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Uniform pulse width modulation closed loop frequency response / PSS and PAC analyses

mohamin

I am trying to simulate a uniform pulse width modulation (UPWM) to extract closed loop frequency response of the UPWM. Surfing the net, I figured out I have to use PSS/PAC. So, I did it but I didn’t get what I expected. 

Just to be clear, I am going to go over on what I’ve done. 

1-      My simulation test bench is shown here with all setting parameters. 

1-      I used vsource/analogLib to be applied to the input.

1-      Non-overlapping clocks (phi1 and phi2) and triangle waveform to be applied to the comparator.

And I used vcvs for the comparator with the voltage gain=1000, maximum output voltage= 1 and minimum output voltage=0. The negative terminals are connected to triangle waveform . 

While I am setting ADE like this:

Here is tran analysis and it seems that thing’s going well. 

BUT PSS/PA C analysis made me unhappy. Since I am setting the amplitude of triangular waveform at 1 and VDD is 1 volt so I am expecting that the gain of 1 (0dB) for UPWM. Also I have to have notches at 2fs , 4fs, 6fs because of double sampling before the conventional PWM.  BUT I cannot see that.

I also traced the differential output before the comparator and I saw this.

Could anyone please help me to figure out what I am doing wrong?

Any help would be really appreciated.

Thank you!

  • Hi,

    I was thinking probably comparator is doing something wrong since the frequency response before the comparator is rational. The blue curve in the figure below shows the frequency response of UPWM before the comparator. gain of 0dB is what I expected and notches at 2n*fs. I thought comparator gave me a suspicious look! Then I blindly played with the gain of the comparator and changed the value to 10. I examined two cases. the first one is a triangular waveform with the amplitude of 0.5 V leads to the gain of (2 or 6dB) for the system. As you can see, the gain is 6dB (the purple profile) and the other, I changed the triangular amplitude to 2 results the gain of (0.5 ot -6dB). The green profile shows that. However notches are not sitting at a correct place! both gain and notches before the comparator are correct ! But what about overall system ? !

    First of all, what's the justification behind this? Changing the gain of the comparator! How come it affects the frequency response?

    Second, any Idea to properly simulate the PWM frequency response?   

    I attached my expectation which comes from this paper "True Filterless Class-D Audio Amplifier"

    Thanks

    Ref; http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=6007063&tag=1

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