Esercizi stadi Cascode e specchi di corrente - Parte I

Esercizi Svolti e Commentati:

Microelectronics (B. Razavi, Wiley 2014)

Capitolo 9 Cascode Stages e

Current Mirrors

Parte I

Cascodes e Mirror di 9

1. Rout = (2 + gm1 ro1) R + ro1

   R = 1/gm2 || ro2

2. Rout = (1 + gm1 (Rp || ro3)) (Rp || ro2) + ro1

3. Rout = (1 + gm1 ro1) (Rp || ro2) + ro1

4. Rout = (1 + gm1 ro1) (Rp || ro2) + ro1

5. IA1 = 0.5uA

   IC1 = 0.5uA

   IC2 = 1uA

   Rout = (1 + gm1 ro1) R + ro1

   R = ro3 || ro2 || rpi

   VA1M = VA1I2 = VA1N

   VA1P = VA1P

6.

Rout = (1 + gm1 ro1) R + ro1

R = ro1 || ((?) ro2)

if Q2 -> biased current Ic1

Rout,1 = ro1 = ro

7. Stack N Q atop each other

Rout ≅ [prod from i=1 to N] gm i ro i for i<N ≅ beta ro

8.

A)

Rout = (1 + gm1 ro1) R + ro1

R = (rpi2 + (RB || rpi1))

No cascade E1 = E2

For cascode E1 = E2

R2 = (1 / (1/(rpi2 + 1/(gm1)) + 1/ro))

B)

Rout = (1 + gm1 ro1)(R2 || ro1)

R2 = ro2

cascade

C)

Ix = Vx/ro + Vx/(rpi + RB) + gm Vx rpi/(rpi + RB)

R2 = Vx/Ix = 1 / (((beta + 1)/(rpi + RB)) + 1/ro) ≅ 1 / (beta/(rpi + RB) + 1/ro2)

R2 = (rpi + RB)/(beta + 1) || ro2

Rout = (1 + gm1 ro1)(R2 || rpi1) + ro1

≅ gm1 ro1 (R2 || rpi1)

D) R2 = ro2 // ro2 ? approx 1/gm1 // ro2

Rout = [1 + gm1(ro1||Rp)](R2||rpi1) + (ro1||Rp)

no cascoda

E) R2 = (1 + gm2 ro2)(Re||rpi2) + ro2

Rout = (1 + gm1 ro1)(R2||rpi1) + ro1

cascoda

F) R2 = ro2

Rout = (1 + gm1 ro1)(R2||rpi1) + ro1

no cascoda

G) Rout = (1 + gm2 ro2)(R1||rpi2) + ro2

R = ro2

no cascoda

9.

Vcc = 2.5V

Ic2 = 0.5mA

beta = 100

Is = 10^-16

Vb2 = Vcc - |Vbe2|

|Vbe2| = VT ln(Ic2/Is) = 0.760V

=> Vb2 = 1.74V

Vx = Vb1 + |Vbe1|

Vbe1 = 0.2 => Vb1 = Vb2 + |Vcb3| (= Vx - Vo2) = 0.94V

Vb1 = Vcc - |Vbe1| = 1.18V

10

V_DS = V_GS -> V_DS > V_GS altijd in pinch-off

I_D = 1/2 μnCox W/L (V_GS - V_TH)

I_REF + I_OUT = I_D

I_OUT = I_D - I_REF -> I_OUT ≈ I_REF I_o -> ∞

13.

I_D = 25uA     R_D = 25kΩ

V_G2 -> Roapin

A_V = ?

R_OUT = R_D || R₂

R₂ = (1 + g_m2r_o2)r_o1 + r_o2 ≈ g_m2r_o1r_o2

≈ g_m2r_o1r_o2

R_OUT,MIN => R₂ ≫ R_D

V_G1S = V_TH + sqrt(2I_D/(μnCox(W/L)₁)) = 0,62V

V_G2X = V_TH + sqrt(2I_D/(μnCox(W/L)₂)) = 0,65V

g_m1 = sqrt(2I_DμnCoxW/L) = 0,00067

g_m2 = 0,0006

V_G2 = V_D2 + V_TH = V_DD - I_DR_D + V_TH = 0,325V

14.

quinto >> 1. SATURATION.

R_OUT = (2 + g_m1r_o1)R + r_o1

R = 1/g_m || r_o = g_mr_o/(g_mg_ro) ≈ 1/g_m

R_OUT = g_m1r_o1/g_m2 + r_o1

(A)

R_OUT = (1 + g_m1r_o1)r_o2 + r_o1 = g_m1r_o1r_o2 + r_o1

(B)

R_OUT = (1 + g_m1r_o1)r_o2 + r_o1

= g_m1r_o1r_o2 + r_o1

C

g_m = g_m1 + g_m3

r_o = r_o1 || r_o3

R_out = (1 + g_m2 r_o) r_o2 + r_o ≈ g_m2 r_o r_o2

D

Tx focus through M1 e M2

I_x = v_y/r_o2 + g_m2v_x

I_x = -g_m1v_y + (v_x - v_y)/r_o2

=> v_y = g_m2v_xr_o2 - I_x

=> I_x = f(g_m1, v_x, r_o1, r_o2, g_m2)

R_out = (g_m2r_o2 + r_o2/r_o1 + 1)/(g_m1g_m2r_o2 + (g_m1 + 1)r_o1) ≈ 1/g_m2

15.

A_v = ?

R_out = ?

w/L = 2/1

λ = 0.05 v^-1

I_D = 125uA

k'm = 100 uA/V²

k'p = 50 uA/V²

R_out = r_o || R₂

R₂ = (1 + g_m2r_o2)r_o1 + r_o2

g_m2 = g_m1