Esercizi risposta in frequenza - Parte II

Esercizi Svolti e Commentati:

Microelectronics (B. Razavi, Wiley 2014)

Capitolo 11 Risposta in Frequenza

Parte II

19.

Cin = Cgs(1 - Ao) + CGD

Cout = CSB + Cgs(1 - 1/Ao)

Ao = +g_mr_o

Vout/Vin = Vx/Vin * Vout/Vx

Vx/Vin = Zin/(R + Zin)

Vout/Vx = Zout/(1/gm + Zout)

(Vout/Vin)(s) = Zin/(R + Zin) * gmZout/(1 + gmZout)

= (sCGD)^-1 / (R + (sCGD)^-1) * gm (sCSB)^-1 / (1 + gm(sCB)^-1)

= gm / ((sCGD R + 1)(sCSB gm + 1))

w_p,in = (CGD R)^-1

w_p,out = (CSB gm)^-1

=> APPROXIMATION DI MILLER.

-> NO APPROXIMATION.

Zin = (CGD s)^-1

ZGS = (CGS s)^-1

Zout = (CSB s)^-1

Igs = Vout/Zout - gm Vgs

Vgs = ZGS Igs = ZGS Vout/Zout - gm Vgs ZGS

Vgs = ZGS Vout/Zout / (1 + gmZGS)

Vg = Vgs + Vs = ZGS Vout/Zout / (1 + gmZGS) + Vout

(Vg - Vin)/R + Vg/Zin + Vgs/ZGS = 0

Vout/Vin = (1 + Cgs s/gm) / (a s² + b s + 1)

a = Rs/gm [CGD CGS + CGD(CSB + Cgs CSB)]

b = RsCGD + (CGD CBB)/gm.

20

Cxy = Cgs. Ef.

Cin = Cgd + Cxy (1 - Av)

Cout = Csb + Cxy (1 - 1/Av)

21.

Av = Av1 . Av2

Av1 = - (Rc||ro) gu1 rtt / (RB + rtt)

Av2 = gu2 ro / (1 + gu2 ro)

Cin = CF (1 - Av) + Ctr1 + Cu1 (1 - Av)

Cx = Ccs1 + Ctr2 (1 - Av2) + Cu2 + Cu1 (1 - 1/Av)

Cout = Ctr2 (1 - 1/Av2) + CF (1 - 1/Av)

2.2.

A)

Cin = Ctr2 + Cu1 (1 - Av)

Cout = Ctr2 + Cu1 (1 - 1/Av) + CL + Ccs1

Av ≈ gu1/gu2

B)

Cin = Ctr1 + Cu2 (1 - Av)

Cout = Cu1 (1 - 1/Av) + CL + Ccs1 + Ctr2

C)

V1

V02

V0

V03

23.

A) B) C) D)

24.

w_T, BJT = g_m / (C_T + C_u) ≈ g_m / C_T    C_u << C_T

w_T, MOS = g_m / (C_GS + C_GD) ≈ g_m / C_GS    C_GD << C_GS.

25.

C_GS ≈ 2/3 C_ox wL

=> 2πf_T = g_m / C_GS = (w/mu) C_ox (V_GS-V_TH) / ((2/3) C_ox wL) = 3/2 mu 1/L² (V_GS-V_TH)

26.

2πf_T = 3/2 · 2πI_D / (wLcox) · 1/V_ov

f_T α V_ov / I_ov ? f_T α V_ov => IN SAT. I_D α V_ov²

27.

R_out(s) = (R_sC_GSs + 1) / (C_GSs + g_m)

29.

A)

wp,in ≈ [RS(CT + Ciu(1 - Av))]^-1

wp,out ≈ [(Ccs + Ciu(1 - 1/Av))Ro]^-1

RT = RS || rpi

RO = RC || ro

Av = -gm(RC || ro)

trascurando (RS + rpi)

B)

wp,in = {RS[Cgs + Cgd(1 - Av)]}^-1

wp,out = {(RC || ro)[CDB + Cgd(1 - 1/Av)]}^-1

Av = -gm(RD || ro)

1/(gmRS + 1/b)

30.

IF NEGLECTING ALL CAPACITANCES EXCEPT Cgs2.

Rout = 1/gm3

Rout = (ro||ro2)Cgs3s + 1 / (Cgs3s + gm3)

Ztot = (sCtot)^-1 || ro1

Itot = Ztot^-1Vx

VGS = -Vx

Zc = [(CAD1 + CDB1 + Cgs2)s]^-1

Req = ro2 || ro1 || 1/gm1 || Zc

Z₁ = Z_eq || (sC_GD)^-1

Z₂ = r_o3 || (sC_SB)^-1

= I_CCS = I_X + g_mV_GS

V_GS = - Z_CCS / (Z₁ + Z_CCS) . V_X => Z_CCS V_X / (Z₁ + Z_CCS) = I_X - g_mZ_CCSV_X / (Z₁ + Z_CCS)

=> - 1 / (Z₁ + Z_CCS) (1 + g_mZ_CCS)V_X = I_X

V_X / I_X = (Z₁ + Z_CCS) / (1 + g_mZ_CCS) || Z₂

3/0.

Z₀ = (r_o2 || g_m2) || Z_CONT

Z_CONT = C_u2 + C_cs2 + C_cs1

MILERSI APPROXIMATION.

H(s) = A₀ / (1 + s/w_p1) (1 + s/w_p2)