# PCM (Peak current mode) controlled Buck converter design example

Ming Sun / December 24, 2022

13 min read • ––– views

## Conditions

**Vin**= 3.8V**Vout**= 1.8V**R**= 1.8Ω**L**= 1µH**C**= 10µF (derated)**fsw**= 3MHz**Rsns**= 0.3Ω**Se**tracks inductor current down-slope

## G_{vc} test bench in Simplis for PCM (peak current mode) Buck converter

In **Ref. 1~2**, we first derived the **G _{vc}** transfer function equation and then designed the Type-II compensator. In this tutorial, we are going to just use Simplis as a tool to design the closed loop transfer function. There is no necessary to derive the

**G**mathematically anymore.

_{vc}^{}

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

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The **G _{vc}** simulation result from Simplis is as shown in

**Fig. 2**.

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We have added two markers on the plot. For the Buck converter, we do not have the limitation of the right half plane zero. Therefore, the cross over frequency can be designed very high. Here our design target is to design the cross over frequency to be around **300kHz** with reasonable amount of phase margin.

## Design Type-II compensator

**Fig. 4** shows a Type-II compensator, where an OTA is being used^{[3]}.

^{[3]}

From **Ref. [3]**, we can sketch the Type-II compensator transfer function as shown in **Fig. 5**.

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**p _{1}** is the dominant pole, which will make sure we have a good DC voltage accuracy at Buck converter's output. Since we have a low frequency pole due to

**G**,

_{vc}**z**has to be placed inside the cross over frequency so that we can have sufficient phase margin. Let us place

_{1}**z**to be

_{1}**1/3**of the cross over frequency, which is

**100kHz**.

First, let us choose **C _{1}** to be

**50pF**and calculate the rest of the compensation network components value. If the calculated results do not quite make sense to integrate the components (resistors or capacitors) in the silicon, we can always come back to pick a new value for

**C**. As a result, the resistor

_{1}**R**value can be calculated as:

_{1}We know the mid-band gain of the Type-II compensator is **g _{m}*R_{1}**. To make sure the cross over frequency is at

**100kHz**, from

**Fig. 3**, we know that:

Where, **α** is the resistor feedback factor. Since output is 1.8V and typically bandgap voltage is 1.2V, the feedback factor can be calculated as:

As a result,

Let us place the **p _{2}** pole to be at switching frequency to suppress the ripple. Therefore, we have:

## Add Type-II compensator into the G_{vc} test bench

Next, let us add the Type-II compensator into the **G _{vc}** test bench. However, we still keep the loop open. In this way, we can plot both the

**G**and

_{vc}**G**(compensator transfer function) into the same AC Bode plot. The schematic is as shown in

_{c}**Fig. 6**.

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The Bode plot for **G _{vc}** and

**G**is as shown in

_{c}**Fig. 7**.

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## Closed-loop PCM Buck converter model

The closed-loop PCM Buck converter model in Simplis is as shown in **Fig. 8**.

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The transient waveforms are as shown in **Fig. 9**.

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The AC simulation results are as shown in **Fig. 10**.

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## References and downloads

[1] PCM (Peak current mode) controlled Boost converter design example

[2] Voltage-mode Buck converter design example

[3] Type-II compensator - OTA based

[4] Gvc test bench for PCM Buck in Simplis - pdf

[5] Gvc test bench for PCM Buck in Simplis - download