Esercizi risposta in frequenza - Parte V

Esercizi Svolti e Commentati:

Microelectronics (B. Razavi, Wiley 2014)

Capitolo 11 Risposta in Frequenza

Parte V

43.

d = 0

M1 A0

A0 = - gm1 (1/gm2 || 1/gm3) = - gm1/(gm2 + gm3)

CIN = Cgs1 + Cgd1 (1 - A0)

Cy = Csb1 + Cdb1 (1 - 1/A0) + Cgs3 + Cdb3 + Csb2

COUT = Cdb2 + Cdb1

|wp,IN| = (Ri CIN)^-1

|wp,OUT| = (RD COUT)^-1

|wp,Y| = (gm2 + gm3)/Cy

44.

wp,IN = 500 MHz * 2pi

wp,OUT = 2 GHz * 2pi

IC = 1uA

betaT = 20 pF

Cu = 5 pF

Cos = 10 pF

VA = oo

RB, RE: Av,min

Miller theorem.

A0 = - gm1 Rc.

CIN = Cpi + Cu(1 - Ao) =

Cout = Cu(1 - VoAo) + Coss =

Av = - Rc / (1/gm1 + RB/betaT)

wp,IN = 1/((RB || rpi)CIN)

wp,OUT = 1/(RE Cout) => Cout Rc = 1/wp,OUT

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

= 5305,15.

Av -> A0 e RB minimize

RB << rpi > RB || rpi ≈ RB

wp,IN = 1/(RB CIN) => RB(Cpi + Cu(1 + gm Rc)) = wp,IN^-1

RB = wp,IN^-1 / CIN = 303,95 ohm.

45.

w_gdb = 2pi (10GHz)

I_C = 1uA

V_A = oo

R_S = 300ohm

C_RT = 20 pF

C_u = 5 pF

C_es = 20 pF

R_C,max -> A_v,max

C_in = C_RT

C_out = C_CS + C_u

R_CC_out >> R_SC_in => w_p,out << w_p,in

=> BW -> w_p,out = 1 / (R_C(C_es+C_u)) = 2pi(10kHz)

=> R_C = 6366,62 ohm.

g_m = I_C/V_T = 0,038 S = (26ohm)^-1

A_v = R_C / (R_S + 1/g_m) = 8,4

46.

C_in <= 50 pF

C_u = 10 pF

C_T = 100 pF

V_A = oo

I_C = 1uA

A_o = - R_L / (R_L + 1/g_m)

C_in = C_u + C_T(1 - R_L / (R_L + 1/g_m))

g_m = 0,038 S = (26ohm)^-1

C_out = C_cs + C_TT(1 + R_L + 1/g_m / R_L)

C_u + C_TT - C_TC R_L / (R_L + g_m^-1) <= 50 pF.

R_L / (R_L + g_m^-1) > 0,6 => R_L > 39,2/g_m = 897,47 ohm.

47.

R_L = 100Ω     I_D = 1 uA

A_V = 98     K'μ = 100 uA/V²

C_ox = 12 fF/'m²     L = 0,18 μm

C_GD ≈ 0

C_SB ≈ 0     C_GS = (2/3) WLC_ox

A_V = R_L / (1 + R_L/g_m)

g_m = 0,038 S = (26 Ω)^-1

C_in = C_GS(1 - 0,8) = 0,2 ⋅ C_GS ⇒ W = 1440 µm.

V_OV = 2I_D/g_m = 52 mV

C_IN,MIN = (0,2 ⋅ 1440 ⋅ 0,18 ⋅ 12 ⋅ 2/3) pF = 0,415 pF.

48.

V_DD

R_D

V_OUT

V_IN

R_G

V_IN

g_m,IN = 2π ⋅ 5 kHz     I_D = 0,5 uA     C_ox = 12 pF/µm²

ω_p,OUT = 2π ⋅ 10 kHz     C_GS = (2/3)WLC_ox     K'μ = 100 uA/V²

λ = 0     L = 0,18 µm     C_GD = C_OW     C_O = 0,2 pF/µm

Max. R_D, R_G, A_V?

r_OV = 0,2V for each transistor.

A₀ = - g_m1/g_m2 = 1     M₁, M₂ identical.

C_IN = C_GS + C_GD(1 + A_V) = C_GS + 2C_GD

C_IN = 82,8 pF

g_m = 2I_D/V_OV = 0,005 S = (200 Ω)^-1

(W/L)² = 2I_D/(K'μV_ov²) = 250

ω_p,IN = (2π ⋅ 5 kHz) = 1/(R_GC_IN) ⇒ R_G = 1/(2π⋅5kHz⋅C_IN) = 384,4 Ω.

C_OUT = C_GD = 9 pF

ω_p,OUT = (R_DC_OUT)^-1 ⇒ R_D = 1/(ω_p,OUTC_OUT) = 1,76 kΩ.