# Full Wave Bridge Rectifier: the RMS current through a diode

#### dvep

Joined Jan 23, 2012
4
Hi,

Could someone point me in the right direction as to how to calculate the RMS current through a diode on a bridge rectifier w/capacitor, starting with an expression for the current using sin and cos, I am completely stuck on how to do this.
These equations are given which are from wiki:

http://i1225.photobucket.com/albums/ee382/jon_jon_19/rmsdiode.jpg

Once this is found I am meant to calculate the rms current through the single phase synchronous generator which follows a cosine v=Vpcoswt. the voltage at the terminals is perfectly sinusoidal and all components are assumed ideal.

Would appreciate any help!
thanks!

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#### bountyhunter

Joined Sep 7, 2009
2,512
If this is a sine wave fed to a FWB followed by a capacitor, the current waveforms through the diodes is an extremely complex calculation which I am not certain can be done in closed form. The diodes only conduct for a narrow time interval in pulses that used to be called haversine pulses and are NOT sinusoidal but look more like a "bent" half of a sine wave. The current pulses change shape based on current because they get wider. I have no idea how to generate equations for them.

#### studiot

Joined Nov 9, 2007
4,998
I am completely stuck on how to do this.
Hello dvep and welcome to All About Circuits.

I am not suprised you are stuck. Please post the question you are attempting, along with any thoughts, rather than some wiki reference.

#### crutschow

Joined Mar 14, 2008
33,342
The peak current through a diode is shown near the page bottom of this reference. The peak diode current is determined by the DC load current, the filter capacitor value, the transformer equivalent winding resistance (secondary plus reflected primary), and the diode resistance. It's not a simple calculation. From that you can calculate the RMS value of this pulse of current. You may want to simplify this calculation using an approximate wave-shape such as a trapezoid pulse.

#### dvep

Joined Jan 23, 2012
4
I have worked the average diode current to be http://i1225.photobucket.com/albums/ee382/jon_jon_19/avdiodei.png
by integrating the diode current and dividing by the period.

However, what are the steps to find the RMS current? And where do those equations come into it?

A small water turbine provides lighting.
In the question I am given a water turbine speed (rpm), the number of poles and RMS output voltage for the generator, and the light bulbs power rating, voltage and allowable ripple.

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#### bountyhunter

Joined Sep 7, 2009
2,512
I have worked the average diode current to be http://i1225.photobucket.com/albums/ee382/jon_jon_19/avdiodei.png
by integrating the diode current and dividing by the period.

However, what are the steps to find the RMS current? And where do those equations come into it?
I recall there is a formal definition of "RMS" which is some sort of squared integral function. Problem is, you need a concise function for the current to do the math on it. I think this is one of those things best solved by a computer that can do point by point integration.

#### MrChips

Joined Oct 2, 2009
29,824
The RMS value is the square-root of the integral of the square of the current over one period.

#### dvep

Joined Jan 23, 2012
4
The RMS value is the square-root of the integral of the square of the current over one period.
Do you mean the root of the integral of the square of the average diode current or the peak current?

#### MrChips

Joined Oct 2, 2009
29,824
The RMS value is the square-root of the integral of the square of the instantaneous current over one period, i.e. the exact current value at that instant. (You need to know the exact shape of the current pulse - which is not easy to find.)

#### thatoneguy

Joined Feb 19, 2009
6,359
A small water turbine provides lighting.
In the question I am given a water turbine speed (rpm), the number of poles and RMS output voltage for the generator, and the light bulbs power rating, voltage and allowable ripple.

Find the current drawn by the light bulb by dividing the wattage of the light bulb by the RMS voltage.

Then use that to calculate ripple with whatever size capacitor you have, taking into account the frequency of the input, derived from the RPM and number of poles.

Does that help?

#### t_n_k

Joined Mar 6, 2009
5,455
If this is a sine wave fed to a FWB followed by a capacitor, the current waveforms through the diodes is an extremely complex calculation which I am not certain can be done in closed form. The diodes only conduct for a narrow time interval in pulses that used to be called haversine pulses and are NOT sinusoidal but look more like a "bent" half of a sine wave. The current pulses change shape based on current because they get wider. I have no idea how to generate equations for them.
Some time ago The Electrician posted a link to what appears to be a valid closed form solution.

http://powerelectronics.com/power_m...ullwave_rectifiers_capacitor_filter_20100101/

The authors themselves concede that a computer based numerical solution of the proposed closed form equations would be preferred to a paper based exact approach.

#### bountyhunter

Joined Sep 7, 2009
2,512
I didn't see anything about the RMS current, but the equations are pretty thick. That really is a job for a computer (or a grad student).

#### t_n_k

Joined Mar 6, 2009
5,455
Yes it looks pretty convoluted. I think one has to first find the conduction time and conduction intervals from the the equations. Then one presumably solves for the current using a transient analysis method.

I've never had the inclination to do the laborious work. Even transcribing the equations into a program to solve them seems hardly worth the effort.

I recollect in the past I used to approximate the capacitor charging current as a triangular shaped spike with some reasonable assumptions used to determine the conduction time/interval.