# PWM in the Frequency Domain

Discussion in 'Math' started by kb1vyi, Jul 8, 2014.

1. ### kb1vyi Thread Starter New Member

Jul 8, 2014
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I am currently working on a project that requires me to use a transfer function of a circuit to manipulate bode plots. Manipulation of the Bode plots will be done by summing multiple input voltage sources together to receive the desired bode plots. This simply being achieved by taking whatever source is necessary and performing the inverse laplace transform.

So ultimately I have two PWM input signals into my circuit as a sinusoidal PWM signal acting differentially. This leads to a sinusoidal output. However, how do I achieve an equation of the PWM signal in the frequency domain. From my understanding it must be done using Fourier analysis and things start to go over my head a little bit.

Any and all help is appreciated in deriving a frequency domain PWM equation.

2. ### MrAl Distinguished Member

Jun 17, 2014
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Hi,

Very often the PWM signal transforms into a simple gain block. This is when the frequency of the PWM is significantly higher than the other frequencies in the system which is very often the case.
For example, for 50 percent duty cycle you would substitute a gain block equal to 1/2.

If the duty cycle is variable, you would take the control signal and convert it to the appropriate voltage, which would involve either just a gain or a gain and offset.
So for example if a 0 to 10 volt signal controls a 0 to 100 percent PWM duty cycle and the input voltage is 20 volts, then for a 5v control signal the output of the PWM is converted to 10 volts because 5v represents 50 percent duty cycle and a 50 percent duty cycle with 20v input would produce 10 volts averaged output.

When you do this with a buck regulator circuit for example, you get a linear regulator response. Thus you can evaluate the behavior of a buck circuit using linear techniques. This is often referred to as the "Averaged AC Response".

Dec 24, 2013
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