Dual Supergravity in D=10, N=1 Superspace with Tree-Level Superstring Corrections

【原创】GAUSSION计算常见错误及解决方案★★★★★★★★★★fegg7502(金币+3,VIP+0):thank you very much! 9-22 23:49zeoliters(金币+2,VIP+0):谢谢分享！9-22 21:56dongdong3881(金币+3,VIP+0):感谢10-28 14:04luoqiquan(金币+2,VIP+0):很好很强大12-23 22:35初学Gaussian03常见出错分析最初级错误1. 自旋多重度错误2. 变量赋值为整数3. 变量没有赋值4. 键角小于等于0度，大于等于180度5. 分子描述后面没有空行6. 二面角判断错误，造成两个原子距离过近7. 分子描述一行内两次参考同一原子,或参考原子共线运行出错1. 自洽场不收敛 SCFa. 修改坐标，使之合理b. 改变初始猜 Guessc. 增加叠代次数SCFCYC=Nd. iop（5/13=1）2. 分子对称性改变a. 修改坐标，强制高对称性或放松对称性b. 给出精确的、对称性确定的角度和二面角c. 放松对称性判据 Symm=loosed. 不做对称性检查iop(2/16=1)3. 无法写大的Scratch文件RWFa. 劈裂RWF文件%rwf=loc1,size1,loc2,size2,……..,locN,-1b. 改变计算方法MP2=Direct可以少占硬盘空间c. 限制最大硬盘maxdisk=N GB4. FOPT出错原因是变量数与分子自由度数不相等。

可用POPT 或直接用OPT5. 优化过渡态只能做一个STEP 原因是负本征数目不对添加iop（1/11）=16. 组态相互作用计算中相关能叠代次数不够，增加叠代次数QCISD（Maxcyc=N）Default.Rou设置•在Scratch文件夹中的Default.Rou文件中设置G03程序运行的省缺参数：• -M- 200MW•-P- 4•-#- MaxDisk=10GB•-#- SCF=Conventional or Direct•-#- MP2=NoDirect or Direct•-#- OPTCYC=200•-#- SCFCYC=200•-#- IOPs 设置如iop（2/16=1）Default.Rou设置中的冲突•Default route: MaxDisk=2GB SCF=Direct MP2=Direct OPTCYC=200 SCFcyc=100 iop(2/16=1) iop(5/13=1)• ------------------• # ccsd/6-31G** opt• ------------------• L903/L905 and L906 can only do MP2.问题在于，ＭP2=Direct！去掉这个设置，CCSD的作业就能进行了。

Chapter 3 Inorganic Chemistry (28)3.1 The Atomic Nature of Matter (28)3.2 Electronic Structure of Atoms (30)3.3 Periodicity of Atomic Properties (32)3.5 Molecular Geometry and Bonding Theories......................................................... 错误！未定义书签。

3.6 Chemical Reactions................................................................................................. 错误！未定义书签。

3.7 The Behavior of Gases ............................................................................................ 错误！未定义书签。

3.8 Aqueous Reactions and Solution Stoichiometry................................................... 错误！未定义书签。

3.9 Chemical Equilibrium ............................................................................................ 错误！未定义书签。

3.10 Thermochemistry.................................................................................................. 错误！未定义书签。

a rXiv:h ep-th/04546v16M a y24Topological mass in seven dimensions and dualities in four dimensions M.Betancourt and A.Khoudeir ∗Centro de F ´isica Fundamental,Facultad de Ciencias,Universidad de los Andes,M´e rida 5101,Venezuela February 1,2008Abstract The massive topologically and self dual theories en seven dimensions are considered.The local duality between these theories is established and the dimensional reduction lead to the different dualities for massive antisymmetric fields in four dimensions.The topological Chern Simons terms have played an important role in several physical models.For instance,they appear in the eleven dimensional supergrav-ity in a natural way [1]and arise in the anomalies cancellation for gauge and string theories.Also,they allow the formulation of genuine gauge theory for gravity.[2].If they are included in the conventional theories for odd dimension D =4k −1,it is possible formulate massive theories which are compatible with gauge invariance.Initially,this goal was formulated in three dimensions pro-vide gauge invariant theories for massive spin 1and spin 2fields [3].These are called massive topologically theories.Alternatively,other formulations describe the same physical dynamics but in a non-gauge invariant way:the self dual theories [4][5]Eventually,it was established that they are essentially two waysfor describing the same physics[6],i.e.,they are related by duality[7].Further-more,the dual equivalence can be shown from the hamiltonian framework[8].The self dual theories are gauged fixed versions of the topologically massive theories.Also,there exist analogues dualities for antisymmetric fields in four dimensions,[9],[10],which constitute alternative manners to describe massive scalar and vectorial fields through of gauge invariant topological BF terms.In this work,we will consider the dual equivalence between the topologically massive and self dual theories in seven dimensions.The basic field is a third order antisymmetric tensor.Recently,it was recognized the importance of these theories,when the eleven dimensional supergravity is dimensionally reduced in a consistent way on A d S 7⊗S 4[11].We perform the Hamiltonian analysis inorder to achieve the local canonical duality between them.Besides,the dualitycan be inferred through the existence of afirst order master action.Finally, we will make the dimensional reduction of the topologically massive and self dual theories in seven dimensions,to obtain the several dualities for massive antisymmetricfields in four dimensions.The topologically massive theory is described by the following actionI T M=−172 d7xεmnpqrst C mnp∂q C rst,(1)where C mnp is a third order antisymmetricfield,G mnpq=∂m C npq+∂n C pmq+∂p C mnq+∂q C nmp itsfield strength andµis a mass parameter.This action is invariant under gauge transformations:δC mnp=∂mΛnp+∂nΛpm+∂pΛmn. Thefield equations for the topologically massive theory are∂m G mnpq=−µ72µ d7xεmnpqrst C mnp∂q C rst−16µεmnpqrst∂q C rst.(4)The thirtyfive components of C mnp can be decomposed in its transverse and longitudinal parts in the following mannerC mnp= C0ij≡b ij=b T ij+ρi b T j−ρj b T i15=10+5C ijk=C T ijk+ρi C T jk+ρj C T ki+ρk C T ij20=10+10,(5) whereρi=∂i/√36 d7xχmnp C mnp−µ12 d7x C mnp C mnp,(6)whereχmnp≡εmnpqrst∂q C rst.(7) Making independent variations on C mnp allow us determine C mnp in terms of C mnpC mnp=1Substituting(8)into(6)wefind the topologically massive action.Meanwhile, independent variations on C mnp tell usεmnpqrst∂q(C rst−µC rst)=0,(9) which can be(locally)solved as C mnp=1δ˙C ijk =172µεijklmn C lmn(10)andπ0ij=δL T M24µεijklmn∂k C lmn≈0.(12)There is no more constraint,because˙φ2ij={φ2ij(x),H(y)}≡0.This set of constraints constitute afirst class abelian gauge algebra:{φαij,φβkl}=0α,β=1,2,(13) which generate the gauge transformations for the topologically massive theory. Finally,the extended Hamiltonian density is given byH T M=3πijkπijk+148G ijkl G ijkl++1∂˙C ijk=1∂˙C0ij=0.(16)3These are primary constraintsψijk=πijk−112C ijk C ijk−C0ij(6∂kφijk+12C0ij≈0,(20) while the preservation of the other primary constraint,lead to the determination of the Lagrange multiplierλijk:λijk=136µεijklmnδ6(x−y),(23) {Θij,ψklm}=112δijlmδ6(x−y).(25)Obviously,we can solve the constraints,for instance,making use of transverse-longitudinal decomposition given by eq.(5).To show the dynamical propagation of C T ijk:( −µ2)C T ijk=0.The Hamiltonian density of the self dual theory can be written down(after redefining C ijk⇒µC ijk)asH SD=1(12)2(εijklmn∂k C lmn)2.(26) Having found the Hamiltonians of the massive topologically and Self Dual The-ories,we can establish the following relationship between themH T M=H SD+3ψijk(ψijk+µThe two Hamiltonian densities are related by a specific combination of the second class constraintψijk of H SD.This result shows the canonical duality equivalence.The self dual theory can be considered as a gaugefixed version of the topologically massive theory.In fact,we observe that148 d4+3x72 d4+3xεMNP QRSTˆC MNPˆG QRST(28) and1I SD=12 d4+3x√With this ansatz,it is straightforward to make the dimensional reduction pro-cess.For the topologically massive theory,we obtain the following reduced action to four dimensionsI1= d4x[−112Hαmnp H mnpα−µG mnpq G mnpq−16εmnpqφG mnpq].(36)48Thefirst integral is nothing but of a triplet of Cremmer-Scherk actions[12]and as is well known,it describes in a gauge invariant way,the dual equivalence between massive vector and second order antisymmetricfields in four dimensions[9].This action allow us to obtain the non abelian Fredman-Townsend[13]model from the self interaction mechanism[14].The second integral is just the gauge invariant master action which allow us to show the dual equivalence between massive scalar and a third order antisymmetricfields in four dimensions[10]On the other hand,the self dual action in seven dimensions is reduced to four dimensions in the following wayI2= d4x[−12Aαm A mα−1C mnp C mnp−16µεmnpqφ∂m C mnp],(37)12from which the dualities just commented above,is easily inferred but in a non gauge invariant way.These dualities in four dimensions are established in a local way.Global aspects of the dual equivalences have been considered in[9] and[10].Summarizing,we have discussed some hamiltonian aspects of the topolog-ically massive and self dual theories in seven dimensions and we have stated that they are dual equivalent from the Hamiltonian framework.Both the-ories describe the same physical situation:the propagation of ten local de-grees of freedom in seven dimensions,contained in the purely transverse part of C MNP(C T ijk).The self dual theory can be considered as afixed gauge version of the topologically massive theory.The dual equivalence can be seen in a covariant way using the master action(6).Since the constraints for higher antisymmetricfield are reducible,these theories deserve a full Hamiltonian treat-ment.It will be interesting the BRST quantization of these theories.We have also obtained the different local dualities between antisymmetricfields in four dimensions,after making the dimensional reduction of the topologically massive and dual theories in seven dimensions.AcknowledgmentThe authors would like to thank to the Consejo de Desarrollo Cient´ıfico y Hu-manistico de la Universidad de los Andes for institutional support under project C-1149-02-05-F.6References[1]E.Cremmer,B.Julia and J.Scherk,Phys.Lett.B76,409(1978)[2]E.Witten,Nucl.Phys.B111,46(1988/89);A.H.Chamseddine,Phys.Lett.B233(1989)291;Nucl.Phys.B346213(1990);M.Ba˜n ados,R.Troncoso and J.Zanelli,Phys.Rev.D542605(1996);R.Troncoso and J.Zanelli,Phys.Rev.D58R101703(1998);J.Zanelli,hep-th0206169.[3]S.Deser,R.Jackiw,and S.Templeton,Phys.Rev.Lett.48,975(1982).[4]P.K.Townsend,K.Pilch,and Van Nieuwenhuizen,Phys.Lett.B136.38(1984).[5]C.Aragone and A.Khoudeir,Phys.Lett.B173,141(1986);Rev.Mexicanade F´isica39819(1993).[6]S.Deser,R.Jackiw,Phys.Rev.Lett..B139,371(1984).[7]J.Stephany,Phys.Lett.B390,128(1997);J.Stephany and P.J.Arias J.Math.Phys.361968(1995).[8]R.Gianvittorio,A.Restuccia and J.Stephany,Mod.Phys.Lett.A62121(1991).[9]P.J.Arias and L.Leal Phys.Lett.B404,49-56(1997).[10]P.J.Arias and A.Khoudeir,Mod.Phys.Lett.A14,2125(1999).[11]H.Nastase,D.Vaman and P.Van Nieuwenhuizen,Nucl.Phys.B581,179(2000).[12]E.Cremmer and J.Scherk,Nucl.Phys..B72,117(1974).[13]D.Z.Freedman and P.K.Townsend,Nucl.Phys..B177,282(1981).[14]A.Khoudeir,Mod.Phys.Lett.A11,2489-2495(1996).7。

Publication Release Date: May 02, 2017Revision D3V 128M-BITSERIAL FLASH MEMORY WITH DUAL/QUAD SPI- 1 -Table of Contents1. GENERAL DESCRIPTIONS ............................................................................................................. 42. FEATURES ....................................................................................................................................... 43.PACKAGE TYPES AND PIN CONFIGURATIONS ........................................................................... 5 3.1 Pin Configuration SOIC 208-mil ........................................................................................... 5 3.2 Pad Configuration WSON 6x5-mm/ 8x6-mm ....................................................................... 5 3.3 Pin Description SOIC 208-mil, WSON 6x5-mm / 8x6-mm ................................................... 5 3.4 Pin Configuration SOIC 300-mil ........................................................................................... 6 3.5 Pin Description SOIC 300-mil ............................................................................................... 6 3.6 Ball Configuration TFBGA 8x6-mm (5x5 or 6x4 Ball Array) ................................................. 7 3.7Ball Description TFBGA 8x6-mm ......................................................................................... 7 4. PIN DESCRIPTIONS ........................................................................................................................ 8 4.1 Chip Select (/CS) .................................................................................................................. 8 4.2 Serial Data Input, Output and IOs (DI, DO and IO0, IO1, IO2, IO3) ..................................... 8 4.3 Write Protect (/WP) .............................................................................................................. 8 4.4 HOLD (/HOLD) ..................................................................................................................... 8 4.5 Serial Clock (CLK) ................................................................................................................ 8 4.6Reset (/RESET) (8)5. BLOCK DIAGRAM ............................................................................................................................ 96.FUNCTIONAL DESCRIPTIONS ..................................................................................................... 10 6.1 Standard SPI Instructions ................................................................................................... 10 6.2 Dual SPI Instructions .......................................................................................................... 10 6.3 Quad SPI Instructions ......................................................................................................... 10 6.4 Software Reset & Hardware /RESET pin ........................................................................... 10 6.5Write Protection (11)6.5.1 Write Protect Features (11)7. STATUS AND CONFIGURATION REGISTERS ............................................................................ 12 7.1Status Registers (12)7.1.1 Erase/Write In Progress (BUSY) – Status Only ................................................................ 12 7.1.2 Write Enable Latch (WEL) – Status Only .......................................................................... 12 7.1.3 Block Protect Bits (BP2, BP1, BP0) – Volatile/Non-Volatile Writable ................................ 12 7.1.4 Top/Bottom Block Protect (TB) – Volatile/Non-Volatile Writable ....................................... 13 7.1.5 Sector/Block Protect Bit (SEC) – Volatile/Non-Volatile Writable ....................................... 13 7.1.6 Complement Protect (CMP) – Volatile/Non-Volatile Writable ............................................ 13 7.1.1 Status Register Protect (SRP, SRL) – Volatile/Non-Volatile Writable ............................... 14 7.1.2 Erase/Program Suspend Status (SUS) – Status Only . (15)Publication Release Date: May 02, 2017- 2 - Revision D7.1.3 Security Register Lock Bits (LB3, LB2, LB1) – Volatile/Non-Volatile OTP Writable .......... 15 7.1.4 Quad Enable (QE) – Volatile/Non-Volatile Writable .......................................................... 15 7.1.5 Write Protect Selection (WPS) – Volatile/Non-Volatile Writable ....................................... 16 7.1.6 Output Driver Strength (DRV1, DRV0) – Volatile/Non-Volatile Writable ........................... 16 7.1.7 Reserved Bits – Non Functional ........................................................................................ 16 7.1.8 W25Q128JV Status Register Memory Protection (WPS = 0, CMP = 0) ............................... 17 7.1.9 W25Q128JV Status Register Memory Protection (WPS = 0, CMP = 1) ............................... 18 7.1.10 W25Q128JV Individual Block Memory Protection (WPS=1) . (19)8. INSTRUCTIONS ............................................................................................................................. 20 8.1Device ID and Instruction Set Tables (20)8.1.1 Manufacturer and Device Identification ................................................................................ 20 8.1.2 Instruction Set Table 1 (Standard SPI Instructions)(1)........................................................... 21 8.1.3 Instruction Set Table 2 (Dual/Quad SPI Instructions) ........................................................... 22 Notes: (22)8.2 Instruction Descriptions (23)8.2.1 Write Enable (06h) ............................................................................................................... 23 8.2.2 Write Enable for Volatile Status Register (50h) .................................................................... 23 8.2.3 Write Disable (04h) ............................................................................................................... 24 8.2.4 Read Status Register-1 (05h), Status Register-2 (35h) & Status Register-3 (15h) .............. 24 8.2.5 Write Status Register-1 (01h), Status Register-2 (31h) & Status Register-3 (11h) .............. 25 8.2.6 Read Data (03h) ................................................................................................................... 27 8.2.7 Fast Read (0Bh) ................................................................................................................... 28 8.2.8 Fast Read Dual Output (3Bh) ............................................................................................... 29 8.2.9 Fast Read Quad Output (6Bh) .............................................................................................. 30 8.2.10 Fast Read Dual I/O (BBh) ................................................................................................... 31 8.2.11 Fast Read Quad I/O (EBh) ................................................................................................. 32 8.2.12 Set Burst with Wrap (77h) .................................................................................................. 34 8.2.13 Page Program (02h) ........................................................................................................... 35 8.2.14 Quad Input Page Program (32h) ........................................................................................ 36 8.2.15 Sector Erase (20h) ............................................................................................................. 37 8.2.16 32KB Block Erase (52h) ..................................................................................................... 38 8.2.17 64KB Block Erase (D8h) ..................................................................................................... 39 8.2.18 Chip Erase (C7h / 60h) ....................................................................................................... 40 8.2.19 Erase / Program Suspend (75h) ......................................................................................... 41 8.2.20 Erase / Program Resume (7Ah) ......................................................................................... 42 8.2.21 Power-down (B9h) .............................................................................................................. 43 8.2.22 Release Power-down / Device ID (ABh) ............................................................................. 44 8.2.23 Read Manufacturer / Device ID (90h) ................................................................................. 45 8.2.24 Read Manufacturer / Device ID Dual I/O (92h) ................................................................... 46 8.2.25 Read Manufacturer / Device ID Quad I/O (94h) ................................................................. 47 8.2.26 Read Unique ID Number (4Bh). (48)- 3 -8.2.27 Read JEDEC ID (9Fh) ........................................................................................................ 49 8.2.28 Read SFDP Register (5Ah) ................................................................................................ 50 8.2.29 Erase Security Registers (44h) ........................................................................................... 51 8.2.30 Program Security Registers (42h) ...................................................................................... 52 8.2.31 Read Security Registers (48h) ........................................................................................... 53 8.2.32 Individual Block/Sector Lock (36h) ..................................................................................... 54 8.2.33 Individual Block/Sector Unlock (39h) .................................................................................. 55 8.2.34 Read Block/Sector Lock (3Dh) ........................................................................................... 56 8.2.35 Global Block/Sector Lock (7Eh) .......................................................................................... 57 8.2.36 Global Block/Sector Unlock (98h) ....................................................................................... 57 8.2.37 Enable Reset (66h) and Reset Device (99h) . (58)9.ELECTRICAL CHARACTERISTICS (59)9.1 Absolute Maximum Ratings (1) ............................................................................................ 59 9.2 Operating Ranges............................................................................................................... 59 9.3 Power-Up Power-Down Timing and Requirements ............................................................ 60 9.4 DC Electrical Characteristics- ............................................................................................. 61 9.5 AC Measurement Conditions .............................................................................................. 62 9.6 AC Electrical Characteristics (6) ........................................................................................... 63 9.7 Serial Output Timing ........................................................................................................... 65 9.8 Serial Input Timing .............................................................................................................. 65 9.9/WP Timing ......................................................................................................................... 65 10. PACKAGE SPECIFICATIONS ........................................................................................................ 66 10.1 8-Pin SOIC 208-mil (Package Code S) .............................................................................. 66 10.2 16-Pin SOIC 300-mil (Package Code F) ............................................................................ 67 10.3 8-Pad WSON 6x5-mm (Package Code P) ......................................................................... 68 10.4 8-Pad WSON 8x6-mm (Package Code E) ......................................................................... 69 10.5 24-Ball TFBGA 8x6-mm (Package Code B, 5x5-1 ball array) ............................................ 70 10.624-Ball TFBGA 8x6-mm (Package Code C, 6x4 ball array) ............................................... 71 11. ORDERING INFORMATION .......................................................................................................... 72 11.1Valid Part Numbers and Top Side Marking (73)12. REVISION HISTORY (74)Publication Release Date: May 02, 2017- 4 - Revision D1. GENERAL DESCRIPTIONSThe W25Q128JV (128M-bit) Serial Flash memory provides a storage solution for systems with limited space, pins and power. The 25Q series offers flexibility and performance well beyond ordinary Serial Flash devices. They are ideal for code shadowing to RAM, executing code directly from Dual/Quad SPI (XIP) and storing voice, text and data. The device operates on a single 2.7V to 3.6V power supply with current consumption as low as 1µA for power-down. All devices are offered in space-saving packages.The W25Q128JV array is organized into 65,536 programmable pages of 256-bytes each. Up to 256 bytes can be programmed at a time. Pages can be erased in groups of 16 (4KB sector erase), groups of 128 (32KB block erase), groups of 256 (64KB block erase) or the entire chip (chip erase). The W25Q128JV has 4,096 erasable sectors and 256 erasable blocks respectively. The small 4KB sectors allow for greater flexibility in applications that require data and parameter storage. (See Figure 2.)The W25Q128JV supports the standard Serial Peripheral Interface (SPI), Dual/Quad I/O SPI: Serial Clock, Chip Select, Serial Data I/O0 (DI), I/O1 (DO), I/O2 and I/O3. SPI clock frequencies of W25Q128JV of up to 133MHz are supported allowing equivalent clock rates of 266MHz (133MHz x 2) for Dual I/O and 532MHz (133MHz x 4) for Quad I/O when using the Fast Read Dual/Quad I/O. These transfer rates can outperform standard Asynchronous 8 and 16-bit Parallel Flash memories.Additionally, the device supports JEDEC standard manufacturer and device ID and SFDP, and a 64-bit Unique Serial Number and three 256-bytes Security Registers.2. FEATURES∙ New Family of SpiFlash Memories – W25Q128JV: 128M-bit / 16M-byte – Standard SPI: CLK, /CS, DI, DO – Dual SPI: CLK, /CS, IO 0, IO 1 – Quad SPI: CLK, /CS, IO 0, IO 1, IO 2, IO 3 – Software & Hardware Reset (1) ∙ Highest Performance Serial Flash – 133MHz Single, Dual/Quad SPI clocks – 266/532MHz equivalent Dual/Quad SPI – 66MB/S continuous data transfer rate – Min. 100K Program-Erase cycles per sector – More than 20-year data retention ∙ Efficient “Continuous Read”– Continuous Read with 8/16/32/64-Byte Wrap– As few as 8 clocks to address memory– Allows true XIP (execute in place) operation ∙ Low Power, Wide Temperature Range– Single 2.7 to 3.6V supply– <1µA Power-down (typ.)– -40°C to +85°C operating range∙ Flexible Architecture with 4KB sectors – Uniform Sector/Block Erase (4K/32K/64K-Byte) – Program 1 to 256 byte per programmable page – Erase/Program Suspend & Resume ∙ Advanced Security Features – Software and Hardware Write-Protect – Power Supply Lock-Down – Special OTP protection – Top/Bottom, Complement array protection – Individual Block/Sector array protection – 64-Bit Unique ID for each device – Discoverable Parameters (SFDP) Register– 3X256-Bytes Security Registers with OTP locks – Volatile & Non-volatile Status Register Bits ∙ Space Efficient Packaging – 8-pin SOIC 208-mil– 16-pin SOIC 300-mil (additional /RESET pin) – 8-pad WSON 6x5-mm / 8x6-mm – 24-ball TFBGA 8x6-mm (6x4/5x5 ball array) – Contact Winbond for KGD and other options Note: 1. Hardware /RESET pin is only available on TFBGA or SOIC16 packages- 5 -3. PACKAGE TYPES AND PIN CONFIGURATIONS3.1 Pin Configuration SOIC 208-milFigure 1a. W25Q128JV Pin Assignments, 8-pin SOIC 208-mil (Package Code S)3.2 Pad Configuration WSON 6x5-mm/ 8x6-mmFigure 1b. W25Q128JV Pad Assignments, 8-pad WSON 6x5-mm/ 8x6-mm (Package Code P/E)3.3 Pin Description SOIC 208-mil, WSON 6x5-mm / 8x6-mmNotes:1. IO0 and IO1 are used for Standard and Dual SPI instructions2.IO0 – IO3 are used for Quad SPI instructions, /HOLD (or /RESET) function is only available for Standard/Dual SPI.Publication Release Date: May 02, 2017- 6 - Revision D3.4 Pin Configuration SOIC 300-milFigure 1c. W25Q128JV Pin Assignments, 16-pin SOIC 300-mil (Package Code F)3.5 Pin Description SOIC 300-milNotes:1. IO0 and IO1 are used for Standard and Dual SPI instructions.2. IO0 – IO3 are used for Quad SPI instructions, /HOLD (or /RESET) function is only available for Standard/Dual SPI.3. The /RESET pin is a dedicated hardware reset pin regardless of device settings or operation states. If the hardware reset function is not used, this pin can be left floating or connected to VCC in the system.3.6Ball Configuration TFBGA 8x6-mm (5x5 or 6x4 Ball Array)Figure 1d. W25Q128JV Ball Assignments, 24-ball TFBGA 8x6-mm (Package Code B/C)3.7Ball Description TFBGA 8x6-mmNotes:1.IO0 and IO1 are used for Standard and Dual SPI instructions2.IO0 – IO3 are used for Quad SPI instructions, /HOLD (or /RESET) function is only available for Standard/Dual SPI.3. The /RESET pin is a dedicated hardware reset pin regardless of device settings or operation states.If the hardware reset function is not used, this pin can be left floating or connected to VCC in the system- 7 -Publication Release Date: May 02, 2017- 8 - Revision D4. PIN DESCRIPTIONS4.1 Chip Select (/CS)The SPI Chip Select (/CS) pin enables and disables device operation. When /CS is high the device is deselected and the Serial Data Output (DO, or IO0, IO1, IO2, IO3) pins are at high impedance. When deselected, the devices power consumption will be at standby levels unless an internal erase, program or write status register cycle is in progress. When /CS is brought low the device will be selected, power consumption will increase to active levels and instructions can be written to and data read from the device. After power-up, /CS must transition from high to low before a new instruction will be accepted. The /CS input must track the VCC supply level at power-up and power-down (see “Write Protection” and Figure 58). If needed a pull-up resister on the /CS pin can be used to accomplish this.4.2 Serial Data Input, Output and IOs (DI, DO and IO0, IO1, IO2, IO3)The W25Q128JV supports standard SPI, Dual SPI and Quad SPI operation. Standard SPI instructions use the unidirectional DI (input) pin to serially write instructions, addresses or data to the device on the rising edge of the Serial Clock (CLK) input pin. Standard SPI also uses the unidirectional DO (output) to read data or status from the device on the falling edge of CLK.Dual and Quad SPI instructions use the bidirectional IO pins to serially write instructions, addresses or data to the device on the rising edge of CLK and read data or status from the device on the falling edge of CLK. Quad SPI instructions require the non-volatile Quad Enable bit (QE) in Status Register-2 to be set. When QE=1, the /WP pin becomes IO2 and the /HOLD pin becomes IO3.4.3 Write Protect (/WP)The Write Protect (/WP) pin can be used to prevent the Status Register from being written. Used in conjunction with the Status Register’s Block Protect (CMP, SEC, TB, BP2, BP1 and BP0) bits and Status Register Protect (SRP) bits, a portion as small as a 4KB sector or the entire memory array can be hardware protected. The /WP pin is active low.4.4 HOLD (/HOLD)The /HOLD pin allows the device to be paused while it is actively selected. When /HOLD is brought low, while /CS is low, the DO pin will be at high impedance and signals on the DI and CLK pins will be ignored (don’t care). When /HOLD is brought high, device operation can resume. The /HOLD function can be useful when multiple devices are sharing the same SPI signals. The /HOLD pin is active low. When the QE bit of Status Register-2 is set for Quad I/O, the /HOLD pin function is not available since this pin is used for IO3. See Figure 1a-c for the pin configuration of Quad I/O operation.4.5 Serial Clock (CLK)The SPI Serial Clock Input (CLK) pin provides the timing for serial input and output operations. ("See SPI Operations")4.6 Reset (/RESET)A dedicated hardware /RESET pin is available on SOIC-16 and TFBGA packages. When it’s driven low for a minimum period of ~1µS, this device will terminate any external or internal operations and return to its power-on state.Note: Hardware /RESET pin is available on SOIC-16 or TFBGA; please contact Winbond for this package.- 9 -5. BLOCK DIAGRAMFigure 2. W25Q128JV Serial Flash Memory Block Diagram6.FUNCTIONAL DESCRIPTIONS6.1Standard SPI InstructionsThe W25Q128JV is accessed through an SPI compatible bus consisting of four signals: Serial Clock (CLK), Chip Select (/CS), Serial Data Input (DI) and Serial Data Output (DO). Standard SPI instructions use the DI input pin to serially write instructions, addresses or data to the device on the rising edge of CLK. The DO output pin is used to read data or status from the device on the falling edge of CLK.SPI bus operation Mode 0 (0,0) and 3 (1,1) are supported. The primary difference between Mode 0 and Mode 3 concerns the normal state of the CLK signal when the SPI bus master is in standby and data is not being transferred to the Serial Flash. For Mode 0, the CLK signal is normally low on the falling and rising edges of /CS. For Mode 3, the CLK signal is normally high on the falling and rising edges of /CS.6.2Dual SPI InstructionsThe W25Q128JV supports Dual SPI operation when using instructions such as “Fast Read Dual Output (3Bh)” and “Fast Read Dual I/O (BBh)”. These instructions allow data to be transferred to or from the device at two to three times the rate of ordinary Serial Flash devices. The Dual SPI Read instructions are ideal for quickly downloading code to RAM upon power-up (code-shadowing) or for executing non-speed-critical code directly from the SPI bus (XIP). When using Dual SPI instructions, the DI and DO pins become bidirectional I/O pins: IO0 and IO1.6.3Quad SPI InstructionsThe W25Q128JV supports Quad SPI operation when using instructions such as “Fast Read Quad Output (6Bh)”,and “Fast Read Quad I/O (EBh). These instructions allow data to be transferred to or from the device four to six times the rate of ordinary Serial Flash. When using Quad SPI instructions, the DI and DO pins become bidirectional IO0 and IO1, with the additional I/O pins: IO2, IO3.6.4Software Reset & Hardware /RESET pinThe W25Q128JV can be reset to the initial power-on state by a software Reset sequence. This sequence must include two consecutive instructions: Enable Reset (66h) & Reset (99h). If the instruction sequence is successfully accepted, the device will take approximately 30µS (t RST)to reset. No instruction will be accepted during the reset period. For the SOIC-16 and TFBGA packages, W25Q128JV provides a dedicated hardware /RESET pin. Drive the /RESET pin low for a minimum period of ~1µS (tRESET*) will interrupt any on-going external/internal operations and reset the device to its initial power-on state. Hardware /RESET pin has higher priority than other SPI input signals (/CS, CLK, IOs).Note:1.Hardware /RESET pin is available on SOIC-16 or TFBGA; please contact Winbond for his package.2.While a faster /RESET pulse (as short as a few hundred nanoseconds) will often reset the device, a 1us minimum isrecommended to ensure reliable operation.3.There is an internal pull-up resistor for the dedicated /RESET pin on the SOIC-16 and TFBGA-24 package. If the reset functionis not needed, this pin can be left floating in the system.6.5Write ProtectionApplications that use non-volatile memory must take into consideration the possibility of noise and other adverse system conditions that may compromise data integrity. To address this concern, the W25Q128JV provides several means to protect the data from inadvertent writes.6.5.1Write Protect Features∙Device resets when VCC is below threshold∙Time delay write disable after Power-up∙Write enable/disable instructions and automatic write disable after erase or program∙Software and Hardware (/WP pin) write protection using Status Registers∙Additional Individual Block/Sector Locks for array protection∙Write Protection using Power-down instruction∙Lock Down write protection for Status Register until the next power-up∙One Time Program (OTP) write protection for array and Security Registers using Status Register** Note:This feature is available upon special order. Please contact Winbond for details.Upon power-up or at power-down, the W25Q128JV will maintain a reset condition while VCC is below the threshold value of V WI, (See Power-up Timing and Voltage Levels and Figure 43). While reset, all operations are disabled and no instructions are recognized. During power-up and after the VCC voltage exceeds V WI, all program and erase related instructions are further disabled for a time delay of t PUW. This includes the Write Enable, Page Program, Sector Erase, Block Erase, Chip Erase and the Write Status Register instructions. Note that the chip select pin (/CS) must track the VCC supply level at power-up until the VCC-min level and t VSL time delay is reached, and it must also track the VCC supply level at power-down to prevent adverse command sequence. If needed a pull-up resister on /CS can be used to accomplish this.After power-up the device is automatically placed in a write-disabled state with the Status Register Write Enable Latch (WEL) set to a 0. A Write Enable instruction must be issued before a Page Program, Sector Erase, Block Erase, Chip Erase or Write Status Register instruction will be accepted. After completing a program, erase or write instruction the Write Enable Latch (WEL) is automatically cleared to a write-disabled state of 0.Software controlled write protection is facilitated using the Write Status Register instruction and setting the Status Register Protect (SRP, SRL) and Block Protect (CMP, TB, BP[3:0]) bits. These settings allow a portion or the entire memory array to be configured as read only. Used in conjunction with the Write Protect (/WP) pin, changes to the Status Register can be enabled or disabled under hardware control. See Status Register section for further information. Additionally, the Power-down instruction offers an extra level of write protection as all instructions are ignored except for the Release Power-down instruction.The W25Q128JV also provides another Write Protect method using the Individual Block Locks. Each 64KB block (except the top and bottom blocks, total of 126 blocks) and each 4KB sector within the top/bottom blocks (total of 32 sectors) are equipped with an Individual Block Lock bit. When the lock bit is 0, the corresponding sector or block can be erased or programmed; when the lock bit is set to 1, Erase or Program commands issued to the corresponding sector or block will be ignored. When the device is powered on, all Individual Block Lock bits will be 1, so the entire memory array is protected from Erase/Program. An “Individual Block Unlock (39h)” instruction must be issued to unlock any specific sector or block.The WPS bit in Status Register-3 is used to decide which Write Protect scheme should be used. When WPS=0 (factory default), the device will only utilize CMP, SEC, TB, BP[2:0] bits to protect specific areas of the array; when WPS=1, the device will utilize the Individual Block Locks for write protection.。

华中师范大学物理学院物理学专业英语仅供内部学习参考！2014一、课程的任务和教学目的通过学习《物理学专业英语》，学生将掌握物理学领域使用频率较高的专业词汇和表达方法，进而具备基本的阅读理解物理学专业文献的能力。

通过分析《物理学专业英语》课程教材中的范文，学生还将从英语角度理解物理学中个学科的研究内容和主要思想，提高学生的专业英语能力和了解物理学研究前沿的能力。

培养专业英语阅读能力，了解科技英语的特点，提高专业外语的阅读质量和阅读速度；掌握一定量的本专业英文词汇，基本达到能够独立完成一般性本专业外文资料的阅读；达到一定的笔译水平。

要求译文通顺、准确和专业化。

要求译文通顺、准确和专业化。

二、课程内容课程内容包括以下章节：物理学、经典力学、热力学、电磁学、光学、原子物理、统计力学、量子力学和狭义相对论三、基本要求1.充分利用课内时间保证充足的阅读量（约1200~1500词/学时），要求正确理解原文。

2.泛读适量课外相关英文读物，要求基本理解原文主要内容。

3.掌握基本专业词汇（不少于200词）。

4.应具有流利阅读、翻译及赏析专业英语文献，并能简单地进行写作的能力。

四、参考书目录1 Physics 物理学 (1)Introduction to physics (1)Classical and modern physics (2)Research fields (4)V ocabulary (7)2 Classical mechanics 经典力学 (10)Introduction (10)Description of classical mechanics (10)Momentum and collisions (14)Angular momentum (15)V ocabulary (16)3 Thermodynamics 热力学 (18)Introduction (18)Laws of thermodynamics (21)System models (22)Thermodynamic processes (27)Scope of thermodynamics (29)V ocabulary (30)4 Electromagnetism 电磁学 (33)Introduction (33)Electrostatics (33)Magnetostatics (35)Electromagnetic induction (40)V ocabulary (43)5 Optics 光学 (45)Introduction (45)Geometrical optics (45)Physical optics (47)Polarization (50)V ocabulary (51)6 Atomic physics 原子物理 (52)Introduction (52)Electronic configuration (52)Excitation and ionization (56)V ocabulary (59)7 Statistical mechanics 统计力学 (60)Overview (60)Fundamentals (60)Statistical ensembles (63)V ocabulary (65)8 Quantum mechanics 量子力学 (67)Introduction (67)Mathematical formulations (68)Quantization (71)Wave-particle duality (72)Quantum entanglement (75)V ocabulary (77)9 Special relativity 狭义相对论 (79)Introduction (79)Relativity of simultaneity (80)Lorentz transformations (80)Time dilation and length contraction (81)Mass-energy equivalence (82)Relativistic energy-momentum relation (86)V ocabulary (89)正文标记说明：蓝色Arial字体（例如energy）：已知的专业词汇蓝色Arial字体加下划线（例如electromagnetism）：新学的专业词汇黑色Times New Roman字体加下划线（例如postulate）：新学的普通词汇1 Physics 物理学1 Physics 物理学Introduction to physicsPhysics is a part of natural philosophy and a natural science that involves the study of matter and its motion through space and time, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic disciplines, perhaps the oldest through its inclusion of astronomy. Over the last two millennia, physics was a part of natural philosophy along with chemistry, certain branches of mathematics, and biology, but during the Scientific Revolution in the 17th century, the natural sciences emerged as unique research programs in their own right. Physics intersects with many interdisciplinary areas of research, such as biophysics and quantum chemistry,and the boundaries of physics are not rigidly defined. New ideas in physics often explain the fundamental mechanisms of other sciences, while opening new avenues of research in areas such as mathematics and philosophy.Physics also makes significant contributions through advances in new technologies that arise from theoretical breakthroughs. For example, advances in the understanding of electromagnetism or nuclear physics led directly to the development of new products which have dramatically transformed modern-day society, such as television, computers, domestic appliances, and nuclear weapons; advances in thermodynamics led to the development of industrialization; and advances in mechanics inspired the development of calculus.Core theoriesThough physics deals with a wide variety of systems, certain theories are used by all physicists. Each of these theories were experimentally tested numerous times and found correct as an approximation of nature (within a certain domain of validity).For instance, the theory of classical mechanics accurately describes the motion of objects, provided they are much larger than atoms and moving at much less than the speed of light. These theories continue to be areas of active research, and a remarkable aspect of classical mechanics known as chaos was discovered in the 20th century, three centuries after the original formulation of classical mechanics by Isaac Newton (1642–1727) 【艾萨克·牛顿】.University PhysicsThese central theories are important tools for research into more specialized topics, and any physicist, regardless of his or her specialization, is expected to be literate in them. These include classical mechanics, quantum mechanics, thermodynamics and statistical mechanics, electromagnetism, and special relativity.Classical and modern physicsClassical mechanicsClassical physics includes the traditional branches and topics that were recognized and well-developed before the beginning of the 20th century—classical mechanics, acoustics, optics, thermodynamics, and electromagnetism.Classical mechanics is concerned with bodies acted on by forces and bodies in motion and may be divided into statics (study of the forces on a body or bodies at rest), kinematics (study of motion without regard to its causes), and dynamics (study of motion and the forces that affect it); mechanics may also be divided into solid mechanics and fluid mechanics (known together as continuum mechanics), the latter including such branches as hydrostatics, hydrodynamics, aerodynamics, and pneumatics.Acoustics is the study of how sound is produced, controlled, transmitted and received. Important modern branches of acoustics include ultrasonics, the study of sound waves of very high frequency beyond the range of human hearing; bioacoustics the physics of animal calls and hearing, and electroacoustics, the manipulation of audible sound waves using electronics.Optics, the study of light, is concerned not only with visible light but also with infrared and ultraviolet radiation, which exhibit all of the phenomena of visible light except visibility, e.g., reflection, refraction, interference, diffraction, dispersion, and polarization of light.Heat is a form of energy, the internal energy possessed by the particles of which a substance is composed; thermodynamics deals with the relationships between heat and other forms of energy.Electricity and magnetism have been studied as a single branch of physics since the intimate connection between them was discovered in the early 19th century; an electric current gives rise to a magnetic field and a changing magnetic field induces an electric current. Electrostatics deals with electric charges at rest, electrodynamics with moving charges, and magnetostatics with magnetic poles at rest.Modern PhysicsClassical physics is generally concerned with matter and energy on the normal scale of1 Physics 物理学observation, while much of modern physics is concerned with the behavior of matter and energy under extreme conditions or on the very large or very small scale.For example, atomic and nuclear physics studies matter on the smallest scale at which chemical elements can be identified.The physics of elementary particles is on an even smaller scale, as it is concerned with the most basic units of matter; this branch of physics is also known as high-energy physics because of the extremely high energies necessary to produce many types of particles in large particle accelerators. On this scale, ordinary, commonsense notions of space, time, matter, and energy are no longer valid.The two chief theories of modern physics present a different picture of the concepts of space, time, and matter from that presented by classical physics.Quantum theory is concerned with the discrete, rather than continuous, nature of many phenomena at the atomic and subatomic level, and with the complementary aspects of particles and waves in the description of such phenomena.The theory of relativity is concerned with the description of phenomena that take place in a frame of reference that is in motion with respect to an observer; the special theory of relativity is concerned with relative uniform motion in a straight line and the general theory of relativity with accelerated motion and its connection with gravitation.Both quantum theory and the theory of relativity find applications in all areas of modern physics.Difference between classical and modern physicsWhile physics aims to discover universal laws, its theories lie in explicit domains of applicability. Loosely speaking, the laws of classical physics accurately describe systems whose important length scales are greater than the atomic scale and whose motions are much slower than the speed of light. Outside of this domain, observations do not match their predictions.Albert Einstein【阿尔伯特·爱因斯坦】contributed the framework of special relativity, which replaced notions of absolute time and space with space-time and allowed an accurate description of systems whose components have speeds approaching the speed of light.Max Planck【普朗克】, Erwin Schrödinger【薛定谔】, and others introduced quantum mechanics, a probabilistic notion of particles and interactions that allowed an accurate description of atomic and subatomic scales.Later, quantum field theory unified quantum mechanics and special relativity.General relativity allowed for a dynamical, curved space-time, with which highly massiveUniversity Physicssystems and the large-scale structure of the universe can be well-described. General relativity has not yet been unified with the other fundamental descriptions; several candidate theories of quantum gravity are being developed.Research fieldsContemporary research in physics can be broadly divided into condensed matter physics; atomic, molecular, and optical physics; particle physics; astrophysics; geophysics and biophysics. Some physics departments also support research in Physics education.Since the 20th century, the individual fields of physics have become increasingly specialized, and today most physicists work in a single field for their entire careers. "Universalists" such as Albert Einstein (1879–1955) and Lev Landau (1908–1968)【列夫·朗道】, who worked in multiple fields of physics, are now very rare.Condensed matter physicsCondensed matter physics is the field of physics that deals with the macroscopic physical properties of matter. In particular, it is concerned with the "condensed" phases that appear whenever the number of particles in a system is extremely large and the interactions between them are strong.The most familiar examples of condensed phases are solids and liquids, which arise from the bonding by way of the electromagnetic force between atoms. More exotic condensed phases include the super-fluid and the Bose–Einstein condensate found in certain atomic systems at very low temperature, the superconducting phase exhibited by conduction electrons in certain materials,and the ferromagnetic and antiferromagnetic phases of spins on atomic lattices.Condensed matter physics is by far the largest field of contemporary physics.Historically, condensed matter physics grew out of solid-state physics, which is now considered one of its main subfields. The term condensed matter physics was apparently coined by Philip Anderson when he renamed his research group—previously solid-state theory—in 1967. In 1978, the Division of Solid State Physics of the American Physical Society was renamed as the Division of Condensed Matter Physics.Condensed matter physics has a large overlap with chemistry, materials science, nanotechnology and engineering.Atomic, molecular and optical physicsAtomic, molecular, and optical physics (AMO) is the study of matter–matter and light–matter interactions on the scale of single atoms and molecules.1 Physics 物理学The three areas are grouped together because of their interrelationships, the similarity of methods used, and the commonality of the energy scales that are relevant. All three areas include both classical, semi-classical and quantum treatments; they can treat their subject from a microscopic view (in contrast to a macroscopic view).Atomic physics studies the electron shells of atoms. Current research focuses on activities in quantum control, cooling and trapping of atoms and ions, low-temperature collision dynamics and the effects of electron correlation on structure and dynamics. Atomic physics is influenced by the nucleus (see, e.g., hyperfine splitting), but intra-nuclear phenomena such as fission and fusion are considered part of high-energy physics.Molecular physics focuses on multi-atomic structures and their internal and external interactions with matter and light.Optical physics is distinct from optics in that it tends to focus not on the control of classical light fields by macroscopic objects, but on the fundamental properties of optical fields and their interactions with matter in the microscopic realm.High-energy physics (particle physics) and nuclear physicsParticle physics is the study of the elementary constituents of matter and energy, and the interactions between them.In addition, particle physicists design and develop the high energy accelerators,detectors, and computer programs necessary for this research. The field is also called "high-energy physics" because many elementary particles do not occur naturally, but are created only during high-energy collisions of other particles.Currently, the interactions of elementary particles and fields are described by the Standard Model.●The model accounts for the 12 known particles of matter (quarks and leptons) thatinteract via the strong, weak, and electromagnetic fundamental forces.●Dynamics are described in terms of matter particles exchanging gauge bosons (gluons,W and Z bosons, and photons, respectively).●The Standard Model also predicts a particle known as the Higgs boson. In July 2012CERN, the European laboratory for particle physics, announced the detection of a particle consistent with the Higgs boson.Nuclear Physics is the field of physics that studies the constituents and interactions of atomic nuclei. The most commonly known applications of nuclear physics are nuclear power generation and nuclear weapons technology, but the research has provided application in many fields, including those in nuclear medicine and magnetic resonance imaging, ion implantation in materials engineering, and radiocarbon dating in geology and archaeology.University PhysicsAstrophysics and Physical CosmologyAstrophysics and astronomy are the application of the theories and methods of physics to the study of stellar structure, stellar evolution, the origin of the solar system, and related problems of cosmology. Because astrophysics is a broad subject, astrophysicists typically apply many disciplines of physics, including mechanics, electromagnetism, statistical mechanics, thermodynamics, quantum mechanics, relativity, nuclear and particle physics, and atomic and molecular physics.The discovery by Karl Jansky in 1931 that radio signals were emitted by celestial bodies initiated the science of radio astronomy. Most recently, the frontiers of astronomy have been expanded by space exploration. Perturbations and interference from the earth's atmosphere make space-based observations necessary for infrared, ultraviolet, gamma-ray, and X-ray astronomy.Physical cosmology is the study of the formation and evolution of the universe on its largest scales. Albert Einstein's theory of relativity plays a central role in all modern cosmological theories. In the early 20th century, Hubble's discovery that the universe was expanding, as shown by the Hubble diagram, prompted rival explanations known as the steady state universe and the Big Bang.The Big Bang was confirmed by the success of Big Bang nucleo-synthesis and the discovery of the cosmic microwave background in 1964. The Big Bang model rests on two theoretical pillars: Albert Einstein's general relativity and the cosmological principle (On a sufficiently large scale, the properties of the Universe are the same for all observers). Cosmologists have recently established the ΛCDM model (the standard model of Big Bang cosmology) of the evolution of the universe, which includes cosmic inflation, dark energy and dark matter.Current research frontiersIn condensed matter physics, an important unsolved theoretical problem is that of high-temperature superconductivity. Many condensed matter experiments are aiming to fabricate workable spintronics and quantum computers.In particle physics, the first pieces of experimental evidence for physics beyond the Standard Model have begun to appear. Foremost among these are indications that neutrinos have non-zero mass. These experimental results appear to have solved the long-standing solar neutrino problem, and the physics of massive neutrinos remains an area of active theoretical and experimental research. Particle accelerators have begun probing energy scales in the TeV range, in which experimentalists are hoping to find evidence for the super-symmetric particles, after discovery of the Higgs boson.Theoretical attempts to unify quantum mechanics and general relativity into a single theory1 Physics 物理学of quantum gravity, a program ongoing for over half a century, have not yet been decisively resolved. The current leading candidates are M-theory, superstring theory and loop quantum gravity.Many astronomical and cosmological phenomena have yet to be satisfactorily explained, including the existence of ultra-high energy cosmic rays, the baryon asymmetry, the acceleration of the universe and the anomalous rotation rates of galaxies.Although much progress has been made in high-energy, quantum, and astronomical physics, many everyday phenomena involving complexity, chaos, or turbulence are still poorly understood. Complex problems that seem like they could be solved by a clever application of dynamics and mechanics remain unsolved; examples include the formation of sand-piles, nodes in trickling water, the shape of water droplets, mechanisms of surface tension catastrophes, and self-sorting in shaken heterogeneous collections.These complex phenomena have received growing attention since the 1970s for several reasons, including the availability of modern mathematical methods and computers, which enabled complex systems to be modeled in new ways. Complex physics has become part of increasingly interdisciplinary research, as exemplified by the study of turbulence in aerodynamics and the observation of pattern formation in biological systems.Vocabulary★natural science 自然科学academic disciplines 学科astronomy 天文学in their own right 凭他们本身的实力intersects相交，交叉interdisciplinary交叉学科的，跨学科的★quantum 量子的theoretical breakthroughs 理论突破★electromagnetism 电磁学dramatically显著地★thermodynamics热力学★calculus微积分validity★classical mechanics 经典力学chaos 混沌literate 学者★quantum mechanics量子力学★thermodynamics and statistical mechanics热力学与统计物理★special relativity狭义相对论is concerned with 关注，讨论，考虑acoustics 声学★optics 光学statics静力学at rest 静息kinematics运动学★dynamics动力学ultrasonics超声学manipulation 操作，处理，使用University Physicsinfrared红外ultraviolet紫外radiation辐射reflection 反射refraction 折射★interference 干涉★diffraction 衍射dispersion散射★polarization 极化，偏振internal energy 内能Electricity电性Magnetism 磁性intimate 亲密的induces 诱导，感应scale尺度★elementary particles基本粒子★high-energy physics 高能物理particle accelerators 粒子加速器valid 有效的，正当的★discrete离散的continuous 连续的complementary 互补的★frame of reference 参照系★the special theory of relativity 狭义相对论★general theory of relativity 广义相对论gravitation 重力，万有引力explicit 详细的，清楚的★quantum field theory 量子场论★condensed matter physics凝聚态物理astrophysics天体物理geophysics地球物理Universalist博学多才者★Macroscopic宏观Exotic奇异的★Superconducting 超导Ferromagnetic铁磁质Antiferromagnetic 反铁磁质★Spin自旋Lattice 晶格，点阵，网格★Society社会，学会★microscopic微观的hyperfine splitting超精细分裂fission分裂，裂变fusion熔合，聚变constituents成分，组分accelerators加速器detectors 检测器★quarks夸克lepton 轻子gauge bosons规范玻色子gluons胶子★Higgs boson希格斯玻色子CERN欧洲核子研究中心★Magnetic Resonance Imaging磁共振成像，核磁共振ion implantation 离子注入radiocarbon dating放射性碳年代测定法geology地质学archaeology考古学stellar 恒星cosmology宇宙论celestial bodies 天体Hubble diagram 哈勃图Rival竞争的★Big Bang大爆炸nucleo-synthesis核聚合，核合成pillar支柱cosmological principle宇宙学原理ΛCDM modelΛ-冷暗物质模型cosmic inflation宇宙膨胀1 Physics 物理学fabricate制造，建造spintronics自旋电子元件，自旋电子学★neutrinos 中微子superstring 超弦baryon重子turbulence湍流，扰动，骚动catastrophes突变，灾变，灾难heterogeneous collections异质性集合pattern formation模式形成University Physics2 Classical mechanics 经典力学IntroductionIn physics, classical mechanics is one of the two major sub-fields of mechanics, which is concerned with the set of physical laws describing the motion of bodies under the action of a system of forces. The study of the motion of bodies is an ancient one, making classical mechanics one of the oldest and largest subjects in science, engineering and technology.Classical mechanics describes the motion of macroscopic objects, from projectiles to parts of machinery, as well as astronomical objects, such as spacecraft, planets, stars, and galaxies. Besides this, many specializations within the subject deal with gases, liquids, solids, and other specific sub-topics.Classical mechanics provides extremely accurate results as long as the domain of study is restricted to large objects and the speeds involved do not approach the speed of light. When the objects being dealt with become sufficiently small, it becomes necessary to introduce the other major sub-field of mechanics, quantum mechanics, which reconciles the macroscopic laws of physics with the atomic nature of matter and handles the wave–particle duality of atoms and molecules. In the case of high velocity objects approaching the speed of light, classical mechanics is enhanced by special relativity. General relativity unifies special relativity with Newton's law of universal gravitation, allowing physicists to handle gravitation at a deeper level.The initial stage in the development of classical mechanics is often referred to as Newtonian mechanics, and is associated with the physical concepts employed by and the mathematical methods invented by Newton himself, in parallel with Leibniz【莱布尼兹】, and others.Later, more abstract and general methods were developed, leading to reformulations of classical mechanics known as Lagrangian mechanics and Hamiltonian mechanics. These advances were largely made in the 18th and 19th centuries, and they extend substantially beyond Newton's work, particularly through their use of analytical mechanics. Ultimately, the mathematics developed for these were central to the creation of quantum mechanics.Description of classical mechanicsThe following introduces the basic concepts of classical mechanics. For simplicity, it often2 Classical mechanics 经典力学models real-world objects as point particles, objects with negligible size. The motion of a point particle is characterized by a small number of parameters: its position, mass, and the forces applied to it.In reality, the kind of objects that classical mechanics can describe always have a non-zero size. (The physics of very small particles, such as the electron, is more accurately described by quantum mechanics). Objects with non-zero size have more complicated behavior than hypothetical point particles, because of the additional degrees of freedom—for example, a baseball can spin while it is moving. However, the results for point particles can be used to study such objects by treating them as composite objects, made up of a large number of interacting point particles. The center of mass of a composite object behaves like a point particle.Classical mechanics uses common-sense notions of how matter and forces exist and interact. It assumes that matter and energy have definite, knowable attributes such as where an object is in space and its speed. It also assumes that objects may be directly influenced only by their immediate surroundings, known as the principle of locality.In quantum mechanics objects may have unknowable position or velocity, or instantaneously interact with other objects at a distance.Position and its derivativesThe position of a point particle is defined with respect to an arbitrary fixed reference point, O, in space, usually accompanied by a coordinate system, with the reference point located at the origin of the coordinate system. It is defined as the vector r from O to the particle.In general, the point particle need not be stationary relative to O, so r is a function of t, the time elapsed since an arbitrary initial time.In pre-Einstein relativity (known as Galilean relativity), time is considered an absolute, i.e., the time interval between any given pair of events is the same for all observers. In addition to relying on absolute time, classical mechanics assumes Euclidean geometry for the structure of space.Velocity and speedThe velocity, or the rate of change of position with time, is defined as the derivative of the position with respect to time. In classical mechanics, velocities are directly additive and subtractive as vector quantities; they must be dealt with using vector analysis.When both objects are moving in the same direction, the difference can be given in terms of speed only by ignoring direction.University PhysicsAccelerationThe acceleration , or rate of change of velocity, is the derivative of the velocity with respect to time (the second derivative of the position with respect to time).Acceleration can arise from a change with time of the magnitude of the velocity or of the direction of the velocity or both . If only the magnitude v of the velocity decreases, this is sometimes referred to as deceleration , but generally any change in the velocity with time, including deceleration, is simply referred to as acceleration.Inertial frames of referenceWhile the position and velocity and acceleration of a particle can be referred to any observer in any state of motion, classical mechanics assumes the existence of a special family of reference frames in terms of which the mechanical laws of nature take a comparatively simple form. These special reference frames are called inertial frames .An inertial frame is such that when an object without any force interactions (an idealized situation) is viewed from it, it appears either to be at rest or in a state of uniform motion in a straight line. This is the fundamental definition of an inertial frame. They are characterized by the requirement that all forces entering the observer's physical laws originate in identifiable sources (charges, gravitational bodies, and so forth).A non-inertial reference frame is one accelerating with respect to an inertial one, and in such a non-inertial frame a particle is subject to acceleration by fictitious forces that enter the equations of motion solely as a result of its accelerated motion, and do not originate in identifiable sources. These fictitious forces are in addition to the real forces recognized in an inertial frame.A key concept of inertial frames is the method for identifying them. For practical purposes, reference frames that are un-accelerated with respect to the distant stars are regarded as good approximations to inertial frames.Forces; Newton's second lawNewton was the first to mathematically express the relationship between force and momentum . Some physicists interpret Newton's second law of motion as a definition of force and mass, while others consider it a fundamental postulate, a law of nature. Either interpretation has the same mathematical consequences, historically known as "Newton's Second Law":a m t v m t p F ===d )(d d dThe quantity m v is called the (canonical ) momentum . The net force on a particle is thus equal to rate of change of momentum of the particle with time.So long as the force acting on a particle is known, Newton's second law is sufficient to。

PACKAGING INFORMATIONOrderableDevice Status (1)Package Type Package DrawingPins Package Qty Eco Plan (2)Lead/Ball Finish MSL Peak Temp (3)5962-7704301VCAACTIVE CDIP J 141TBD A42SNPB Level-NC-NC-NC 77043012A ACTIVE LCCC FK 201TBD POST-PLATE Level-NC-NC-NC7704301CA ACTIVE CDIP J 141TBD A42SNPB Level-NC-NC-NC 7704301DA ACTIVE CFP W 141TBD A42SNPB Level-NC-NC-NC 77043022A ACTIVE LCCC FK 201TBD POST-PLATE Level-NC-NC-NC7704302CA ACTIVE CDIP J 141TBD A42SNPB Level-NC-NC-NC JM38510/11005BCAACTIVE CDIP J 141TBD A42SNPB Level-NC-NC-NC LM124AFKB ACTIVE LCCC FK 201TBD POST-PLATE Level-NC-NC-NCLM124AJ ACTIVE CDIP J 141TBD A42SNPB Level-NC-NC-NC LM124AJB ACTIVE CDIP J 141TBD A42SNPB Level-NC-NC-NC LM124D ACTIVE SOIC D 1450TBD CU NIPDAU Level-3-245C-168HR LM124DR ACTIVE SOIC D 142500TBD CU NIPDAU Level-3-245C-168HR LM124FKB ACTIVE LCCC FK 201TBD POST-PLATE Level-NC-NC-NCLM124J ACTIVE CDIP J 141TBD A42SNPB Level-NC-NC-NC LM124JB ACTIVE CDIP J 141TBD A42SNPB Level-NC-NC-NC LM124N OBSOLETE PDIP N 14TBD Call TI Call TILM124W ACTIVE CFP W 141TBD A42SNPB Level-NC-NC-NC LM124WB ACTIVE CFP W 141TBD A42SNPB Level-NC-NC-NC LM224AD ACTIVE SOIC D 1450Green (RoHS &no Sb/Br)CU NIPDAU Level-1-260C-UNLIM LM224ADE4ACTIVE SOIC D 1450Green (RoHS &no Sb/Br)CU NIPDAU Level-1-260C-UNLIM LM224ADR ACTIVE SOIC D 142500Green (RoHS &no Sb/Br)CU NIPDAU Level-1-260C-UNLIM LM224ADRE4ACTIVE SOIC D 142500Green (RoHS &no Sb/Br)CU NIPDAU Level-1-260C-UNLIM LM224AN ACTIVE PDIP N 1425Pb-Free (RoHS)CU NIPDAU Level-NC-NC-NC LM224D ACTIVE SOIC D 1450Green (RoHS &no Sb/Br)CU NIPDAU Level-1-260C-UNLIM LM224DE4ACTIVE SOIC D 1450Green (RoHS &no Sb/Br)CU NIPDAU Level-1-260C-UNLIM LM224DR ACTIVE SOIC D 142500Green (RoHS &no Sb/Br)CU NIPDAU Level-1-260C-UNLIM LM224DRE4ACTIVE SOIC D 142500Green (RoHS &no Sb/Br)CU NIPDAU Level-1-260C-UNLIM LM224KAD ACTIVE SOIC D 1450Green (RoHS &no Sb/Br)CU NIPDAU Level-1-260C-UNLIM LM224KADE4ACTIVE SOIC D 1450Green (RoHS &no Sb/Br)CU NIPDAU Level-1-260C-UNLIM LM224KADR ACTIVE SOIC D 142500Green (RoHS &no Sb/Br)CU NIPDAU Level-1-260C-UNLIM LM224KADRE4ACTIVE SOIC D 142500Green (RoHS &no Sb/Br)CU NIPDAU Level-1-260C-UNLIM LM224KANACTIVEPDIPN1425Pb-Free (RoHS)CU NIPDAULevel-NC-NC-NCPACKAGE OPTION ADDENDUM9-Aug-2005Addendum-Page 1OrderableDeviceStatus (1)Package Type Package Drawing Pins Package Qty Eco Plan (2)Lead/Ball Finish MSL Peak Temp (3)LM224KANE4ACTIVE PDIP N 1425Pb-Free (RoHS)CU NIPDAU Level-NC-NC-NC LM224KDACTIVE SOIC D 1450Green (RoHS &no Sb/Br)CU NIPDAU Level-1-260C-UNLIM LM224KDE4ACTIVE SOIC D 1450Green (RoHS &no Sb/Br)CU NIPDAU Level-1-260C-UNLIM LM224KDRACTIVE SOIC D 142500Green (RoHS &no Sb/Br)CU NIPDAU Level-1-260C-UNLIM LM224KDRE4ACTIVE SOIC D 142500Green (RoHS &no Sb/Br)CU NIPDAU Level-1-260C-UNLIM LM224KNACTIVE PDIP N 1425Pb-Free (RoHS)CU NIPDAU Level-NC-NC-NC LM224KNE4ACTIVE PDIP N 1425Pb-Free (RoHS)CU NIPDAU Level-NC-NC-NC LM224NACTIVE PDIP N 1425Pb-Free (RoHS)CU NIPDAU Level-NC-NC-NC LM2902DACTIVE SOIC D 1450Green (RoHS &no Sb/Br)CU NIPDAU Level-1-260C-UNLIM LM2902DE4ACTIVE SOIC D 1450Green (RoHS &no Sb/Br)CU NIPDAU Level-1-260C-UNLIM LM2902DG4ACTIVE SOIC D 1450Green (RoHS &no Sb/Br)CU NIPDAU Level-1-260C-UNLIM LM2902DRACTIVE SOIC D 142500Green (RoHS &no Sb/Br)CU NIPDAU Level-1-260C-UNLIM LM2902DRE4ACTIVE SOIC D 142500Green (RoHS &no Sb/Br)CU NIPDAU Level-1-260C-UNLIM LM2902DRG4ACTIVE SOIC D 142500Green (RoHS &no Sb/Br)CU NIPDAU Level-1-260C-UNLIM LM2902KAVQDRACTIVE SOIC D 142500Pb-Free (RoHS)CU NIPDAU Level-2-250C-1YEAR/Level-1-235C-UNLIM LM2902KAVQPWRACTIVE TSSOP PW 142000TBD CU NIPDAU Level-1-250C-UNLIM LM2902KDACTIVE SOIC D 1450Green (RoHS &no Sb/Br)CU NIPDAU Level-1-260C-UNLIM LM2902KDBACTIVE SSOP DB 1480Green (RoHS &no Sb/Br)CU NIPDAU Level-1-260C-UNLIM LM2902KDBE4ACTIVE SSOP DB 1480Green (RoHS &no Sb/Br)CU NIPDAU Level-1-260C-UNLIM LM2902KDBRACTIVE SSOP DB 142000Green (RoHS &no Sb/Br)CU NIPDAU Level-1-260C-UNLIM LM2902KDBRE4ACTIVE SSOP DB 142000Green (RoHS &no Sb/Br)CU NIPDAU Level-1-260C-UNLIM LM2902KDE4ACTIVE SOIC D 1450Green (RoHS &no Sb/Br)CU NIPDAU Level-1-260C-UNLIM LM2902KDRACTIVE SOIC D 142500Green (RoHS &no Sb/Br)CU NIPDAU Level-1-260C-UNLIM LM2902KDRE4ACTIVE SOIC D 142500Green (RoHS &no Sb/Br)CU NIPDAU Level-1-260C-UNLIM LM2902KNACTIVE PDIP N 1425Pb-Free (RoHS)CU NIPDAU Level-NC-NC-NC LM2902KNE4ACTIVE PDIP N 1425Pb-Free(RoHS)CU NIPDAU Level-NC-NC-NC 9-Aug-2005OrderableDeviceStatus (1)Package Type Package Drawing Pins Package Qty Eco Plan (2)Lead/Ball Finish MSL Peak Temp (3)LM2902KNSRACTIVE SO NS 142000Green (RoHS &no Sb/Br)CU NIPDAU Level-1-260C-UNLIM LM2902KNSRE4ACTIVE SO NS 142000Green (RoHS &no Sb/Br)CU NIPDAU Level-1-260C-UNLIM LM2902KPWACTIVE TSSOP PW 1490Green (RoHS &no Sb/Br)CU NIPDAU Level-1-260C-UNLIM LM2902KPWE4ACTIVE TSSOP PW 1490Green (RoHS &no Sb/Br)CU NIPDAU Level-1-260C-UNLIM LM2902KPWRACTIVE TSSOP PW 142000Green (RoHS &no Sb/Br)CU NIPDAU Level-1-260C-UNLIM LM2902KPWRE4ACTIVE TSSOP PW 142000Green (RoHS &no Sb/Br)CU NIPDAU Level-1-260C-UNLIM LM2902KVQDRACTIVE SOIC D 142500Pb-Free (RoHS)CU NIPDAU Level-2-250C-1YEAR/Level-1-235C-UNLIM LM2902KVQPWRACTIVE TSSOP PW 142000TBD CU NIPDAU Level-1-250C-UNLIM LM2902NACTIVE PDIP N 1425Pb-Free (RoHS)CU NIPDAU Level-NC-NC-NC LM2902NE4ACTIVE PDIP N 1425Pb-Free (RoHS)CU NIPDAU Level-NC-NC-NC LM2902NSRACTIVE SO NS 142000Green (RoHS &no Sb/Br)CU NIPDAU Level-1-260C-UNLIM LM2902NSRG4ACTIVE SO NS 142000Green (RoHS &no Sb/Br)CU NIPDAU Level-1-260C-UNLIM LM2902PWACTIVE TSSOP PW 1490Green (RoHS &no Sb/Br)CU NIPDAU Level-1-260C-UNLIM LM2902PWE4ACTIVE TSSOP PW 1490Green (RoHS &no Sb/Br)CU NIPDAU Level-1-260C-UNLIM LM2902PWG4ACTIVE TSSOP PW 1490Green (RoHS &no Sb/Br)CU NIPDAU Level-1-260C-UNLIM LM2902PWLEOBSOLETE TSSOP PW 14TBD Call TI Call TI LM2902PWRACTIVE TSSOP PW 142000Green (RoHS &no Sb/Br)CU NIPDAU Level-1-260C-UNLIM LM2902PWRE4ACTIVE TSSOP PW 142000Green (RoHS &no Sb/Br)CU NIPDAU Level-1-260C-UNLIM LM2902PWRG4ACTIVE TSSOP PW 142000Green (RoHS &no Sb/Br)CU NIPDAU Level-1-260C-UNLIM LM2902QNOBSOLETE PDIP N 14TBD Call TI Call TI LM324ADACTIVE SOIC D 1450Green (RoHS &no Sb/Br)CU NIPDAU Level-1-260C-UNLIM LM324ADBLEOBSOLETE SSOP DB 14TBD Call TI Call TI LM324ADBRACTIVE SSOP DB 142000Green (RoHS &no Sb/Br)CU NIPDAU Level-1-260C-UNLIM LM324ADBRE4ACTIVE SSOP DB 142000Green (RoHS &no Sb/Br)CU NIPDAU Level-1-260C-UNLIM LM324ADE4ACTIVE SOIC D 1450Green (RoHS &no Sb/Br)CU NIPDAU Level-1-260C-UNLIM LM324ADRACTIVE SOIC D 142500Green (RoHS &no Sb/Br)CU NIPDAU Level-1-260C-UNLIM LM324ADRE4ACTIVE SOIC D 142500Green (RoHS &no Sb/Br)CU NIPDAU Level-1-260C-UNLIM LM324AN ACTIVE PDIP N 1425Pb-FreeCU NIPDAU Level-NC-NC-NC 9-Aug-2005OrderableDevice Status (1)PackageType Package Drawing Pins Package Qty Eco Plan (2)Lead/Ball Finish MSL Peak Temp (3)(RoHS)LM324ANE4ACTIVE PDIPN 1425Pb-Free (RoHS)CU NIPDAU Level-NC-NC-NC LM324ANSR ACTIVE SONS 142000Green (RoHS &no Sb/Br)CU NIPDAU Level-1-260C-UNLIM LM324ANSRE4ACTIVE SONS 142000Green (RoHS &no Sb/Br)CU NIPDAU Level-1-260C-UNLIM LM324APW ACTIVE TSSOPPW 1490Green (RoHS &no Sb/Br)CU NIPDAU Level-1-260C-UNLIM LM324APWE4ACTIVE TSSOPPW 1490Green (RoHS &no Sb/Br)CU NIPDAU Level-1-260C-UNLIM LM324APWG4ACTIVE TSSOPPW 1490Green (RoHS &no Sb/Br)CU NIPDAU Level-1-260C-UNLIM LM324APWLE OBSOLETE TSSOPPW 14TBD Call TI Call TI LM324APWR ACTIVE TSSOPPW 142000Green (RoHS &no Sb/Br)CU NIPDAU Level-1-260C-UNLIM LM324APWRE4ACTIVE TSSOPPW 142000Green (RoHS &no Sb/Br)CU NIPDAU Level-1-260C-UNLIM LM324APWRG4ACTIVE TSSOPPW 142000Green (RoHS &no Sb/Br)CU NIPDAU Level-1-260C-UNLIM LM324D ACTIVE SOICD 1450Green (RoHS &no Sb/Br)CU NIPDAU Level-1-260C-UNLIM LM324DE4ACTIVE SOICD 1450Green (RoHS &no Sb/Br)CU NIPDAU Level-1-260C-UNLIM LM324DG4ACTIVE SOICD 1450Green (RoHS &no Sb/Br)CU NIPDAU Level-1-260C-UNLIM LM324DR ACTIVE SOICD 142500Green (RoHS &no Sb/Br)CU NIPDAU Level-1-260C-UNLIM LM324DRE4ACTIVE SOICD 142500Green (RoHS &no Sb/Br)CU NIPDAU Level-1-260C-UNLIM LM324DRG4ACTIVE SOICD 142500Green (RoHS &no Sb/Br)CU NIPDAU Level-1-260C-UNLIM LM324KAD ACTIVE SOICD 1450Green (RoHS &no Sb/Br)CU NIPDAU Level-1-260C-UNLIM LM324KADG4ACTIVE SOICD 1450Green (RoHS &no Sb/Br)CU NIPDAU Level-1-260C-UNLIM LM324KADR ACTIVE SOICD 142500Green (RoHS &no Sb/Br)CU NIPDAU Level-1-260C-UNLIM LM324KADRG4ACTIVE SOICD 142500Green (RoHS &no Sb/Br)CU NIPDAU Level-1-260C-UNLIM LM324KAN ACTIVE PDIPN 1425Pb-Free (RoHS)CU NIPDAU Level-NC-NC-NC LM324KANE4ACTIVE PDIPN 1425Pb-Free (RoHS)CU NIPDAU Level-NC-NC-NC LM324KANS PREVIEW SONS 1450Green (RoHS &no Sb/Br)CU NIPDAU Level-1-260C-UNLIM LM324KANSR ACTIVE SONS 142000Green (RoHS &no Sb/Br)CU NIPDAU Level-1-260C-UNLIM LM324KANSRE4ACTIVE SONS 142000Green (RoHS &no Sb/Br)CU NIPDAU Level-1-260C-UNLIM LM324KAPW ACTIVE TSSOP PW 1490Green (RoHS &CU NIPDAU Level-1-260C-UNLIM 9-Aug-2005OrderableDevice Status (1)PackageType Package Drawing Pins Package Qty Eco Plan (2)Lead/Ball Finish MSL Peak Temp (3)no Sb/Br)LM324KAPWG4ACTIVE TSSOPPW 1490Green (RoHS &no Sb/Br)CU NIPDAU Level-1-260C-UNLIM LM324KAPWR ACTIVE TSSOPPW 142000Green (RoHS &no Sb/Br)CU NIPDAU Level-1-260C-UNLIM LM324KAPWRG4ACTIVE TSSOPPW 142000Green (RoHS &no Sb/Br)CU NIPDAU Level-1-260C-UNLIM LM324KD ACTIVE SOICD 1450Green (RoHS &no Sb/Br)CU NIPDAU Level-1-260C-UNLIM LM324KDE4ACTIVE SOICD 1450Green (RoHS &no Sb/Br)CU NIPDAU Level-1-260C-UNLIM LM324KDR ACTIVE SOICD 142500Green (RoHS &no Sb/Br)CU NIPDAU Level-1-260C-UNLIM LM324KDRE4ACTIVE SOICD 142500Green (RoHS &no Sb/Br)CU NIPDAU Level-1-260C-UNLIM LM324KN ACTIVE PDIPN 1425Pb-Free (RoHS)CU NIPDAU Level-NC-NC-NC LM324KNS PREVIEW SONS 1450Green (RoHS &no Sb/Br)CU NIPDAU Level-1-260C-UNLIM LM324KNSR ACTIVE SONS 142000Green (RoHS &no Sb/Br)CU NIPDAU Level-1-260C-UNLIM LM324KNSRE4ACTIVE SONS 142000Green (RoHS &no Sb/Br)CU NIPDAU Level-1-260C-UNLIM LM324KPW ACTIVE TSSOPPW 1490Green (RoHS &no Sb/Br)CU NIPDAU Level-1-260C-UNLIM LM324KPWE4ACTIVE TSSOPPW 1490Green (RoHS &no Sb/Br)CU NIPDAU Level-1-260C-UNLIM LM324KPWR ACTIVE TSSOPPW 142000Green (RoHS &no Sb/Br)CU NIPDAU Level-1-260C-UNLIM LM324KPWRE4ACTIVE TSSOPPW 142000Green (RoHS &no Sb/Br)CU NIPDAU Level-1-260C-UNLIM LM324N ACTIVE PDIPN 1425Pb-Free (RoHS)CU NIPDAU Level-NC-NC-NC LM324NE4ACTIVE PDIPN 1425Pb-Free (RoHS)CU NIPDAU Level-NC-NC-NC LM324NSR ACTIVE SONS 142000Green (RoHS &no Sb/Br)CU NIPDAU Level-1-260C-UNLIM LM324NSRE4ACTIVE SONS 142000Green (RoHS &no Sb/Br)CU NIPDAU Level-1-260C-UNLIM LM324NSRG4ACTIVE SONS 142000Green (RoHS &no Sb/Br)CU NIPDAU Level-1-260C-UNLIM LM324PW ACTIVE TSSOPPW 1490Green (RoHS &no Sb/Br)CU NIPDAU Level-1-260C-UNLIM LM324PWE4ACTIVE TSSOPPW 1490Green (RoHS &no Sb/Br)CU NIPDAU Level-1-260C-UNLIM LM324PWG4ACTIVE TSSOPPW 1490Green (RoHS &no Sb/Br)CU NIPDAU Level-1-260C-UNLIM LM324PWLE OBSOLETE TSSOPPW 14TBD Call TI Call TI LM324PWR ACTIVE TSSOPPW 142000Green (RoHS &no Sb/Br)CU NIPDAU Level-1-260C-UNLIM LM324PWRE4ACTIVE TSSOP PW 142000Green (RoHS &CU NIPDAU Level-1-260C-UNLIM 9-Aug-2005Orderable Device Status (1)PackageTypePackage Drawing Pins Package Qty Eco Plan (2)Lead/Ball Finish MSL Peak Temp (3)no Sb/Br)LM324PWRG4ACTIVE TSSOPPW 142000Green (RoHS &no Sb/Br)CU NIPDAU Level-1-260C-UNLIM LM324YOBSOLETE XCEPT Y 0TBD Call TI Call TI (1)The marketing status values are defined as follows:ACTIVE:Product device recommended for new designs.LIFEBUY:TI has announced that the device will be discontinued,and a lifetime-buy period is in effect.NRND:Not recommended for new designs.Device is in production to support existing customers,but TI does not recommend using this part in a new design.PREVIEW:Device has been announced but is not in production.Samples may or may not be available.OBSOLETE:TI has discontinued the production of the device.(2)Eco Plan -The planned eco-friendly classification:Pb-Free (RoHS)or Green (RoHS &no Sb/Br)-please check /productcontent for the latest availability information and additional product content details.TBD:The Pb-Free/Green conversion plan has not been defined.Pb-Free (RoHS):TI's terms "Lead-Free"or "Pb-Free"mean semiconductor products that are compatible with the current RoHS requirements for all 6substances,including the requirement that lead not exceed 0.1%by weight in homogeneous materials.Where designed to be soldered at high temperatures,TI Pb-Free products are suitable for use in specified lead-free processes.Green (RoHS &no Sb/Br):TI defines "Green"to mean Pb-Free (RoHS compatible),and free of Bromine (Br)and Antimony (Sb)based flame retardants (Br or Sb do not exceed 0.1%by weight in homogeneous material)(3)MSL,Peak Temp.--The Moisture Sensitivity Level rating according to the JEDEC industry standard classifications,and peak solder temperature.Important Information and Disclaimer:The information provided on this page represents TI's knowledge and belief as of the date that it is provided.TI bases its knowledge and belief on information provided by third parties,and makes no representation or warranty as to the accuracy of such information.Efforts are underway to better integrate information from third parties.TI has taken and continues to take 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1I N N O V A T I O N | M A N U F A C T U R E R | D E S I G N | S O L U T I O NDELTA DUAL V4/V6INSTALLATION GUIDEJ U L Y 2022DUAL V4/V6 INSTALLATION GUIDECommissioning DetailsEquipment InstalledApproved Installer Date of commissioning Commissioning engineerStatus Warranty period Signature of engineerConditionsFully commissioned in accordance with the manufacturers instructions 12 months from commissioningEquipment must be on a current service agreement with approved service organisationSERVICING PLANSSump pumps must be maintained. We recommend a qualified engineer exam ines and services equipment every year. Pumps running frequently due to higher water table, water drainage, or weather conditions should be examined more frequently, we recommend every 6 months. Sump pumps, being mechanical devices, may fail if not maintained which could lead to a flooded basement and costly repairs. Regular servicing of sump pumps will increase efficiency and extend the life of the pump. All Delta Membrane pump systems can be maintained and serviced by our recommended service companies or installing contractor.COMMISSIONINGAll sump pumps require commissioning. Commissioning provides peace of mind, knowing that the system is installed correctly and in compliance with warranty conditions. All Delta Membrane pump systems can be commissioned by our recommended service companies or installing contractor.THIS MANUAL SHOULD BE KEPT WITH THEPUMP STATION OR THE HOMEOWNER1123567894V4/V6 Overview1.0 OVERVIEW 1.1 TECHNICAL INFORMATION 1.2 CHAMBER OVERVIEW 1.3 PARTS INCLUDED 1.4OPTIONAL EXTRASDischarge Pipework & Fittings2.0 DISCHARGE PIPEWORK & FITTINGS 2.1SPARE PARTSPump Chamber Depth Limits3.0PUMP CHAMBER DEPTH LIMITSInstallation Guidelines4.0 INSTALLATION GUIDELINES 4.1 PUMP STATION LOCATIONS 4.2RC BOX DIMENSIONSInstallation Of Chamber5.0 INSTALLATION OF CHAMBER - SECTION A 5.1 INSTALLATION OF CHAMBER - SECTION B 5.2 INSTALLATION OF CHAMBER - SECTION C 5.3 INSTALLATION OF CHAMBER - SECTION D15.4 INSTALLATION OF CHAMBER - SECTION D25.5 INSTALLATION OF CHAMBER - SECTION D35.6 INSTALLATION OF CHAMBER - SECTION E 5.7 INSTALLATION OF CHAMBER - SECTION F 5.8INSTALLATION OF CHAMBER - SECTION GWiring Diagram6.0 WIRING DIAGRAM 6.1WIRING DIAGRAMMaintenance7.0 MAINTENANCE 7.1HEALTH & SAFETYGuarantee8.0 GUARANTEETroubleshooting9.0 TROUBLESHOOTING01992523523|***********************|Contents1.0 DUAL V4/V6 OVERVIEWThe Delta Dual V4/V6 is a packaged pump station designed to collect ground water via perimeter channel , modular drainage and/or clear opening to the top of the chamber - please visit our website for water collection details. Typically, the Dual V4/V6 would be used to collect ground water from a basement up to 150m² and/or surface water from a light well up to 12m² to a maximum head of 7m and 9m respectively.The pump station has been specifically designed for below ground applications. The chamber is manufactured from HDPE and when installed correctly, it is able to withstand hydrostatic forces encountered in high water tables.The pump station is delivered as a complete package including, the chamber, internal pipework and two powerful V4/V6 pumps. It is designed to be installed by contractors with competent building, plumbing and electrical skills. The pumps operate by fixed arm floats, the duty pump is set at a standard height (210mm to base of float) and the backup pump is set at a high level (380mm to base of float). The high level alarm (where fitted) will operate if the duty pump fails leaving the backup pump to discharge water.An AlertMaxx2 EC - High water level alarm (DMS-598) is offered as a recommended extra to alert the property occupant when the water level in the chamber becomes too high. A Hi-PowerMaxx (DMS-364-1) is recommended to power the pumps during power outage. Please see section 1.4 for more details about optional extras designed for the Dual V4/V6 pump station.1.1 TECHNICAL INFORMATIONDUAL V4/V6 INSTALLATION GUIDE231.2 CHAMBER OVERVIEW1.4 OPTIONAL EXTRAS•2 x V4/V6 Pumps• 2” Discharge Male Iron & low pressure Male Iron for temp. site installation. 2” Cable Duct Male Iron• AlertMaxx2 EC High Level Alarm (DMS-598)• Hi-PowerMaxx2 Battery Backup (DMS-364-1)• 1.25” Discharge Pipework and various fittings •2” Discharge Pipework and various fittings01992523523|***********************|2. Discharge Pipework & Fittings2.0 DISCHARGE PIPEWORK & FITTINGSA selection of discharge pipework and fittings are available for the Dual V4/V6 pump station.Should you require to place an order for any of these items, please complete the form below, scan and email to ***************************************************.Name:Company Name:Delivery/Site Address:Email:Phone No.:Mobile No.: Sign.:Date.: ********************************************************* 4DUAL V4/V6 INSTALLATION GUIDE52. Discharge Pipework & Fittings2.1 SPARE PARTS01992523523|***********************|3. Pump Chamber Depth LimitsIf the inlet does not allow the pump chamber to be within depth limits, please contact Delta***********************************************************************.> 500mmA pump chamber installed more than500mm below floor finishes cannotbe serviced safely in accordance withCDM regulations.X6DUAL V4/V6 INSTALLATION GUIDE74. Installation Guidelines01992523523|***********************|4.0 INSTALLATION GUIDELINESThe following instructions are for guidance only and it is the contractors responsibility to ensure that the installation is in accordance with the prevailing ground conditions and good building practice, to eliminate any potential damage to the pump station either during or after installation.Please read these instructions carefully prior to installing the chamber. If there is anything that is unclear, please contact our technical help desk on 01992 523 5234.1 PUMP STATION LOCATIONThis station requires routine maintenance, therefore it is important that careful consideration is taken to position the chamber in a location that allows permanent access to the chamber.4.2 RC BOX DIMENSIONS85. Installation of Chamber5.0 INSTALLATION OF CHAMBER - SECTION AConstruction of reinforced concrete boxExcavate hole for chamber. Refer to section 4.2 for RC box internal dimensions.Install re-bar as per structural engineer’s drawings.Lay inlet and discharge pipework. Allow pipework to protrude into RC box by a minimum of 100mm.Pour concrete to form RC box as per structural engineer’s drawings.DUAL V4/V6 INSTALLATION GUIDE12345.1 INSTALLATION OF CHAMBER - SECTION B1Connecting 110mm inlet pipeworkSaw off socket end/s, where inlet pipe/s are to be connected.Position chamber in RC box.Fit push fit coupler.Connect inlet pipework to the required chamber spigot.56785.2 INSTALLATION OF CHAMBER - SECTION B2Connecting perimeter channel to chamberTo be followed when installing perimeter channel directly into upper side of chamber.Mark perimeter channel position on side of chamber.Drill holes in the corners inside the area marked in red.Cut around the marked line outlining the perimeter channel using a jigsaw.Insert the perimeter channel into the chamber allowing 35mm of overhang inside the chamber.910 11125.3 INSTALLATION OF CHAMBER - SECTION B3Connecting perimeter channel via a 1.5”/40mm inlet pipeMark position of the 40mm pipe on the side of the chamber and cut out the marked line using a 1.5”/40mm Cut 40mm pipe to length allowing an overhang of 35mm inside the chamber.13145.4 INSTALLATION OF CHAMBER - SECTION CConnecting discharge and cable ductWrap the thread on a DMS-0153 high pressure male iron with PTFE tape.Screw the high pressure male iron into the female iron.Apply DMS-0158 solvent cement around the first 20mm of the external face of the discharge and cable duct pipe and internal side of their respective male iron.Push discharge and cable duct pipe into their respective male iron, twisting the pipe as it is pushed into the male iron to remove any trapped air.1516 17185.4 INSTALLATION OF CHAMBER - SECTION CConnecting discharge and cable duct19Ensure a draw cord is pulled through thecable duct as the cable duct is built.5.5 INSTALLATION OF CHAMBER - SECTION D1Backfill around chamber with concreteTo be followed when installing chamber in an RC box.Check all pipes are connected to the chamber correctly.Completely fill chamber with water.Fill void between RC box and chamber with concrete (min. C35 grade) or as per engineer’s drawings.2021225.6 INSTALLATION OF CHAMBER - SECTION D2Backfill around chamber with concreteTo be followed when installing chamber in the ground.2324Completely fill chamber with water.Fill void between soil and chamber withconcrete (min. C35 grade) or as perengineer’s drawings.25Allow concrete to cure.5.7 INSTALLATION OF CHAMBER - SECTION D3Backfill around chamber with concreteTo be followed when installing chamber in the ground with a reinforced cage.2627Completely fill chamber with water.Fill void between soil and chamber withconcrete (min. C35 grade) or as perengineer’s drawings.28Allow concrete to cure.5.8 INSTALLATION OF CHAMBER - SECTION EInstalling pumps in chamber and AlertMaxx2 EC or Delta HLAPump out water from chamber.Manually remove any debris from chamberand residual water using a wet vacuum.Remove discharge arms from ‘Y’ piece manifold and screw ‘Y’ piece on to gate valve. Ensure gate valve is fully open.Wrap PTFE tape around thread located on male irons at the bottom of the discharge arms and screw discharge arms on to pumps.2930 3132Installing pumps in chamber and AlertMaxx2 ECFill chamber half full with water Lower pumps in to chamber. Ensure ‘O’ ringsare correctly seated in unions and screwdischarge arms to ‘Y’ piece manifold.When installing an AlertMaxx2 EC high level alarm, refer to the AlertMaxx2 EC installation instructions.Pull pump and AlertMaxx2 EC cables through cable duct.5.8 INSTALLATION OF CHAMBER - SECTION E33343536195. Installation of ChamberInstalling pumps in chamber and AlertMaxx2 ECIsolate main supply and connect each pump to a separate non-switched fused spur.When installing an AlertMaxx2 EC, follow the wiring diagram on page 20.Turn mains supply on and lift each pumps float arm to test water is discharging correctly.To test float switch, refer to the AlertMaxx2 EC installation instructions.Re-fit temporary site cover to protect the pump station.01992523523|***********************|373839405.8 INSTALLATION OF CHAMBER - SECTION E6.0 WIRING DIAGRAM20DUAL V4/V6 INSTALLATION GUIDE6.1 WIRING DIAGRAMThe electrical installation must comply with the requirements ofBS 7671:2018 ‘Requirements forElectrical Installations’ incorporating amendment 3:20152101992523523|***********************|7. Maintenance7.0 MAINTENANCESump pumps must be maintained. We recommend a qualified engineer examines and services equipment every year.Pumps running frequently due to higher water table, water drainage, or weather conditions should be examined more frequently, we recommend every 6 months. Sump pumps, being mechanical devices, may fail if not maintained which could lead to a flooded basement and costly repairs.Regular servicing of sump pumps will increase efficiency and extend the life of the pump. All Delta Membrane pump systems can be maintained by our recommended pump service providers or installing contractor.7.1 HEALTH & SAFETYIn order to minimise the risk of ill health or accidents when installing and/or servicing pump chambers, workers must be fully trained, competent and follow the health and safety guidelines below:• Do not work without a risk assessment being in place.• Work in accordance with the control measures identified in the risk assessment.• All personnel must be vaccinated against diseases to which they may be exposed to, i.e. Tetanus, Polio, Hepatitis A&B, etc.• At the time of writing, due to there being no vaccine against leptospirosis/weil’s disease, where rats may be present, ensure appropriate personal protective equipment (skin protection) is worn and ensure any cuts or abrasions are fully covered.• There should be no eating or drinking during works and only afterwards following a change of clothing and washing.• Ensure electrical power to the pump is turned off/isolated before carrying out installation or maintenance.• A suitable first aid kit must be close to hand.8. Guarantee8.0 GUARANTEEThe Delta Dual V4/V6 pump chamber is offered with an 18-month component guarantee from the date of commissioning.Pump chambers that have not been commissioned by a suitable qualified engineer are offered with an 18-month component guarantee from the date of delivery.This guarantee does not cover defects caused by incorrect installation, installation/installer error, abnormal working conditions, misuse, or neglect.Any defects or malfunctions should be reported to Delta Membrane Systems Limited immediately to avoid any subsequential damage to other components of the system. All broken components should be returned to Delta Membrane Systems Limited at customer cost.TomakeaPumporPumpingAccessoryWarrantyClaim,***********************************.Formsareavailable for download from our website .In no event shall we be liable for any consequential damage, penalties, loss, or expenses howsoever arising, out of or in connection with incorrect installations, including, without limitation, direct or indirect loss, consequential loss or damage, loss of profit or goodwill, loss arising from any errors or omissions in the pump chamber as a result of, incorrect installation, installation/installer error, abnormal working conditions, misuse, or neglect.We shall not accept liability if the pumping system fails due to being incorrectly specified by any third parties not employed by Delta Membrane Systems Limited.We shall not accept liability if the pump system fails due to discharge of inappropriate fluids/solids including, but not limited to, building debris or materials.22DUAL V4/V6 INSTALLATION GUIDE9. Troubleshooting9.0 TROUBLESHOOTINGPlease ensure the installation process has been completed thoroughly and all steps have been followed correctly.Use the table below to assist with troubleshooting and if problems still occur, please contact the Delta TechnicalDepartmenton01992523523from9:00am-5:***********************************2301992523523|***********************|2410. AncillariesDUAL V4/V6 INSTALLATION GUIDE90° DEGREE BEND1.25”2.0” 2.5”3.0”DMS 0145DMS 0155DMS 315DMS-SP-S1PLAIN SOCKET1.25”2.0” 2.5”3.0”DMS 0147DMS 0157DMS 317DMS-SP-S1THREADED SOCKET1.25”2.0” 2.5”3.0”DMS 331DMS 339NA NA T PIECE1.25”2.0” 2.5”3.0”DMS 318DMS 212DMS-SP-S1DMS-SP-S1PIPE1.25”2.0” 2.5”3.0”DMS 0144DMS 0154DMS 313DMS-SP-S145° BEND1.25”2.0” 2.5”3.0”DMS 0146DMS 0156DMS 316DMS-SP-S1PLAIN THREADED SOCKET1.25”2.0” 2.5”3.0”DMS 358DMS 359NA NA UNION1.25”2.0” 2.5”3.0”DMS 0148DMS 0160DMS 353DMS-SP-S1HIGH PRESSURE SOLVENT CEMENT500ml DMS 0158110MM ADAPTOR1.25”2.0” 2.5”3.0”DMS 340DMS 341DMS 342NA HOSE TAIL1.25”2.0” 2.5”3.0”DMS 062NA NA NA SEMI RIGID HOSE1.25”2.0” 2.5”3.0”DMS 065NA NA NA NON-RETURN SWING CHECK VALVES1.25”2.0” 2.5”3.0”NA DMS 327DMS-SP-S1DMS-SP-S1NON-RETURN BALL VALVES1.25”2.0” 2.5”3.0”DMS 328DMS-SP-S1DMS-SP-S1DMS-SP-S1VALVES GATE- BRASS1.25”2.0” 2.5”3.0”DMS 329DMS-SP-S1DMS-SP-S1DMS-SP-S1100M SADDLE CLAMPS1.25”2.0” 2.5”3.0”DMS 0141DMS 0151NA NA 150MM SADDLE CLAMPS 1.25” 2.0” 2.5” 3.0”DMS 0142DMS 0152NANA26Drainage Channel Without UpstandCornerPieces11. Drainage Channel Components01992523523|***********************|HEAD OFFICEDelta House, Merlin Way, North Weald, Epping, Essex, CM16 6HR01992523523|***********************|© 2022 Delta Membrane Systems Ltd All Rights Reserved28。

1POST OFFICE BOX 655303 •DALLAS, TEXAS 75265>2.3 V at V CC = 3.3 V, T A = 25°CDSupport Mixed-Mode Voltage Operation on All Ports− 200-V Machine Model (A115-A)− 1000-V Charged-Device Model (C101)12345671413121110981CLR 1D 1CLK 1PRE 1Q 1Q GNDV CC 2CLR 2D 2CLK 2PRE 2Q 2QSN54LV74A ...J OR W PACKAGE SN74LV74A ...D, DB, DGV, NS,OR PW PACKAGE(TOP VIEW)32120199101112134567818171615142D NC 2CLK NC 2PRE1CLK NC 1PRE NC 1Q1D C L R N C 2Q 2QV C L R1Q G N D N C SN54LV74A ...FK PACKAGE(TOP VIEW)C CNC − No internal connectionSN74LV74A ...RGY PACKAGE(TOP VIEW)11478234561312111092CLR 2D 2CLK 2PRE 2Q1D 1CLK 1PRE 1Q 1Q1C L R2QV G N DC Cdescription/ordering informationThese dual positive-edge-triggered D-type flip-flops are designed for 2-V to 5.5-V V CC operation.ORDERING INFORMATIONT APACKAGE †ORDERABLEPART NUMBER TOP-SIDE MARKING QFN − RGY Reel of 1000SN74LV74ARGYR LV74A SOIC D Tube of 50SN74LV74AD SOIC − D Reel of 2500SN74LV74ADR LV74A SOP − NSReel of 2000SN74LV74ANSR 74LV74A −40°°SSOP − DB Reel of 2000SN74LV74ADBR LV74A 40C to 85CTube of 90SN74LV74APW TSSOP − PW Reel of 2000SN74LV74APWR TSSOP PW Reel of 250SN74LV74APWT LV74A TVSOP − DGV Reel of 2000SN74LV74ADGVR LV74A CDIP − JTube of 25SNJ54LV74AJ SNJ54LV74AJ −55°°CFP − W Tube of 150SNJ54LV74AW SNJ54LV74AW 55C to 125CLCCC − FKTube of 55SNJ54LV74AFKSNJ54LV74AFK†Package drawings, standard packing quantities, thermal data, symbolization, and PCB design guidelines are available at /sc/package.Copyright © 2005, Texas Instruments IncorporatedUNLESS OTHERWISE NOTED this document contains PRODUCTION DATA information current as of publication date. Products conform to specif ications per the terms of Texas Instruments standard warranty.Production processing does not necessarily include testing o all parameters.Please be aware that an important notice concerning availability, standard warranty, and use in critical applications of Texas Instruments semiconductor products and disclaimers thereto appears at the end of this data sheet.SN54LV74A, SN74LV74ADUAL POSITIVE-EDGE-TRIGGERED D-TYPE FLIP-FLOPSSCLS381L − AUGUST 1997 − REVISED APRIL 20052POST OFFICE BOX 655303 •DALLAS, TEXAS 75265description/ordering information (continued)A low level at the preset (PRE) or clear (CLR) inputs sets or resets the outputs, regardless of the levels of the other inputs. When PRE and CLR are inactive (high), data at the data (D) inputs meeting the setup-time requirements is transferred to the outputs on the positive-going edge of the clock pulse. Clock triggering occurs at a voltage level and is not directly related to the rise time of the clock pulse. Following the hold-time interval,data at the D input can be changed without affecting the levels at the outputs.These devices are fully specified for partial-power-down applications using I off . The I off circuitry disables the outputs, preventing damaging current backflow through the devices when they are powered down.FUNCTION TABLE INPUTSOUTPUTSPRE CLR CLK D Q Q L H X X H L H L X X L H L L X X H †H †H H ↑H H L H H ↑L L H HHLXQ 0Q 0†This configuration is nonstable; that is, it does not persist when PRE or CLR returns to its inactive (high) level.logic diagram, each flip-flop (positive logic)PRE DCLRQQSN54LV74A, SN74LV74ADUAL POSITIVE-EDGE-TRIGGERED D-TYPE FLIP-FLOPSSCLS381L − AUGUST 1997 − REVISED APRIL 20053POST OFFICE BOX 655303 •DALLAS, TEXAS 75265absolute maximum ratings over operating free-air temperature range (unless otherwise noted)†Supply voltage range, V CC −0.5 V to 7 V . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Input voltage range, V I (see Note 1) −0.5 V to 7 V . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Voltage range applied to any output in the high-impedanceor power-off state, V O (see Note 1) −0.5 V to 7 V . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Output voltage range, V O (see Notes 1 and 2) −0.5 V to V CC + 0.5 V . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Input clamp current, I IK (V I < 0) −20 mA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Output clamp current, I OK (V O < 0) −50 mA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Continuous output current, I O (V O = 0 to V CC ) ±25 mA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Continuous current through V CC or GND ±50 mA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Package thermal impedance, θJA (see Note 3):D package 86°C/W. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (see Note 3):DB package 96°C/W . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (see Note 3):DGV package 127°C/W . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (see Note 3):NS package 76°C/W . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (see Note 3):PW package 113°C/W . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (see Note 4):RGY package 47°C/W. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Storage temperature range, T stg −65°C to 150°C. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . †Stresses beyond those listed under “absolute maximum ratings” may cause permanent damage to the device. These are stress ratings only, and functional operation of the device at these or any other conditions beyond those indicated under “recommended operating conditions” is not implied. Exposure to absolute-maximum-rated conditions for extended periods may affect device reliability.NOTES: 1.The input and output negative-voltage ratings may be exceeded if the input and output current ratings are observed.2.This value is limited to 5.5 V maximum.3.The package thermal impedance is calculated in accordance with JESD 51-7.4.The package thermal impedance is calculated in accordance with JESD 51-5.SN54LV74A, SN74LV74ADUAL POSITIVE-EDGE-TRIGGERED D-TYPE FLIP-FLOPSSCLS381L − AUGUST 1997 − REVISED APRIL 20054POST OFFICE BOX 655303 •DALLAS, TEXAS 75265recommended operating conditions (see Note 5)SN54LV74A SN74LV74A MINMAX MIN MAX UNIT V CCSupply voltage2 5.52 5.5VV CC = 2 V1.5 1.5High level input voltage V CC =2.3 V to 2.7 V V CC ×0.7V CC ×0.7V IHHigh-level input voltageV CC = 3 V to 3.6 V V CC ×0.7V CC ×0.7VV CC = 4.5 V to 5.5 V V CC ×0.7V CC ×0.7V CC = 2 V0.50.5Low level input voltage V CC = 2.3 V to 2.7 V V CC ×0.3V CC ×0.3V ILLow-level input voltageV CC = 3 V to 3.6 V V CC ×0.3V CC ×0.3V V CC = 4.5 V to 5.5 VV CC ×0.3V CC ×0.3V I Input voltage 0 5.50 5.5V V OOutput voltage0V CC 0V CC V V CC = 2 V−50−50μA High level output current V CC = 2.3 V to 2.7 V −2−2I OHHigh-level output currentV CC = 3 V to 3.6 V −6−6V CC = 4.5 V to 5.5 V −12−12mA V CC = 2 V5050μA Low level output current V CC = 2.3 V to 2.7 V 22I OLLow-level output currentV CC = 3 V to 3.6 V 66V CC = 4.5 V to 5.5 V 1212mA V CC = 2.3 V to 2.7 V200200V CC = 3 V to 3.6 V 100100Δt/Δv Input transition rise or fall rate V CC = 4.5 V to 5.5 V2020ns/V T AOperating free-air temperature−55125−4085°C NOTE 5:All unused inputs of the device must be held at V CC or GND to ensure proper device operation. Refer to the TI application report,Implications of Slow or Floating CMOS Inputs , literature number SCBA004.electrical characteristics over recommended operating free-air temperature range (unless otherwise noted)TEST CONDITIONS SN54LV74A SN74LV74A PARAMETERTEST CONDITIONS V CC MIN TYPMAXMIN TYPMAXUNITI OH = −50 μA2 V to 5.5 VV CC −0.1V CC −0.1I OH = −2 mA 2.3 V 22V OHI OH = −6 mA 3 V 2.48 2.48VI OH = −12 mA 4.5 V 3.83.8I OL = 50 μA2 V to 5.5 V0.10.1I OL = 2 mA 2.3 V 0.40.4V OLI OL = 6 mA 3 V 0.440.44V I OL = 12 mA4.5 V 0.550.55I I V I =5.5 V or GND 0 to 5.5 V ±1±1μA I CC V I = V CC or GND,I O = 05.5 V2020μA I off V I or V O = 0 to 5.5 V 055μA =V or GND 3.3 V 22C iV I = VCC or GND 5 V22pF PRODUCT PREVIEW information concerns products in the formative ordesign phase o f development. Characteristic data and other specifications are design goals. Texas Instruments reserves the right to change or discontinue these products without notice.SN54LV74A, SN74LV74ADUAL POSITIVE-EDGE-TRIGGERED D-TYPE FLIP-FLOPSSCLS381L − AUGUST 1997 − REVISED APRIL 20055POST OFFICE BOX 655303 •DALLAS, TEXAS 75265timing requirements over recommended operating free-air temperature range, V CC = 2.5 V ±0.2 V (unless otherwise noted) (see Figure 1)T A = 25°C SN54LV74A SN74LV74A PARAMETERMIN MAXMIN MAXMIN MAXUNIT Pulse duration PRE or CLR low 899t w Pulse durationCLK 899ns Setup time before CLK Data899t su Setup time before CLK ↑PRE or CLR inactive777ns t hHold time, data after CLK ↑0.50.50.5nstiming requirements over recommended operating free-air temperature range, V CC = 3.3 V ±0.3 V(unless otherwise noted) (see Figure 1)T A = 25°C SN54LV74A SN74LV74A PARAMETERMIN MAXMIN MAXMIN MAXUNIT Pulse duration PRE or CLR low 677t w Pulse durationCLK 677ns Setup time before CLK Data677t su Setup time before CLK ↑PRE or CLR inactive555ns t hHold time, data after CLK ↑0.50.50.5nstiming requirements over recommended operating free-air temperature range, V CC = 5 V ±0.5 V(unless otherwise noted) (see Figure 1)T A = 25°C SN54LV74A SN74LV74A PARAMETERMIN MAXMIN MAXMIN MAXUNIT Pulse duration PRE or CLR low 555t w Pulse durationCLK 555ns Setup time before CLK Data555t su Setup time before CLK ↑PRE or CLR inactive333ns t hHold time, data after CLK ↑0.50.50.5nsswitching characteristics over recommended operating free-air temperature range,V CC = 2.5 V ± 0.2 V (unless otherwise noted) (see Figure 1)FROMTO LOADT A = 25°C SN54LV74A SN74LV74A PARAMETER(INPUT)(OUTPUT)CAPACITANCE MIN TYP MAXMIN MAXMIN MAXUNIT C L = 15 pF 50*100*40*40f max C L = 50 pF 30702525MHz PRE or CLRQ Q 15pF 9.8*14.8*1*17*117t pd CLK Q or Q C L = 15 pF 11.1*16.4*1*19*119ns PRE or CLRQ or Q =50pF1317.4120120t pdCLKQ or QC L = 50 pF 14.220123123ns* On products compliant to MIL-PRF-38535, this parameter is not production tested.PRODUCT PREVIEW information concerns products in the formative ordesign phase o fdevelopment. Characteristic data and other specifications are design goals. Texas Instruments reserves the right to change or discontinue these products without notice.SN54LV74A, SN74LV74ADUAL POSITIVE-EDGE-TRIGGERED D-TYPE FLIP-FLOPSSCLS381L − AUGUST 1997 − REVISED APRIL 20056POST OFFICE BOX 655303 •DALLAS, TEXAS 75265switching characteristics over recommended operating free-air temperature range,V CC = 3.3 V ± 0.3 V (unless otherwise noted) (see Figure 1)FROMTO LOADT A = 25°C SN54LV74A SN74LV74A PARAMETER(INPUT)(OUTPUT)CAPACITANCE MIN TYP MAXMIN MAXMIN MAXUNIT C L = 15 pF 80*140*70*70f max C L = 50 pF 50904545MHz PRE or CLRQ or Q 15pF 6.9*12.3*1*14.5*114.5t pd CLK Q or Q C L = 15 pF 7.9*11.9*1*14*114ns PRE or CLRQ or Q =50pF9.215.8118118t pdCLKQ or QC L = 50 pF 10.215.4117.5117.5ns* On products compliant to MIL-PRF-38535, this parameter is not production tested.switching characteristics over recommended operating free-air temperature range,V CC = 5 V ± 0.5 V (unless otherwise noted) (see Figure 1)FROMTO LOADT A = 25°C SN54LV74A SN74LV74A PARAMETER(INPUT)(OUTPUT)CAPACITANCE MIN TYP MAXMIN MAXMIN MAXUNIT C L = 15 pF 130*180*110*110f max C L = 50 pF 901407575MHz PRE or CLRQ Q 15pF 5*7.7*1*9*19t pd CLK Q or Q C L = 15 pF 5.6*7.3*1*8.5*18.5ns PRE or CLRQ or Q =50pF6.69.7111111t pdCLKQ or QC L = 50 pF 7.29.3110.5110.5ns* On products compliant to MIL-PRF-38535, this parameter is not production tested.noise characteristics, V CC = 3.3 V, C L = 50 pF, T A = 25°C (see Note 6)SN74LV74A PARAMETERMINTYP MAX UNIT V OL(P)Quiet output, maximum dynamic V OL 0.10.8V V OL(V)Quiet output, minimum dynamic V OL 0−0.8V V OH(V)Quiet output, minimum dynamic V OH 3.2V V IH(D)High-level dynamic input voltage 2.31V V IL(D)Low-level dynamic input voltage0.99VNOTE 6:Characteristics are for surface-mount packages only.operating characteristics, T A = 25°CPARAMETERTEST CONDITIONS V CC TYP UNIT Power dissipation capacitance =50pFf =10MHz 3.3 V 21C pdPower dissipation capacitanceC L = 50 pF, f = 10 MHz5 V23pFSN54LV74A, SN74LV74ADUAL POSITIVE-EDGE-TRIGGERED D-TYPE FLIP-FLOPSSCLS381L − AUGUST 1997 − REVISED APRIL 20057POST OFFICE BOX 655303 •DALLAS, TEXAS 75265PARAMETER MEASUREMENT INFORMATIONV CC V CC0 V0 VVOLTAGE WAVEFORMS SETUP AND HOLD TIMESData InputInputOut-of-PhaseOutputIn-Phase OutputTiming InputVOLTAGE WAVEFORMS PROPAGATION DELAY TIMESINVERTING AND NONINVERTING OUTPUTSOutput ControlOutput Waveform 1S1 at V CC (see Note B)OutputWaveform 2S1 at GND (see Note B)V OLV OH ≈V CC0 V≈0 V V CCVOLTAGE WAVEFORMS ENABLE AND DISABLE TIMES LOW- AND HIGH-LEVEL ENABLINGt PLH /t PHL t PLZ /t PZL t PHZ /t PZH Open DrainOpen V CC GND V CCTEST S1V CC0 VVOLTAGE WAVEFORMS PULSE DURATIONInputNOTES: A.C L includes probe and jig capacitance.B.Waveform 1 is for an output with internal conditions such that the output is low, except when disabled by the output control.Waveform 2 is for an output with internal conditions such that the output is high, except when disabled by the output control.C.All input pulses are supplied by generators having the following characteristics:PRR ≤ 1 MHz, Z O = 50 Ω, t r ≤3 ns, t f ≤ 3 ns.D.The outputs are measured one at a time, with one input transition per measurement.E.t PLZ and t PHZ are the same as t dis .F.t PZL and t PZH are the same as t en .G.t PHL and t PLH are the same as t pd .H.All parameters and waveforms are not applicable to all devices.From Output Under TestLOAD CIRCUIT FOR3-STATE AND OPEN-DRAIN OUTPUTSFrom Output Under TestLOAD CIRCUIT FOR TOTEM-POLE OUTPUTS Open Figure 1. Load Circuit and Voltage WaveformsPACKAGING INFORMATIONOrderable Device Status(1)PackageType PackageDrawingPins PackageQtyEco Plan(2)Lead/Ball Finish MSL Peak Temp(3)SN74LV74AD ACTIVE SOIC D1450Green(RoHS&no Sb/Br)CU NIPDAU Level-1-260C-UNLIMSN74LV74ADBLE OBSOLETE SSOP DB14TBD Call TI Call TISN74LV74ADBR ACTIVE SSOP DB142000Green(RoHS&no Sb/Br)CU NIPDAU Level-1-260C-UNLIMSN74LV74ADBRE4ACTIVE SSOP DB142000Green(RoHS&no Sb/Br)CU NIPDAU Level-1-260C-UNLIMSN74LV74ADBRG4ACTIVE SSOP DB142000Green(RoHS&no Sb/Br)CU NIPDAU Level-1-260C-UNLIMSN74LV74ADE4ACTIVE SOIC D1450Green(RoHS&no Sb/Br)CU NIPDAU Level-1-260C-UNLIMSN74LV74ADG4ACTIVE SOIC D1450Green(RoHS&no Sb/Br)CU NIPDAU Level-1-260C-UNLIMSN74LV74ADGVR ACTIVE TVSOP DGV142000Green(RoHS&no Sb/Br)CU NIPDAU Level-1-260C-UNLIMSN74LV74ADGVRE4ACTIVE TVSOP DGV142000Green(RoHS&no Sb/Br)CU NIPDAU Level-1-260C-UNLIMSN74LV74ADGVRG4ACTIVE TVSOP DGV142000Green(RoHS&no Sb/Br)CU NIPDAU Level-1-260C-UNLIMSN74LV74ADR ACTIVE SOIC D142500Green(RoHS&no Sb/Br)CU NIPDAU Level-1-260C-UNLIMSN74LV74ADRE4ACTIVE SOIC D142500Green(RoHS&no Sb/Br)CU NIPDAU Level-1-260C-UNLIMSN74LV74ADRG4ACTIVE SOIC D142500Green(RoHS&no Sb/Br)CU NIPDAU Level-1-260C-UNLIMSN74LV74ANSR ACTIVE SO NS142000Green(RoHS&no Sb/Br)CU NIPDAU Level-1-260C-UNLIMSN74LV74ANSRG4ACTIVE SO NS142000Green(RoHS&no Sb/Br)CU NIPDAU Level-1-260C-UNLIMSN74LV74APW ACTIVE TSSOP PW1490Green(RoHS&no Sb/Br)CU NIPDAU Level-1-260C-UNLIMSN74LV74APWE4ACTIVE TSSOP PW1490Green(RoHS&no Sb/Br)CU NIPDAU Level-1-260C-UNLIMSN74LV74APWG4ACTIVE TSSOP PW1490Green(RoHS&no Sb/Br)CU NIPDAU Level-1-260C-UNLIM SN74LV74APWLE OBSOLETE TSSOP PW14TBD Call TI Call TISN74LV74APWR ACTIVE TSSOP PW142000Green(RoHS&no Sb/Br)CU NIPDAU Level-1-260C-UNLIMSN74LV74APWRE4ACTIVE TSSOP PW142000Green(RoHS&no Sb/Br)CU NIPDAU Level-1-260C-UNLIMSN74LV74APWRG4ACTIVE TSSOP PW142000Green(RoHS&no Sb/Br)CU NIPDAU Level-1-260C-UNLIMSN74LV74APWT ACTIVE TSSOP PW14250Green(RoHS&no Sb/Br)CU NIPDAU Level-1-260C-UNLIMSN74LV74APWTE4ACTIVE TSSOP PW14250Green(RoHS&no Sb/Br)CU NIPDAU Level-1-260C-UNLIMSN74LV74APWTG4ACTIVE TSSOP PW14250Green(RoHS&no Sb/Br)CU NIPDAU Level-1-260C-UNLIMSN74LV74ARGYR ACTIVE VQFN RGY143000Green(RoHS&CU NIPDAU Level-2-260C-1YEAROrderable Device Status(1)PackageType PackageDrawingPins PackageQtyEco Plan(2)Lead/Ball Finish MSL Peak Temp(3)no Sb/Br)SN74LV74ARGYRG4ACTIVE VQFN RGY143000Green(RoHS&no Sb/Br)CU NIPDAU Level-2-260C-1YEAR(1)The marketing status values are defined as follows:ACTIVE:Product device recommended for new designs.LIFEBUY:TI has announced that the device will be discontinued,and a lifetime-buy period is in effect.NRND:Not recommended for new designs.Device is in production to support existing customers,but TI does not recommend using this part in a new design.PREVIEW:Device has been announced but is not in production.Samples may or may not be available.OBSOLETE:TI has discontinued the production of the device.(2)Eco Plan-The planned eco-friendly classification:Pb-Free(RoHS),Pb-Free(RoHS Exempt),or Green(RoHS&no Sb/Br)-please check /productcontent for the latest availability information and additional product content details.TBD:The Pb-Free/Green conversion plan has not been defined.Pb-Free(RoHS):TI's terms"Lead-Free"or"Pb-Free"mean semiconductor products that are compatible with the current RoHS requirements for all6substances,including the requirement that lead not exceed0.1%by weight in homogeneous materials.Where designed to be soldered at high temperatures,TI Pb-Free products are suitable for use in specified lead-free processes.Pb-Free(RoHS Exempt):This component has a RoHS exemption for either1)lead-based flip-chip solder bumps used between the die and package,or2)lead-based die adhesive used between the die and leadframe.The component is otherwise considered Pb-Free(RoHS compatible)as defined above.Green(RoHS&no Sb/Br):TI defines"Green"to mean Pb-Free(RoHS compatible),and free of Bromine(Br)and Antimony(Sb)based flame retardants(Br or Sb do not exceed0.1%by weight in homogeneous material)(3)MSL,Peak Temp.--The Moisture Sensitivity Level rating according to the JEDEC industry standard classifications,and peak solder temperature.Important Information and Disclaimer:The information provided on this page represents TI's knowledge and belief as of the date that it is provided.TI bases its knowledge and belief on information provided by third parties,and makes no representation or warranty as to the accuracy of such information.Efforts are underway to better integrate information from third parties.TI has taken and continues to take reasonable steps to provide representative and accurate information but may not have conducted destructive testing or chemical analysis on incoming materials and chemicals.TI and TI suppliers consider certain information to be proprietary,and thus CAS numbers and other limited information may not be available for release.In no event shall TI's liability arising out of such information exceed the total purchase price of the TI part(s)at issue in this document sold by TI to Customer on an annual basis.OTHER QUALIFIED VERSIONS OF SN74LV74A:•Automotive:SN74LV74A-Q1•Enhanced Product:SN74LV74A-EPNOTE:Qualified Version Definitions:•Automotive-Q100devices qualified for high-reliability automotive applications targeting zero defects•Enhanced Product-Supports Defense,Aerospace and Medical ApplicationsTAPE AND REELINFORMATION*All dimensionsare nominalDevicePackage Type Package Drawing Pins SPQReel Diameter (mm)Reel Width W1(mm)A0(mm)B0(mm)K0(mm)P1(mm)W (mm)Pin1Quadrant SN74LV74ADBR SSOP DB 142000330.016.48.2 6.6 2.512.016.0Q1SN74LV74ADGVR TVSOP DGV 142000330.012.4 6.8 4.0 1.68.012.0Q1SN74LV74ADR SOIC D 142500330.016.4 6.59.0 2.18.016.0Q1SN74LV74ANSR SO NS 142000330.016.48.210.5 2.512.016.0Q1SN74LV74APWR TSSOP PW 142000330.012.4 6.9 5.6 1.68.012.0Q1SN74LV74APWR TSSOP PW 142000330.012.47.0 5.6 1.68.012.0Q1SN74LV74APWRG4TSSOP PW 142000330.012.4 6.9 5.6 1.68.012.0Q1SN74LV74APWT TSSOP PW 14250330.012.4 6.9 5.6 1.68.012.0Q1SN74LV74ARGYRVQFNRGY143000330.012.43.753.751.158.012.0Q1PACKAGE MATERIALS INFORMATION14-Jul-2012*All dimensionsare nominalDevice Package TypePackage DrawingPins SPQ Length (mm)Width (mm)Height (mm)SN74LV74ADBR SSOP DB 142000367.0367.038.0SN74LV74ADGVR TVSOP DGV 142000367.0367.035.0SN74LV74ADR SOIC D 142500367.0367.038.0SN74LV74ANSR SO NS 142000367.0367.038.0SN74LV74APWR TSSOP PW 142000367.0367.035.0SN74LV74APWR TSSOP PW 142000364.0364.027.0SN74LV74APWRG4TSSOP PW 142000367.0367.035.0SN74LV74APWT TSSOP PW 14250367.0367.035.0SN74LV74ARGYRVQFNRGY143000367.0367.035.0PACKAGE MATERIALS INFORMATION14-Jul-2012Pack Materials-Page 2IMPORTANT NOTICETexas Instruments Incorporated and its subsidiaries(TI)reserve the right to make corrections,enhancements,improvements and other changes to its semiconductor products and services per JESD46C and to discontinue any product or service per JESD48B.Buyers should obtain the latest relevant information before placing orders and should verify that 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Chapter 1414.1 80(max) 4.5(max)56.25 mV o d io i v A v v v ==−=⇒=So(max)i rms v = ______________________________________________________________________________________14.2(a) 2 4.50.028125 mA 1604.5 4.5 mA 1L i i ==== Output Circuit 4.528 mA = 4.50.05625 V 80o i i v v v A −=−=⇒=−(b) 4.515 mA (min)300o o L L L v i R R R ≈==⇒=Ω______________________________________________________________________________________14.3 (1)2 V o v = (2)212.5 mV v = (3)4210OL A =× (4) 18 V v μ=(5)1000OL A =______________________________________________________________________________________14.4(a) ()42857.216.512012−=−=−=∞R R A CL 42376.211042857.22142857.215−=+−=CL A ()%0224.0%10042857.2142857.2142376.21−=×−−−− (b) ()634146.142.812012−=−=−=∞R R A CL 63186.1410634146.151634146.145−=+−=CL A ()%0156.0%100634146.14634146.1463186.14−=×−−−− ______________________________________________________________________________________14.5(a) (i) 90863.710291176.7191176.71028.647118.647144=×+=×⎟⎠⎞⎜⎝⎛+++=CL A (ii) %03956.0%10091176.791176.790863.7−=×− (b) (i) 84966.71091176.7191176.73=+=CL A (ii) %785.0%10091176.791176.784966.7−=×− ______________________________________________________________________________________14.6(a) 12091.151050005.1102110.15121241231212=⇒⎟⎠⎞⎜⎝⎛×+−=×⎟⎠⎞⎜⎝⎛++−=−−R R R R R R R R R R (b) 1160.1510512091.16112091.154−=×+−=CL A ______________________________________________________________________________________14.7()()5109991.890190900001.01×=⇒+=−OL OLA A ______________________________________________________________________________________14.8()()499911110002.01=⇒+=−=OL OLCL A A A ______________________________________________________________________________________14.9(a) ()()001.0121001.0121012±±=+=R R A 02.10979.2021.210max ==A 98.9021.2179.209min ==A So 02.1098.9≤≤A (b) 009.101002.11102.104max =+=A 969.91098.10198.94min =+=A So 009.10969.9≤≤A ______________________________________________________________________________________14.1010110012010011212and so that 111I L iL I i v v v v v v A R R R v v A v v v R R R R R −−=+=−=−⎛⎞+=++⎜⎟⎝⎠1vSo 01201211111I L i v v R R A R R R ⎡⎤⎛⎞=−+++⎢⎥⎜⎟⎝⎠⎣⎦ Then 012012(1/)11111CL I L i v R A v R A R R R −==⎡⎤⎛⎞+++⎢⎥⎜⎟⎝⎠⎣⎦ From Equation (14.20) for and L R =∞00R =02(1)1111L if i A R R R +=+⋅ a. For1 k i R =Ω 33(1/20)11111100201001100.05[0.01 1.0610]CL A −−=⎡⎤⎛⎞+++⎜⎟⎢⎥⎝⎠⎣⎦−=+×or3 4.521111090.8 1100CL if if A R R ⇒=−+=+⇒=Ω b. For10 k i R =Ω 34(1/20)111111002010010100.05[0.01 1.610]CL A −−=⎡⎤⎛⎞+++⎜⎟⎢⎥⎝⎠⎣⎦−=+× or 4.92CL A ⇒=−31111098.9 10100if if R R +=+⇒=Ω c. For100 k i R =Ω 35(1/20)1111110020100100100.05[0.01710]CL A −−=⎡⎤⎛⎞+++⎜⎟⎢⎥⎝⎠⎣⎦−=+×or 3 4.9651111099.8 100100CL if if A R R ⇒=−+=+⇒=Ω ______________________________________________________________________________________14.1121211111o CL i OL R R v A v R A R ⎛⎞+⎜⎟⎝⎠==⎡⎤⎛⎞++⎢⎥⎜⎟⎝⎠⎣⎦ For the ideal: 210.10150.002R R ⎛⎞+==⎜⎟⎝⎠0 ()(0.10)(10.001)0.0999ov actual =−= So 0.09995049.9510.0021(50)OL A ==+which yields 1000OLA = ______________________________________________________________________________________14.12From Equation (14.18) 211121111OL o o vf L o A R R v A v R R R ⎛⎞−−⎜⎟⎝⎠==⎛⎞++⎜⎟⎝⎠ Or 331131151011100(4.9999910)111 1.111011004.50449510o o v v v v ⎛⎞×−−⎜⎟−×⎝⎠=⋅=⎛⎞++⎜⎟⎝⎠=−×⋅1v ⋅ Now 11111i v v i K v R v −=≡Then 11i v v KR v −=1 which yields 111i v v KR =+ Now, from Equation (14.20) 3311510111011101001101005.001110(0.1)(0.01)45.154951.11K ⎡⎤+×+⎢⎥=+⎢⎥⎢⎥++⎢⎥⎣⎦⎡⎤×=+=⎢⎥⎣⎦Then ()()145.15495101452.5495i i v v v ==+We find31 4.50449510452.5495i o v v ⎡⎤=−×⎢⎥⎣⎦ Or 119.9536o vf i v A v ==− For the second stage,L R =∞ 332131111151011100 4.9504851011110011151049.6148511010011001(49.61485)(10)1497.1485o o o o v v K v v v v KR ⎛⎞×−−⎜⎟⎝⎠′′=⋅=−⎛⎞+⎜⎟⎝⎠⎡⎤⎢⎥+×≡+=⎢⎥⎢⎥+⎢⎥⎣⎦′===++1v ×⋅ Then 321 4.950485109.95776497.1485o o v v −×==−So 2(9.9536)(9.95776)99.12o vf vf iv A A v ==−−⇒= ______________________________________________________________________________________14.13a.10113120I i v v v v v R R R R −−++=+ (1) 0131223111I i i v v v R R R R R R R ⎡⎤++=+⎢⎥++⎣⎦00001020L d L v v A v v v R R R −−++= (2) or 010*******L dL A v v v R R R R R ⎡⎤++=+⎢⎥⎣⎦ 13I d i i v v v R R R ⎛⎞−=⋅⎜⎟+⎝⎠ (3)So substituting numbers:011110201040401020I v v v 1⎡⎤++=+⎢⎥+⎣⎦+ (1)or10[0.15833][0.025][0.03333]I v v v =+ 410(10)11110.540400.5d v v v ⎡⎤++=+⎢⎥⎣⎦ (2) or[][]()4013.0250.025210dv v =+×v ()11200.66671020I d v v v v −⎛⎞=⋅=⎜⎟+⎝⎠I v − (3)So[][]()()()4013.0250.0252100.6667I v v v =+×−1v (2) or []44013.025 1.33310 1.33310I v v =×−×v ) From (1):()(100.15790.2105I v v v =+ Then []()()44003403.025 1.33310 1.333100.15790.21052.107810 1.052410I I I v v v v v v =×−×+⎡⎤⎣⎦⎡⎤⎡⎤×=×⎣⎦⎣⎦or 0 4.993CL I v A v == To find:if R Use Equation (14.27) ()31210.50.5114010110.50.50.51104014040(40)(1.5125){(0.125)(1.5125)0.0003125}25I d I d i v v i v ⎛⎞++⎜⎟⎝⎠⎧⎫⎛⎞⎛⎞=+++−−⎨⎬⎜⎟⎜⎟⎝⎠⎝⎠⎩⎭=−v −or (1.5125){0.18875}25I I d i v =−v I Nowand(20)d I i I v i R i ==1(20)I I v v i =− So(1.5125)[(20)][0.18875]25(20)[505.3](0.18875)I I I I I i v i i i v =−⋅−= or 2677 k I I v i =Ω Now 102677 2.687 M if if R R =+⇒=ΩTo determine 0:f R Using Equation (14.36)30200111110400.5111020L f i A R R R R R ⎡⎤⎡⎤⎢⎥⎢⎥⎢⎥⎢⎥=⋅=⋅′⎢⎥⎢⎥++⎢⎥⎢⎥⎣⎦⎣⎦or0 3.5 f R ′=Ω Then 0 1 k f R =ΩΩ0 3.49 f R ⇒=Ωb. Using Equation (14.16) 35(10)(0.05)%10CL CL CL CL dA dA A A ⎛⎞=−⇒=−⎜⎟⎝⎠ ______________________________________________________________________________________14.14(a)(b) (i)()o O I OL O i O I R A R υυυυυ−−=− ⎟⎟⎠⎞⎜⎜⎝⎛++=+o OL o iO o I OL i IR A R R R A R 11υυυ ⎟⎟⎠⎞⎜⎜⎝⎛×++=⎟⎟⎠⎞⎜⎜⎝⎛×+110511101110510133O I υυ()(33100011.5100001.5×=×O I υυ) 9998.0=IO υυ (ii) ()ix o x OL x x R V R V A V I +−−= 101110511113+×+=++==i o OL of x x R R A R V IΩ≅2.0of R______________________________________________________________________________________14.151011210121201040111201040201040I I I I v v v v v v v v v v −−−+=⎡⎤++=++⎢⎥⎣⎦ andso that 00L v A =−1v 010L v v A =−Then 1203200120000117(0.05)(0.10)4040210[2.5087510]1.993 3.9862 1.9930.352I I I I v v v v v v v v v %v v −⎧⎫⎛⎞+=−+⋅⎨⎬⎜⎟×⎝⎠⎩⎭=−×⇒=−−ΔΔ−=⇒= ______________________________________________________________________________________14.16224040.840105B v v v ⎛⎞⎛⎞===⎜⎟⎜⎟+⎝⎠⎝⎠2v (1) 011040A A v v v v −−= 011110401040A v v v ⎛⎞+=+⎜⎟⎝⎠ (2)10(0.1)(0.025)(0.125)A v v v += 000()L d L B A v A v A v v ==−(3)or002020020[0.8]0.80.8L A A LA L v A v v v v v A v v v A =−−=−⇒=−Then 01020120320021(0.1)(0.025)(0.125)0.80.125(0.1)(0.1)0.02510[2.512510]3.98010.01990.49754L d d d v v v v A v v v v v A v v A %A −⎡⎤+=−⎢⎥⎣⎦⎡⎤−=−+⎢⎥⎣⎦=−×⇒==−Δ⇒=⇒ ______________________________________________________________________________________14.17a. Considering the second op-amp and Equation (14.20), we have 211111001010.101100.1(0.1)(11)10.1if R ⎡⎤⎢⎥+=+⋅=+⎢⎥⎢⎥+⎢⎥⎣⎦ So 20.0109 k if R =ΩThe effective load on the first op-amp is then 120.10.1109 k L if R R =+=Ω Again using Equation (14.20), we have 11100111110.0170.11090.101110111.01710.11091if R ++=+⋅=+++ so that 99.1 if R =Ω b. To determine 0:f RFor the first op-amp, we can write, using Equation (14.36) 020101111100401111||10||L f i A R R R R R ⎡⎤⎡⎤⎢⎥⎢⎥⎢⎥⎢⎥=⋅=⋅⎢⎥⎢⎥++⎢⎥⎢⎥⎣⎦⎣⎦ which yields010.021 k f R =Ω For the second op-amp, then020*******()||11000.1011(0.121)||10L f f i A R R R R R R ⎡⎤⎢⎥⎢⎥=⋅⎢⎥+⎢⎥+⎣⎦⎡⎤⎢⎥⎢⎥=⋅⎢⎥+⎢⎥⎣⎦ or018.4 f R =Ω c. To find the gain, consider the second op-amp.0122202()0.10.1d d d i v v v v v R −−−−+= (1) 010221110.10.1100.10.1d v v v ⎛⎞+++=−⎜⎟⎝⎠ or 01202(10)(20.1)(10)d v v v +=−02020220()00.1L d d v A v v v R −−−+= (2) 0202202210010110.10.1(11)(90)0d d v v v v v ⎛⎞−−+⎜⎟⎝⎠−==−or 202(0.1222)d v v = Then Equation (1) becomes010202(10)(0.1222)(20.1)(10)v v v += or0102(1.246)v v =− Now consider the first op-amp.1110()11I d d d i v v v v v R −−−−+=1 (1) 10111(1)(1)1101I d v v v ⎛⎞+++=−⎜⎟⎝⎠1(1)(2.1)(1)v v v +=− or101I d 010*******()00.11091L d d v v A v v v R −−−++= (2) 011011111100100.11091111(11.017)(99)0d d v v v v ⎛⎞⎛++−−=⎜⎟⎜⎝⎠⎝−=⎞⎟⎠−or 101(0.1113)d v v = Then Equation (1) becomes0101(1)(0.1113)(2.1)I v v v += or01(1.234)I v v =− We had0102(1.246)v v =− So02(1.246)(1.234)I v v = or 020.650I v v =d. Ideal021Iv v = So ratio of actual to ideal0.650.=______________________________________________________________________________________14.18(a) For the op-amp. 60310L dB A f ⋅= 6341050 Hz 210dB f ==× For the closed-loop amplifier. 631040 kHz 25dB f == (b) Open-loop amplifier.444310A f f ==×=10 Closed-loop amplifier330.2524.255dB dB f f f f −===⇒______________________________________________________________________________________14.19dB,100=o A 510=⇒o A dB,38=A 43.79=A Then 2451011043.79⎟⎟⎠⎞⎜⎜⎝⎛+=PD f 94.743.79101054=⇒≅PD PD f f Hz Hz()()551094.794.710×==GBW ______________________________________________________________________________________14.20(a) 11151501112=⎟⎠⎞⎜⎝⎛+=⎟⎟⎠⎞⎜⎜⎝⎛+=R R A CLO kHz()10911102.1336=⇒=×=−−dB dB T f f f (b) ()()()()⎥⎦⎤⎢⎣⎡±±+=05.011505.011501CLO A ()05.1225.145.1571max =+=CLO A ()05.1075.155.1421min =+=CLO A Then05.1205.10≤≤CLO AkHz ()6.9905.12102.1336=⇒=×=−−dB dB T f f f kHz()4.11905.10102.1336=⇒=×=−−dB dB T f f f Then kHz4.1196.993≤≤−dB f ______________________________________________________________________________________14.21The open loop gain can be written as 006()11510L PD A A f f f j j f =⎛⎞⎛⎞+⋅+⋅⎜⎟⎜⎟×⎝⎠⎝⎠ where 50210.A =× The closed-loop response is 001L CL LA A A β=+ At low frequency, 552101001(210β×=+×) So that39.99510.β−=× Assuming the second pole is the same for both the open-loop and closed-loop, then116tan tan 510PD f f f φ−−⎛⎞⎛⎞=−−⎜⎟⎜⎟×⎝⎠⎝⎠ For a phase margin of80 ,°100.φ=−°So 1610090tan 510f −⎛⎞−=−−⎜⎟×⎝⎠ or58.81610 Hz f =× Then051L A == or 558.81610 1.969610PD f ×≅× or 4.48 HzPD f = ______________________________________________________________________________________14.22(a) 1st stage33(10) 1 100dB dB f MHz f kHz −−=⇒= 2nd stage33(50) 1 20dB dB f MHz f kHz −−=⇒= Bandwidth of overall system20 kHz ≅(b) If each stage has the same gain, so 250022.36K K =⇒= Then bandwidth of each stage33(22.36) 1 44.7dB dB f MHz f kHz −−=⇒= ______________________________________________________________________________________14.23(a) 9978.91051110.101141212−=×+−=⎟⎠⎞⎜⎝⎛++−=O CLO A R R R R A kHz()033.1509978.9105.1336=⇒=×=−−dB dB T f f f (b) ()34.9999978.93−=−=CLO A At ; dB f −364.706234.999==⇒CL AThen 323310033.150134.99964.706⎥⎥⎦⎤⎢⎢⎣⎡⎟⎟⎠⎞⎜⎜⎝⎛×+=−dB f 49.7664.70634.99910033.1501323233=⇒⎟⎠⎞⎜⎝⎛=⎥⎥⎦⎤⎢⎢⎣⎡⎟⎟⎠⎞⎜⎜⎝⎛×+−−dB dB f f kHz ______________________________________________________________________________________14.24466333(510)1020 (25)1040 1PD PD dB dB vov v dB f f Hzf f kHzA A A fj f −−−×=⇒=⇒==⇒=+ At 30.520 dB f f k −==Hz22.36v AAt 3280 dB f f k −==Hz11.18v A = ______________________________________________________________________________________14.25 36(2010)1050vf vf MAX MAX A A ×⋅=⇒= ______________________________________________________________________________________14.26(a) ()159521052max 6max =⇒×==f V SR f PO ππkHz (b) ()5.5305.12105max 6max =⇒×=f f πkHz (c) ()99.14.02105max 6max =⇒×=f f πMHz ______________________________________________________________________________________14.27a. Using Equation (14.55), 6038102(25010)P V π×=× or 0 5.09 V P V =b.Period 6311410 s 25010T f −===××One-fourth period 1 sμ= 00Slope 8 V/s 18 VP P V SR s V μμ===⇒= ______________________________________________________________________________________14.28 PO V SR f π2max = V/s()()531054.71012102×=×=πSR Or V/754.0=SR μs______________________________________________________________________________________14.29(a) 0.521063.0102063max =⇒×=×=PO POV V f πV (b) ()87.231020210336=××=πPO V V ______________________________________________________________________________________14.30For input (a), maximum output is 5 V. 1 V/μs S R =soFor input (b), maximum output is 2 V.For input (c), maximum output is 0.5 V so the output is______________________________________________________________________________________14.31 For input (a),01max 3 V.v =Then02max 3(3)9 V v ==For input (b),01max 1.5 V.v =Then()02max 31.5 4.5V v ==______________________________________________________________________________________14.32111exp ,BE S T V I I V ⎛⎞=⎜⎟⎝⎠ 222exp BE S T V I I V ⎛⎞=⎜⎟⎝⎠ Want so12,I I = 1411214212510(1)exp 1510(1)exp (1)exp (1)BE T BE T BE BE T V x V I I V x V V V x x V −−⎛⎞×+⎜⎟⎝⎠==⎛⎞×−⎜⎟⎝⎠⎛⎞−+=⎜⎟−⎝⎠Or 211exp exp 10.0025exp 1.100.026OS BE BE T T V V V x x V ⎛⎞⎛−+==⎜⎟⎜−⎝⎠⎝⎛⎞==⎜⎟⎝⎠V ⎞⎟⎠Now 1(1)(1.10)x x +=−⇒ 0.0476 4.76%x =⇒______________________________________________________________________________________14.33(a) Balanced circuit, A154105−×=S I (b) From Eq. (14.62), 51=CE υV, 4.42.16.52=−=CE υV⎟⎠⎞⎜⎝⎛+⎟⎠⎞⎜⎝⎛+⋅=++802.111204.41806.011205143S S I I()()015.1036667.10075.1041667.143⋅=S S I I 1544310939.40123.1−×=⇒=S S S I I I A (c) 51=CE υV, 1.35.26.52=−=CE υV ⎟⎠⎞⎜⎝⎛+⎟⎠⎞⎜⎝⎛+⋅=++805.211201.31806.011205143S S I I()()03125.1025833.10075.1041667.143⋅=S S I I 1544310811.403937.1−×=⇒=S S S I I I A ______________________________________________________________________________________14.34μ150=n K A/V 2()()μx x x K n 30011501150=−−+=ΔA/V2 ⎟⎟⎠⎞⎜⎜⎝⎛Δ=n n n Q OS K K K I V 221()01837.08165.015030015022002110153=⇒=⎟⎠⎞⎜⎝⎛=×−x x x ______________________________________________________________________________________14.35(a) V()()3310603001021030−−×±−=×±−=O υ So 240.0360.0−≤≤−O υV (b) V()06.0310*******±−=×±−=−O υ So 94.206.3−≤≤−O υ V______________________________________________________________________________________14.36()2sin 2530±−=t O ωυmV06.0sin 75.0±−=t O ωυVSo ()(06.0sin 75.006.0sin 75.0)+−≤≤−−t t O ωυω V______________________________________________________________________________________14.373840.510510 10I A −−×==×Also 01i o o dV I I C V Idt t dt C C =⇒==∫⋅Then 836510511010t t s −−×=⇒=×0______________________________________________________________________________________14.38(a) (31010011±⎟⎠⎞⎜⎝⎛+=O υ) mV, 33331≤≤−O υmV ()33310502±±⎟⎠⎞⎜⎝⎛−=O υ mV, 1801802≤≤−O υmV (b) ()()310111±=O υ mV, 143771≤≤⇒O υmV()730314352−=+−=O υmV()37037752−=−−=O υmVSo 37.073.02−≤≤−O υV(c) ()()3100111±=O υ mV133.1067.11≤≤O υV()68.5003.0133.152−=+−=O υV()32.5003.0067.152−=−−=O υVSo 32.568.52−≤≤−O υV______________________________________________________________________________________14.39 due to 0v I v 01(0.5)10.9545 V 1.1v ⎛⎞=+=⎜⎟⎝⎠ Wiper arm at (using superposition) 10 V,V +=151154||0.0909(10)(10)||0.0909100.090R R v R R R ⎛⎞⎛⎞==⎜⎟⎜⎟++⎝⎠⎝⎠= Then 011(0.090)0.0901v ⎛⎞=−=−⎜⎟⎝⎠Wiper arm in center, and10v =020v = Wiper arm at10 V,V −=−10.090v =− So030.090v = Finally, total output (from superposition)0:v Wiper arm at,V + 00.8645 Vv = Wiper arm in center, 00.9545 V v = Wiper arm at,V − 0 1.0445 V v = ______________________________________________________________________________________14.40 a.120.5||250.490 k R R ′′===Ω or 12490 R R ′′==Ωb. From Equation (14.75), 6114621412510(0.026) ln (0.125)21012510(0.026) ln (0.125)2.210R R −−−−⎛⎞×′+⎜⎟×⎝⎠⎛⎞×′=+⎜⎟×⎝⎠12210.586452(0.125)0.583974(0.125)0.002478(0.125)()R R R R ′′+=+′′=−So210.0198 k 19.8 R R ′′−=Ω⇒Ω Then 2121(1)0.0198(1)(0.5)(1)(50)(0.5)(50)0.0198(0.5)(1)(50)(0.5)(50)25(1)250.019850.5500.550(0.550)(2525)(25)(50.550)0.0198(50.550)(0.550)x x x xR x R R R R x R R xR x x x x x x x xx x x x x x −×−=+−+−−=+−+−−=−++−−−=−+{}{}{}{}22222250.50.5505050.5500.019825.252525252500250.50.019825.25250025000.50.019998 1.98 1.981.98 2.980.4802x x x x x x x x x x x x x x x x x −+−−+=+−−−=+−−=+−−+==So 0.183x = and 10.81x −=7ΩΩ ______________________________________________________________________________________14.411122||150.5||150.4839 k ||350.5||350.4930 k R R R R ′===′=== From Equation (14.75), 121122341221121112222211222(0.026) ln (0.026) ln (0.026) ln (0.026) ln 1(0.026) ln (0.4930)1(0.9815)C C C C S S C C C C C C C C C C C C C C i i i R i R I I i i R i R i i i R i R i i R i i i i i ⎛⎞⎛⎞′′+=+⎜⎟⎜⎟⎝⎠⎝⎠⎛⎞′′=−⎜⎟⎝⎠′⎛⎞⎡⎤′=−⋅⎜⎟⎢⎥′⎝⎠⎣⎦⎛⎞=−⎜⎟⎝⎠⎡⎤⎛⎞⎢⎥⎜⎟⎝⎠⎣⎦ By trial and error: 1252 A C i μ= and 2248 A C i μ=or 12 1.0155C C i i = ______________________________________________________________________________________14.42(a) ()()()2.010********=×=−A O μυV Insert resistor3R ()()09.92020011022.03362=⇒⎟⎠⎞⎜⎝⎛+×−=−=−R R A O μυk Ω (b) ()()()16.010200108.0368.0=××=−A O μυV ()()09.29202001105.016.03365.0=⇒⎟⎠⎞⎜⎝⎛+×−=−=−R R A O μυk Ω ______________________________________________________________________________________14.43(a) V ()()3.010*********−=××−=−=−R I B O υ(b) ()5.03.002.015150−=−−=O υV (c) ()1.03.002.015150−=−−−=O υV (d) ()3.13.01.015150−=−−=O υV ______________________________________________________________________________________14.44(a) V ()()15.010250106.036=××=−O υ(b) ()()478.015.0008.041=+=O υV(c) ()()0065.015.00035.041=+−=O υV(d) ()()15.0sin 205.015.0sin 005.041+=+=t t O ωωυ (V)______________________________________________________________________________________14.45a.For 2 1 A,B I μ= then()(6401010v −=−) or00.010 Vv =− b. If a 10 resistor is included in the feedback loop k ΩNow021(10)(10)0B B v I I =−+= Circuit is compensated if12.B B I I =______________________________________________________________________________________14.46From Equation (14.83), we haveΩ 020S v R I = where and 240 k R =0 3 A.S I μ= Then()(3604010310v −=××) or 00.12 V v = ______________________________________________________________________________________14.47a. Assume all bias currents are in the same direction and into each op-amp.()()()6501101100 k 10100.1 V B v I v −=Ω=⇒=Then ()()()()()(020******* k 0.15105100.50.05B v v I −=−+Ω=−+×=−+)or 020.45 V v =− b. Connect resistor to noninverting terminal of first op-amp, and310||1009.09 k R ==ΩΩ resistor to noninverting terminal of second op-amp.310||508.33 k R ==______________________________________________________________________________________14.48a. For a constant current through a capacitor. 001 t v I C =∫dt or 60060.110(0.1)10v t v −−×=⋅⇒=t b.At10 s,t =0 1 V v = c. Then 1240010010(10)10v t v −−−×=⋅⇒=t At10 s,t =0 1 mV v = ______________________________________________________________________________________14.49(a) V()()15.010********=××=−O υ 15.02=O υV ()()()09.010*******.02020363−=××+−=−O υV (b) 33.85010==A R k Ω 102020==B R k Ω(c) V()()015.0103.01050631±=××±=−O υ 015.02±=O υVV()()021.0015.0103.01020633±=±××±=−O υ______________________________________________________________________________________14.50a. Using Equation (14.79),Circuit (a),()()()()63630500.81050100.8102510150v −−⎛⎞=××−××+⎜⎟⎝⎠ or 00v = Circuit (b),()()()()636302500.81050100.81010150410 1.6v −−−⎛⎞=××−×+⎜⎟⎝⎠=×− or 0 1.56 V v =− b. Assume 10.7 AB I μ= and 20.9 A,B I μ= then using Equation (14.79): Circuit (a),()()()()63630500.71050100.91025101500.0350.045v −−⎛⎞=××−××+⎜⎟⎝⎠=− or00.010 V v =−Circuit (b), ()()()()63660500.71050100.910101500.035 1.8v −−⎛⎞=××−×+⎜⎟⎝⎠=− or 0 1.765 Vv =−______________________________________________________________________________________14.51(a) For : OS V ()333101001±=±⎟⎠⎞⎜⎝⎛+=O υmV For : B I ()()()043.010*******.0max 36=××=−O υ V()()()037.010*******.0max 36=××=−OυVSo 764≤≤O υmV(b) For : OS V 33±=O υmV For : VOS I ()()006.010*******.036±=××±=−O υSo 3939≤≤−O υmV(c) ()039.02.0101001±⎟⎠⎞⎜⎝⎛+=O υ So 239.2161.2≤≤O υV______________________________________________________________________________________14.52a. 2(15)0.010 V i i R R R ⎛⎞=⎜⎟+⎝⎠ 22150.00066671515(10.0006667)0.0006667 R R =+−= Then 222.48 M R =Ωb.11||15||10 6 k i F R R R R ==⇒=Ω ______________________________________________________________________________________14.53a. Assume the offset voltage polarities are such as to produce the worst case values, but the bias currents are in the same direction.Use superposition:Offset voltages 010********||1(10)110 mV ||1050||(5)(110)1(10)10||610 mV v v v v ⎛⎞=+==⎜⎟⎝⎠⎛⎞=++⎜⎟⎝⎠⇒=Bias Currents: 6301(100 k )(210)(10010)0.2 V B v I −=Ω=××= Then6302(5)(0.2)(210)(5010)0.9 V v −=−+××=− Worst case: is positive and is negative, then01v 02v 010.31 V v = and 021.51 V v =−b. Compensation network:If we want20 mV and 10 V 8.33(10)0.0208.33B B C C R V V R R R ++⎛⎞==⎜⎟+⎝⎠⎛⎞=⎜⎟+⎝⎠ or 4.15 M C R ≅Ω______________________________________________________________________________________14.54(a) Offset voltage: ()122105011±=±⎟⎠⎞⎜⎝⎛+=O υmV 142122±=±±=O υmV ()()()16221220203±=±+±⎟⎠⎞⎜⎝⎛−=O υmV Bias current:V()()0105.010501021.0361=××=−O υ or V ()()0095.010501019.0361=××=−O υ 12O O υυ= ()()()()0042.010201021.0113613+−=××+−=−O O O υυυor()()0038.010201019.013613+−=××+−=−O O O υυυ By superposition5.225.21≤≤−O υmV5.245.42≤≤−O υmV7.103.223≤≤−O υmV(b) Bias currents:()()()110501002.010*******±=⇒××±=×±=−O OS O I υυmV()()()4.010201002.010*******±=⇒××±=×±=−O OS O I υυmVBy superposition: ()4.02213±±±=O O υυ13131≤≤−O υmV15152≤≤−O υmV4.174.173≤≤−O υmV______________________________________________________________________________________14.55For circuit (a), effect of bias current:390(5010)(10010) 5 mV v −=××⇒ Effect of offset voltage 050(2)1 4 mV 50v ⎛⎞=+=⎜⎟⎝⎠ So net output voltage is09 mV v = For circuit (b), effect of bias current:Let then from Equation (14.79),2550 nA,B I =1450 nA,B I = 93960250(45010)(5010)(55010)(10)1502.2510 1.1v −−−⎛⎞=××−×+⎜⎟⎝⎠=×− or0 1.0775 V v =− If the offset voltage is negative, then0(2)(2)4mV v =−=− So the net output voltage is 0 1.0815 Vv =− _____________________________________________________________________________________14.56a. At so the output voltage for each circuit is25C,T =°0 2 mV S V = 0 4 mV v = b. Forthe offset voltage for is 50C,T =° 0 2 mV (0.0067)(25) 2.1675 mV S V =+= so the output voltage for each circuit is 0 4.335 mVv = ______________________________________________________________________________________14.57 a. At then25C,T =°0 1 mV,S V = 010150(1)1 6 mV 10v v ⎛⎞=+⇒=⎜⎟⎝⎠and 020********(1)120206(4)(1)(4)28 mV v v v ⎛⎞⎛⎞=+++⎜⎟⎜⎟⎝⎠⎝⎠=+⇒= b. Atthen 50C,T =°01(0.0033)(25) 1.0825 mV,S V =+= 0101(1.0825)(6) 6.495 mV v v =⇒=and 02(6.495)(4)(1.0825)(4)v =+ or 0230.31 mVv = ______________________________________________________________________________________14.580025C;500 nA,200 nA50C,500 nA (8 nA /C)(25C)700 nA200 nA (2 nA /C)(25C)250 nA B S B S I I I I °==°=+°°==+°°= a. Circuit (a): For ,B I bias current cancellation, 00v =Circuit (b): For ,B I Equation (14.79), 93960050(50010)(5010)(50010)(10)1500.025 1.000.975 V v v −−⎛⎞=××−×+⎜⎟⎝⎠=−⇒=− b. Due to offset bias currents.Circuit (a): 930(20010)(5010)0.010 V v −=××⇒=0vCircuit (b): 21Let 600 nA400 nA B B I I == Then93960050(40010)(5010)(60010)(10)1500.020 1.20 1.18 V v v −−⎛⎞=××−×+⎜⎟⎝⎠=−⇒=−c. Circuit (a): Due to ,B I 0v = Circuit (b): Due to ,B I93960050(70010)(5010)(70010)(10)1500.035 1.40 1.365 V v v −−⎛⎞=××−×+⎜⎟⎝⎠=−⇒=−Circuit (a): Due to 0,S I930(25010)(5010)0.0125 V v v −=××⇒=0Circuit (b): Due to0,S I 21Let 825 nA575 nA B B I I == Then 93960050(57510)(5010)(82510)(10)1500.02875 1.65 1.62 Vv v −−⎛⎞=××−×+⎜⎟⎝⎠=−⇒=− ______________________________________________________________________________________14.590025C; 2 A,0.2 A 50C, 2 A (0.020 A /C)(25C 2.5 A 0.2 A (0.005 A /C)(25C)0.325 A B S B S I I I )I μμμμμμμμ°==°=+°°==+°°= a. Due to :B I (Assume bias currents into op-amp). 630101(50 k )(210)(5010)0.10 VB v I v −=Ω=××⇒= 020*********(60 k )(50 k )12020(0.1)(4)(210)(6010)(210)(6010)4B B v v I I −−⎛⎞⎛⎞=++Ω−Ω+⎜⎟⎜⎟⎝⎠⎝⎠=+××−××3 or020.12 V v = b. Due to0:S I1121st op-amp. Let 2.1 A2nd op-amp. Let 2.1 A1.9 A B B B I I I μμμ===6301101(50 k )(2.110)(5010)0.105 V B v I v −=Ω=××⇒= 020112636360601(60 k )(50 k )12020(0.105)(4)(2.110)(6010)(1.910)(5010)(4)B B v v I I −−⎛⎞⎛⎞=++Ω−Ω+⎜⎟⎜⎟⎝⎠⎝⎠=+××−×× or 020.166 V v =c. Due to :B I 63010101026363(2.510)(5010)0.125 V60601(60 k )(50 k )12020(0.125)(4)(2.510)(6010)(2.510)(5010(4)B B v v v v I I −−=××⇒=⎛⎞⎛⎞=++Ω−Ω+⎜⎟⎜⎟⎝⎠⎝⎠=+××−×× or 020.15 V v =Due to0:S I12Let 2.625 A2.3375 A B B I I μμ== 6301101(50 k )(2.662510)(5010)1.133 V B v I v −=Ω=××⇒= 020112636360601(60 k )(50 k )12020(0.133)(4)(2.662510)(6010)(2.337510)(5010)(4)B B v v I I −−⎛⎞⎛⎞=++Ω−Ω+⎜⎟⎜⎟⎝⎠⎝⎠=+××−×× or 020.224 Vv = ______________________________________________________________________________________14.60(a) 0.51050==d A For common-mode, 21I I υυ=From Chapter 9, 12431211R R R R R R A cm −⎟⎟⎠⎞⎜⎜⎝⎛+⎟⎟⎠⎞⎜⎜⎝⎛+= If , ()75.50015.1502==R ()85.9015.01101=−=R, ()85.9015.01103=−=R ()75.50015.1504==R Then 610046.515228.519409.115228.685.975.5075.5085.9185.975.501−×=−=−++=cm A If , ()15.10015.1103==R ()25.49015.01504=−=R Then 051268.015228.520609.115228.685.975.5025.4915.10185.975.501−=−=−++=cm A If , 25.492=R 15.101=R Then 04877.085222.419409.185222.515.1025.4975.5085.9115.1025.491+=−=−++=cm A Now ()8.39051268.05log 20min 10=⎟⎠⎞⎜⎝⎛=dB CMRR dB (b) , ()5.5103.1502==R ()70.997.0101==R, ()5.4897.0504==R ()3.1003.1103==R。