数字集成电路习题答案

CHAPTER 2P2.1. a) The solution for the NMOS case is based on Example 2.4: The equation for V T0 is: 02BT FB F OXQ V V C φ=-- Calculate each individual component.1710()1362OX 077200611196310ln 0.026ln 0.44 V 1.4100.440.550.99 V 4 3.510 F/cm1.610 F/cm 310310/0.188 V 1.610610 1.6100.1.610i FpA GC Fp G gate OXB B OX OX OX n kT q NC Q Q C cmC Q C φφφφεε-------⨯==-=-⨯=-=--=-==⨯=⨯⨯=⨯==⨯⨯⨯⨯==⨯TO 06 V V 0.99(0.88)(0.188)0.0600.018 V=------=+ For the PMOS device:1710()77200611196TO 310ln 0.026ln 0.44 V 1.4100.440.550.99 V 310310/0.188 V1.610610 1.6100.06 V 1.610V 0.99(0.88)(0.188)0.0600.138 D Fn i GC Fn G gate B B OX OX OX N kT q n Q Q C cmC Q C φφφφ-----⨯===⨯=-=+=+⨯=⨯==⨯⨯⨯⨯==⨯=---=-Vb) The magnitude of V T0 would be higher. Since the device is PMOS this means that V T0 islowered. Since the only thing that’s been changed is the doping of the gate, only G φ changes. The new V T0 then becomes:00.110.880.1880.6 1.24V T V =----=-c) Since V T0 will be adjusted with implanted charge (Q I ):60.40.0180.382(1.610)(0.382)IOXIOXI Q C Q V C Q V -=-==⨯To calculate the threshold implant level N I :I I I I qN Q Q N q==For the NMOS device from part(a):6122190.610 3.8210/1.610I I Q N ions cm q --⨯=-=-=⨯⨯ (p-type) For the PMOS device from part(a):612219(1.610)(0.40.138)2.6210/1.610I I Q N ions cm q --⨯-=-=-=⨯⨯ (n-type) For the PMOS device from part(b):612219(1.610)(1.240.4)8.410/1.610I I Q N ions cm q --⨯-=-=-=⨯⨯ (p-type)d) The advantage of having the gate doping be n + for NMOS and p + for PMOS could be seen from analysis above. Doping the gates in such a way leads to devices with lower threshold voltages, but enables the implant adjustment with the same kind of impurities that used in the bulk (p-type for NMOS and n-type for PMOS). If we were to use the same kind of doping in gate as in the body (i.e. n + for PMOS and p + for NMOS) that would lead to higher un-implanted threshold voltages. Adjusting them to the required lower threshold voltage would necessitate implantation of the impurities of the opposite type near the oxide-Si interface. This is not desirable. Also, the doping of the poly gate can be carried out at the same time as the source and drain and therefore does not require an extra step.P2.2. First, convert ox t to units of cm:810100cm222210cm 10ox t -=⨯=ÅÅNow, using the mobility equation:()()20 1.8568130/V70cm0.8114102210pep nGS T ox cm V s V V t μμθ--==≈⎛⎫⎛⎫-+ ⎪⎪+ ⎪⎝⎭⎝⎭P2.3. a) For each transistor, derive the region of operation. In our case, for 0V,0.4V GS V =, thetransistor is in the cutoff region and there is no current. For 0.8V,1.2V GS V =, firstcalculate the saturation voltage Dsat V using:()GS T C DSAT GS T C V V E L V V V E L-=-+For our transistors, this would be:Next, we derive the IV characteristics using the linear and saturation current equations,we get the graphs shown below.IV Characteristic of NMOS01020304050607000.20.40.60.811.2Volts (V)C u r r e n t (u A )IV Characteristic of PMOSVolts (V)C u r r e n t (u A )To plot DS I vs. GS V , first identify the region of operation of the transistor. For GS T V V <, the transistor is in the cutoff region, and there is negligible current. For GS T V V > and GS DS V V ≤, the transistor is in the saturation region and saturation current expression should be used. The graphis shown below. Clearly, it is closer to the linear model.Ids vs. Vgs of NMOS010********607000.20.40.60.811.21.4Vgs (V)I d s (V )P2.4. For each transistor, first determine if the transistor is in cutoff by checking to see if V GS isless than or greater than V T . V T may have to be recalculated if the source of the transistor isn’t grounded. If V GS is less than V T , then it is in cutoff, otherwise, it is in either triode or saturation.To determine if it is in the triode saturation region, check to see if V DS is less than or greater than V DSAT . If V DS is less than V DSAT , then it is in triode, otherwise, it is in saturation. a. Cutoff00.200.2V0.4V GS G S T T GS TV V V V V V V =-=-===∴<b. Cutoff01.2 1.20V0.4V GS G S T T GS TV V V V V V V =-=-===∴<c. Linear01.20 1.2V0.4V GS G S T T GS TV V V V V V V =-=-===∴>The transistor is not in the cutoff region.()()()()()()1.20.460.20.48V 1.20.460.20.2V GS T C DSATGS T C DS DS DSATV V E L V V V E L V V V --===-+-+=∴<d. Saturation: In this case, because D G V V > the transistor is in the saturation region. To see this, recognize that in a long-channel transistor if D G V V >, the transistor is in saturation. Since the saturation drain voltage Dsat V is smaller in a velocity-saturated transistor than in a long-channel transistor, if the long-channel saturation region equation produces a saturated transistor, than the velocity-saturated saturation region equation will also.P2.5. In both cases, the first step it to calculate the maximum value of X V given G V . If thevoltage at the drain is higher than this maximum value, then ,max X X V V =, otherwise,X D V V =. The maximum value of X V is G T V V - but 0T T V V ≠ because of body effect andwe consider its effect.(),max 0001.20.40.988X G T G T G T G T V V V V V V V V V γγγγ=-=-+=--=--+=--=-There are two ways to calculate this, either through iteration or through substitution. Iteration:For the iteration method, we need a starting value for V X,max . A good starting value would be 0 1.20.40.8V G T V V -=-=. We plug this value on the RHS of the equation, calculate a new V X,max and repeat until we reach a satisfactory converged value.Old Vx,max New Vx,max 0.800 0.728 0.728 0.734 0.734 0.734In this, only three iterations are needed to reach 0.734V. Substitution:The term makes things a bit tricky, we get around this by making the following substitution:2,max 2,max 0.880.88X X x V V x =+∴=-Therefore:,max 220.9880.880.98800.2 1.87X V x x x =--=-=+-2,max 1.27, 1.470.880.733,1.28X x V x ===-=-= We use the first value since second value is above V DD . a. Since ,max D X V V >, ,max 0.733V X X V V ==. b. Since ,max D X V V <, ,max 0.6V X X V V ==. P2.6.a. Initially, when 0V in V =, the transistor is in the cutoff region and 0V X V =. Thisvalue is constant until V in exceeds V t 0. From then, X in T V V V =- and body effect must be taken into account. This trend continues until 0.7V X D V V ==, and the value of V inat that point must be calculated. From then on, 0.7V X D V V ==. To plot V X in the second region, we first derive an expression for V X vs. V in.(),max 0000.40.212X G T G T in T in T in in V V V V V V V V V V V γγγγ=-=-+=---=--=--=--Substituting:2,max2,max 0.880.88X X x V V x =+∴=-Therefore:,max 220.2120.880.21200.20.66X in in in V V x V x x V =---=--=+--220.880.88XxV x====-=-⎝⎭Since this is a quadratic function, there will be two graphs of V X. Only one of thesegraphs intersects with V X in the first region. In this case, plug 0.4inV= and see which one gives 0V. In our case, it would be the ‘+’ version of the quadratic.To see where region 3 begins, we simply isolate V in:()()()22220.880.2 2.710.2 2.71440.2 2.711.16V4XinVV=-⎝⎭-+-==+-==The final graph is shown in Figure 错误！未找到引用源。

浙江工业大学 / 学年第一学期 《数字电路和数字逻辑》期终考试试卷 A姓名 学号 班级 任课教师一、填空题（本大题共10小题，每空格1分，共10分）请在每小题的空格中填上正确答案。

错填、不填均无分。

1．十进制数（68）10对应的二进制数等于 ；2．描述组合逻辑电路逻辑功能的方法有真值表、逻辑函数、卡诺图、逻辑电路图、波形图和硬件描述语言（HDL ）法等，其中 描述法是基础且最直接。

3．1A ⊕可以简化为 。

4．图1所示逻辑电路对应的逻辑函数L 等于 。

A B L≥1&CYC图1 图25．如图2所示，当输入C 是（高电平，低电平） 时，AB Y =。

6．两输入端TTL 与非门的输出逻辑函数AB Z =，当A =B =1时，输出低电平且V Z =0.3V ，当该与非门加上负载后，输出电压将(增大，减小) 。

7．Moore 型时序电路和Mealy 型时序电路相比， 型电路的抗干扰能力更强。

8．与同步时序电路相比，异步时序电路的最大缺陷是会产生 状态。

9．JK 触发器的功能有置0、置1、保持和 。

10．现有容量为210×4位的SRAM2114，若要将其容量扩展成211×8位，则需要 片这样的RAM 。

二、选择题（本大题共10小题，每小题2分，共20分）在每小题列出的四个备选项中只有一个是符合题目要求的，请将其代码填写在题后的括号内。

错选、多选或未选均无分。

11．十进制数（172）10对应的8421BCD 编码是 。

【 】A ．（1111010）8421BCDB ．（10111010）8421BCDC ．（000101110010）8421BCD D ．（101110010）8421BCD12．逻辑函数AC B A C B A Z +=),,(包含 个最小项。

【 】A ．2B ．3C ．4D ．513．设标准TTL 与非门AB Z =的电源电压是+5V ，不带负载时输出高电平电压值等于+3.6V ，输出低电平电压值等于0.3V 。

自我检测题1．在存储器结构中，什么是“字”什么是“字长”，如何表示存储器的容量解：采用同一个地址存放的一组二进制数，称为字。

字的位数称为字长。

习惯上用总的位数来表示存储器的容量，一个具有n字、每字m位的存储器，其容量一般可表示为n ×m位。

2．试述RAM和ROM的区别。

解：RAM称为随机存储器，在工作中既允许随时从指定单元内读出信息，也可以随时将信息写入指定单元，最大的优点是读写方便。

但是掉电后数据丢失。

ROM在正常工作状态下只能从中读取数据，不能快速、随时地修改或重新写入数据，内部信息通常在制造过程或使用前写入，3．试述SRAM和DRAM的区别。

解：SRAM通常采用锁存器构成存储单元，利用锁存器的双稳态结构，数据一旦被写入就能够稳定地保持下去。

动态存储器则是以电容为存储单元，利用对电容器的充放电来存储信息，例如电容器含有电荷表示状态1，无电荷表示状态0。

根据DRAM的机理，电容内部的电荷需要维持在一定的水平才能保证内部信息的正确性。

因此，DRAM在使用时需要定时地进行信息刷新，不允许由于电容漏电导致数据信息逐渐减弱或消失。

4．与SRAM相比，闪烁存储器有何主要优点解：容量大，掉电后数据不会丢失。

5．用ROM实现两个4位二进制数相乘，试问：该ROM需要有多少根地址线多少根数据线其存储容量为多少解：8根地址线，8根数据线。

其容量为256×8。

6．简答以下问题：（1）CPLD和FPGA有什么不同FPGA可以达到比 CPLD更高的集成度，同时也具有更复杂的布线结构和逻辑实现。

FPGA 更适合于触发器丰富的结构，而 CPLD更适合于触发器有限而积项丰富的结构。

在编程上 FPGA比 CPLD具有更大的灵活性；CPLD功耗要比 FPGA大；且集成度越高越明显；CPLD比 FPGA有较高的速度和较大的时间可预测性，产品可以给出引脚到引脚的最大延迟时间。

CPLD的编程工艺采用 E2 CPLD的编程工艺，无需外部存储器芯片，使用简单，保密性好。

CHAPTER 3P3.1. The general approach for the first two parameters is to figure out which variables shouldremain constant, so that when you have two currents, you can divide them, and every variable but the ones you want to calculate remain. In this case, since the long-channel transistor is in saturation for all values of V GS and V DS , only one equation needs to be considered:()()2112DS N OX GS T DS W I C V V V Lμλ=-+ For the last two parameters, now that you have enough values, you can just choose oneset of numbers to compute their final values.a. The threshold voltage, V T0, can be found by choosing two sets of numbers with the same V DS ’s but with different V GS ’s. In this case, the first two values in the table can be used.()()()()()()211122222201022001121121.2 1.210000.82800.8DS N OX GS T DS DS N OX GS T DS T DS T DS T T W I C V V V L W I C V V V LV I V I V V μλμλ=-+=-+-⎛⎫-===⎪--⎝⎭ 00.35V T V ∴=b. The channel modulation parameter, λ, can be found by choosing two sets of numberswith the same V GS ’s but with different V DS ’s. In this case, the second and third values in the table can be used.()()221 1.225010.8247DS DS I I λλ+==+ -10.04V λ∴=c. The electron mobility, µn , can now be calculated by looking at any of the first three sets of numbers, but first, let’s calculate C OX .631062-31m 10μm22?.210μm1m 10 0.0351 1.610/2.210OX OX t C F cm--=⨯⨯===⨯Now calculate the mobility by using the first set of numbers.()()()()()()()()()()()()22111021262101111 1.21 1.222210002cm 348V-s 1.610(4.75)1.20.3510.04 1.21DS N OX GS T DS N OX T DS N OX GS T DS W W I C V V V C V L LA I W C V V V L μλμλμμλ-=-+=-+===⨯-+-+d. The body effect coefficient gamma, γ, can be calculated by using the last set of numbers since it is the only one that has a V SB greater than 0V.()()()()244124414411221 1.20.468VDS N OX GS T DS DS GS T N OX DS GS T T GS W I C V V V LI V V W C V LV V V V μλμλ=-+-=+-==-==12000.6VT T T T V V V V γγγ=+-====P3.2. The key to this question is to identify the transistor’s region of operation so that gatecapacitance may be assigned appropriately, and the primary capacitor that will dischargedat a rate of V It C ∂∂= by the current source may be identified. Then, because the nodes arechanging, the next region of operation must be identified. This process continues until the transistor reaches steady state behavior. Region 1:Since 0V GS V = the transistor is in the cutoff region. The gate capacitance is allocated to GB C . Since no current will flow through the transistor, all current will come from the source capacitor and the drain node remains unchanged.68-151010V V 6.67100.6671510s nsSB V I I t C C -∆⨯====⨯=∆⨯ The source capacitor will discharge until 1.1V GS T V V == when the transistor enters thesaturation region. This would require that the source node would be at 3.3 1.1 2.2V S G GS V V V =-=-=.()15961510 3.3 2.2 1.6510s 1.65ns 1010C t V I ---⨯∆=∆=-=⨯=⨯ Region 2:The transistor turns on and is in saturation. The current is provided from the capacitor atthe drain node, while the source node remains fairly constant. The capacitance at the drain node is the same as the source node so the rate of change is given by:68-151010V V 6.67100.6671510s nsSB V I I t C C -∆⨯====⨯=∆⨯ Since the transistor is now in the saturation region, GS V can be computed based on thecurrent flowing through the device.()22 1.1 1.37V 3.3 1.37 1.93VGS T GST S G GS kW I V V LV V V V V =-==+==-=-=This is where the source node settles. This means that most of the current is discharged through the transistor until the drain voltage reaches a value that puts the transistor at the edge of saturation.3.3 1.1 2.2VDS GS TD G T V V V V V V =-=-=-=If we assume that all the current comes from the transistor, and the source node remains fixed, the drain node will then discharge at a rate equal to that of the source node in the first region. Region 3:The transistor is now in the linear region the gate capacitance is distributed equally to both GS C and GD C . and both capacitors will discharge at approximately the same rate.-151510V0.28621510510nsV I A t C μ-∆===∆⨯⨯+⨯The graph is shown below.00.511.522.533.5024681012Time (ns)V o l t a g e (V )P3.3. The gate and drain are connected together so that DS GS V V = which will cause thetransistor to remain in saturation. This is a dc measurement so capacitances are not required. Connect the bulk to ground and run SPICE. P3.4. Run SPICE. P3.5. Run SPICE. P3.6. Run SPICE. P3.7. Run SPICE.P3.8. First, let’s look at the various parameters and identify how they affect V T .∙ L – Shorter lengths result in a lower threshold voltage due to DIBL. ∙ W – Narrow width can increase the threshold voltage.∙ V SB – Larger source-bulk voltages (in magnitude) result in a higher threshold voltage. ∙ V DS –Larger drain-source voltages (in magnitude) result in a lower threshold voltage due to DIBL. The transistor with the lowest threshold voltage has the shortest channel, larger width, smallest source-bulk voltage and largest drain-source voltage. This would be the first transistor listed.The transistor with the highest threshold voltage has the longest channel, smallest width,largest source-bulk voltage and smallest drain-source voltage. This would be the last transistor listed. P3.9. Run SPICE.P3.10. Run SPICE. The mobility degradation at high temperatures reduces I on and the increasemobile carriers at high temperatures increase I off . P3.11. The issues that prompted the switch from Al to Cu are resistance and electromigration.Copper wires have lower resistances and are less susceptible to electromigration problems. Copper on the other hand, reacts with the oxygen in SiO 2 and requires cladding around the wires to prevent this reaction.For low-k dielectrics, the target value future technologies is 2.High-k dielectrics are being developed as the gate-insulator material of MOSFET’s. This is because the current insulator material, SiO 2, can not be scaled any longer due to tunneling effects.P3.12. Self-aligned poly gates are fabricated by depositing oxide and poly before the source anddrain regions are implanted. Self-aligned silicides (salicides) are deposited on top of the source and drain regions using the spacers on the sides of the poly gate. P3.13. To compute the length, simply use the wire resistance equation and solve for L .LR TWRTWL ρρ==First convert the units of ρ to terms of μm. Aluminum:2.7μΩρ=cm 6Ω10μΩ⨯610μm100cm ⨯()()()0.027Ωμm1000.812963μm 2.96mm0.027RTWL ρ=====Copper:1.7μΩρ=cm 6Ω10μΩ⨯610μm100cm ⨯()()()0.017Ωμm1000.814706μm 4.71mm0.017RTWL ρ=====P3.14. Generally, the capacitance equation in terms of permittivity constants and spacing is:k C WL tε=a. 4k = ()()()()230048.8510 3.541100SiO k k C WL TL t S S Sεε-====b. 2k = ()()()()30028.8510 1.771100k k C WL TL t S SSεε-====The plots are shown below.Capacitance vs. Spacing01234567800.511.522.533.544.555.5Spacing (um)C a p a c i t a n c e (f F)。

1、在数字集成电路中，以下哪个元件常用于存储二进制信息？A、电阻B、电容C、触发器D、电感（答案：C）2、模拟集成电路中，用于放大电信号的主要元件是？A、二极管B、晶体管C、电阻D、电容（答案：B）3、以下哪种逻辑门电路可以实现“与”运算？A、NOT门B、OR门C、AND门D、XOR门（答案：C）4、在数字电路中，时钟信号的主要作用是？A、提供电源B、控制信号同步C、放大信号D、转换信号格式（答案：B）5、模拟集成电路中，常用于稳定输出电压的元件是？A、运算放大器B、比较器C、稳压二极管D、晶体管（答案：C）6、数字集成电路中，D触发器的输出在何时更新？A、时钟信号上升沿B、时钟信号下降沿C、随时更新D、根据输入信号变化（答案：A，注：也可能是B，具体取决于触发器类型，但此题通常按常见上升沿触发考虑）7、以下哪种电路常用于将模拟信号转换为数字信号？A、放大器B、滤波器C、模数转换器（ADC）D、数模转换器（DAC）（答案：C）8、在模拟集成电路中，用于产生稳定电流源的元件或电路是？A、电流镜B、电压源C、电阻网络D、电容器（答案：A）9、数字集成电路中，用于实现计数功能的电路是？A、加法器B、寄存器C、计数器D、译码器（答案：C）10、以下哪种电路或元件在模拟集成电路中常用于信号的滤波？A、放大器B、比较器C、滤波器D、振荡器（答案：C）。

懂得1、Please illustrate the meaning of its voltage transfer characteristic to a logic gate, and describe the static behaviors showed in the voltage transfer characteristic curves.The electrical function of a gate is best expressed by its voltage transfer characteristic (VTC),which plots the output voltage as a function of the input voltage Vout=f(Vin).The high and low nominal voltage Voh and Vol;The gate or switching threshold voltage Vm,that is define as Vm=f(Vm)(The gate threshold voltage presents the midpoint of the switching characteristics,which is obtained when the output of a gate is short circuited to the input);The high and low input voltage Vih and Vil are defined by the point where the gain (=dVout/dVin)of the VTC equals -12、Please draw the voltage transfer characteristic curve of the inverter and label the static operation points in the VTC.3、Please describe the definition of noise margin and its physical significance(物理意义), then draw the figure of definition of noise margins.The noise margins represent the levels of noise that can be sustained(所允许的) when gates are cascaded. A measure of the sensitivity of a gate to noise is given by the noise margins NML(noise margin low) and NMH(noise margin high), which quantize the size of the legal “0” and “1”, respectively, and set a fixed maximum threshold on the noise value4、Please describe the meaning of the regenerative property and the conditions of a gate with regenerative property.A gate with regenerative property ensures that a disturbed signal converges back to a nominal voltage level after passing through a number of logical stages. The VTC should have a transient region (or undefined region) with a gain greater than 1 in absolute value, bordered by the two legal zones, where the gain should be less than 1 in absolute value5、What are the definitions of the fan-out and fan-in properties?The number that can be driven is termed the fan-out of circuit, that denotes the number of load gates N that are connected to the output of the driving gate. The fan-in of a gate is defined as the number of independent input nodes to the gate.6、How to describe the performance of a digital IC? Please illustrate the parameters used to characterize the transient performance of a logic family, and draw the associated figure of the definition of these parP ropagation delay time and rise/fall time can be used to characterize the transient performance of a logic family .Propagation delay time of a gate expresses the delay experienced by a signal when passing through a gate,which represent how quickly the gate responds to the changes at its inputs.Rise/fall time express how fast a signal transits between the different levels. Propagation delay time is defined as the period between the 50%transition points of the input and output signals.Rise/fall time is defined as the period between the 10% and 90% points of the total voltage transition at the output waveforms.1、Illustrate the basic structure and simple operation principle of MOS transistor.Four terminals:source, drain, gate, body; Vertical Structure: gate electrode, insulator, semiconductor substrate; Horizontal Structure: source region, channel region, drain region2、Illustrate the basic function of each terminal of MOS device, and describe the general terminal connections of NMOS and PMOS transistor, respectively.The source and the drain are the electrodes conducting the current. The gate electrode is thecontrolling terminal. The function of the body is secondaryIn NMOS devices, the source is defined as the n+ region which has a lower potential(电势) than the other n+ region, the drain. The source is the terminal with the higher potential in PMOS devices, The body is generally connected to a DC supply that is identical for all devices of the same type (GND for NMOS, VDD for PMOS).3、What does the transition (or input) characteristic of MOS transistor mean? And what conclusions we can find from the characteristic curve?It describes the relationship between the gate-source voltage and the drain-source current with the certain drain-source voltage .When the gate-source voltage is less than the threshold voltage, the conducting current is zero, that is, the NMOS transistor is in cutoff operation. When is larger than, the NMOS transistor is on.4、What does the current-voltage (or output) characteristic of MOS transistor mean? And what conclusions we can find from the I-V characteristic curve?.It describes the relationship between the drain-source voltage and the drain-source current with a certain gate-source voltageVgs > Vt , 0<VDS <VGS -VT : Linear modeThe inversion layer forms a continuous current path between the source and the drain.A drain current proportional to Vds will flow from the drain to the source through the conducting channel. The channel region acts as a voltage-controlled linear resister.5、Describe the operation modes of NMOS and PMOS transistors respectively, and define the corresponding ideal current equations.1、Explain the channel-length modulation, sub-threshold conduction, short-channel effect and narrow-channel effect. And illustrate their corresponding chief impacts on the device.This simple current equation prescribes a linear drain-bias dependence for the current in MOS transistors, determined by the empirical model parameter λ, called the channel-length modulation coefficientOne typical condition, which is due to the two-dimensional nature of channel current flow, is the sub-threshold conduction in small-geometry MOS transistors.As a working definition, a MOS transistor is called a short-channel device if its channel length is on the same order of magnitude as the depletion region thicknesses of the source and drain junctions.The short-channel effects that arise in this case are attributed to two physical phenomena: the limitations imposed on electron drift characteristics in the channel; the modification of the threshold voltage due to the shortening channel lengthMOS transistor that have channel widths on the same order of magnitude as the maxium depletion region thickness are defined as narrow channel devices.For MOSFET with small channel widths,the actual threshold voltage increases as a result of this extra depletion charge of the fringe depletion region.This fact is called narrow channel effect.2、Describe the three main components of the load capacitanceCL, when a logic gate is driving other fan-out gates. And sketch the capacitance model of NMOS transistor.Gate capacitances (of other inputs connected to out)Diffusion(or junction) capacitances (of drain/source regions)Routing capacitances (output to other inputs)1,Describe the basic structure and operation of a static CMOS inverter. Then draw theassociated transistor schematicThis structure consists of an enhancement-type NMOS transistor and an enhancement-type PMOS transistor, operating in complementary mode. So this configuration is called Complementary MOS (CMOS). The gate terminals of the PMOS and NMOS transistors are connected to form the inverter input. The drain terminals of the PMOS and NMOS transistors are connected to form the inverter output. The source and the substrate of the NMOS transistor are connected to the ground, while the source and body of PMOS transistor are connected to VDD The circuit topology is complementary push-pull in the sense that: For high input the NMOS transistor drives (pulls down) the output node while the PMOS transistor acts as the load, and for low input the PMOS transistor drives (pulls up) the output node while the NMOS transistor acts as the load.When the input is at VDD: The NMOS is on (conducting) while the PMOS is off (cut-off). A direct path exists between Vout and the ground node, resulting in a steady-state value of 0V at the output. When the input is at ground:The NMOS is off while the PMOS is on. A direct path exists between VDD and Vout, yielding a high output voltage (equal to VDD).Static CMOS logic:structure:The static CMOS style is really an extension of the static CMOS inverter to multiple inputs. A logic function in static CMOS must be implemented in both NMOS and PMOS transistors. It is the combination of the pull-up network(PUN) and the pull-down network(PDN). Each input always connects to PUN and PDN simultaneously. The function of the PUN is to provide a connection between the output and VDD anytime the output of the logic gate is meant to be 1 (based on the inputs). The function of the PDN is to connect the output to VSS when the output of the logic gate is meant to be 0.Opreation: The pull-down net should be “on” when the pull-up net is “off” and vice versa. For any given input combination, the output is connected either to VDD or to ground via a low-resistance path. A DC current path between the VDD and ground is not established for any of the input combinations. With the complementary nature of NMOS and PMOS, the pull-up or the pull-down is “on” alternately to implement the logic operation.Discuss the main problems for high fan-in static CMOS gates and the associated techniques for fast complex gates.tpHL = 0.69 Reqn(C1+2C2+3C3+4CL); Propagation delay deteriorates(恶化) rapidly as a function of fan-in quadratically in the worst case, Gates with a fan-in greater than 4 become excessively slow and must be avoided.tPLH increases linearly due to the linearly increasing value of the diffusion capacitance;tPHL increase quadratically due to the simultaneous increase the resistance and internal capacitance in serial part.Transistor sizing: as long as fan-out capacitance dominatesProgressive transistor sizing: This approach reduces the dominant resistance, while keeping the increase in capacitance within boundsTransfer gate:Configuration:The source and drain nodes serve as inputs and outputs, while the gate node serves as the control input, the body node is connected to the power/ground Operation: For NMOS transfer gate,it turns on while the gate control terminal goes high, and the input signal will be delivered to the output node; it turns off while the gate control terminal goes low, and the output node will be impedance.CMOS transmission gate:Configuration: The CMOS transmission gate consists of one NMOS and one PMOS transistor, with the source and drain connected in parallel; The gate voltages appliedto these two transistors are also set to be complementary signals. The substrate terminal of the NMOS transistor is connected to ground and the substrate terminal of the PMOS transistor is connected to Vdd.Operation: If the control signal C is logic-high (equal to Vdd), then both transistors are turned on and provide a low-resistance current path between the input and output nodes. If the control signal C is logic-low, then both transistors will be off, and the path between the input and output nodes will be in the high-impedance state. The weakness of one device is overcome by the strength of the other device, whether the output is transmitting a high or low value. This is a clear advantage of the CMOS transfer gate over the single transistor counterpart.DCVLS:Operation: Assume now that, for a given set of inputs, PDN1 conducts while PDN2 does not, and that Out and out are initially high and low, respectively. Turning on PDN1: Causes Out to be pulled down (below VDD−|VTP |); Out is in a high impedance state, as M2 and PDN2 are both turned off. At the point M2 turns on and starts charging out非to VDD — eventually turning off M1; This in turn enables Out to discharge all the way to GND.XOR/XNOR: When the signals A and B have the same values, there is one conducting path either AB or A非B非; Then the output F is pulled down;At the same time, the other pull-down paths connected to the F非are both turned off. When F is pulled down below VDD−|VTP |, M2 t urns on and starts charging F非to VDD —eventually turning off M1 and pulling down F to Gnd. When the signals A and B have the different values, there is one conducting path either AB非or A非B; Then the output F非is pulled down; At the same time, the other pull-down paths connected to the F are both turned off. When F非is pulled down below VDD−|VTP |, M1 turns on and starts charging F to VDD —eventually turning off M2 and pulling down F非to Gnd.Precharge-Evaluate dynamic CMOS:Operation: Precharge (when the clock signal Φ= 0)：The PMOS precharge transistor MP is conducting while the complementary NMOS transistor MN is off. The output load capacitance is precharged to VDD by MP, then VOH=VDD；The input voltages have no influence yet upon the output level since the complementary NMOS transistor MN is off. Evaluate (when the clock signal Φ=1)：The precharge transistor MP turns off while the NMOS evaluate transistor MN turns on. The output node voltage may now remain at the logic-high level or drop to a logic low, depending on the input voltage levels: If the input signals create a conducting path between the output node and the ground, PDN is on, and the output capacitance will discharge toward VOL=0;Otherwise, when PDN is off, the output voltage remains at VOH= VDD.Domino dynamic CMOS logic:When Φ=0, during precharge: The output of the n-type dynamic gate is charged up to VDD, and the output of the inverter is set to 0. When Φ=1, during evaluation: The dynamic gate conditionally discharges, and there are two possibilities: The output node of the dynamic CMOS stage is either discharged to a low level through the NMOS circuitry (1 to 0 transition), or it remains high. Consequently, the inverter output voltage can also make at most one transition during the evaluation phase, from 0 to 1.TSPC dynamic CMOS logic:Configuration:If one constrains a NORA stage to have only n-precharge gates, and not static gates, then a p-channel transistor can be eliminated from the clocked latch; The dynamic circuit technique to be presented in that it uses only one-phase clock signal, so no clock skew problem exists. The NORA design style can be simplified so that a single clock is sufficient. For the doubled n-C2MOS latch, when φ= 1, the latch is in the transparent evaluate mode and corresponds to 2 cascaded inverters (non-inverting); For the doubled n-C2MOS latch, when φ= 0, both inverters are disabled (hold mode) -- only the pull-up network is still active.Pipelined NORA dynamic CMOS system:Configuration: Consists of an np-CMOS logic sequence and a clocked CMOS output buffer; A pipelined system can be constructed by simply cascading alternating φ-section and φ -section, meaning that evaluation occurs during active φ and φ respectively;Operation:φ=0, during hold mode :N block performs the precharge operation and pulls node Out1 up to VDD through the p-type device Mp1, while p block performs the discharge operation and pulls the node Out2 down to zero through the n-type device Mn2; The clocked CMOS latch will not be in operation and the previous output voltage will be stored on the output load capacitor CL. φ=1, during evaluate mode:All cascaded NMOS and PMOS blocks evaluate output levels one after the other, and then the signal Out2 will be inversed to the output node by the clocked CMOS latch in operation;Operation Mode: Evaluate―Hold: All logic stages perform the precharge-discharge operation when the clock is high, and all stages evaluate output levels when the clock is low. Therefore, wewill call this circuit a section, meaning that evaluation occurs during active .Clocked CMOS dynamic circuit:Basic Structure:A pair of PMOS and NMOS transistors controlled by the complementary clock signals are cascaded in the pullup and pulldown paths of the static CMOS gate, respectively, then a CMOS logic gate can be synchronized with a clock. Operation: φ=1, during evaluation mode：The transistors Mp1 and Mp2 are both turned on, then this gate can evaluate normally as a CMOS inverter to generate the logic output In非; φ=0 , during hold mode: Both transistors Mp1 and Mp2 are off, decoupling the output from the input. The CMOS circuit cannot conduct and evaluate, then the output Q retains its previous value stored on the output capacitor CL.Sequential logic:Virtually all useful systems require storage of state information, leading to another class of circuits called sequential logic circuits. In these circuits, the output not only depends upon the current values of the inputs, but also upon preceding output values. In other words, a sequential circuit remembers some of the past history of the system; A sequential circuit consists of a combinational circuit and a memory block in the feedback loop.Combination logic:In all logic circuits described so far, the output is directly related to the input. Typically, there are no feedback loops between the output and the input in these circuits (also classified as non-regenerative circuits), so the outputs are always a logical combination of the inputs. As a class, these circuits are known as combinational logic circuits. Combinational logic circuits, described earlier, have the property that the output of a logic block is only a function of the current input values, assuming that enough time has elapsed for the logic gates to settle. Static storage:preserve state as long as the power is on;are built using positive feedback or regeneration with an intentional connection between the output and the input;useful when updates are infrequent (clock gating)Dynamic storage:store state on parasitic capacitors;only hold state for short periods of time (milliseconds);require periodic refresh to annihilate charge leakage;usually simpler, so higher speed and lower power;useful in datapath circuits that require high performance levels and are periodically clockedLatch: level sensitive circuit that passes inputs to Q when the clock is high (or low);input sampledon the falling edge of the clock is held stable when clock is low (or high)Register or Flip-flops (edge-triggered): edge sensitive circuits that only sample the inputs on a clock transitionpositive edge-triggered: 0- 1negative edge-triggered: 1 -0built using latches (e.g., master-slave flip-flops)。

《数字集成电路基础》作业答案第一次作业1、查询典型的TTL与CMOS系列标准电路各自的VIH、VIL、VOH和VOL，注明资料出处。

2、简述摩尔定律的内涵，如何引领国际半导体工艺的发展。

第二次作业1、说明CMOS电路的Latch Up效应；请画出示意图并简要说明其产生原因；并简述消除“Latch-up”效应的方法。

答：在单阱工艺的MOS器件中（P阱为例），由于NMOS管源与衬底组成PN结，而PMOS 管的源与衬底也构成一个PN结，两个PN结串联组成PNPN结构，即两个寄生三极管(NPN 和PNP)，一旦有因素使得寄生三极管有一个微弱导通，两者的正反馈使得电流积聚增加，产生自锁现象。

影响：产生自锁后，如果电源能提供足够大的电流，则由于电流过大，电路将被烧毁。

消除“Latch-up”效应的方法：版图设计时：为减小寄生电阻Rs和Rw，版图设计时采用双阱工艺、多增加电源和地接触孔数目，加粗电源线和地线，对接触进行合理规划布局，减小有害的电位梯度；工艺设计时：降低寄生三极管的电流放大倍数：以N阱CMOS为例，为降低两晶体管的放大倍数，有效提高抗自锁的能力，注意扩散浓度的控制。

为减小寄生PNP管的寄生电阻Rs，可在高浓度硅上外延低浓度硅作为衬底，抑制自锁效应。

工艺上采用深阱扩散增加基区宽度可以有效降低寄生NPN管的放大倍数；具体应用时：使用时尽量避免各种串扰的引入，注意输出电流不易过大。

2、什么是器件的亚阈值特性，对器件有什么影响？答：器件的亚阈值特性是指在分析MOSFET时，当Vgs<Vth时MOS器件仍然有一个弱的反型层存在，漏源电流Id并非是无限小，而是与Vgs呈现指数关系，这种效应称作亚阈值效应。

影响：亚阈值导电会导致较大的功率损耗，在大型电路中，如内存中，其信息能量损耗可能使存储信息改变，使电路不能正常工作。

3、什么叫做亚阈值导电效应？并简单画出logI D-V GS特性曲线。

答：GS在分析MOSFET时，我们一直假设：当V GS下降到低于V TH时器件会突然关断。

第1章数字电路和集成逻辑门电路习题解答思维题和习题1-1填空题1)三极管截止条件为UBE ≤0V三极管饱和导通条件为IB≥IBS三极管饱和导通的IBS为IBS ≥ (VCC-UCES)/β RC2)当栅极电路输出为高电平时的负载是拉电流负载，当输出为低电平时的负载是填充电流负载3)当晶体管用作电子开关时，其工作状态必须是饱和或关断4)74LTL电路的电源电压值和输出电压的高低电平值分别约为5V、2.7V和0.5V74TTL电路的电源电压值和输出电压的高低电平值分别约为5V、2.4V和0.4V5)OC门被称为开集电极门。

多个OC门输出可以并联实现线路和功能CMOS门电路的输入电流始终为零7)不能暂停CMOS门电路的空闲输入。

与门应连接到高电平，或门应连接到低电平。

1-2选择题1) abc常用于以下电路中的总线应用A。

TSL门电路、0C门电路、漏极开路门电路、互补金属氧化物半导体与非门(2)TTL与非门有n个同类门电路，低电平输入电流为1.5毫安，高电平输入电流为10毫安，最大填充电流为15毫安，最大拉电流为400毫安。

选择正确答案n和最多b。

a . n = 5b . n = 10c . n = 20d . n = 403)与TTL数字集成电路相比，CMOS数字集成电路的突出优势是ACD A。

当三极管用作开关时，为了提高开关速度，da .降低饱和深度b .增加饱和深度c .采用有源漏极电路d .采用反饱和三极管5)进行TTL与非门空闲输入处理，可以使用ABDa。

连接到电源b，连接到电源c，连接到地d，通过电阻3kω并联连接到有用输入6)。

光盘可以在以下电路中实现“线和”功能当A与非门b三态输出门c打开集电极门d打开漏极门7)三态门输出高阻抗状态时，ABD是正确的a .使用电压表测量指针不动b .相当于暂停c .电压不是高或低d .测量电阻指针不动8)已知正向电压降UD = 1.7V，参考工作电流ID = 10mA，TTL门的输出高和低电平分别为UOH = 3.6V，UOL = 0.3V，允许充电电流和牵引电流分别为IOL = 15mA，IOH = 4mA那么电阻r应该选择d。

数字集成电路第二版答案【篇一：《数字集成电路》期末试卷a(含答案)】考试试卷 a姓名学号班级任课教师一、填空题（本大题共10小题，每空格1分，共10分）请在每小题的空格中填上正确答案。

错填、不填均无分。

1．十进制数（68）10对应的二进制数等于；2．描述组合逻辑电路逻辑功能的方法有真值表、逻辑函数、卡诺图、逻辑电路图、波形图和硬件描述语言（hdl）法等，其中描述法是基础且最直接。

3．a?1可以简化为4．图1所示逻辑电路对应的逻辑函数l等于。

abc≥1lcy图1图25．如图2所示，当输入c是（高电平，低电平）时，y?ab。

6．两输入端ttl与非门的输出逻辑函数z?ab，当a=b=1时，输出低电平且vz=0.3v，当该与非门加上负载后，输出电压将(增大，减小)。

7．moore型时序电路和mealy型时序电路相比，型电路的抗干扰能力更强。

8．与同步时序电路相比，异步时序电路的最大缺陷是会产生 9．jk触发器的功能有置0、置1、保持和的ram。

二、选择题（本大题共10小题，每小题2分，共20分）在每小题列出的四个备选项中只有一个是符合题目要求的，请将其代码填写在题后的括号内。

错选、多选或未选均无分。

11．十进制数（172）10对应的8421bcd编码是。

【】a．（1111010）8421bcdb．（10111010）8421bcdc．（000101110010）8421bcd d．（101110010）8421bcd12．逻辑函数z(a,b,c)?ab?ac包含【】a．2 b．3c．4d．513．设标准ttl与非门z?ab的电源电压是+5v，不带负载时输出高电平电压值等于+3.6v，输出低电平电压值等于0.3v。

当输入端a、b电压值va=0.3v，vb=3.6v和va=vb=3.6v两种情况下，输出电压值vz分别为。

a．5v，5v c．3.6v，0.3v【】b．3.6v，3.6v d．0.3v ，3.6v14．图3所示电路的输出逻辑函数z1等于。

P4.1. Problem should refer to Figure P4.2.a. All inverters but the CMOS inverter consume static power then the output is high.Notice that in the first three inverters when the input is high, there is always a directconnection from V DD to G ND .b. None of the static inverters consumes power when the input is low because there is nopath from V DD to G ND .c. All inverters but the saturated enhancement inverter has a V OH of 1.2 V.d. Only the CMOS inverter has a V OL of 0 V.e. Except for the CMOS inverter, all the other inverte rs’ functionality depend on therelative sizes of the transistors.P4.2. Problem should refer to Figure P4.1a. Resistive loadb. Saturated-enhancement loadIterate to produce:To compute V OL we can ignore body effect and equate currents:Solve for 0.03OL V V ≈c. Linear-enhancement loadIterate to produce:This tells us that V GG should have been above 1.6V <closer to 1.7 V>.To compute V OL we can ignore body effect and equate currents. Note that the load issaturated even though we call it a linear-enhancement load. The driver is alsosaturated due to the device sizes used.Solve for 0.69V OL V ≈d. CMOSP4.3. For this problem, you are required to use the formulae:We already know that V OH =1.2 V and V OL =0 V. For V S use:Next V IL and V IH are estimated as follows:ThereforeWhen we cut the size of the PMOS device in half, the VTC shifts to the left. So V IL , V S , and V IH will all shift to the left. The recalculation of the switching threshold produces V S =0.566V. We can compute V IL to be roughly 0.533V and V IH to be roughly 0.667V.ThereforeP4.4. Similar approach as in P4.3. Run SPICE to check results.P4.5. First, set up the equation.Now solve for χ.This implies that a very large <W/L>P is needed to reach the desired value. It also reveals the limitations of the models. SPICE would be needed to obtain an acceptable solution if the switching threshold of 0.9V is truly desired.P4.6. SPICEP4.7. The advantages of the pseudo-PMOS is that it can reach a V OH of V DD while the pseudo-NMOS V OH can never reach that value. Additionally, the pseudo-NMOS’s V OH dependson the relative sizings of the inverters.The disadvantage is the dual of its advantage. The pseudo-PMOS inverter can never reach a V OL of 0 V. In addition, the pseudo-PMOS device will have to be approximately twice as large as a pseudo-NMOS device with comparable characteristics. This is due to the unequal mobility of holes and electrons. The pseudo-PMOS’s NMOS pull -down device is twice as strong as the pseudo-NMOS’s PMOS pull -up device, that means that the pseudo-PMOS’s PMOS wi ll have to be bigger than the NMOS device in a pseudo-NMOS.P4.8. a> Circuit is a buffer with degraded outputs.Output swing calculation:When IN DD V V =, output voltage is OH DD TN V V V =-. Since the source of NMOS transistor is not connected to substrate <ground>, we must take into account body effect.When 0IN V V =, output voltage is ||OL TP V V =. Since the source of PMOS transistor is not connected to substrate <V DD >, we must take into account body effect.Therefore the output swing is DD TN V V - to ||TP V with full accounting for body effect.b> Assume that the input is at 0 and the output is at |V TP |. As the input is increased, the output will stay constant until the NMOS device turns on. That will occur at V IN =|V TP |+V TN . The upper transistor behaves as a source follower and will pull the output along as the input rises until the output reaches V DD -V TN . However, as the input is reduced in value the output stays at its highvalue until the PMOS device turns on. This occurs at V IN=V DD-< |V TP|+V TN>. Then the PMOS device acts as a source follower and the output drops linearly to |V TP| as the input is reduced.c> The gain of the circuit is close to unity but slightly below this value. The circuit has poor noise rejection properties as it lacks the regenerative properties <this is a consequence of low gain>.d> SPICE run.P4.9.Resistive Load inverter:Saturated Enhancement Load inverter <ignoring body-effect>:Linear Enhancement Load inverter <ignoring body-effect>:The linear enhancement load inverter requires the largest pull-down device since it has the strongest pull up device. The resistive load inverter is next and the saturated enhancement load requires the smallest pull-down device.P4.10.We will illustrate the process and estimate the solutions for this problem.We already know that V OH=1.2 V and V OL=0 V. For V S use:Next V IL and V IH are estimated as follows:We can compute V IL to be roughly 0.533V.We can compute V IH to be roughly 0.667V.When we double the size of the PMOS device, the VTC shifts to the right. So V IL, V S, and V IH will all shift to the right. The recalculation of the switching threshold produces V S=0.6V.We can compute V IL to be roughly 0.55V and V IH to be roughly 0.65V.P4.11.The peak current would occur when both devices are in saturation and when V out=V in=V S.We can easily compute V S as:P4.12.As the required V OL becomes smaller, the W D/W L ratio becomes larger.P4.13.SPICEP4.14.The expression for the switching threshold of a CMOS inverter is:Solving for χ.Now solving for the ratio of sizes.Solving for χ.Now solving for the ratio of sizes.In the first case <0.6S DD V V >, the PMOS is much larger than the NMOS, so t PLH issmaller and t PHL is larger. The reverse is true for the second case.P4.15 <a> It does not have the regenerative property since the gain is less than one.<b> The last inverter would have an output of about 0.8V.<c> It is not possible to define the noise margin for this gate. Even a properinput eventually produces the incorrect output.P4.16 Both gates would work as a tristate buffer. However, as we shall find out in Chapter 7, the second one is prone to charge-sharing. That is, when the output is high and the EN signal is low, if the input goes high, the output may drop slightly in value due to loss of charge to the adjacent internal node.。

CHAPTER 5P5.1. For each problem, restate each Boolean equation into a form such that it can be translatedinto the p and n-complex of a CMOS gate.a. ()()Out ABC BD ABC BD A B C B D =+=+=+++b. ()()()Out AB AC BC AB AC BC A B A C B C =++=++=+++c. ()()Out A B CD A AB C D A A B CD A A B CD A =+++=++=+++=++AbVddVddAb BbAAbVddP5.2.AP5.3. First, convert the equation into its p and n-complex.()()()()()()()()()()()Out A B C BC AB AB C BC AB AB C BC AB AB C BC AB AB C BC AB AB C B C =⊕+=++=++=+=++=+++VddP5.4. The truth table is given below in terms of voltages. The function is F A B =The worse case V OH is V DD and the worse case V OL is 0V.P5.5. The first circuit is a NOR gate while the second is a NAND gate. The V OL and V OHcalculated are for the worst-case scenario. To find this, assume only one transistor turns on, this just reduces to a pseudo-NMOS/PMOS inverter, so the other transistors are not important.a. The V OL for the pseudo-NMOS (in 0.18μm) is:()()()2,1N N OXNSAT OX P GSP TPP SATOL W C L N DD TN GSP TP CP PDD TN SAT P N OX v C W V V I V k V V V V E L V V v W L C μ-==--+-=()2DD TP N N OX V V W C μ-()()()()()20.1DD TP CP P DD TN SAT P N DD TPDDN N DD TP CP P DD TN V V E L V V v W L V V V W V V E L V V μ-+--==-+-()()()()()()()()()()()()226440.18100.2100.210 1.80.50.14μm=1.40.11.8270 1.80.5240.2 1.80.5SAT P N DD TPN DD N DD TP CP P DD TN v W L V V W V V V E L V V μλ---=-+-⨯⨯⨯-==-+-Since the minimum width is 2λ, we make that the width. The V OH for the pseudo-PMOS (in 0.18μm) is:()()()()()()2221SDPSDP CP PN P V P OX P SGP TP SDP SAT OX N GSN TN V GSN TN CN N N E L SAT OX I sat I lin C W V V V v C W V V V V E L L v C μ=---=-++()2P OX N DD TN DD TN CN NC W V V V V E L μ-=-+()()()()()()2201DD OH DD OH CP PV V P DD TPDDOH V V P E L W V V VV L ------+()()()()()()20.1824620.184.8(70) 1.80.50.180.2(10)(810)1.80.51.80.5 1.21P P W L ---⨯-=-++4.2P W λ≈The pseudo-PMOS circuit will have bigger devices than the pseudo-NMOS.P5.6. The steps to solving this question are the same as the pseudo-NMOS question in Chapter4.a. For V OH , recognize that GS T V V >= for operation so the output can only be as high asDD T V V -. Since 0SB V ≠, body effect must be taken into account and the full equationis:()()()001.20.40.2OH DD T DDT V V V V Vγγ=-+=-+=-+ Iteration produces V OH =0.73V.b. For V OL , we must first recognize that the worst-case V OL occurs when only one of the pull-down transistors is on. Next we identify the regions of operation of the transistors. In this case, the pull-up transistor is always in saturation and the pull-down is most likely in the linear region since it will have a high input (high V GS ) and a low output (low V DS ). Then, we equate the two currents together and solve for V OL :()()()()()()()()221222222211111224620.61(1)(270)1.20.4(0.13)(10)(810)1.20.42(1.20.42)0.61DS DS CN OL OLV N OX GS T DS sat OX GS T V GS T CN E LV OL OL V OL I sat I lin W C V V V W v C V V V V E LL V V V μ-=---=-++--⨯--=--++Using a programmable calculator or a spreadsheet program, V OL = 0.205V. The dc current with the output low is:()()()()2222222260.20520.2050.61(1)(270)(1.610)1.20.4(0.205)146.5DS DS CN V N OX GS T DS DS V ELW C V V V I L Aμμ---=+⨯--=+=The power with the output low is:(46.5)(1.2)55.8DS DD P I V A V W μμ===P5.7. See Example 5.2 which is based on the NAND gate. This question is the same except thatit addresses the NOR gate.With both inputs tied together, 88N P W W λλ==2χ=== ()()1.80.520.50.77V 112DD TP TNS V V V V χχ-+-+===++In the SPICE solution, the reason why the results vary for input A and B is due to body-effect.P5.8. The solution is shown below. Notice that there is no relevance with the lengths andwidths of the transistors when it comes to V OH , although they the do matter when calculating V OL.01.80.50.3 2.51Vout GG T GG out T V V V V V V γ=-=++=++=P5.9. For t PLH , we need to size the pull-up PMOS appropriately.()()()()15120.70.720.70.73010010845010PLH eqp LOAD p SQLOAD PLHLt RC R C WL W R C k t λλ--====Ω⨯=⨯For V OL :()()()()()()()()()()()()()2246660.1220.10.63 4.210810 1.610 1.20.4 1.08mA1.20.4240.1(270)(1.610)1.20.40.11138.577377232(3OLOL CN P sat OX GS T P GS T CP V N N OX OL TN OLN P V N N E LNN NW v C V V I sat V V E LW C V V V W I sat L L W W W stack L μλλλ---⨯⨯⨯--===-+-+--⨯--==++===⨯=2)155(2)W stack λ=P5.10. The circuit is shown below:()()()()()()()()31512315120.720.70.7301075106350100.720.70.712.510751026.6275010PLH EQP LOAD PP EQPLOAD PLHPHL EQN LOAD NN EQNLOAD PHLLt RC R C W L W R C t Lt RC R C W L W R C t λλλλλ----====⨯⨯=⨯====⨯⨯=≈⨯Because the number of transistors in series is more than one, we must multiply the widths by the appropriate number. Here, all the NMOS transistors will have a width of 54λ. The PMOS transistors will have widths of 126λ and 190λ, respectively.P5.11. We estimate the dc power and dynamic switching power for this problem.a. The circuit’s dc power can be computed by computing the dc current when the output is low. This is given by I DS =550uA/um x 0.1um=55uA. Then P DC =66uW when the output is low.b. Its dynamic power can be calculated by simply using the equation 2dyn DD P CV f α=. Therefore, P dyn =(50fF)(V DD -V TN )(V DD )(100MHz)=4.4uW.P5.12. The pseudo-NMOS inverter has static current when the output is low. We can estimate itas:()()()()()()()()224660.110810 1.610 1.20.425.6A 1.20.4240.1P sat OX GS T P GS T CP W v C V V I sat V V E Lμ--⨯⨯⨯--===-+-+Then the average static power is P stat =(25.6uA)(1.2)/2 =15.4uW.The dynamic power is dyn DD swing avg P CV V f ==(50fF)(1.2)(1.1)f avg assuming that V OL is 0.1V.For the CMOS inverter, the static power is almost zero: P stat =I sub V DD . It is far less than the pseudo-NMOS case. The dynamic power dyn DD swing avg P CV V f ==(50fF)(1.2)2f avg is slightly larger than the pseudo-NMOS case.VVINCMOS InverterV V INPseudo-NMOSP5.13. Model development to compute αsc .P5.14. The energy delivered by the voltage source is:()()200202DDDDV C sourceDD DD L L DDCL DDV CDDcap C LC L C C LdvE i t V dt V C dt C V dvC V dt dv V E i t v dt C v dt C v dv C dt∞∞∞∞========⎰⎰⎰⎰⎰⎰As can be seen, only half the energy is stored in the capacitor. The other half was dissipated as heat through the resistor.P5.15. The average dynamic power does not depend on temperature if the frequency stays thesame. However, the short-circuit current will increase as temperature increases. In addition, the subthreshold current increases as temperature increases. So the overall power dissipation will be higher. P5.16. The circuit is shown below. The delay should incorporate both Q and Qb settling in400ps. All NMOS and PMOS devices are the same size in both NAND gates.QQW()()()()()()()()15331220.70.70.70.720.71001030100.1212.5100.10.72400101μm N P P PHL PLH UP LOAD DOWN LOAD LOAD eqp eqn P N LOAD eqp eqn LOAD eqp eqn PL Lt t t R C R C C R R W W C R L R L WC R L R L W t --⎛⎫=+=+=+ ⎪⎝⎭+=++==≈P5.17. The small glitch in J propagates through the flop even though it is small. This is due tothe fact that the JK-flop of Figure 5.20 has the 1’s catching problem. P5.18. The small glitch in J does not propagate through the flop since the edge-triggeredconfiguration does not have a 1’s catching problem.P5.19. The positive-edge triggered FF is as follows:QQDS(a) With CK=D=0 and S=R=1, the outputs are(b) Now CK=0。

1Chapter 11 Problem SetChapter 11PROBLEMS1.[E, None, 11.6] For this problem you are given a cell library consisting of full adders and two-input Boolean logic gates (i.e. AND, OR, INVERT, etc.).a.Design an N-bit two's complement subtracter using a minimal number of Boolean logicgates. The result of this process should be a diagram in the spirit of Figure 11.5 . Specifythe value of any required additional signals (e.g., C in ).b.Express the delay of your design as a function of N , tcarry , t sum , and the Boolean gate delays(t and , t or , t inv , etc.).2.[M, None, 11.6] A magnitude comparator for unsigned numbers can be constructed using fulladders and Boolean logic gates as building blocks. For this problem you are given a celllibrary consisting of full adders and arbitrary fan-in logic gates (i.e., AND, OR, INVERTER,etc.).a.Design an N -bit magnitude comparator with outputs and A = B using a minimalnumber of Boolean logic gates. The result of this process should be a diagram in the spiritof Figure 11.5. Specify the value of any required control signals (e.g., C in ).b.Express the delay of your design in computing the two outputs as a function of N , tcarry ,t sum , and the Boolean gate delays (t and , t or , t inv , etc.).3.3.[E, None, 11.6] Show how the arithmetic module in Figure 0.1 can be used as a comparator.Derive an expression for its propagation delay as a function of the number of bits.4.[E, None, 11.6] The circuit of Figure 11.2 implements a 1-bit datapath function in dynamic(precharge/evaluate) logic.a.Write down the Boolean expressions for outputs F and G . On which clock phases are out-puts F and G valid?b.To what datapath function could this unit be most directly applied (e.g., addition, subtrac-tion, comparison, shifting)?5.[M, None, 11.3] Consider the dynamic logic circuit of Figure 0.2 .a.What is the purpose of transistor M1? Is there another way to achieve the same effect, butwith reducing capacitive loading on the clock Φ?A B ≥Figure 0.1Arithmetic module.a i a ib j b jc jd jc j +1j+1c 0c 1d 0d 1c 1c 2d 1d 2c 2c 3d 2d 3c 3c 4d 3d 4a 0b 0a 1b 1a 2b 2a 3b 32Chapter 11 Problem Setb.How can the evaluation phase of F be sped up by rearranging transistors? No transistorsshould be added, deleted, or resized.c.Can the evaluation of G be sped up in the same manner? Why or why not?6.[M, SPICE, 11.3] The adder circuit of Figure 0.3 makes extensive use of the transmissiongate XOR. V DD = 2.5 V.a.Explain how this gate operates. Derive the logic expression for the various circuit nodes.Why is this a good adder circuit?b.Derive a first-order approximation of the capacitance on the C o -node in equivalent gate-capacitances. Assume that gate and diffusion capacitances are approximately identical.Compare your result with the circuit of Figure 11-6 .c.Assume that all transistors with the exception of those on the carry path are minimum-size. Use 4/0.25 NMOS and 8/0.25 PMOS devices on the carry-path. Using SPICE simu-lation, derive a value for all important delays (input-to-carry, carry-to-carry, carry-to-sum).A C inB B A ΦΦA B C in ABC inF GFigure 0.2Datapath module bit-slice.M 1Figure 0.3Quasi-clocked adder circuit.A A iV C oC i Signal setup Carry generationSum generationDigital Integrated Circuits - 2nd Ed 37.[M, None, 11.3] The dynamic implementation of the 4-bit carry-lookahead circuitry from Fig.11-21 can significantly reduce the required transistor count.a.Design a domino-logic implementation of Eq. 11.17 . Compare the transistor counts of thetwo implementations.b.What is the worst-case propagation delay path through this new circuit?c.Are there any charge-sharing problems associated with your design? If so, modify yourdesign to alleviate these effects.8.[C, None, 11.3] Figure 0.4 shows a popular adder structure called the conditional-sum adder.Figure 0.4.a shows a four-bit instance of the adder, while 0.4.b gives the schematics of thebasic adder cell. Notice that only pass-transistors are used in this implementation.a.Derive Boolean descriptions for the four outputs of the one-bit conditional adder cell.b.Based on the results of describe how the schematic of 0.4.a results in an addition.c.Derive an expression for the propagation delay of the adder as a function of the number ofbits N . You may assume that a switch has a constant resistance R on when active and thateach switch is identical in size.9.[M, None, 11.3] Consider replacing all of the NMOS evaluate transistors in a dynamicManchester carry chain with a single common pull-down as shown in Fgure 0.5.a. Assumethat each NMOS transistor has (W /L )N = 0.5/0.25 and each PMOS has (W /L )P = 0.75/0.25.Further assume that parasitic capacitances can be modeled by a 10 fF capacitor on each of theFigure 0.4Conditional-sum adder.A A B B A A B S 0A A B B AA B S 1AB A A AC 0ABA AAC 1(b) Conditional adder cell (a) Four-bit conditional-sum adderS 0S 1S 2S 3C out Conditional Cell Conditional Cell Conditional Cell ConditionalCellC 1C 0S 1S 0C 1C 0S 1S 0C 1C 0S 1S 0C 1C 0S 1S 0B 3A 3B 2A 2B 1A 1B 0A 04Chapter 11 Problem Setinternal nodes: A , B , C , D , E , and F . Assume all transistors can be modeled as linear resistorswith an on-resistance, R on = 5 k Ω.a.Does this variation perform the same function as the original Manchester carry chain?Explain why or why not.b.Assuming that all inputs are allowed only a single zero-to-one transition during evalua-tion, will this design involve charge-sharing difficulties? Justify your answer.plete the waveforms in Figure 0.5b for P 0 = P 1 = P 2 = P 3 = 2.5 V and G 0 = G 1 = G 2 =G 3 = 0 V. Compute and indicate t pHL values for nodes A , E , and F . Compute and indicate10.[M, None, 11.3] Consider the two implementations of Manchester carry gates in Figure 11-8.pare the delay per segment of the two implementationsb.Compare the layout complexities of the two gates using stick diagrams.c.In the precharged Manchester carry chain using the gate from b. find the probability thatthe carry signal is propagated from the 15th to the 16thbit of a 32-bit adder, assuming ran-dom inputs.11.[C, None, 11.3] Consider the Radix-4 and Radix-2 Kogge-Stone adders from Figures 11-22and 11-27 extended to 64-bits. All gates are implemented in domino and all gates in a stagehave the same size. The adders have an overall fanout (electrical effort) of 6.ing logical effort, identify the critical path.b.Size the gates for minimum delay (hint: don't forget to factor in branching). Which adderis faster?c.Let's now consider sparse versions of each of the above trees. In a tree with a sparseness of2, only every other carry is computed and it is used to select 2 sums. Similarly, a tree witha sparseness of 4 computes every fourth carry - and that carry signal is used to select 4sums. Repeat a. and b. for Radix-2 and Radix-4 trees with sparseness of 2 and 4 and com-pare their speed. Which adder is fastest?pare the switching power of all adders analyzed in this problem.12.[C, None, 11.3] In this problem we will analyze a carry-lookahead adder proposed by H. Lingmore than 20 years ago, but still among the fastest adders available. In a conventional adder,in order to add two numbersA = a n −12n −1 + a n −22n −2 + .... + a 020B = b n −12n −1 + b n −22n −2 + .... + b 020we first compute the local carry generate and propagate terms:P 0C in P 1G 0P 2G 1P 3G 2G 3φφV DD Figure 0.5Alternative dynamic Manchester carry-chain adder.A B C D E F (a) Circuit schematic (b) Partial waveformsφAEFCDigital Integrated Circuits - 2nd Ed 5g i = a i b i pi = a i + b ithen, with a ripple or a tree circuit we form the global carry-out terms resulting from the recurrence relation:G i = g i + p i G i −1Finally, we form the sum of A and B using local expressions:In the conventional adder, the terms G i have, as described, a physical significance. However,an arbitrary function could be propagated, as long as sum terms could be derived. Ling'sapproach is to replace G i with:H i = G i + Gi −1i.e. H i is true if "something happens at bit i " - there is a carry out or a carry in. H i is so-called"Ling's pseudo-carry".a.Show that:H i = g i + ti −1H i −1where p i = a i + b i (it was Ling’s idea to change the notation).b.Find a formula for computing the sum out of the operands and Ling's pseudo-carry.c.Unroll the recursions for G i and H i for i = 3. You should get the expressions fpr G 3 and H 3as a function of the bits of input operands. Simplify the expressions as much as possible.d.Implement the two functions using n-type dynamic gates. Draw the two gates and size thetransistors. Which one helps us build a faster adder? Explain your answer.13.[M, None, 11.4] An array multiplier consists of rows of adders, each producing partial sumsthat are subsequently fed to the next adder row. In this problem, we consider the effects ofpipelining such a multiplier by inserting registers between the adder rows.a.Redraw Figure 11-31 by inserting word-level pipeline registers as required to achievemaximal benefit to throughput for the 4x 4 multiplier. Hint: you must use additional regis-ters to keep the input bits synchronized to the appropriate partial sums.b.Repeat for a carry-save, as opposed to ripple-carry, architecture.c.For each of the two multiplier architectures, compare the critical path, throughput, andlatency of the pipelined and nonpipelined versions.d.Which architecture is better suited to pipelining, and how does the choice of a vector-merging adder affect this decision?14.[M, None, 11.4] Estimate the delay of a 16x16 Wallace tree multiplier with the final adderimplemented using a Radix-4 tree. One FA has a delay of t p , a HA 2/3*t p and a CLA stage½*t p .15.[E, None, 11.5] The layout of shifters is dominated by the number of wires running through acell. For both the barrel shifter and the logarithmic shifter, estimate the width of a shifter cellas a function of the maximum shift-width M and the metal pitch p .16.[E, None, 11.7] Consider the circuit from Figure 0.7 . Modules A and B have a delay of 10 nsand 32 ns at 2.5V, and switch 15 pF and 56 pF respectively. The register has a delay of 2 nsand switches 0.1 pF. Adding a pipeline register allows for reduction of the supply voltagewhile maintaining throughput. How much power can be saved this way? Delay with respectto V DD can be approximated from Figure 11-57.17.[E, None, 11.7] Repeat Problem 16, using parallelism instead of pipelining. Assume that a 2-to-1 multiplexer has a delay of 4 ns at 2.5 V and switches 0.3 pF. Try parallelism levels of 2and by 4. Which one is preferred?S i p i G i 1–⊕=6Chapter 11 Problem Set DESIGN PROBLEMUsing the 0.25 µm CMOS technology, design a static 32-bit adder, with the fol-lowing constraints:1.input capacitance on each bit is limited to not more than 50fF.2.each bit is loaded with 100fF.Use a carry lookahead tree of your choice for implementation. The goal is toachieve the shortest propagation delay.Determine the logic design of the adder and W and L of all transistors.Initially size the design using the method of logical effort. Estimate the capaci-tance of carry signal wires based on the floorplan. Verify and optimize thedesign using SPICE. Compute also the energy consumed per transition. If youhave a layout editor available, perform the physical design, extract the real cir-cuit parameters, and compare the simulated results with the ones obtained ear-lier. For implementation use the 144λ.bit-slice pitch, that corresponds to 36metal-1 tracks. Use metal 1 for cell-level power distrbution and intra-cell rout-ing, metal-2 for short interconnect and metal-3 and metal-4 for long carries.R e g is t er Re gis t e r Figure 0.6Pipelined datapath.A B In Out。

北京大学信息学院考试试卷考试科目： 数字集成电路原理 考试时间 姓名： 学号：题 号 一 二三四五六七八九 十总分分 数 阅卷人以下为答题纸，共 6 页一、填空1、（4分）CMOS 逻辑电路中NMOS 管是（ 增强 ）型，PMOS 管是（增强）型； NMOS 管的体端接（ 地 ），PMOS 管的体端接（ VDD ）。

2、（8分）CMOS 逻辑电路的功耗由3部分组成，分别是（ 动态功耗 ）、（开关过程中的短路功耗）和（ 静态功耗 ）；增大器件的阈值 电压有利于减小（ 短路功耗和静态 ）功耗。

3、（6分）饱和负载NMOS 反相器的3个主要缺点是：（ 输出高电平有阈值损失 ）,( 输出低电平不是0，与比例因子Kr 相关 ), ( 输出低电平时有静态功耗 ) 。

4、（3分）三态输出电路的3种输出状态是：（ 高电平 ）， （ 低电平 ）和（ 高阻态 ）。

二、（12分）画出实现ABC D C B A Y +++=)(的静态CMOS 电路，如果所有MOS管的导电因子都是K ,分析几个输入同步变化的等效反相器的导电因子（K Neff 和K Peff ），在什么输入状态下电路有最小的低电平噪声容限。

Kneff = 1/(1/3k + 1/k) + k/3 = 3k/4 + k/3 = （13/12）K;Kpeff = 1/(1/3k + 1/k) + k/3 = （13/12）K;当 D = 1 ，A、B、C 同步变化时，上拉通路3个串联的PMOS 管起作用，下拉支路所有NMOS 都起作用，Kneff 最大 ， Kpeff 最小，传输特性曲线在最左边。

三、（12分）分析下面2个电路的逻辑功能，若所有输入高电平都是5V、输入低电平都是0V，电源电压是5V，所有MOS 管的阈值电压绝对值都是0.8V，分析2个电路的输出高、低电平和主要优缺点。

（1） （2） 电路 1） ⎩⎨⎧=======+=VB A VB A Vol B A AB Y 2.4Voh 15Voh 0,0,时，时， ，电路 2） B A B A B A AB Y +=++=，低电平0V ，高电平 4.2V 电路1）结构简单，节省面积，逻辑电平与输入状态相关，驱动能力差，噪声容限小。

思考题与习题1-1 填空题1）三极管截止的条件是U BE ≤0V。

三极管饱和导通的条件是I B≥I BS。

三极管饱和导通的I BS是I BS≥（V CC－U CES）/βRc。

2）门电路输出为高电平时的负载为拉电流负载，输出为低电平时的负载为灌电流负载。

3）晶体三极管作为电子开关时，其工作状态必须为饱和状态或截止状态。

4） 74LSTTL电路的电源电压值和输出电压的高、低电平值依次约为 5V、2.7V、0.5V 。

74TTL电路的电源电压值和输出电压的高、低电平值依次约为 5V、2.4V、0.4V 。

5）OC门称为集电极开路门门，多个OC门输出端并联到一起可实现线与功能。

6） CMOS 门电路的输入电流始终为零。

7） CMOS 门电路的闲置输入端不能悬空，对于与门应当接到高电平，对于或门应当接到低电平。

1-2 选择题1）以下电路中常用于总线应用的有 abc 。

A.TSL门B.OC门C.漏极开路门D.CMOS与非门2）TTL与非门带同类门的个数为N，其低电平输入电流为1.5mA，高电平输入电流为10uA，最大灌电流为15mA，最大拉电流为400uA，选择正确答案N最大为 B 。

A.N=5B.N=10C.N=20D.N=403）CMOS数字集成电路与TTL数字集成电路相比突出的优点是 ACD 。

A.微功耗B.高速度C.高抗干扰能力D.电源范围宽4）三极管作为开关使用时，要提高开关速度，可 D 。

A.降低饱和深度B.增加饱和深度C.采用有源泄放回路D.采用抗饱和三极管5）对于TTL与非门闲置输入端的处理，可以 ABD 。

A.接电源B.通过电阻3kΩ接电源C.接地D.与有用输入端并联6）以下电路中可以实现“线与”功能的有 CD 。

A.与非门B.三态输出门C.集电极开路门D.漏极开路门7）三态门输出高阻状态时， ABD 是正确的说法。

A.用电压表测量指针不动B.相当于悬空C.电压不高不低D.测量电阻指针不动8）已知发光二极管的正向压降U D = 1.7V ，参考工作电流I D = 10mA ， 某TTL 门输出的高低电平分别为U OH = 3.6V ，U OL = 0.3V ，允许的灌电流和拉电流分别为 I OL = 15mA ，I OH = 4mA 。

课时4数字集成电路一、基础巩固篇1.下列对于MOS管的描述，不恰当．．．的是()A.MOS管属于电压控制元件B.栅极G用来控制导通与截止C.漏极D通常接地D.MOS管作为开关时工作在截止与导通状态2.数字集成电路有多种类型，最常用的有TTL和CMOS两种，它们各有优缺点，适用于不同的场合中。

下列不是．．TTL电路优点的是()A.速度快B.允许负载流过的电流较大C.抗静电能力强D.功耗小3.下列有关如图所示的数字集成电路芯片的说法中，正确的是()A.该芯片的名称是双4输入与门B.7脚接电源正极，14脚接地C.该芯片能实现或逻辑关系D.如果工作的电压为12 V，则该芯片为CMOS型电路4.如图所示是CT74LSO4集成芯片引脚图，共有____个门电路，每个门电路有____个输入端、____个输出端。

横线上分别应该填()A.6、6、6B.6、1、1C.1、6、6D.1、1、15.晶体管电路如图所示，请完成以下任务：(1)三极管型号是________(在①NPN型；②PNP型中选择合适的选项，将序号填写在“______”处)；(2)将开关断开，LED1和LED2分别为________和________(在①熄灭；②点亮中选择合适的选项，将序号填写在“________”处)；将开关闭合，LED1和LED2分别为______和______(在①熄灭；②点亮中选择合适的选项，将序号填写在“______”处)；(3)开关闭合时，三极管基极和发射极之间的电压为__________ V，三极管处于__________状态(在①饱和；②截止中选择合适的选项，将序号填写在“________”处)；集电极和发射极之间________(在①导通；②截止中选择合适的选项，将序号填写在“______”处)，LED2被________(在①短路；②开路中选择合适的选项，将序号填写在“______”处)。

二、素养提升篇1.如图所示是数字集成电路CC4001引脚排列及功能图，在实际使用中，下列说法中不正确．．．的是()A.该集成电路是TTL类型B.如果电路中只需用一个或非门，可任选其中一组C.把其中一组或非门的两个输入端并接后，可以实现非门的功能D.把该集成块中的或非门加以组合，可以实现与门功能2.如图所示的集成逻辑门电路引脚图(V CC＝5 V)，关于该电路描述错误．．的是()A.该集成电路属于TTL类型B.该集成电路的名称为四2输入与非门C.该集成电路由普通晶体三极管构成D.该集成电路的四个与非门作用各不相同3.如图a所示为小明设计的湿度警示实验电路，R S为负系数湿敏电阻，电路中所用芯片为四2输入与非门74LS00。