Ripple factor and efficiency

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Derive the Ripple factor and efficiency in case of half wave and full wave rectifier circuit. 

Ripple factor: - Ripple factor is the ratio of RMS value of AC component present in the rectified output to the average value of rectified output. it is  dimensionless quantity. 

Rectification efficiency:- it is a quantitative measurement of rectifier efficiency . it is ratio of DC power output to AC power input to the rectifier. it is denoted and expressed in percentage. 

Derivation of Ripple factor:
By definition, The RMS value of total load current is given by

Irms = √(Idc)^2+ (Iac) ^2

(or)

Iac = √Irms ^2+ Idc^2

When the above equation is divided by using Idc then we can get the following equation.

Iac / Idc = 1/ Idc √I2rms + I2dc

However, here Iac / Idc is the ripple factor formula

R.F = 1/ Idc √I2rms + I2dc = √ (Irms / Idc)2 -1

Ripple Factor of Half Wave Rectifier
For half-wave rectifier,

Irms = Im/2

Idc = Im/ π

We know the formula of R.F = √ (Irms / Idc)2 -1

Substitute the above Irms & Idc in the above equation so we can get the following.

R.F = √ (Im/2 / Im/ π)2 -1 = 1.21

Ripple Factor of Full Wave Rectifier
For full-wave rectifier,

Irms = Im/√ 2

Idc = 2Im / π

We know the formula of R.F = √ (Irms / Idc)2 -1

Substitute the above Irms & Idc in the above equation so we can get the following.

R.F = √ (Im/√ 2/ 2Im / π)2 -1 = 0.483

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