# Gvc simulation for peak current mode controlled Boost converter in Simplis

Ming Sun / December 23, 2022

9 min read • ––– views

## G_{vc} transfer function for PCM (peak current mode) Boost converter

In **Ref. [1]**, we have derived the **G _{vc}** transfer function for PCM controlled Boost converter.

Where, the DC gain is:

The dominant pole is:

The subhamonic oscillation pole is:

The quality factor **Q** is:

The right half plane zero is:

In this tutorial, let us create the **G _{vc}** test bench in Simplis and verify the above equations.

## G_{vc} test bench in Simplis for PCM Boost converter

The PCM controlled Boost converter is as shown in **Fig. 1**.

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The transient waveforms from Simplis simulation are as shown in **Fig. 2**.

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The AC simulation result of **G _{vc}** is as shown in

**Fig. 3**.

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## Comparison between Matlab and Simplis

The following Matlab script can be used to compare the **G _{vc}** transfer function between Matlab and Simplis.

```
clc; clear; close all;
Vg = 3.8;
V = 20;
L = 1e-6;
C = 10e-6;
fsw = 3e6;
Rsns = 0.3;
R = 20;
Dp = Vg/V;
D = 1-Dp;
Ts = 1/fsw;
Se = (V-Vg)/L*Rsns;
Sr = Vg/L*Rsns;
s = tf('s');
Gvc0 = R*Dp/(2*Rsns + Dp^3*R*Se*Ts/Vg);
wp = 2/R/C;
wn = pi*fsw;
Q = 1/pi/(Dp*(1+Se/Sr)-0.5);
wrhpz = R*Dp^2/L;
Gvc = Gvc0*(1-s/wrhpz)/(1+s/wp)/(1+s/wn/Q+s^2/wn^2);
h = bodeplot(Gvc); % Plot the Bode plot of G(s)
setoptions(h, 'FreqUnits', 'Hz'); % change frequency scale from rad/sec to Hz
set(findall(gcf,'type','line'),'linewidth',2);
p = getoptions(h);
p.PhaseMatching = 'on';
p.PhaseMatchingFreq = 1;
p.PhaseMatchingValue = 0;
setoptions(h,p);
grid on;
hold on;
% read simplis simulation results from csv file
data = csvread("simplis.csv", 1, 0);
freq = data(:,1);
mag = data(:,2);
phase = data(:,3);
ax = findobj(gcf, 'type', 'axes');
phase_ax = ax(1);
mag_ax = ax(2);
% append simplis plot to bode plot
plot(phase_ax, freq, phase, 'r--', 'LineWidth', 2);
plot(mag_ax, freq, mag, 'r--', 'LineWidth', 2);
legend('Math', 'Simplis')
xlim([100, 1.67e6]);
```

The comparison result from Matlab is as shown in **Fig. 4**.

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In the above condition, we let compensation ramp to track the inductor current down slope. As a result, **Eq. 5** can be written as:

We can run another condition, where we reduce the compensation ramp slope. As a result, the quality factor **Q** should be increased and we will see higher peaking introduced by the subhamonic poles. The new **G _{vc}** plot from AC simulation with reduced compensation ramp slope is as shown in

**Fig. 5**.

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## References and downloads

[1] Modeling of peak current mode controlled Boost converter

[2] Gvc test bench for PCM controlled Boost converter schematic - pdf

[3] Gvc test bench for PCM controlled Boost converter schematic - download