A derivation of the Vdc in a fullwave rectifier with smoothing?

[patric44]

Homework Statement

i had an assignment of deriving the Vdc in a fullwave rectifier with smoothing capacitor

Relevant Equations

Vdc = V average of the discharging part

i was trying to derive the Vdc in a fullwave rectifier with smoothing capacitor , i guess i had it right as my final equation matches the book equation :

Vdc~(1-(1/2fRC))Vp , but i am not really sure that my attempt was completely right as i assumed that Vdc is the average value of the discharging function neglecting the charging part , and i had to take the first 3 terms of the Taylor approximation to get the answer ,
i just want some one to verify my attempt :

 

[patric44]

Any help , i will really appreciate it

 

[patric44]

i just want to know if assuming that the vdc is the average of the discharging function is a good approximation
or not .

 

[rude man]

Yes it is. The diode resistances are very much smaller than the load resistance so the charge-up time is very small compared to the discharge time.

But the charge time is not zero, and depends not only on diode forward voltage drops but also transformer winding resistances. and leakage inductances.