Esercizi stadi Cascode e specchi di corrente - Parte IV

Esercizi Svolti e Commentati:

Microelectronics (B. Razavi, Wiley 2014)

Capitolo 9 Cascode Stages e

Current Mirrors

Parte IV

39.

Iref = Ic,ref + I / p = Ic,ref + 1/p (Ic,ref / p + IcQ1,1 / p + IcQ1,2 / p)

IcQ1,2 = 6/2 IcQ1,1.

IcQ1,1 = Ic,ref / 2

=> Iref = 2 IcQ1,1 + 2 IcQ1,1 / p² + IcQ1,1 / p² + 6/ p² IcQ1,1

= IcQ1,1 (2 + 9/p²)

IcQ1,1 = Iref / (2 + 9/p²)

IcQ1,2 = 6 IcQ1,1.

40.

VDD = 3V

VTH1 = 0,4V

kn = 20 uA/V²

R = 1k

IREF = 2uA.

VGS1,REF = sqrt(2 IREF / kn (W/L)) + VTH = VDS = VDD - IREF R.

IREF = 1/2 kn (W/L) VOV²

(W/L) = 556.

41.

If IO = 10 uA => (W/L)₂ ?

IO = (W/L)₂ / (W/L)_REF IREF. => (W/L)₂ = 5 (W/L)₁.

43.

lambda != 0

M1, M2 identical

I_REF = (1/2) mu_n Cox (W/L)_ref (VGS,1REF - Vtn)² (1 + lambda VDS1)

I_COPY = (1/2) mu_n Cox (W/L)_copy (VGS,1copy - Vtn)² (1 + lambda VDS2)

I_REF = I_COPY => (W/L)_copy (1 + lambda VDS2) = (W/L)_ref (1 + lambda VDS1)

I_REF = (kN/2) (VGS,1REF - Vth)² (1 + lambda VDS1) VGS,1REF = VDS,1REF.

= (kW/2) (VX - Vth)² (1 + lambda VX)

sqrt(2 I_REF / kN) = (VX - Vth) sqrt(1 + lambda VX)

I_O / I_REF = ((W/L)₂ / (W/L)₁) ((1 + lambda VDS2) / (1 + lambda VDS1)) = (1 + lambda VD2) / (1 + lambda VGS)

IF EDGE OF SAT. VDS = VOV

=> I_O / I_REF = 1 - (lambda VTH) / (1 + lambda VGS) = 1 <=> (lambda VTH) / (1 + lambda VGS) << 1

=> VOV >> -1/lambda => VGS > Vth - 1/lambda

44.

A) RE = 300Ω

VBE1 = VT ln(IC/IS) = 0,732V

Vb = VBE + VE = 1,232V

ROUT,A = (1 + gm1 ro1)(RE || rπ1) + ro1

≈ gm1 ro1 RE

Ibias = 1uA

VRE ≈ 0,5V = VCE2 (Q2)

B) ROUT,B = (1 + gm2 ro2) ro1 + ro2

≈ gm2 ro2 ro1

VBE1 = 0,732V

VBE2 = VBEQ - 0,5 = VT ln(IC/IS)

Vb2 = 1,232V

45.

ROUT = 200kΩ

Ibias = 0,5uA

A) λ = 0,1V^-1 => (W/L)1 = (W/L)2?

B) Vb2 ?

ro1 = ro2 = 1/λID = 20kΩ

=> ((ROUT - ro1)/ro2 - 1) 1/ro1 = gm1 = 0,0004 S = (2,5kΩ)^-1

gm1 = √(2 ID un Cox W/L)

=> (W/L) = gm1²/(2I0unCox) ≈ 1,6

B) Vb2 = √(2ID/(un Cox (W/L))) + Vth = 2,9V

46.

Av = 500beta = 100Av approx -Va/(VT + Va/beta) => Va^2 + Va(VT/Av) + (AvVT)^2 = 0.

Av approx 9,quasi 10, quasi (80,1 kHz)

VA approx 0,65V

VIN,BIAS = VT ln(IBIAS/IS) approx 0,71V

VCE,1 = 0,5V = VC1

VB1 = VBE1 + VE2 = VBE1 + VC1 = 0,71 + 0,5 = 1,21V.

47.

P = 2mW   VCC = 2,5V.

A) VB2, VB3 -> Q1, Q4 VBC = 0,2V

B) Av = ?

IBIAS = P/VCC = 0,8 uA.

VBC1 = VB1 - VC1 = 0,2

=> VC1 = VB1 - 0,2

VB1 = VBE1 = VT ln(IC/IS) = 0,725V

VC1 = 0,525V

VBE2 + VC1 = VB2 = 1,25V

VCB4 = VC4 - (VBE4 + VE) = 0,2

VC4 = VCB4 + 0,2 + VE = 3,425V.

VB3 = VCC - 0,725 = 1,775V

Av = -gm1 (gmi2 ro2 ro1 || gmi3 ro3 ro4)x 740