# ripplle factor from fourier analysis

#### aragon1971

Joined Apr 7, 2008
126
Hi
i m trying to find the ripple factor in full wave rectifier circuit with a capacitor filter
i find a results can check that ?

thank you
George

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#### Jerry-Hat-Trick

Joined Aug 31, 2022
366
Hi George,
I struggled to follow the maths, but the way I work out the expected ripple is to consider how fast the capacitor will discharge before the next voltage peak comes along. So long as the capacitor is large enough you can assume that the voltage drop is linear with time and the next peak will come along (for a full rectified AC) after half the period of the full wave. So the ripple voltage is close to Vpeak times the time between peaks divided by the load resistance divided by the capacitor value.

The fact that the voltage drop is not quite linear and the falling voltage is picked up by the next peak before the time between peaks means that the ripple voltage is slightly less than this

#### Papabravo

Joined Feb 24, 2006
20,399
You can also simulate it and get the simulator to measure it for you. If all three methods give approximately the same result, then you can choose the most convenient method.

ETA: Here is a simulation of a DC supply with an undersized capacitor and a high impedance load. The droop is about 41% here. You can not see the full wave rectified waveform without removing the capacitor entirely, but that is why you are seeing a cycle between the positive peaks of the AC waveform.

ETA2: Oh, but thanks to waveform arithmetic there is a way to see it:

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#### aragon1971

Joined Apr 7, 2008
126
hI
I lnow this approximately solution but i m looking if thera an most exact solution

#### ericgibbs

Joined Jan 29, 2010
18,053
hi a1971,
This PDF has some interesting information that may help.
E

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#### Papabravo

Joined Feb 24, 2006
20,399
hI
I lnow this approximately solution but i m looking if thera an most exact solution
An exact solution may be a difficult hill to climb especially when our modeling of the situation is less than perfect. Is it really your contention that knowing the amount of ripple to 9 or 10 significant figures is better than 3 or 4?

#### Ian0

Joined Aug 7, 2020
8,407
Hi
i m trying to find the ripple factor in full wave rectifier circuit with a capacitor filter
i find a results can check that ?

thank you
George
Your approach would be valid if you had a filter circuit that was been driven by a voltage source V=|Vo.sin(ωt)| with a source impedance of Rs. Unfortunately that is not the case. Current can only flow when Vs>Vo because of the diode. For your maths to be correct current must be able to flow back to the source when Vo>Vs. Fourier analysis works on linear circuits, and this isn't.
In most cases the approximation Vripple_peak-to-peak = It/C will suffice. If Rs is high then it will be less accurate as it assumes that the capacitor charges instantly once per half cycle, and the current is a δ-function.

#### Papabravo

Joined Feb 24, 2006
20,399
Your approach would be valid if you had a filter circuit that was been driven by a voltage source V=|Vo.sin(ωt)| with a source impedance of Rs. Unfortunately that is not the case. Current can only flow when Vs>Vo because of the diode. For your maths to be correct current must be able to flow back to the source when Vo>Vs. Fourier analysis works on linear circuits, and this isn't.
In most cases the approximation Vripple_peak-to-peak = It/C will suffice. If Rs is high then it will be less accurate as it assumes that the capacitor charges instantly once per half cycle, and the current is a δ-function.
In fact, the leading edge of the diode current is sharp and after reaching its peak, the falling "edge" has a distinctly rounded aspect. The width of the current pulse is not approximated very well by a delta function. This can also be seen in the simulation.

ETA: I saw the diode waveform but did not include it in the image I posted. I can do that upon request.

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#### Ian0

Joined Aug 7, 2020
8,407
In fact, the leading edge of the diode current is sharp and after reaching its peak, the falling "edge" has a distinctly rounded aspect. The width of the current pulse is not approximated very well by a delta function. This can also be seen in the simulation.
But if the tolerance on your smoothing cap is +80%-20% then it is probably close enough.

#### aragon1971

Joined Apr 7, 2008
126
But if the tolerance on your smoothing cap is +80%-20% then it is probably close enough.
thank you!!! is valid for RL filter ??

#### ericgibbs

Joined Jan 29, 2010
18,053
thank you!!! is valid for RL filter ??
Hi 1972,
The tolerances of all smoothing components effects all types of ripple reduction.

E

#### Ian0

Joined Aug 7, 2020
8,407
thank you!!! is valid for RL filter ??
- unlikely, because it is a non-linear system because of the diode.