Esercizi risposta in frequenza - Parte I

Esercizi Svolti e Commentati:

Microelectronics (B. Razavi, Wiley 2014)

Capitolo 11 Risposta in Frequenza

Parte I

FREQUENCY RESPONSE - CAP. II.

1.

-3dB BW = 1GHz

Av = 1,8    P = 2,5 mWVcc = 2,5    VA = oo

Z = 1/sCL

T1 = R1C/1 => w = 1/(R1CL)

2pi p = 1/(R1CL) => ZL = 1/(2pi p CL)

Av = -gm (R1||ZL) = -gm R1ZL/(ZL+R1) = -gm R1/(1+sCR1)

|Vout/Vin|_3dB = gmR1/(3/2)

Av,max = gmR1 = 1,8

Ic = 1uA

R1 = 1,8 Vf/Ic = 46,8

CL = 3,40 pF.

2.

RD = 1,5kOhmCL = 1,5 pFVA = oo

Av(3GHz) = A0 . 0,02

Vout(s)/Vin(s) = -gmRD/(1 + sCLRD)

|Vout(s)/Vin(s)| = gmRD/sqrt(1 + CL²R²D w²)

A(3GHz) = A0 . 0.02 => A/A0 = 2%

A minus 98%

3.

A

VA = oo

t = RoutCL

Rout = rt/gm2

w3dB = 1/(RoutCL)

B

Rout = (1/gm2 + RB/(beta + 1))

w3dB = 1/(RoutCL)

C

lambda > 0

Rout = ro1|| (1/gm2 || ro2)

w3dB = 1/(RoutCL)

D

Rout = ro1 || (gm2 || ro2)

w3dB = 1/(Rout CL)

E

Rout = ro2 || ro1

w3dB = 1/(Rout CL)

8.

INPUT POLE Vin = 0    l = 0

Rx = Rs || Req, D

Req, D = 1/gm1

=> wp,in = 1/(Rx CIn)

OUTPUT:

wp,out = 1/(RD CL)

9.

INPUT:

RIN = RS || (RP + 1/gm1)

wp,in = 1/(RIN CIn)

OUTPUT

wp,out = 1/(RD CL)

10.

F.O.M. = GAIN * BW / P

Av = gm1 RD = 2ID RD / Vov

Vov = Vgs - Vth

w3d = 1/(RD CL)

P = ID VDD

F.O.M. = 2ID RD * 1/(RD CL) * 1/(ID VDD) = 2/(Vov VDD CL)

N.B. Vov > Vt -> BJT F.O.M > F.O.M MOS.

11.

w_p,in = [(R_S || 1/g_m) C_IN]^-1

w_p,out = [R_D || (R_P || r_o) C_L]^-1

|V_out/V_in(s)| = g_mR_D / sqrt((1 + w²/w_p1²)(1 + w²/w_p2²))

12.

w_p,in = (R_CC_IN)^-1

w_p,out = (R_DC_L)^-1

13.

F.O.M. CS = GAIN BW / P = 2I_DR_D / (V_DDI_DV_ov R_DC_L) = 2 / (V_ovC_LV_DD).

14.

MILLER'S THEOREM

Z₁ = Z_F / (1 - A_v)

Z₂ = Z_F(1 - 1/A_v)^-1

Z_F = 1 / Cs

A_v = -A₀

C_IN = C_F(1 + A₀)

C_OUT = C_F(1 + 1/A₀)

w_p,in = (R_AC_IN)^-1

w_p,out = (R_DC_OUT)^-1

15.

d = 0

RF -> oo : vout/vx = RL/(RL + gout^-1)

A₀ = RL/(RL + gout^-1)

Ri = RF/(1 - RL/(RL + gout^-1))

Ro = RF 1/(1 - 1/A₀) = RF/(1 - (RL + gout^-1)/RL)

16.

Zin = [s(CGS + (1 + A_o)C_GD)]^-1

Zout = RD || [s(CDB + CGD + 1/(A₀))]^-1

17.

l = 0

w_p,x = [RD(CDB + CGD)]^-1

w_p,x = [RS(CSB + CAS)]^-1

18.

Cin = CF(1 + A_o) = CF(1 - g_mr_o)

A₀ = -g_mr_o

Cout = CF(1 + 1/(g_mr_o))