Ming Sun – Silicon achitect, design lead, researcher.

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_vc mathematically anymore.

Fig. 1Gvc test bench for PCM controlled Buck converter in Simplis

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

Fig. 2Transient waveforms of PCM Buck converter (open-loop) in Simplis

The G_vc simulation result from Simplis is as shown in Fig. 2.

Fig. 3Gvc Bode plot for PCM Buck converter in Simplis

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].

Fig. 4Type-II compensator block diagram^[3]

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

Fig. 5Type-II compensator Bode plot illustration

p₁ 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, z₁ has to be placed inside the cross over frequency so that we can have sufficient phase margin. Let us place z₁ to be 1/3 of the cross over frequency, which is 100kHz.

First, let us choose C₁ 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 C₁. As a result, the resistor R₁ value can be calculated as:

`R_1 = 1/(z_1C_1) = 1/(6.28*100k*50p) = 32kΩ`

(1)

We know the mid-band gain of the Type-II compensator is g_m*R₁. To make sure the cross over frequency is at 100kHz, from Fig. 3, we know that:

`g_mR_1*alpha = 15.2dB`

(2)

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:

`alpha = 1.2/1.8 = 2/3`

(3)

As a result,

`g_m = 10^(15.2/20)/(2/3*32k) = 270µS`

(4)

Let us place the p₂ pole to be at switching frequency to suppress the ripple. Therefore, we have:

`C_2 = 1/(p_2*R_1) = 1/(6.28*3M*32k) = 1.66pF`

(5)

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_vc and G_c (compensator transfer function) into the same AC Bode plot. The schematic is as shown in Fig. 6.