0 Operation principle of power semiconductors

中文2540字Laser driver circuitSmall cha nges will directly semic on ductor laser drive curre nt to the output inten sity fluctuati on. To stabilize the output power semicon ductor laser, Voltage negative feedback principle to design a constant current driving circuit comprises a soft start ing and curre nt limiti ng protect ion circuit based on; At the same time, accord ing to the n eed of the light source is modulated to elim in ate the in flue nee of background light and, integrated laser modulation circuit comprises a crystal oscillati on circuit and divider circuit desig n. Making the specific circuit and complete the releva nt experime ntal. The experime ntal results show that the circuit can provide a driving current of high stability, Current stability up to 0.05%; Soft start and curre nt-limiti ng protecti on circuit can protect the semic on ductor laser and enhance the impact capability. Modulati on circuit gen erates a carrier sig nal n eeded for laser diode modulation and direct to complete the output light modulation, The switch can be convenien tly realized from 256Hz to 512kHz range of 12 kinds of com monly used modulati on freque ncy selecti on.Semic on ductor laser with its excelle nt characteristics, high efficie ncy, simple structure, small is widely used in scientific research, national defense, medical, and other areas of process in g, its drive tech no logy becomes more and more importa nt. Semic on ductor laser is the ideal electro n - phot on direct conv ersi on devices, qua ntum efficiency is very high, the current small changes will lead to a great change, the output light inten sity of the therefore, semic on ductor laser drive curre nt requireme nts is very high. Driving tech no logy of semic on ductor laser usually adopts con sta nt curre nt drive mode, this work, through the prin ciple of n egative feedback con trol loop, directly provide the effective control of the drive current. In addition, the transient current or voltage spikes, and overcurrent, overvoltage will damage the semic on ductor laser drive circuit, therefore should be con sidered in the protecti on circuit aga inst electric shock measures and special.In some applicati ons, DC semic on ductor lasers produce DC drive light in the measurementprocess is vulnerable to interferenee from ambient light slow change, which could not be separated from the en vir onment light required DC optical sig nal, the signal-to-noise ratio is too small, so to carry on the modulation. When the high-speed modulated semic on ductor lasers, there will be dyn amic characteristics is complex, such as the relaxation oscillation, since the pulse and multi-pulse phe nomena. In thispaper, experime nts were con ducted to study the characteristics of low freque ncy modulati on. Semic on ductor laser output is stable, and can be directly modulated, it has bee n widely applied in optical system, is the preferred source sen sor system. This paper describes the design of a high stability driving current, modulation, simple operation and low cost driving circuit for the light source of optical fiber systems.In this paper, the desig n of driv ing the semic on ductor laser modulati on circuit composed of four parts, including constant current circuit, a soft start, current limit protect ion and modulatio n sig nal gen erat ing circuit. The con sta nt curre nt circuit to gen erate a high stable drive curre nt. Soft start is the role of elim in at ing surge may be prese nt in the circuit, to preve nt the harm of surge for laser. To avoid damage due to overcurre nt caused by semic on ductor laser can not be restored, the n addi ng current-limiting protection in a driver circuit. Circuit to realize the modulation and freque ncy can be adjusted to gen erate a modulated sig nal.The constant current circuit is shown in figure 1, The in-phase end voltage refere nce Vr into A1 op amp, the operati onal con trol amplifier con duct ing level, and thus to obta in the corresp onding output curre nt. The output curre nt gen erated by sampling voltage sampling resistor Rs, the sampling voltage is amplified as the in vert ing in put voltage feedback voltage feedback amplifier A1, and voltage and the in-phase in put end of comparis on, Q2 to adjust the output voltage through the triode, adjustme nt and output curre nt of semic on ductor lasers, so that the whole closed-loop feedback system in the dyn amic bala nce.Figure 1 Constant current mapBecause the switch in sta ntan eous in power supply gen eratesa voltage, curre nt surge, as well as the surge interference effects are likely to cause the breakdown and the damage of the semic on ductor laser, and therefore must be in the desig n of soft start circuit drive laser, namely the use of the charge and discharge of RC circuit, delay time, the specific circuit as shown in Figure 2 as shown in. Switch S1 is closed, thecurrent through the resistor R1 and capacitor C3 to charge, the base electrode of the triode Q voltage gradually rises. As the capacitor chargi ng and the con duct ion of the triode, output voltage V is achieved from 0 to the maximum rise slowly, until the capacitor charge saturation, the voltage and current stabilizing. When the power supply is disc onn ected, the process of reverse, so as to realize the curre nt and voltageFigure 2 Soft start circuit diagramLaser soft start time and the chargi ng capacitor and the corresp onding resista nee, when the capacitor charging tends to saturation, the output voltage soft start circuit can achieve maximum. Power supply voltage is V I, the capacitor voltage is V o, the capacitor charging formula:_ 1V厂V j（1 - e「RC）Accord ing to this formula can calculate the electric charge and discharge time.Semic on ductor laser with other devices, have no rmal worki ng curre nt, if the curre nt exceeds this ran ge, the laser will be damaged, therefore must restrict curre nt laser in the set ran ge.Emitter voltage tran sistor Q2 as the feedback voltage term inal phase in A3 op amp, when the feedback voltage is less than the limit voltage VA3 op amp output low level, the transistor Q1 is turned on, this time by a triode Q2 output voltage feedback voltage is greater than the limit; when the voltage of V A3 op amp output high, triodeQ1 cutoff, this limits the triode Q2 emissi on in creases very curre nt, and is limited to a specific value. So even if the current caused by Vr control voltage exceeds the set value, the triode Q1 and Q2 are connected in series, so the total current will be clamped in the setting current value.Modulation signal generating circuit is composed of a crystal oscillating circuit and divider circuit is composed of two parts, used to generate the high stability of frequency, duty cycle square wave signal is stable. Crystal oscillating circuit directlygenerated by the active oscillator, oscillation frequency is 1MHz. Frequency divider circuit composed of a CMOS integrated circuit 4040.1MHz pulse signal after the frequency by 4040, pin output frequency from the switch is selected, the duty cycle is 50%, amplitude is 5V square wave signal. The modulation frequency dividing frequency were 256Hz, 512Hz, 1kHz, 2kHz,4kHz,8kHz,16kHz,32kHz, 64kHz128kHz, 256kHz, 512kHz..Driving an important technical parameters of circuit for current stability. Current stability is in a certain period of time, several measurements through the current size of the semiconductor laser, namely the ratio of output current stability for the relative change amount and input current, stability calculation, there will be current relative change is defined as the measurementof the maximum and minimum values, will measure the average value as the input current value.Drive circuit based on voltage negative feedback principle, by constant current drive mode to realize the control of the injection current and output power of semiconductor laser, and it can provide high stable output current, current stability0.05%. Drive circuit with soft start, current limit circuit protection, reduce the damage of semiconductor laser to surge breakdown and current, the modulation circuit and the drive circuit effectively combined, realize the frequency is, the development of new technology of optical fiber communication is essential.The causes of dispersion: One is the light emitted by the light source is not monochromatic light; two is the modulation signal has a certain bandwidth.The dispersion of the classification: By different modes or different frequency (or wavelength) light signal components, transmission in optical fibers, due to the physical phenomenon of different group velocities cause signal distortion is called fiber dispersion. The fiber dispersion is divided into mode dispersion (or intermodal distortion), material dispersion and waveguide dispersion. After two kinds of dispersion is the dispersion a pattern, also known as intra-modal dispersion.Dispersion harm: Fiber dispersion in optical signal waveform distortion, performance for the pulse width, it is the time domain characteristics of optical fiber.In digital communication system, pulse broadening of optical signal is an important index. Pulse broadening is too large can cause adjacent pulse gap decreases,the adjacent pulse will overlap and regenerative repeater decision errors occur, which increases the BER, transmission bandwidth narrowing, limit the transmission capacity of optical fiber.Said method of dispersion: Commonly used dispersion representation hasmaximum time delay for $S, pulse width R and optical bandwidth of 3dB B three. The maximum time delay difference delay description fiber in the fastest and most slow wave component. Used to describe the effect of fiber dispersion on the transmission signal pulse broadening and optical fiber bandwidth. A section of optical fiber as a network analysis of the dispersion characteristics, the available time domain method and frequency domain method. When in the time domain analysis, dispersion effect is represented by the pulse broadening, and analyzed in the frequency domain, the transmission bandwidth said.激光器驱动电路半导体激光器驱动电流的微小变化将直接导致其输出光强的波动。

Superconducting Magnetic Energy Storage forPower System Applications电力系统设备的超导磁储能Abstract-A survey of the technology of superconducting mag-netic energy storage (SMES) was made. This technology is at-tractive for its high efficiency and fast response, but also dubious for the capital investment. Research made in the USA and Japan resulted in several conceptual designs for the utility scale SMES systems. Experiments on power system models proved that SMES systems offer other benefits in addition to energy storage. Economic evaluations showed that the SMES is competitive with pumped hydro, especially when the energy price hikes. A power flow program is used to verify the application of a SMES plant to the Taiwan power (Taipower) system摘要——一个关于超导磁能储存的技术被研发出来了。

这项技术涉它高效且响应速度快，但是相关投资经费却被怀疑。

在美国和日本的研究导致了几项公共事业项目SMES系统的概念设计。

一个新的对于无约束非凸优化问题渐近的算法陈汝栋;吴成玉【摘要】For the optimization of nonconvex functions in mathematical programming,according to the know nconvex function optimization results and the corresponding algorithm,a new im-proved asymptotic algorithm is constructed,and by using Kurdyka-Lojasiewicz property,the convergence analysis of unconstrained nonconvex optimization problems for real lower semicon-tinuous nonconvex functions is considered.The sequence generated by the improved asymptotic algorithm has finite length and converges to a critical point of the function are obtained.Mean-while,the result representation of the convergence rate of the sequence is given.%针对数学规划中的非凸函数的优化问题,根据已知的凸函数的优化结果及相应算法,构造新的渐进算法,并运用Kurdyka-Lojasiewicz不等式,对真下半连续的非凸函数的无约束非凸优化问题进行了收敛分析,得到了由改进的渐进算法生成的序列具有有限长且收敛于该函数的一个临界点.同时给出了序列收敛速率的结果表示.【期刊名称】《纺织高校基础科学学报》【年(卷),期】2018(031)001【总页数】8页(P55-62)【关键词】渐近算法;Kurdyka-Lojasiewicz性质;无约束非凸优化问题;收敛速率【作者】陈汝栋;吴成玉【作者单位】天津工业大学理学院,天津 300387;天津工业大学理学院,天津300387【正文语种】中文【中图分类】O1770 引言在数学规划中,研究的大多数是凸函数的优化问题,而非凸函数优化很少涉及．非凸函数优化还是一个新兴的研究方向,发展较为缓慢,且主要应用于非凸优化方面的算法,Martient[1]和Rockafellar[2]在对极大单调算子的变分不等式的研究中引进渐近算法和在凸优化中引进一个渐近正则方法.文献[3-8]给出了凸优化中的非单调算子.文献[9-13]给出了关于非凸函数的概念以及非凸条件下的优化理论.文献[14]研究了f:X→(-∞,∞]和g:Y→(-∞,∞] 是真下半连续函数(未必是凸的)的优化问题,其中X⊂⊂Rn是闭凸集,目的在于找到关于下列函数的临界点f(x)+g(y),(1)使得min(f(x)+g(y)).(2)引进交替方向法去解决非凸的线性约束问题,其中目标函数是真下半连续的非凸函数构造的迭代方法如下:(3)通过收敛性分析,得到了交替方向法生成的序列{(xk,yk)}收敛于目标函数的一个临界点{(x*,y*)}以及{(xk,yk)}具有有限长.但所是构造的迭代方法中的罚参数的控制条件比较严格,且没有给出收敛速率的结果．本文借鉴文献[14]研究非凸函数无约束的优化问题,构造了新的渐进算法，并在适当条件下检验改进的迭代算法的收敛性.1 预备知识设H是一个定义了内积〈·,·〉和范数‖·‖的希尔伯特空间.命题1 (ⅰ) domf:={x∈Rn:f(x)<+∞}表示f的定义域;(ⅱ) 对于一点表示f在x的Fre′chet次微分,它是关于向量x*∈Rn的集合,该集合满足(ⅲ) ∂f(x)表示f在x∈Rn处的极限次微分,定义为∂f(x):={x*∈Rn:∃∀x∈Rn,显然有⊂∂f(x).其中第一个集合是闭的和凸的, 然而第二个集合是闭的. 用critf来表示f的临界点的集合, 即若0∈∂f(x)：则有x∈crit.命题2 设f:Rn→(-∞,+∞]是一个真下半连续函数.如果C是Rn的一个闭子集,对x∈Rn,x到C的距离dist(x,C):=inf{‖x-y‖:y∈C}.(4)如果C是空的, 对所有的x∈Rn,有dist(x,C)=∞.若dist(x,C)=0,则x∈C.命题3 如果C是Rn中的一个闭子集,用δC表示其指示函数, 即对所有x∈Rn,有(5)在C上的投影PC(x):=argmin{‖x-z‖:z∈C}来表示.命题4 设η∈(0,+∞].用Φη来表示所有凹函数和连续函数φ:[0,η)→R+,该函数满足下列条件:(ⅰ) φ(0)=0;(ⅱ) φ在(0,η)上是C1和在0是连续的;(ⅲ) ∀x∈(0,η),φ′(x)>0.引理1[15] 设f:Rn→(-∞,+∞]是真下半连续函数,如果x∈Rn是f的局部极小值,则有0∈∂f(x).引理2(KL性质)[16] 设f:Rn→(-∞,+∞]是真下半连续函数.则(ⅰ) 设Dom∂f(x):={x∈Rn:∂f(x)≠φ}.f在具有Kurdyka-Lojasiewicz(KL)性质,如果∃η∈(0,+∞],对于的一个邻域U和一个函数φ∈Φη,使得∀(6)有(7)(ⅱ) 如果一个凹函数f在关于Dom∂f(x)的每一点满足KL性质,则f被称为KL函数.2 迭代算法首先构造与式(1)有关的目标函数:(8)然后,给出该方法的迭代序列:(9)上述方法就是所构造的新的渐近算法．针对不同非凸问题的渐近算法和相关知识可以参考文献[17-22].假设满足的条件如下:(H1) 式(9)的解集是非空的且(H2) f和g是下有界的KL函数;(H3) ∀k≥0,序列{λk}，{μk}属于(λ-,λ+).引理3 假定满足(H1)-(H3),设由式(9)生成的序列是{(xk,yk)},且则(Δx,k,Δy,k)∈∂Ψ(xk,yk).故存在一个常数M>0,使得‖(Δx,k,Δy,k)‖≤M(‖xk-xk-1‖+‖yk-yk-1‖).证明由式(9),得(10)设αk∈∂f(xk),可得关于式(10)的优化条件为同理,(11)因为∂xΨ(xk,yk-1)=αk+‖xk-yk-1‖和∂yΨ(xk,yk)=βk-‖xk-yk‖, 有最后因此得到(Δx,k,Δy,k)∈∂Ψ(xk,yk).根据三角不等式,有其中3 收敛性分析定理1 假定满足(H1)～(H3), 由式(9)生成的序列是{(xk,yk)}. 则下面的假设成立: (ⅰ) 序列{Ψ(xk,yk)}是递增的且存在一个常数M1>0, 使得M1(‖xk+1-xk‖2+‖yk+1-yk‖2)≤Ψ(xk,yk)-Ψ(xk+1,yk+1)(12)(ⅱ)如果{(xk,yk)}是有界的, 则此外,和是有限的,则证明(ⅰ)由式(9)知(13)(14)∀k≥1,式(13)和(14)相加可得(15)根据Ψ(x,y)的定义, 有(16)这表明{Ψ(xk,yk)}是非增的. 其中(ⅱ) 对不等式(16)从0到N(N≥0)求和，得(17)因为{(xk,yk)}是有界的,∀ε1>0, 存在N1>0使得∀k>N1 dist((xk,yk),(x*,y*))<ε1.由f的下半连续性知(18)从式(9)知因(xk,yk)→(x*,y*)且{λk}是有界的, 设k→∞,则有(19)结合式(18)和(19), 得到同理故(20)即∀ε2>0,∃N2>0, 使得∀k>N2‖Ψ(xk,yk)-Ψ(x*,y*)‖<ε2.(21)因{Ψ(xk,yk)}是非增序列, 则可得∀k≥1Ψ(x*,y*)<Ψ(xk,yk).设N=max{1,N1,N2},∀k>N,有(xk,yk)∈ {(xk,yk)|dist((xk,yk),(x*,y*))<ε1}∩(Ψ(x*,y*)<Ψ(xk,yk)<Ψ(x*,y*)+ε2).由KL性质知, 有φ′(ψ(xk,yk)-ψ(x*,y*))dist((0,0),∂Ψ(xk,yk))≥1.(22)由引理3得(23)由φ的凹性有φ(Ψ(xk,yk)-Ψ(x*,y*))-φ(Ψ(xk,yk)-Ψ(x*,y*))≥φ,(Ψ(xk,yk)-Ψ(x*,y*))(Ψ(xk,yk)-Ψ(xk+1,yk+1)).(24)∀k>N, 由式(22),式(11)式和φ的凹性可得(25)其中Ωk,k+1=φ(Ψ(xk,yk)-Ψ(x*,y*))-φ(Ψ(xk,yk)-Ψ(x*,y*)).根据(a+b)2≤2a2+2b2和有2(‖xk+1-xk‖+‖yk+1-yk‖)≤M2Ωk,k+1+(‖xk-xk-1‖+‖yk-yk-1‖).(26)其中将式(26)从k=N+1,N+2,…,n相加,化简得到其中ΩN+1,n+1=ΩN+1,q+Ωq,n+1(q是一个正整数).然后由ΩN+1,n+1的定义和φ∈Φη,可得+M2φ(Ψ(xN+1,yN+1)-Ψ(x*,y*)).(27)设n→∞,根据式(27)可得到因此,由于得到是有限的.最终4 收敛结果定理2(收敛定理) 假定满足(H1)～(H3), 由式(9)生成的序列记作{(xk,yk)}. 用{(x*,y*)}表示关于Ψ(xk,yk)的极限点, 则{(xk,yk)}收敛于一个临界点{(x*,y*)}.证明设m>n>N,得到(28)式(28)表明{(xk,yk)}是一个收敛序列，从定理1(ⅱ)知,由引理2和定理1(ⅱ),有(Δx,k,Δy,k)∈∂Ψ(xk,yk),(Δx,k,Δy,k)→(0,0)当k→∞.因此,由∂Ψ的封闭性可知(0,0)∈∂Ψ(x*,y*),这表明(x*,y*)是Ψ的一个临界点.推论1 假定Ψ满足(H1)～(H3)且在处具有Kurdyka-Lojasiewicz性质,且是Ψ一个局部极小点.则∃ε3>0和υ>0，使得(ⅰ)(ⅱ) minΨ<Ψ(x0,y0)<minΨ+υ.这表明以(x0,y0)为起始点的序列(xk,yk)具有有限长性质且收敛于(x*,y*), 即Ψ(x*,y*)=minΨ.证明从定理1知(xk,yk)收敛于(x*,y*), 一个临界点Ψ满足minΨ<Ψ(x0,y0)<minΨ+υ,∀k>0.如果由引理2知这与(0,0)∈∂Ψ(x*,y*)矛盾.定理3(收敛速率定理) 假设Ψ(x,y)满足(H1)～(H3).假定(xk,yk)收敛于(x∞,y∞),Ψ(x,y)在(x∞,y∞)具有Kurdyka-Lojasiewicz性质.φ(s)=cs1-θ,θ∈[0,1),c>0.其中θ是关于(x∞,y∞)的一个Lojasiewicz指数. 则下列假设成立: (ⅰ) 如果θ=0,序列(xk,yk)收敛于有限步长;(ⅱ) 如果使得‖(xk,yk)-(x∞,y∞)‖≤cτk.(ⅲ) 如果证明(ⅰ) 假设θ=0. 如果Ψ(xk,yk)是固定的, 根据定理2,(xk,yk)收敛于有限步长.如果Ψ(xk,yk)不是固定的, 则对于任意k充分大, 由Kurdyka-Lojasiewicz不等式可得cdist((0,0),∂Ψ(xk,yk))≥1.这与(0,0)∈∂Ψ(x k,yk)矛盾.(ⅱ) 假设θ>0.∀k≥0, 设由定理1知它是有限的. 因为Δk≥‖xk-x∞‖+‖yk-y∞‖,估计Δk就足够了. 接下来有Δk≤Δk-1-Δk+M2Ωk,k+1.由Kurdyka-Lojasiewicz不等式可得φ′[Ψ(xk,yk)-Ψ(x*,y*)]dist[(0,0),∂Ψ(xk,yk)]=c(1-θ)[Ψ(xk,yk)-Ψ(x*,y*)]-θdist[(0,0),∂Ψ(xk,yk)]≥1.因此(Ψ(xk,yk)-Ψ(x*,y*))θ≤c(1-θ)dist[(0,0),∂Ψ(xk,yk)].又因为dist((0,0),∂Ψ(xk,yk))≤ ‖Δx,k,Δy,k‖≤M(‖(xk-1-xk)‖+‖(yk-1-xk)‖)≤M(Δk-1-Δk).最后得到然后由Ωk,k+1的定义可得Ωk,k+1≤φ(Ψ(xk,yk)-Ψ(x*,y*))=[c(Ψ(xk,yk)-Ψ(x*,y*))]1-θ.最后给出其中再结合文献[23]可以得到(ⅱ)和(ⅲ).5 结束语研究解决无约束非凸可分离规划的算法, 该目标函数是真下半连续的, 但未必是凸的. 目标函数具有KL性质,证明了算法的收敛性,也获得了收敛速率结果.通过Lojasiewicz指数相关的函数获得了收敛速率的结果.参考文献(References):[1] MARTINET B. Regularisation d′inequations variationnelles par approximations successives(French)[J].Rev Francaise informat.Recherche Operationnelle, 1970,4(4):154-158.[2] ROCKAFELLAR R T.Augmented Lagrangians and applications of the proximal point algorithm in convex programming[J].Mathematics ofOperations Research 1976,1(2):97-116.[3] COMBETTES P,PENNANEN T. Proximal methods for cohypomonotone operators[J].SIAM J Control Optim,2004,43(2):731-742.[4] KAPLAN A,TICHATSCHKE R.Proximal point methods and nonconvex optimization[J].Journal of Globl Optimization,1998,13(4):389-406.[5] MIETTNEN M,MKEL M M,HASLINGER J.On numerical solution of hemivariational inequalities by nonsmooth optimizationmethods[J].Journal of Global Optimization,1995,6(4):401-425.[6] MIFFLIN R,SAGASTIZABAL C.νμ-smoothness and proximal point results for some nonconvex functions[J].Optimization Methods &Software,2004,19(5):463-478.[7] PENNANEN T.Local convergence of the proximal point algorithm and multiplier methods without monotonicity[J].Mathematics of Operations Research,2002,27(1):170-191.[8] Spingarn J E.Submonotone mappings and the proximal point algorithm[J].Numerical Functional Analysis & Optimization,1982,4(2):123-150.[9] ATTOUCH H,SOUBEYRAN A.Inertia and reactivity in decision making as cognitive variational inequalities[J].Journal of ConvexAnalysis,2006,13(13):207-224.[10] CLARKE F H,STERN R J,LEDYAEV Y S,et al.Nonsmooth analysis and control theory[J].Graduate Texts in Mathematics,1998,178(7):137-151. [11] MORDUKHOVICH B S.Maximum principle in the problem of time optimal response with nonsmooth constraints[J].Journal of AppliedMathematics and Mechanics,1976,40(6):960-969.[12] MORDUKHOVICH B.Variational analysis and generalized differentiation[M].Heidelberg:Springer,1998.[13] ROCKAFELLAR R T,WETS R.Variationalanalysis[M].Heidelberg:Springer,1998.[14] WANG X Y,LI S J,KOU X P,et al.A new alternating direction method for linearly constrained nonconvex optimization problems[J].Journal of Global Optimization,2015,62(4):695-709.[15] NOCEDAL J,WRIGHT S J.Numerical optimization[M].NewYork:Springer,2006.[16] BOLTE J,DANIILIDIS A,LEWIS A.The Lojasiewicz inequality for nonsmooth subanalytic functions with applications to subgradient dynamical systems[J].SIAM Journal of Optimization,2006,17(4):1205-1223.[17] REDONT P,SOUBEYRAN A.Proximal alternating minimization and projection methods for nonconvex problems:An approach based on the Kurdyka-jasiewicz inequality[J].Mathematics of Operations Research,2010,35(2):438-457.[18] BOLTE J,SABACH S,TEBOULLE M.Proximal alternating linearized minimization for nonconvex and nonsmooth problems[J].Mathematical Programming,2014,146(1-2):459-494.[19] LEMAIRE B.The proximal algorithm[J].New Methods in Optimization and Their Industrial Uses,International Series of Numerical,1987,87:73-87.[20] ROCKAFELLAR R T.Monotone operators and the proximal point algorithm[J].Siam Journal on Control & Optimization,1976,14(5):877-898.[21] SPINGARN J E.Submonotone mappings and the proximal point algorithm[J].Numerical Functional Analysis & Optimization,1982,4(2):123-150.[22] ATTOUCH H,BOLTE J,SVAITER B F.Convergence of descent methods for semi-algebraic and tame problems:Proximal algorithms,forward-backward splitting, and regularized Gauss-Seidel methods[J].Mathematical Programming, 2013,137(1-2):91-129.[23] ATTOUCH H,BOLTE J.On the convergence of the proximal algorithm for nonsmooth functions involving analytic features[J].Mathematical Programming,2009,116(1-2):5-16.。

ElectricityElectronicsBipolar TransistorsMEASURE THE CHARACTERISTIC CURVES RELEVANT TO AN NPN TRANSISTORUE308020006/16 UDFig. 1: Experiment set-up (Example: input characteristic).GENERAL PRINCIPLESA bipolar transistor is an electronic component com-posed of three alternating p-doped and n-doped semi-conductor layers called the base B, the collector C and the emitter E. The base is between the collector and emit-ter and is used to control the transistor. In principle a bipolar transistor resembles two diodes facing opposite directions and sharing an anode or cathode. Bipolarity arises from the fact that the two varieties of doping allow for both electrons and holes to contribute to the transport of charge.Fig. 2: Design of an npn transistor in principle, including ac-companying circuit symbol plus indications of voltage and currentDepending on the sequence of the layers, the transistor may either be termed npn or pnp (Fig. 2). Bipolar transistors are operated as quadripoles in three basic circuits, distinguished by the arrangement of the terminals and called common emit-ter, common collector and common base. The names indicate which of the terminals is common to both the input and the output.Only npn transistors are considered in the following treatment. There are four operating modes for an npn transistor, depend-ing on whether the base-emitter or base-collector junctions are aligned in a conducting or forward-bias direction (U BE , U BC > 0) or a non-conducting or reverse bias (U BE , U BC < 0) direc-tion (see Table 1). In forward-bias mode, electrons from the emitter migrate into the base across the transistor’s forward -biased base-emitter junction (U BE > 0) while holes from the base move into the emitter. Since the emitter has much higher doping than the base, more electrons will migrate than holes, which minimises recombination between the two. Because the width of the base is shorter than the diffusion length of the electrons, which count as minority carriers within the base itself, the electrons diffuse through the base into the depletion layer between the base and the collector before drifting further towards the collector itself. This is because the depletion layer only forms a barrier for majority carriers. This results in a transfer current I T from the emitter into the collector, which is the major contributor to the collector current I C in forward-bias mode. The transistor can therefore be regarded as a voltage controlled current source whereby the I C at the output can be controlled by the voltage U BE at the input. Electrons which recombine in the base emerge from there in a base current I B which guarantees a constant transfer current I T , thereby en-suring that the transistor remains stable. A small input current I B can therefore control a much greater output current I C (I C ≈ I T ), which gives rise to current amplification.Table 1: Four operating modes of an npn transistorTable 2: Four characteristics of an npn transistor in normal mode.The response of a bipolar transistor is described by four char-acteristics, the input characteristic, the transfer or base char-acteristic, the output characteristic and the feedback charac-teristic (see Table 2). This experiment involves measuring, by way of example, input, transfer and output characteristics for an npn transistor and plotting them as a graph.LIST OF EQUIPMENT1 Plug-In Board for Components 1012902 (U33250) 1 Set of 10 Jumpers, P2W19 1012985 (U333093) 1 Resistor, 1 kΩ, 2 W, P2W19 1012916 (U333024) 1 Resistor, 47 kΩ, 0.5 W, P2W19 1012926 (U333034) 1 Potentiometer, 220 Ω,3 W, P4W50 1012934 (U333042) 1 Potentiometer, 1 kΩ, 1 W, P4W50 1012936 (U333044) 1 NPN Transistor, BD 137, P4W50 1012974 (U333082) 1AC/DC Power Supply, 0…12 V / 3 A @230V 1002776 (U117601-230)or1 AC/DC Power Supply, 0…12 V /3 A@115V 1002775 (U117601-115) 3 Escola 30 Analogue Multimeter 1013526 (U8557330) 1 Set of 15 Experiment Leads,75 cm, 1 mm² 1002840 (U13800)+++N P N BC ESET-UP AND EXPERIMENT PROCEDURE Notes:In all of these circuits, a 1 kΩresistor acts as a protective resistor and must be plugged in at all times.Only turn on the power supply and turn up the voltage once the circuits have been fully assembled.For all experiments, set the voltage on the power supply to 5 V.Select the variables which need to be measured on the ana-logue multimeters (voltage, current) and choose suitable measuring ranges for them. Be careful to get the polarities the right way round.Input characteristic∙Set up the circuit as shown in Fig. 3. The two analogue multimeters in the circuit are for the purpose of measuring the base-emitter voltage U BE and the base current I B.∙Adjust the 1 kΩpotentiometer in such a way that the base-emitter voltage is 0 V.∙Use the potentiometer to slowly increase the base-emitter voltage in suitable steps. For each of these steps, meas-ure the base current and enter the values into Table 3.Transfer characteristic∙Set up the circuit as shown in Fig. 4. The three analogue multimeters in the circuit are for the purpose of checking the collector-emitter voltage U CE while measuring the base current I B and collector current I C.∙Read off the collector-emitter voltage and make a note of it.∙Adjust the 1 kΩpotentiometer in such a way that the base current is as low as possible.∙Use the potentiometer to slowly increase the base current in suitable steps. For each of these steps, measure the collector current and enter the values into Table 4.Output characteristic∙Set up the circuit as shown in Fig. 5. Replace the 1 kΩpotentiometer with a 47 kΩresistor. Also insert a 220 Ωpotentiometer just before the collector. The three ana-logue multimeters in the circuit are for the purpose of checking the base current I B while measuring the collec-tor-emitter voltage U CE and collector current I C.∙Read off the base current and make a note of it.∙Adjust the 220 Ωpotentiometer in such a way that the collector-emitter voltage is as low as possible.∙Use the potentiometer to slowly increase the collector-emitter voltage in suitable steps. For each of these steps, measure the collector current I C and enter the values into Table 5.Fig. 3: Sketch of circuit for recording input characteristic.Fig. 4: Sketch of circuit for recording transfer characteristic.Fig. 5: Sketch of circuit for recording output characteristic.SAMPLE MEASUREMENTTable 3: Input characteristic – measurements of U BE and I B.Table 4: Transfer characteristic – measurements of I B and I C, U CE = 5.2 V.Table 5: Output characteristic – measurements of U CE and I C,I B = 4.2 mA.3B Scientific GmbH, Rudorffweg 8, 21031 Hamburg, Germany, EVALUATIONThe input characteristic (Fig. 6), as expected, is the same as the forward-bias characteristic of a silicon diode. A semicon-ductor diode starts to conduct in the forward-bias direction once a voltage threshold has been reached. To determine what this threshold is from our measurements, the sharply rising part of the input characteristic is extrapolated back to the x-axis and then the voltage U S where it crosses the axis is read off:(1) S 720mV 0.72V U ==.This value is well in agreement with the typical value for sili-con, 0.7 V.The transfer characteristic (Fig. 7) is almost linear, although the gradient decreases slightly once the collector current is greater than I C ≈ 300 mA. The current gain is calculated using the following formula:(2) CBI B I =Its average value is about 240. The maximum value for it under defined test conditions is specified to be 250.The output characteristic (Fig. 8) rises sharply as U CE in-creases until the voltage is about 200 mV but then gradually flattens out until it is nearly horizontal. The power dissipation is calculated as follows:(3) CE C P U I =⋅Where the curve is roughly horizontal, this corresponds to about 0.5 W. The absolute maximum value specified is 8 W.Fig. 6: Input characteristicFig. 7: Transfer characteristic for U CE = 5.2 VFig. 8: Output characteristic for I B = 4.2 mAI B / mAU BE / mVI C / mAI B / mAI C / mAU CE / mV。

pn junction 英文介绍An Introduction to p-n JunctionsA p-n junction is a fundamental building block of semiconductor devices, serving as the core component in a wide range of electronic and optoelectronic applications.It is formed by the interface between a p-type semiconductor and an n-type semiconductor, creating a unique junction that exhibits remarkable electrical properties.In a p-type semiconductor, the majority charge carriers are positively charged holes, while in an n-type semiconductor, the majority charge carriers are negatively charged electrons. When these two types of semiconductors are brought into contact, a depletion region is formed at the interface, where the majority charge carriers from each side are depleted, leaving behind ionized dopant atoms.The formation of the depletion region creates a built-in electric field, which is directed from the n-type region to the p-type region. This electric field establishes a potential barrier that opposes the further flow of chargecarriers across the junction, resulting in a state of equilibrium.The unique properties of a p-n junction can be observedin its current-voltage (I-V) characteristics. When aforward bias is applied, the potential barrier is reduced, allowing a significant flow of current through the junction. Conversely, when a reverse bias is applied, the potential barrier is increased, and the junction exhibits a very high resistance, allowing only a small amount of current to flow.The rectifying behavior of a p-n junction is the foundation for many semiconductor devices, such as diodes, transistors, and integrated circuits. Diodes, for example, are p-n junction devices that allow current to flow in one direction but not the other, making them useful for converting alternating current (AC) to direct current (DC)in power supplies and other electronic circuits.Transistors, on the other hand, are more complex semiconductor devices that utilize p-n junctions to control the flow of current. They can be used as amplifiers, switches, and logic gates, and are the fundamental building blocks of modern digital electronics and computers.In addition to their electronic applications, p-n junctions are also the basis for optoelectronic devices, such as light-emitting diodes (LEDs) and photodetectors. When a p-n junction is forward-biased, it can emit light, which is the principle behind LEDs. Conversely, when lightis absorbed by a p-n junction, it can generate electron-hole pairs, leading to the development of photodetectorsand solar cells.The versatility and importance of p-n junctions in modern electronics and optoelectronics cannot be overstated. They are the foundation for a wide range of semiconductor devices that have revolutionized our lives, from smartphones and computers to medical imaging equipment and renewable energy technologies.p-n 结的介绍p-n 结是半导体器件的基本构建块,作为广泛电子和光电应用的核心组件。