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Registered Member #190
Joined: Fri Feb 17 2006, 12:00AM
Location:
Posts: 1567
I know that the voltage on a capacitor subjected to a step-impulse is
V = Vmax*(1 - exp(-t/RC)) where Vmax is the charging voltage.
Is there a formula when the charging function is a rectified sine function? I want to know the theoretical expression for controlling the peak voltage I can obtain on a capacitor if it is constantly being discharged by a load resistor while charging.
If I remember correctly from mathematics I should be able to deveop a laplace transform for the RC circuit and apply a sine function. I just don't know where my book is now. If I find it I will post my own solution.
Edit: Not a transform function, but this may be close enough:
Registered Member #162
Joined: Mon Feb 13 2006, 10:25AM
Location: United Kingdom
Posts: 3141
A rectified sinewave feeding a capacitor and load is not a simple analysis; the reference that you gave assumes zero source/diode/capacitor impedance - which is unlikely,
With very light loading there will be almost no ripple and Vdc = srqt(2) x Vac Useful for instrumentation purposes. The load (resistor) is to allow Vdc to decay quickly enough to follow decreasing changes in Vac Increasing Vac will immediately result in increased Vdc.
With heavy loading such as a simple transformer/rectifier/capacitor/load the waveforms (especially current) are quite complex so they are normally considered separately; -Ripple Voltage (approximated as per the reference you gave) Required to ensure a minimum source/supply voltage and appropriate ripple rejection. -Ripple current to choose capacitor size/type -dc current to choose the rectifier(s) -Transformer regulation to estimate dc output drop with increasing load -etc. etc.
Usually take Transformer VAR = Vac x Iac, Vdc=1.4 x Vac and Idc=0.62 Iac
Registered Member #32
Joined: Sat Feb 04 2006, 08:58AM
Location: Australia
Posts: 549
IamSmooth wrote ...
If I remember correctly from mathematics I should be able to deveop a laplace transform for the RC circuit and apply a sine function. I just don't know where my book is now. If I find it I will post my own solution.
The trouble is, the Laplace transformation is for linear analysis. A diode used for rectification is very nonlinear.
I think I know what you mean but would you please draw the exact circuit you have in mind?
Registered Member #32
Joined: Sat Feb 04 2006, 08:58AM
Location: Australia
Posts: 549
The only reason the average DC value of the output would be different from that of a usual rectified sine wave is if the voltage source has an output impedance. Of course, it does but you need to model that.
To work this out in practice, I'd think about the long term average current entering and leaving the circuit.
Edit: That first paragraph isn't completely true. I've also been thinking about how to work this out analytically. There might be a simpler way but this is complicated. I really suggest you play with a simulation but if you really want I'll post some of my thoughts.
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putting a cap on the peak capacitor voltage
