Esercizi coppie differenziali - Parte IV

Esercizi Svolti e Commentati:

Microelectronics (B. Razavi, Wiley 2014)

Capitolo 10 Coppie Differenziali

Parte IV

44.

R_up = [1 + g_m5(r_o5 || R)] r_o7 + (r_o5 || R₁) = 15,3 Meg.

R_un = g_m3 r_o3 r_o2 = 900 Meg.

A_v = -g_m1 R_up || R_un = 150 k.

45 -> 44 with BST.

R_up = [1 + g_m5(r_o5 || R)] (R_oz || r_t5) + (r_o5 || R₁)

R_un = (1 + g_m3 r_o3)(r_o1 || r_t3) + r_o3.

46

v_PI1 = v_IN

I_C1 = g_m v_in + v_PI2/r_o1

v_PI2 = - I_out /(g_m + 1/r_o3)

I_out = - g_m v_in2 - v_in2/r_o3 => v_in2 (- g_m - 1/r_o3) = I_out

v_in2 = - I_out /(g_m + 1/r_o3)

I_C1 = g_m v_IN - I_out /(g_m + 1/r_o3) · 1/r_o1

+ I_out /(g_m + 1/r_o3) = g_m v_in + I_out /(g_m + 1/r_o3) · 1/r_o1 + I_out

v_IN / I_OUT = 1/g_m [ 1/(g_m + 1/r_o3) (1 + r_o1/r_o1) + 1 ]

R

A_v = - g_m R_up || R_o1

R_up = r_o3,

4f.

v_PI = ± v_x = v_BE

I_x = - I_E = (g_m v_PI + v_PI/r_o) + v_PI/r_PI

- I_x = - g_m v_x - v_x/r_o - v_x/r_PI

I_x/v_x = g_m + 1/r_o + 1/r_π

A_v = - g_m R_up / (1 + R_SS/2)

48.

Floating.

AV = - g_m r_o1

49. Telephonic cascode.

AV = - g_m1 [g_m3 r_o3 (r_o1 || r_o3)] [g_m5 r_o6 (r_o7 || r_o11)]

AV = 800

beta_m = 2 beta_p

V_A,n = 2 V_A,p

=> 800 = 1/(5V^-2) (V_A,n (V_A,n || 2,6)) => V_A,n = 2,245 V.

V_A,p = 1,225 V.

50.

V_TN = 0,4V   k'n = 100uA/V²

λn = 0,02V^-1   (W/L)_n = 15

V_TP = -0,4V   k'p = 50uA/V²

λp = 0,02V^-1   V_DD = 5V

I_A = 250 uA.

THEVENIN:

SYMNETRY

⇒ V_THEV = - g_mn r_on (V₁ - V₂)

(i_x - g_m1v₁r_o1) r_o1 + (i_x + g_m2v₂)r_o2 = v_x

v₁ = v₂ => R_THEV = 2 r_on.

Ix = -gmVgs - (VE - VX)/ro

VE = RE Ix

Vgs = -VX + VE

=> Ix = -gm (VE - VX) - RE Ix/ro + VX/ro

Ix = gm RE Ix + gm VX - RE Ix/ro + VX/ro

(1 + gm RE + RE/ro) Ix = (gm + 1/ro) VX.

=> (1 + gm ro) RE + ro.

ro + gm ro RE + RE = (gm ro + 1)

CASCODE CURRENT MIRROR -> Rout approx gm ro1 ro2

rout2

rout1

vout

RThev

VThev

RThev