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

Ming Sun / December 24, 2022

12 min read • ––– views

## Conditions

**Vin**= 3.8V**Vout**= -5V**R**= 10Ω**L**= 1µH**C**= 10µF (derated)**fsw**= 3MHz**Rsns**= 0.3Ω**Se**tracks inductor current down-slope

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

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

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We know that for a IBB converter, its right half plane zero can be expressed as:

For a IBB converter, we know that:

Therefore, duty cycle **D** can be calcuated to be 0.568. As a result, the right half plane zero frequency can be calculated as:

We know that right half plane zero can not be compensated in the frequency domain. This is because in order to compensate right half plane zero we need to have a right half plane pole, which does not exist in a stable circuit. Therefore, the closed loop cross over frequency of the PCM controlled Boost converter has to be less than the right half plane zero frequency. As a result, let us choose the cross over frequency to be **150kHz**.

The **G _{vc}** transfer function simulated result is as shown in

**Fig. 2**

^{[1]}.

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Next, we are going to design the Type-II compensator to make the PCM Boost converter stable.

## Type-II compensator design

**Fig. 3** shows a Type-II compensator, where an OTA is being used^{[2]}.

^{[3]}

From **Ref. [3]**, we can sketch the Type-II compensator transfer function as shown in **Fig. 4**.

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**p _{1}** is the dominant pole, which will make sure we have a good DC voltage accuracy at Boost 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

**50kHz**.

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

**150kHz**, from

**Fig. 2**, we know that:

Where, **α** is the resistor feedback factor. Since the IBB converter output is a negative voltage, we need to level shift it as shown in **Fig. 5**.

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Therefore, the ratio between resistor **R _{1}** and

**R**can be calculated as:

_{2}In the small signal model, the DC voltage **1.2V** will be AC grounded. Therefore, 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:

## PCM IBB closed loop model

The PCM controlled IBB converter model in Simplis is as shown in **Fig. 6**.

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The closed-loop transfer function, compensation network transfer function and **G _{vc}** transfer function are as shown in

**Fig. 7**.

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The transient waveform is as shown in **Fig. 7**.

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## References and downloads

[1] Power stage transfer function cheatsheet

[2] Type-II compensator - OTA based

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

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