Analog Integrated Circuit Design --- Problem Answers Textbook by David Johns and Ken Martin, Wiley, 1997.
Solutions by Khoman Phang and Ali Sheikholeslami
Chapter 1:
1) n:10e25 carriers/m^3, p:3.6e8 carriers/m^3
2) 0.87V, decreases
3) 140fC
4) t_fall=0.37ns, t_rise=0.48ns
5) t_fall=0.37ns, t_rise=0.44ns
7) 143uA
8) r_ds=145kohms, lambda=0.3
9) r_ds=182kohms, gm=230uA/V, gs=44uA/V
10) Cgs=86fF, Cgd=10fF, Cdb=60fF, Csb=74fF
12) 1.25ns, 3.33ns
13) 0.977V
14) gm=3.8mA/V, r_pi=26kohms, r_e=260ohms, r_o=800kohms, gmr_o=3000
15) t_fall=690ps, t_rise=7.8ns
16) t_fall=850ps, t_rise=10.3ns
Chapter 2:
8) 2 lambda
12) Cdb=0.019pF, Csb=0.034pF
13) Cdb=0.016pF, Csb=0.44pF
14) y2=2.415x1, x2=0.631x1
15) 98.4%
16) 350 Ohm
Ohm, height=24um, width=152um
17) 379.26
Chapter 3:
1) I_out=20uA, R_out=640kohms, Max. Vout=170mV
2) gain = -4800*sqrt(2*un*Cox*W*L/Ibias)
3) w_3dB = Ibias/(4800*L*C_l)
5) 2*PI*1.05MHz
6) 1/R_out = gm1 + gs + g_ds1 + g_ds2
7) 1/R_out = gm1 + gs
8) a) w_o=2*PI*35MHz, Q=0.332, w_z=2*PI*844MHz
b) w_o=2*PI*33MHz, Q=0.570, w_z=2*PI*844MHz
9) a) C_1=0.125pF, R_1=4780ohms, p_1=2*PI*3.61MHz, p_2=2*PI*281MHz
b) C_1=0.144pF, R_1=4780ohms, p_1=2*PI*3.61MHz, p_2=2*PI*244MHz
10) 2*PI*770kHz
11) R_out = 2*r_ds1
12) V_out >= 1.33V
13) R_out = r_ds4*[1+ r_ds2(gm4+gs4+g_ds4)]
16) 2*PI*57kHz
17) 2*PI*80MHz
陶瓷添加剂
22) R=22kohms, R_out=400kohms
23) gain=-V_a/[2*V_t*(1+I_bias/((beta+2)*V_t)+R_s)]
25) gain=0.9993, R_out=52ohms
26) gain=beta*R_e*(R_l//R_c)/[(beta+1)*(re*Rs+Re*Rs+re*Re)], Rin=re//Re
31) gain = 116, w_3dB=2*PI*10kHz
Chapter 4:
1) dBm(50 Ohm)=dBm(75 Ohm)+1.76
2) a)-18.24dBm, b)-17.16dBm, c)-15.35dBm, d)-30.67dBm
3) -44.77dBm, 0.058mV/root_Hz
6) they are equal.
7) 34.2uV rms
8) 2
10) b)0.32uV rms, c)infinity
11) 10.2uV rms
12) 125uV rms
13) 0.5uV rms
14) 0.14uV rms, 1/f rule: 0.13uV rms
16) a: 41.94dB, b: 57.7dB
17) 44.24uV rms, 67.08dB
18) 5.75 nV/root_Hz, 4.84 nV/root_Hz
Chapter 5:
1) a)2*PI*1.1kHz, b)2*PI*14MHz, c)10V/us
2) 25V/us
3) Width of Q7 must be halved
4) 0.7mV
5) Maximum: Vout=3.9V, V_incm=3.8V
Minimum: Vout=-4.9V, V_incm=-4.99V
7) Maximum: Vout=2.9V, V_incm=3.7V
Minimum: Vout=-4.9V, V_incm=-6.8V
9) 2*PI*72MHz
10) 0.5pF
11) 63fF
12) w1=1.8e4 rads/s, wt=1.43e8 rads/s
13) A(s)=Ao*(1+s*Tz)/[T1*T2*[s^2+s*(1/T2+Ao*beta*Tz/(T1*T2))+Ao*beta/(T1*T2)]] wo= sqrt(Ao*beta/(T1*T2)), Q= sqrt(T1*T2/(Ao*beta))/Tz
15) Rb=5.2k
ohms, Veff=0.31V
Chapter 6:
1) 1/gm
2) W1=W2=W3=W4=43.5um, W5=5.76um
3) VDS3=0.39V, VDS4=0.57V
4) RB=5.43KOhm
5) 0.29V
6) 0.23V
8) upper limit r0(1+beta), independent of A.
9) 238MOhm, 47 times larger.
10) 30.2MHz, 12.5 V/us, 19.8V/us (with clamp xtors)
11) f2=306.7MHz, 2.71pF, 46.1V/us, 73V/us (with clamp xtors)
12) 0.69pF, 526 Ohm, 438MHz, 181V/us, 287V/us (with clap xtors)
13) wt=(K*Itotal)/((K+1)(Veff*CL))
14) Av0=K*(4*a^2*L^2)/(Veff1*Veff8)
15) wt(folded_cas.)/wt(current_mir.)=root((K+3)/(2K(K+1)))
16) 19.5ns
17) yes, 98%, 30.6ns, 24ns
18) +SR=8V/us, -SR=4V/us, for current_mir., +SR=-SR=16V/us
19) KIbias/CL
20) wt=(K/CL)*root((2/(2+K))*Itotal*un*Cox*(W/L)4)
21) Veff=0.78V, Vout+(max)=1.1V, Vout+(min)=-1.1V
22) Veff=0.68V, Vout+(max)=0.96V, Vout+(min)=-0.96V
23) (1+R2/R1)+R2(gm1+gm2)
25) Tmin=(1/Kgm)*2.5ps
Chapter 7:
1) 99mV
2) -7.2uV
3) reset: 0.17ns, comparison: 0.77ns
5) V_ioff=(Verr3+Voff3/(1-A3))/(A1*A2)
6) 54MHz at 71dB
7) L=0.8um, W1=W2=25um, W3=W4=100um, W5=W6=30um, W7=W8=5um, W9=W10=2.4um
Wtrk=25um, Wcmfb=12um
8) tau=1ns, settling time is 3ns
9) 3.65ns
10) 1.7V
11) 2.6V
Chapter 8:
2) 0.63ns
3) 13mV, -13mV
4) 0.03ns
6) Vo=(A/(A+1))Vin+(A/(A+1)^2)Vos
7) Vo[nT]=(1/(C1+C2))*{C2Vo[nT-T]+C1Vin[nT-T]}
9) 57.2mV, 0.178mV/K
10) 10.35
12) R1=5.5kOhm, R2=1kOhm, R3=900Ohm, R4=10kOhm
14) 50uA < I1 < 400uA, io1(peak) < 30uA
15) I1: delta_io=-0.05io, I2: delta_io=0
16) delta_i
o=(0.05/(2*Beta))*i2
Chapter 9:
2) 6
6) poles: 0.8+i0.1, 0.8-i0.1, all zeros at infinity
7) 0.544+i0
8) DC gain=0dB, gain at w=PI is -26.4dB, w_3dB=0.051rads/sec
9) y(n)= 0 when n=0, y(n)=(-0.3)^(n-1) for n>0
10) H(z)=0.095*(z+1)/(z-0.8098)
11) H(z)=9.45e-4*(z+1)^2/(z^2-1.91*z+0.915)
12) output sequence: 1 1 0 0 1 1 0 0
- 3dB attenuation with a phase shift of 45 degrees.
13) 100Hz:1V, 300Hz:0.33V, 500Hz:0.2V, 700Hz:0.14V
14) 100Hz:1V, 9.9kHz:10.1mV, 10.1kHz:9.9mV
15) 100Hz:998mV, 99.9kHz:0.999mV, 100.1kHz:0.997mV
16) -20dB is provided, an additional 60dB is required
Chapter 10:
2) Vo(z)/Vi(z)=(-C1/C2)/(1-1/z)
3) Vo(z)/Vi(z)=(C1/C2+Cp1/(C2z))/(1-1/z)
5) C1=0, C2=-8.75pF, C3=8.75pF, the new gain=-0.304
6) C1=0, C2=-6.71pF, C3=6.71pF, -24.025dB
7) H(z)=0.1z/(1.1z-1)
8) H(z)=-(C1-(C1+C2)/z)/((CA+C3)-CA/z)
37, high_Q: 20
10) low_Q: 6
Chapter 11:
1) 1.023V
2) SNR=64.5dB, Vin=0.6mV(peak to peak)
3) Vout = Vref[-b1*2^-1 + b2*2^-2 + b3*2^-3 + ... + bn*2^-N
5) Extend word by copying MSB to new bit locations.
7) offset=-0.01LSB, gain_err=0.09LSB, max. INL_err=-0.091LSB, max. DNL_err=-0.073LSB
8) max abs error = 0.08LSB (6.6bits accuracy)
max rel error = -0.091LSB (6.5bits accuracy)
9) 200uV/C
10) offset=0.01LSB, gain_err=0.01LSB, max abs err=-0.03LSB
max rel err=-0.047LSB(6.4bits accuracy)
11) 1.22mV
n 0.24ns
12) less tha
Chapter 12:
1) 2(2^N-1)
3) 2^N+2^(N/2)
4) output opamps: 2.5mV, middle opamps: 80mV
5) 512
6) b2: 2 times, b3: 4 times, b4: 8 times
7) 0.75LSB
8) resistance_ratio improvement=2^(N/2)
9) 8, 2
11) 0.08LSB, 0.005LSB
12) w(3dB)=2*pi*17.9MHz
13) 0.0375V, 2.0625V, 3.8375V
14) 31mV
17) 0.027, 5nA
18) 0.27, 50nA
Chapter 13:
1) 105ms
2) 2620Mohms
3) Bout= (vin+err)/(Vref-Voff1) where err=R1*C1*Voff2/T1
4) 0.002LSB offset
5) multiples of 15.3Hz are completely attenuated. Attenuation at 60Hz is 34dB.
6) multiples of 1.53Hz are completely attenuated. Attenuation at 60Hz is 46dB.
7) Bout=0110 binary
8) Bout=0110 binary
9) Bout=0110 binary. Parasitics attenuate gain by 1/3.
11) Invert the MSB
12) Vx1=-1.35e-2*Vref
13) Vx2=-2.7e-3*Vref
14) 3.44usec
17) a differential input of 67mV is required. The resolution is 5bits.
18) 0.3125V < Vin < 0.4375V
20) 2^N
21) 2^(N-F)
22) A reduction factor of 8, and 8 resistors needed between input comparators Chapter 14:
1) 33.345GHz!
2) fs/10
5) 512MHz
6) 18.88MHz, 10.98MHz
7) 760kHz, 100.8kHz
8) 1/7
9) G(z)-1=(1/z)(1/z-2)
12) time-invariant versus a time-varying system
Chapter 15:
2) Gm1=4.71mA/V, Gm2=0.47mA/V
3) C_A=C_B=2pF, Gm1=0.13mA/V, Gm2=0.13mA/V,
Gm3=0.13mA/V, Gm4=0.63mA/V, Gm5=0mA/V
4) Cx = k2*Cb, Gm1=k1*Cb, Gm2=k0*Ca/k1, Gm3=k1*Cb*wo^2/k0, wo*Q=k0/k1
5) Gm = beta/[(beta+1)*(Re+(2*re+Re)/A)]
6) 2.1V, 2.8V
7) 4/Re
8) I1=625uA, I2=156uA
9) -5.3% error
10) a)Gm=0.46mA/V, b)io1=46uA and 230uA,
c)io1=45uA(2% error) and 160uA(-30% error)
11) L=1um, W1=W2=67um, W3=10um
12) Gm=36uA/V
14) 36mV
16) W1=0.39*L, W2=0, W3=0.49*L, W4=0.2*L, W5=0.31*L
17) 0.12%
18) -14dBm
19) OIP3 = 22dBm, IIP3=16dBm, Id1=-3dBm,
SFDR=55dB, Id1=-5dBm if No=-60dBm
Chapter 16:
1) C1=100nF, R2=1kOhm, R1=2.5MOhm, delta_phi=1.19rad,
未载入sso模块2.5MHz < f(osc) < 17.5 MHz, C2=10nF
2) A=2/3, C1=10nF, R2=847Ohm, R1=2333Ohm
the lock range will increase if not limited by the vco!
3) w0=0.93w0(original), Q=1.07Q(original)
5) C1=62.5pF, C2=6.25pF, R=20kOhm
7) Cosc=0.5pF, I1=14uA, f(fr at Tnom+20)=10.6MHz,
8) 0.1Tosc(5V)
9) f(osc)=Ib/(n*Vref*CL*ln(2)) n is the # of stages.
10) f(osc)=Vcntl/(n*Vref*R*CL*ln(2)), f(osc)=36MHz, Kosc=2pi*36MHz/s.V
11) f(osc)=RC1C2(VDD-Vref)/(Vcntl*(C1+C2))
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