数字集成电路习题答案
数字集成电路分析与设计 第二章答案
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。
《数字集成电路》期末试卷(含答案)
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 。
5大规模数字集成电路习题解答
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。
数字集成电路习题答案
1.5 115 106
0.63 3 0.06 0.1
30 106
1.0
21.05
VIL
VM
VDD VM g
1.25 2.5 1.25 21.05
1.19V
VIH
VM
VM g
1.25 1.25 21.05
1.31V
NVH VDD VIH 2.5 1.31 1.19 NM L VIL 1.19
115 (2.072 2.072 )(1 0.06 2.5) 2
283.3A
(2) pmos :
VGT VGS VT 0 0.5 0.4 0.1 VDS
pmos处于饱和区,Vmin 0.1v
ID
kn'
(W L
) (VGTVm in
Vm2in 2
)(1
VDS
)
30 (0.1 0.05) 0.1 (1 0.11.25)
VT0(V) 0.43 -0.4
(V0.5) 0.4 -0.4
VDSAT(V) 0.63 -1
k’(A/V2) 115×10-6 -30×10-6
(V-1) 0.06 -0.1
1.假设设计一个通用0.25m CMOS工艺的反相器，其中PMOS晶体管的 最小尺寸为(W=0.75m，L=0.25m，即W/L=0.75/0.25) , NMOS晶体管
2.如下图所示，由NMOS组成的反相器，输出电容 CL=3pF,W/L=1.5um/0.5um,求tpHL,tpLH和tp
t pHL
ln 2ReqnCL
0.69 13k 3
3 pF
8.97ns
t pLH ln 2RLCL 0.69 75k 3 pF 155.25ns
数字集成电路习题
带入延迟公式可得，反相器链的延迟
t p N t p 0 (1
N
F
) 5 70 ps (1
5
2000 ) 1960 ps 2ns 1
c． 方法 a 的延迟时间
t p t p 0 (1
j 1
N
C g , j 1
C g , j
) t p 0 (1
解：VGS=VDS=2.5V，管子工作在饱和区。 栅沟电容 CGC=W*L*Cox=0.36um*0.24um*6fF/um2=0.52fF 栅与源漏区的交叠电容 Cov=CGSO=CGDO=W*Co=0.36um*0.31fF/um=0.11fF 栅电容 CG=CGC+2Cov=0.52 fF +2*0.11 fF=0.74fF 栅源电容 CGS=2CGC/3+Cov=2*0.52fF/3+0.11=0.46fF 栅漏电容 CGD=Cov=0.11fF 管子的源区和衬底都接地，所以源衬底扩散结处于零偏状态。有 Cs,bottom=W*LD*Cj0=0.36um*0.625um*2fF/um2=0.45fF Cs,sw=(W+2LD)*Cjsw0=(0.36um+2*0.625um)*0.28um/fF=0.45fF CSB= Cs,bottom + Cs,sw =0.45fF+0.45fF=0.9fF 管子的漏区接 2.5V，衬底接地，所以漏衬底扩散结处于反偏状态。有 CD,bottom=W*LD*Cj0/(1-VD/φ b)mj =0.36um*0.625um*2(fF/um2)/[1-(-2.5V)/0.9V]0.5 =0.23fF CD,sw=(W+2LD)*Cjsw0/(1-VD/φ bsw)mjsw =(0.36um+2*0.625um)*0.28(um/fF)/[1-(-2.5V)/0.9]0.44 =0.25fF CDB= CD,bottom + CD,sw =0.23fF+0.25fF=0.48fF
数字集成电路分析与设计 第三章答案
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)。
数字集成电路模拟集成电路考试题库
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）。
数字集成电路设计与系统分析答案
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)。
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2.如下图所示，由NMOS组成的反相器，输出电容 CL=3pF,W/L=1.5um/0.5um,求tpHL,tpLH和tp
t pHL
ln 2ReqnCL
0.69 13k 3
3 pF
8.97ns
t pLH ln 2RLCL 0.69 75k 3 pF 155.25ns
tp
8.97
155.25 2
CP D Q Q′
1.假设设计一个通用0.25m CMOS工艺的反相器，其中PMOS晶体管的 最小尺寸为(W=0.75m，L=0.25m，即W/L=0.75/0.25) , NMOS晶体管
的最小尺寸为(W=0.375m，L=0.25m，即W/L=0.375/0.25)
求出g,VIL,VIH,NML,NMH
NMOS PMOS
VT0(V) 0.43 -0.4
(V0.5) 0.4 -0.4
VDSAT(V) 0.63 -1
k’(A/V2) 115×10-6 -30×10-6
(V-1) 0.06 -0.1
1.假设设计一个通用0.25m CMOS工艺的反相器，其中PMOS晶体管的 最小尺寸为(W=0.75m，L=0.25m，即W/L=0.75/0.25) , NMOS晶体管
(R1 R2 R5 )C5 9RC
DCLK 3 R1C1 R1C2 (R1 R3 )C3 R1C4 R1C5
(5R R3)C R3 4R
8
DB Ck RBk k 1 R1C1 R1C2 (R1 R3 )C3 R1C4 (R1 R3 )C5 (R1 R3 R6 )C6 (R1 R3 )C7 (R1 R3 R6 R8 )C8 0.25* 250 0.25*750 (0.25 0.5) * 250 0.25* 250 (0.25 0.5) *1000 (0.25 0.5 1) * 250 (0.25 0.5) *500 (0.25 0.5 11000) * 250 62.5 187.5 187.5 62.5 750 437.5 375 250437.5 0.2525(ns)
习题答案
▪ 简述CMOS工艺流程
1.已知电路如图1所示，使用一阶二极管模型，即 VDon 0.7V 求解 I D
习题1电路图
解：
(R1 R2 )ID 2VDon 2.5 (4000 4000)ID 2*0.7 2.5 ID 0.275(mA)
2.已知
NMOS : kn' 115A /V 2,VT 0 0.43V , 0.06V 1,VGS 2.5V ,VDS 2.5V PMOS : kn' 30A /V 2,VT 0 0.4V , 0.1V 1,VGS 0.5V ,VDS 1.25V
82.11ns
注：NMOS和PMOS的等效电阻可由表3.3查出
1.写出下图的逻辑函数式
X ( AB CDE )F G
2、写出下图的逻辑函数式，确定电路中晶体管的尺寸，使它的tpLH和 tpHL与具有以下尺寸的反相器近似相等： NMOS为W/L=4, PMOS: W/L=8
习题1：一上升沿触发的D触发器，设初态为1，试在给定CP 、D下，画出Q和Q′波形。
的最小尺寸为(W=0.375m，L=0.25m，即W/L=0.375/0.25)
求出g,VIL,VIH,NML,NMH
NMOS PMOS
VT0(V) 0.43 -0.4
(V0.5) 0.4 -0.4
VDSAT(V) 0.63 -1
k’(A/V2) 115×10-6 -30×10-6
(V-1) 0.06 -0.1
ID
(VM
)
kn'
W L
[(VGSn
VTn
)VDSATn
V2 DSATn 2
](1
VDSn )
1.5115106 0.63 (1.25 0.43 0.63 / 2)(1 0.061.25)
59106 AVp DSATp
ID (VM )
n p
1 59 106
1.5 115 106
0.63 3 0.06 0.1
30 106
1.0
21.05
VIL
VM
VDD VM g
1.25 2.5 1.25 21.05
1.19V
VIH
VM
VM g
1.25 1.25 21.05
1.31V
NVH VDD VIH 2.5 1.31 1.19 NM L VIL 1.19
W /L 1
根据VGS和VDS确定其处于线性、饱和还是截止状态，并求 I D
的值。
解：(1)nmos : VGT VGS VT 0 2.5 0.43 2.07 VDS
nmos处于饱和区,Vmin VGT 2.07
ID
kn'
(W L
) (VGTVm in
V2 m in 2
)(1
VDS
)
115 (2.072 2.072 )(1 0.06 2.5) 2
283.3A
(2) pmos :
VGT VGS VT 0 0.5 0.4 0.1 VDS
pmos处于饱和区,Vmin 0.1v
ID
kn'
(W L
) (VGTVm in
Vm2in 2
)(1
VDS
)
30 (0.1 0.05) 0.1 (1 0.11.25)
(R1 R2 R5 )C5
DCLK 3 R1C1 R1C2 (R1 R3 )C3 R1C4 R1C5
（b）
DCLK1 R1C1 (R1 R2 )C2 R1C3 (R1 R2 R4 )C4 (R1 R2 )C5
9RC
DCLK 2 R1C1 (R1 R2 )C2 R1C3 (R1 R2 )C4
0.169A
3.简述MOS管的电容分布，及其模型
N
（a）
Di
Ck Rik
k 1
DCLK1 R1C1 (R1 R2 )C2 R1C3 (R1 R2 R4 )C4
(R1 R2 )C5
DCLK 2 R1C1 (R1 R2 )C2 R1C3 (R1 R2 )C4