Retroazione nei cicuiti analogici

Tesi sulla retroazione

Tesi sulla retroazione

y=

E=x-Ky

=x-K(Az-A1

(x-y)K)

y=KA2

-xA2-A1

(x-yK)

y =

X Az

X = -A2-A1

1-A1k

=x-Ky

=X-K(Az

...

E=x-KAz

=x

=X

=

=-KA2

1-KA1

...

=Σ

X =

...

y=

=EΣ=x

E=x-KAzY=x

X =

E=

X

...

=EA1=A1(X-YA2K=

Y=X

...

=X

=X(1-A1)

=1

x-Ky

=X(1

=1+y)

=

=x

-1+A=v/X

1+K1(1-A1)K

X

=X=E(K

E=w)

=w=x

...

y

X

=

...

=KA1

1+K

(K-A1)K

E

X

=K(A1

...

E=

K(K(A1

E=x-K=x

)

Z-A

=-x+y(K-1)

=xK(K=K)

1-(1-A1)A1)

=X- X

=E{1(X-1)

3. LOOP-GAIN - IDEAL COMPONENTS (Zin opamp → ∞, A=0)

A)

V_n = -K_A1 V_es

V_n = y_f R2 / R1 + R2

⇒ +K_A1 = -V_es / V_es

Y = -K V_es

= R2 / R1 + R2

B)

B = -g_m V_es R_D A2

Y = g_m V_es R_D A1

V_in = R2 / R1 + R2 g_m V_D A1 V_es

K_A1 = -V_ic / V_es = g_m + R_D Ω₂ A1 / R1 R2

C)

Y = -g_m R_D A1

K_A1 = g_m R_D A1

D)

Y = g_m R2 / 1 + g_m R2

B = -V_es A1

⇒ K_A1 = g_m R2 A1 / 1 + g_m R2

4.

Y = (X - X_F) A₁

X_F = Y R₂ / (R₁ + R₂)

Y = XA₁ - A₁ R₁ Y / (R₁ + R₂)

X = V₀ sin(ωt)

V₀ = 2 µV   R₁/R₂ = 7   A₁ = 500

Y₀ = V₀ A₁ = A₁ ¹⁄_{R1/R2 + 1} = θ 1,5 µV

X_F0 = 1,97 µV

X ≈ X_F

5.

(1 - 10%) A₀ = [A(ω - ω_ds)]

0.9 A₀ = ^A₀⁄_{√(1 + (ω - ωb)/ω0)²}

ω₀ → -3 dB

ω - ω_ds ≈ 0,1 ω_bW0

Closed-loop gain

^A₀⁄_{1 + ε L} = 0.9 = ^|Y|⁄_{|X|(ωbW+ωds)} → ω_ds = 0.9 ω (1 + KA)

Bandwidth is boosted by (1 + KA) in closed loop gain.

6.

K'_m → ±10%

λ → ±20%

ε_L G_m → ±5%

V_out = - g_m r_o ε = -g_m r_o (V_in - K V_out)

^V_out⁄_Vin = - ^{g_m r_o}⁄_{1 + K gm ro} = - ¹⁄_{λ TD}

d ω_bWE = - dλ

(1 + λ_r) = 20% ~ < 5% → 3

7.

λ = 0

A₀ = -g_m₁r_o

A₀(s) = -g_m₁r_o||(sC_L)⁻¹

V_o = -g_m2V_o2

E = V_IN + g_m2r_o2

V_out = -g_m1r_o/(1 + r_oε_Ls)

V_oUTT(s) / V_IN(s) =

(A₀ / 1 + K A₀) / (1 + S / (1 + KA₀) ω_A)

K A₀ = g_m1r_o / 1 + r_oε_Ls

DC: CLG = A₀ / 1 + KA₀}

|V_out / V_IN(ωL)

8.

A₀ = -g_m1(R_D||r_o)

K A₀ = -V_oER / V_ESR = +g_m1 (r_o||R_D)

Z_CL = C₁ / C₁ + C₂

A = A₀ / 1 + KA₀}

9.

G_m1 = A₁ / 1 + KA₁ ≈ K (1 - 1 / KA₁)

G_m2 = A₂ / 1 + KA₂ ≈ 1 / K(1 - 1 / KA₂)

K A₁ ≫ 1

K A₂ ≫ 1

G_m1 - G_m2 / G_X1 < 0,05 ⇒ K > 1 / Z₁₀₀

A₂ = 138,16

A₂ = 131,25

10.

y = d₁x - d₂x³

A)   ∂y/∂x = d₁ - 3d₂x²

&ems