Half Wave Rectifier Circuit Diagram & Working Principle
Half Wave Rectifier Formula
We will now derive the various formulas for a half wave rectifier based on the preceding theory and graphs above.
Ripple Factor of Half Wave Rectifier
‘Ripple’ is the unwanted AC component remaining when converting the AC voltage waveform into a DC waveform. Even though we try out best to remove all AC components, there is still some small amount left on the output side which pulsates the DC waveform. This undesirable AC component is called ‘ripple’.
To quantify how well the half-wave rectifier can convert the AC voltage into DC voltage, we use what is known as the ripple factor (represented by γ or r). The ripple factor is the ratio between the RMS value of the AC voltage (on the input side) and the DC voltage (on the output side) of the rectifier.
The formula for ripple factor is:
Which can also be rearranged to equal:
The ripple factor of half wave rectifier is equal to 1.21 (i.e. γ = 1.21).
Note that for us to construct a good rectifier, we want to keep the ripple factor as low as possible. This is why we use capacitors and inductors as filters to reduce the ripples in the circuit.
Efficiency of Half Wave Rectifier
Rectifier efficiency (η) is the ratio between the output DC power and the input AC power. The formula for the efficiency is equal to:
The efficiency of a half wave rectifier is equal to 40.6% (i.e. ηmax = 40.6%)
RMS value of Half Wave Rectifier
To derive the RMS value of half wave rectifier, we need to calculate the current across the load. If the instantaneous load current is equal to iL = Imsinωt, then the average of load current (IDC) is equal to:
Where Im is equal to the peak instantaneous current across the load (Imax). Hence the output DC current (IDC) obtained across the load is: