Derive the small-signal dynamic equations that model the

Question

Question 1. An ideal boost converter operates in the continuous conduction mode.

(a) Determine the nonlinear averaged equations of this converter.

(b) Now construct a small-signal ac model. Let

(vg(t))_Ts = V_g + V^{^}g(t)

d(t)= D + d^(t)

(i(t))T_s = V + v(t)

where V_g, D, I, and V are steady-state dc values: V^_g(t) and d^(t) are small ac variations in the power and control inputs: i^(t) and v^(t) are the resulting small ac variations in he inductor current and output voltage, respectively. Show that the following model results:

Large-signal dc components

O = -D'V + V_g

O = -D'I -V/R

Small-signal ac components

Ldi^(t)/dt = -D'v^(t) + Vd^(t) + V^_g(t)

Cdv^(t)/dt = -D'i^(t) - id^(t) -V^(t)/R

2. Consider the Cuk converter shown in Fig 1

Fig 1 Cuk Converter

a) Derive the small-signal dynamic equations that model the ideal Cuk converter.
b) Construct a complete small-signal equivalent circuit model for the converter

3. Express the gains represented by the asymptotes of Fig.2 (a) to (c) in factored pole- zero form. You may assume that all poles and zeros have negative real parts.

Fig. 2 Gain asymptotes

Q.4. Plot the Bode magnitude and phase for the system with transfer function

G(s) = 2000(s + 0.5)/s(s+10)(s+50)

Q5. a) Derive the small-signal dynamic equations that model the inverse Sepic converter shown in Fig. 3.

Figure 3 Inverse Sepic Converter

b) Construct a complete small-signal equivalent circuit model for the inverse-SEPIC.