Esercizi Svolti Feedback - Parte II

31.

beta -> infinity

GioL = giu2 Rc giu1

K = RM

K GioL = RM Rc giu2 giu1

Gic,L = GioL / (1 + K GioL)

Rin o.l = 1 / giu1

Rin c.c. = 1 / giu1 (1 + K GioL)

Rout = 1 / giu2

Rout,c.c. = 1 / giu2 (1 + K GioL)

32.

A) Vin T Vx Vout? I - Vx? positivo.

Vin - IRF = IE2

Vin = IRF

B) Va = giu2 RD = Vb => - Vb / Va = - giu2 RD positivo. feedback.

Iz / Vi = - 1 / RF

Esercizi Svolti e Commentati:

Microelectronics (B. Razavi, Wiley 2014)

Capitolo 12 Feedback

Parte II

33.

(A)

K = 1

Ao = -gmu1(ro1 || ro3) - gmu5 ro5

= gmu1 gmu5 (ro1 || ro3) ro5

Rout,0 = 1/gmu5 || ro5

Rout,cl = Rout,0 / (1 + KAo)

(B)

Ao = gmu1 gmu5 (ro1 || ro3) ro5

34.

Ao = gmu1 (R1 + R2)

REDARRE factor

V2 / Vi = R1 / (R1 + R2)

Rin,0 = 1/gmu1

Rout,0 = R1 + R2

Rin,cl = Rin,0 (1 + KAo)

Rout,cl = Rout,0 / (1 + KAo)

35.

R1 + R2 non veri caricobeta >> 1rA = inf

Ao = gm RT rpi / (R1 || R2 + rpi)RT = RC || (R1 + R2)

k = R2 / (R1 + R2)

Rin,eq = 1 / gmi + (R1 || R2) / (beta + 1)

Rout,0 = RC || (R1 + R2)Rout,eq = Rout,0 / (1 + kAo)

36. RC -> inf => Rout,0 = R1 + R2

37.

VL = inf

Ao = + gm2 Req * RD1 * Req / (1 / gmi + (R1 || R2)) . (R1 + R2) / (1 / gmi2 + Rp)

RIN,0 = rpi + (R1 || R2)Rout,0 = (R1 + R2)k = R2 / (R1 + R2)

Req = rpi2 + (beta + 1)Re

38.

lambda = 0

Ao = + gm2 RD1 / (1 / gmi1 + (R1 || R2)) . gm2(R1 + R2)

k = R2 / (R1 + R2)

Rin,0 = infRout,0 = (R1 + R2)

40.

R_O1 = v_out / I_IN = v_out / v_x · v_x / I_IN

v_x / I_IN

{ [R_E + (R₁ || R₂)] || r_pi } I_IN = V_IN

A₀ = v_x / v_IN = g_m1 r_pi2 ⇒ R_O1 = g_m1 r_pi2 · (R_E + R₁ || R₂) || r_pi1

A_0,2 = v_out / v_x = - g_m2 (R₁ + R₂ || R_E)

=> G_BO = R_O1 · A_0,2

I₁ = [R₁ + (R₂ || R_E)]^-1 V₁ = V₁ / [R₁ + R₂ || R_E]

I₂ = -I₁ · R₂ /(R₁ + R₂) = - V₁ / [R₁ + R₂ || R_E] · R₂ /(R₁ + R₂)

K = - (R₂ || R_E) · R₂ / [R₁ + (R_E || R₂)] (R₁ + R_E)

K A₀ > 0 OK.

R_OUT1 = [R₁ + (R₂ || R_E)] / [1 + K B₀]

R_IN = [R_E + (R₁ || R₂) || r_pi1] / [1 + K B₀]

41.

R_O = V_out / I_in = V_x / I_in    V_out / V_x

I_in [ 1/g_m1 || R_F + (R₁ || R₂) ] = V_in

A_0,1 = V_x / V_in = + g_m1 R_D

=> R_O,1 = g_m1 R_D · { 1/g_m1 || [ R_F + (R₁ || R₂) ] }

A_0,2 = V_out / V_x = - g_m2 { R₁ + (R_F || R₂) }

R_O = - g_m1 R_D · { 1/g_m1 || [ R_F + (R₁ || R₂) ] } · g_m2 { R₁ + (R_F || R₂) }

K = - R₂ / (R₁ + R_F || R₂) · 1 / (R₂ + R_F)

R_IN,0 = (1/g_m1 || [ R_F + (R₁ || R₂) ]) / (1 + kR_O)

R_OUT,0 = R₁ + R₂ || R_F / (1 + kR_O)

42.

V_x = (R_E || r_pi) I_IN

R_O = - g_m1 (R_C || R_F) (R_F || r_pi)

R_IN,0 = (R_E || r_pi) / (1 + kR_O)

R_OUT,0 = (R_C || R_P) / (1 + kR_O)

I₂ / V₁ = - R_E^-1 = K

43.

VA << oo

VIN = (RF || ri) IIN

Ro = Vx/Ix = Vout/Ix = - gui(RF||ri1)(RP||ri1) · gmu2 RF||ro2 / (1 + gmu2(RF||ro2))

K = I2/Vx = -1/RF

RIN,0 = (RF || ri1)

Rout,0 = RF || ro2 || (RC||ro1 + 1/gm1)

44.

45.

VA << oo

Iout = gui Vx ro / (Rt + Rh + Rg)

= +A1 Vin gmu1 ro0 / (ro + ra + roa)

K = V2/I = RM

Rout = roL + RM

46.

Qm - Q2 FEEDBACK TOPOLOGY

A_I = I_OUT / I_IN = I_OUT / V_X · V_X / I_IN.

V_X / I_IN = R_D

I_OUT = I_M2 · r_o2 / (R_F + r_o2)

I_M2 = g_m2 V_X

A_I,0 = g_m2 R_D r_o2 / (R_F + r_o2)

R_IN,0 = 1/g_m1 || r_o1

R_OUT,0 = r_o2

A_I,CL = A_I,0 / (1 + kA_I,0)

R_IN,CL = R_IN,0 / (1 + kA_I,0)

R_OUT,CL = R_OUT,0 · (1 + kA_I,0)

47.

V_A = oo

A_I,0 = g_m2

R_IN,0 = 1/g_m1

R_OUT,0 = oo

R_IN,CL = R_IN,0 / (1 + kA_I,0)

k = -1

48.

V_a = inf

Vx/Iin = -beta [Re || (Rf(beta+1) + rpi)]

Iout/Vx = + gm2(ro2 || (R? || ro2?)) / (1 + gm2(R? + r?))

Ai = -beta [Re || ((Rf + Rl) beta + rpi)]

Rini0 = rpi1

Rout0 = Rf + 1/gm2

K = -1

49.

A

VDD

VIN

VOUT

VOUT +

VOUT

Vx

I1

Iin

Ro,0 = - gm1/gm2 ro1

VIN = Iin/gm2

Rin,0 = 1/gm2

Rout,0 = ro1

Rin,CL = Rin,0/(1 + kRo)

Rout,CL = Rout,0/(1 + kRo)

RcL = Rc/(1 + kRo)

B

R_o = -g_m1(r_o1 || r_o2 || 1/g_m2) * r_o2

R_inv,o = r_o2

R_out,o = 1/g_m2 || r_o2 || r_o1

R_o,c = R_o / (1 + kR_o)

R_in,c = R_in,o / (1 + kR_o)

R_out,c = R_out,o / (1 + kR_o)

C

R_o = r_o2 * [1 + g_m1r_o1] / (1 + g_m1r_o1)

R_in,o = r_o2 || 1/g_m1 || r_o1

R_out,o = r_o2(1 + g_m1r_o1) + r_o1

k = I_z / V₁ = +g_m2

50.

|H|

40

-20 dB

-40 dB

wp1 wp2 wp3 w

0 -45 -90 -135 -170 -215 -270

<H

|K H(jw)| > 1

< H(jw) = -180°

Wqx < Wep not oscillate

PM = <H(jw_a) + 180° = -35°

B

|H|

40

-20

-40

-20

wpi wp2 wp1 wp3 w

0 -45 -90 -135 -180

<H

C

60 dB

+20

-20

-40

-wz 0 wp1 wp2 w

90 0

51.

Vin

VDD

Vout

λ = 0 H(s) = ?

H(s) = -(gm R_D)³ / (1 + s/wp)³

wp = 1 / (R_D C_L)

<H = 0 - 3 tan^-1(w/wp)

<H(0,w_p) = -|7i|°

<H(w_p) = -3 tan^-1(1) = -135°

<H(10wp) = -253°