The rectifier charges the filter capacitor to the peak value of the input sine wave minus any IR drop from the transformer and the forward drop of the rectifier(s).Hi!
I'm studying Full-wave rectifier. How would one mathematicaly descibe effect of smoothing capacitor on output voltage waveform?
Hi,Hi!
I'm studying Full-wave rectifier. How would one mathematicaly descibe effect of smoothing capacitor on output voltage waveform?
Here is Full-wave rectifier circuit.Electronic engineers have been doing this for over 100 years. What do you mean you cannot find analytical expression?
http://hyperphysics.phy-astr.gsu.edu/hbase/electronic/rectct.html#c3
How about deriving this yourself by determining the phase angles at which time the rectifier diodes conduct?
As has been stated several times, you model each part of the waveform separately and determine the transition points. If you want to find the Fourier series for this, then use the definition of the Fourier series on the resulting equations.I want to represent rectified waveform mathematically (in terms of Fourier series if it is possible) and then to analyse circuit with capacitor placed in parallel to load resistor in order to find analytical expression for output voltage (red colour). I hope you understand what I mean.
Hi there,Here is Full-wave rectifier circuit.
View attachment 78539
Here are input AC and output DC voltage waveforms:
View attachment 78538
If we put capacitor parallel to our load resistor, output DC voltage waveform would be like this:
View attachment 78540
I want to represent rectified waveform mathematically (in terms of Fourier series if it is possible) and then to analyse circuit with capacitor placed in parallel to load resistor in order to find analytical expression for output voltage (red color). I hope you understand what I mean.
Hi MrAL,Hi there,
I think i understand what you want to do here. It is interesting to do this but it may not relate to the real life circuit as well as we would like to see because the diodes conduct in a very strange way.
To do it the way you want to do it, first note that you would be taking the absolute value of the sine wave to mimic the full wave rectification:
Vs=Vpk*sin(w*t)
Vx=abs(Vpk*sin(w*t))=Vpk*abs(sin(w*t))
Vx is now the full wave rectified sine.
Next, you would find the Fourier series for abs(sin(w*t)) and multiply by Vpk.
Once you have that you would push all the components through the filter one by one, but to make this work you have to assume some series resistance.
The series resistance together with the capacitor and load resistor form the filter:
Vout=Vin*RL/(s*C*RL*Rs+RL+Rs)
where Rs might be very low like 0.1 ohms.
You must compute the effect of the filter for every significant harmonic using that filter equation, and that provides you with an amplitude and phase angle for each harmonic. You can then reconstruct the time wave using those results knowing the time equation for each harmonic is A*sin(n*w*t+ph).
Try this yourself first and see what you can come up with. You should get a DC output with some ripple.
What this does not model is the relatively high impedance of the rectifier bridge when the cap has a higher voltage than the input sine wave. To do that you would have to solve for the start and end of the conduction time and only integrate from the start to end when computing the Fourier series. If you are not interested in too much accuracy this is easy to estimate.