Esercizi risposta in frequenza - Parte IV

Esercizi Svolti e Commentati:

Microelectronics (B. Razavi, Wiley 2014)

Capitolo 11 Risposta in Frequenza

Parte IV

38.

Vin

Vb

VDD

CL

Cgd + Cgs

39.

CASCADE STAGE

Vin

VB

Vout

RD

M2

M1

Cgd2 + Cdb2

Cgs2 + Cdb1 (1 + gm1r0/gm2) + Cdb1 + Cgs2

Cgs1 + Cdb1 (1 + gm1r0/gm2)

ZiN = 1/Rg + Cgs1 + Cdb1 (1 + gm1r0/gm2) s

Zo = [(Cgd2 + Cdb2) s]^-1

ZoT = RD || Zo || Zsec

Zsec = (1 + gm1r0) ZH1 + r0 = oo | v0 = oo

ZoT = RD || Zo = 1 / (1/RD + (Cgd2 + Cdb2) s) = RD / (1 + (Cgd2 + Cdb2) RD s)

ZiN = Rg / [1 + Rg (Cgs1 + Cdb1 (1 + gm1/gm2) s)]

40.

I_x = - I_C + I_M

I_x + g_m v_gs + v_in/(Z_B + Z_pi) = 0

I_x = (g_m + 1/(Z_B + Z_pi)) V_x

Z_out = 1/g_m || (Z_B + Z_pi)

Z_B = R_B/(1 + R_BC_us)

Z_pi = r_pi/(1 + r_piC_pis)

= 1/(g_m + (1 + R_BC_us)(1 + r_piC_pis)/((1 + r_piC_pis)R_B + r_pi(1 + R_BC_us)))

Z_out,DC = r_pi + R_B

s → ∞   Z_out(s) → 0

ω_z = (r_pi + R_B)/(r_piC_uR_B + R_BC_ur_pi) → ∞

ω_p,1

ω_p,2

41.

I_C3 = 0,75 I_C1

I_C2 = 0,25 I_C1

MILLER'S THEOREM -> Q₁ AMPLIFIER A₀

C_IN = C_PI1 + C_u1(1-A₀)

C_Y = C_u3 + C_CS3 + C_u2 + C_CS1

C_B = C_Y + C_i1(1-A₀)

C_OUT = C_u2 + C_CS2

A₀ ≈ -(r_pi2||g_m2) g_m1 ≈ g_m1/g_m2

I_C2 = 0,25 I_C1 -> g_m2 = 0,25 g_m1 -> A₀ = 4

ω_p,in = 1/((R_B||r₁)C_IN)

ω_p,B = 0,25 g_m1/(C_Y + C_i1(1-A₀))

ω_p,Y = g_m2/C_Y

ω_p,OUT = 1/(R_C C_OUT)

DC GAIN IS INCREASED -> MILLER EFFECT IS MORE SIGNIFICANT.

42.

C_OUT = C_ob2 + C_db2

C_Y = C_gs2 + C_gd1 (1+g_m2/g_m1) + C_sb1 + C_sb2

C_IN = C_gs1 + C_gd1 (1+g_m1/g_mL)

λ = 0.

|ω_p,IN| = 1/(R_D C_IN)

|ω_p,OUT| = g_m/(R_S || r_o C_OUT)

|ω_p,Y| = g_m2/C_Y

43.

lambda = 0

M1 Ao

Ao = - gmu1 (1/gmu2 || 1/gmu3) = - gmu1/(gmu2 + gmu3)

Cin = Cgs1 + Cgd1 (1 - Ao)

Cy = Csb1 + Cgd2 (1 - Vi/Ao) + Cgs3 + Csb3 + Csb2

Cout = Cdb2 + Cgd2

|wp,in| = (Ri Cin)^-1

|wp,out| = (RD Cout)^-1

|wp,y| = (gmu2 + gmu3)/Cy

44.

wp,in = 500 MHz * 2pi

wp,out = 2 GHz * 2pi

IC = 1 uA

beta = 20 pF

Cu = 5 pF

Cos = 10 pF

VA = oo

RB Rc = Av, min

Miller theorem.

Ao = - gmu1 Rc.

Cin = Cpi + Cu (1 - Ao) =

eout = Cu (1 - vAo) + Cos =

Av = - Rc / (1/gmu1 + RB/beta+1)

wp,in = 1 / ((RB || rin) Cin)

wp,out = 1 / (Re Cout) => Cout Rc = 1 / wp,out

eth Re + ecg Rc + gmu Cue = wp,out^-1

= 5305,15.

gmu = IC / VT = 0,038 S = (26 ohm)^-1

Av -> Ao e=> RB minimale RB << rin => RB || rin = RB

wp,in = 1 / (RB Cin) => RB (Cpi + Cu (1 + gmu Rc)) = wp,in^-1

RB = wp,in^-1 / Cth = 303,95 ohm.