Esercizi coppie differenziali - Parte II

Esercizi Svolti e Commentati:

Microelectronics (B. Razavi, Wiley 2014)

Capitolo 10 Coppie Differenziali

Parte II

19.

V_P = 0.

r_o1 = r_o2 = ∞ ⇒ KCL at P

i_p/R_EE + (v_P - v_in1)/r_pi1 + g_mi1(v_P - v_in1) + (v_P - v_in2)/r_pi2 + g_mi2(v_P - v_in2) = 0

Since v_in1 = -v_in2, r_pi1 = r_pi2, g_mi1 = g_mi2.

⇒ v_P/R_EE + 2v_P/r_pi1 + 2g_mi1v_P = 0 ⇐⇒ v_P = 0. P node constant

A_v = -g_mR_C.

20.

R_C = 40k

R_E = 8k

r_s = 9k

r_o = 400k

r_Pi = 45k

β = 2200

A_v = (g_mr_Pi)/(R_S + r_Pi) (r_o || R_C)

no voltage node P is constant ⇒ the GND.

v_pi = + r_Pi/(R_S + r_Pi) v_in

g_mv_pi = - v_out/(r_o || R_C)

⇒ g_mr_Pi/(R_S + r_Pi) v_in = -v_out/(r_o || R_C)

⇒ - (r_o || R_C) g_mr_Pi/(R_S + r_Pi)

21

Acm-Ax = _Vout/_Vin,cm = - _Rd/(r_out + 2R_EE) x _RD/(2R_SS) -> RESISTANCE EMITTER.

CMRR is = Ax/Acm-Ax.

ΔVach/ΔVch = Rc/(2REE + 1/gmu). common-mode gain

22.

I_C3 = 3uA

VEE = -5V

VO = 5V

RC = 1K

beta = 90

CMRR = 120

rpi = 25

Adx = -gmuRc

Acm = Rc/(1/gmu + 2REE)

REE = (1+gmu3 r03)(RE || rpi3) + r03

23.

B

Ax = -gmu1(R || Rc || ro)

Ay = -gmu1 ro1 || Rop

Rout = Vo/Vtest = r03 || (R + rpi3) || (1 + R/rpi3)/gmu3

Av = r_out/v_x . v_x/v_in

Rup:

Rup = I_x = + v_x/r_o + v_x/r_pi + g_mv_x

=> v_x/I_x = r_o || r_pi || 1/g_m ≈ 1/g_m

v_x/v_in = -g_m1(r_o3 || r_o5) || r_o1

v_o/v_x = (1 + r_pi/R_C)^-1 = R_C/(r_pi+R_C)

Av = -g_m1 R_C/(r_pi+R_C) . (r_o3 || r_o5)||r_o1

Av = -g_m1 r_o1 || Rup

Rup ≈ (r_pi2+R) || r_o3 || 1/g_m3

24.

Vcc    VA = oo

A) Av = - (Rc + 1/g_m3) / (1/g_m1 + RE/2)

B) Rc >> 1/g_m3    U    RE >> 2/g_m1

=> Av ≈ -2Rc/RE    independent of the tail currents.

25.

Rout = Rc || [ (1 + g_m1r_o1)(RE || r_o2) + r_o1 ]

v_E = -r_o(I₀ - g_mv_it)

v_t = v_i - v_E

=> v_E = (-r_oI₀ + r_og_mv_i) / (1 + r_og_m)

(v_i - v_E) / r_t + I_or = v_E / R_E

=> G_m = i_o / v_IN = - g_m1r_o1 / (g_m1r_o1R_E + r_o1 + R_E)

26.

V1 = V2 = VCM

(VGS - VTH)_EQM = square root of (2ISS / (mu n Cox W / L))

VX = VY = VDD - ISS/2 RD = VO,CM

VT = VCM - VGS1 = VCM - VTH - square root of (ISS / (mu n Cox W / L))

VT increases with (W/L) and decreases with ISS and with Cox

27.

VCM = 1 V

ISS = 2uA

RD = 1 kOhm

VCC,MIN -> Q1,Q2 saturation

VTH = 0.5 V

VDD - ISS/2 RD >= VCM - VTH

VDD > VCM - VTH + ISS/2 RD = 1

VDD,MIN = 1

28.

Av = 7

RD = 400

W/L = 1400

d = 0

VDD = 2 V

VCM,MINIMUM

|Av| = gm RD => gm = |Av|/RD = 0,0175

VCM - VTH < VCM,OUT = VDD - RD ISS/2

gm = square root of (2 mu n Cox W / L ISS / 2)

VCM,MIN < VCM,OUT + VTH

VCM,MAX = VT + VDD - RD 500/2

VCM,MIN -> sufficient voltage drop on tail current generator to make it work.

VCM,MIN = -VSS + VCS + VT + VOV