Question

BUCK FILTER TRANSFER FUNCTION (CCM) USING MATLAB

I. State-space Modelling and Transfer Function of Ideal Buck Converter

1. Write the AC state-space for an ideal Buck Converter under CCM, given
the state-variables iL^(t) and vc^(t),
input variables d^(t) and vs^(t), and
output variables iL^(t) and vc^(t).

2. Create the state-space model in Matlab using R=5/3 ohms, L=10 uH, C=242 uF, Vs=Vin= 20 V, Vo = 5 V, D=5/20

3. Extract the transfer functions from the state-space model.
vo^(s)/vs^(s),
vo^(s)/d^(s),
iL^(s)/vs^(s),
iL^(s)/d^(s)

4. Write the expressions for the transfer functions.

5. Plot the pole-zero maps, step-responses, and Bode plots of the transfer functions.

II. State-space Modelling and Transfer Function of Buck Converter with Parasitics

1. Write the AC state-space for an ideal Buck Converter under CCM, given
the state-variables iL^(t) and vc^(t),
input variables d^(t) and vs^(t), and
output variables iL^(t) and vo^(t).

2. Create the state-space model in Matlab using R=5/3 ohms, L=10 uH, C=242 uF, Vs=Vin = 20 V, Vo = 5 V, D=5/20, rL=25mohm, rC=25mohm

3. Extract the transfer functions from the state-space model.
vo^(s)/vs^(s),
vo^(s)/d^(s),
iL^(s)/vs^(s),
iL^(s)/d^(s)

4. Write the expressions for the transfer functions.

5. Plot the pole-zero maps, step-responses, and Bode plots of the transfer functions.

Answer 1

5. plot the pole-zero map, step response and bode plot of transfer functions

(i) Transfer function Gvd

Matlab code : pzmap(Gvd); step(Gvd); bode(Gvd)

The results are

(ii) Transfer function Gid

Matlab code : pzmap(Gid); step(Gid); bode(Gid)

The results are

(iii) Transfer function Gvg

Matlab code : pzmap(Gvg); step(Gvg); bode(Gvg)

The results are

(iv) Transfer function Gig

Matlab code : pzmap(Gig); step(Gig); bode(Gig)

The results are

II.

5. Plot the pole-zero maps, step-responses, and Bode plots of the transfer functions.

(i) Transfer function Gvd

Matlab code : pzmap(Gvd); step(Gvd); bode(Gvd)

The results are

(ii) Transfer function Gid

Matlab code : pzmap(Gid); step(Gid); bode(Gid)

The results are

(iii) Transfer function Gvg

Matlab code : pzmap(Gvg); step(Gvg); bode(Gvg)

The results are

(iv) Transfer function Gig

Matlab code : pzmap(Gig); step(Gig); bode(Gig)

The results are