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I am new with PWM methods and there is a subject that I cant find an answer to and decided to ask here.

For a varying frequency PWM (VF-PWM) I have found that by using the following spectral modultion:

enter image description here

I am able to use some wave form reference (here cos wave) with a carrier (here sawtooth) and obtain the PWM output as shown below:

enter image description here

However, it all works fine if I know what shape my reference is and what is the frequency of it.

If for example I have a control system which outputs the following signal and I would like to insert it into a PWM to obtain pulses:

enter image description here

Is there some mathematical formula as shown above for a different case or some method to obtain the PWM for unregular reference shapes?

Thank you very much.

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  • \$\begingroup\$ What sampling frequency (aka time resolution) do you require your signal to be converted. If you don’t understand why or what I’m saying then you ought to do some background research. Google will help plenty. \$\endgroup\$ – Andy aka Sep 21 '18 at 19:14
  • \$\begingroup\$ The control system (in this case autopilot) will give me as an output data with about 100-500Hz sampling frequency. This data I had like to insert into a PWM converter in order to activate some ON/OFF part. \$\endgroup\$ – Ben Sep 21 '18 at 19:18
  • \$\begingroup\$ LTC6992 sounds like a way to go. \$\endgroup\$ – Andy aka Sep 21 '18 at 20:06
  • \$\begingroup\$ Thank you Andy. I am now concentrating on performing simulations and understanding the math behind it and was hoping if there is some double fourier model just like I posted earlier but for my case. \$\endgroup\$ – Ben Sep 21 '18 at 20:09
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The constraint for amplitude is the signal may reach but not exceed the sawtooth in a comparator.

Whenever your Amplifier saturates like in your scope wave, the loop incremental gain automatically goes to 0 since it is no longer can vary when saturated. Ie nonlinear. So on average the overall gain is effectively reduced for step response. Lead/lag compensation or Nyquist root analysis needs to correct that.

Other info

Navigation servo analysis gets complicated when you push the spectral boundary where PWM side bands introduce jitter or the integration of force into velocity into position for stabilization maneuvers creates excess delay from a 3rd order system from integration. So the multiple forms of feedback with predictor-correction targets to minimize maneuver control spectrum, and gryo+accelerometers in 3 axis and drift calibration are complex when non-linearity is added.

Phase shift in the compensation network must not lag too much as delay must be much less than the inverse BW desired. This often leads to DSP’s with digital filters.

Once the scope of a design broadens to optimize sensors , transfer functions and specs, then a math simulation can be useful. But you need to start with specs. PWM ought to be a linear function after you choose and optimize the spectrum and bandstop and bandpass requirements.

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