

Frequency Component of single-phase Half-Wave Rectifier Voltage and Current
The load current IL consist of a dc component IL(dc) and an ac component IL(ac). The Fourier series of the Half-Wave rectifier rectified current following through the load is found to be
iL = ILM(1/ π + sinωt/2 – 2 cos 2 ωt/3π – 2 cos 4 ωt /15 π + ……………)
As seen the Half-Wave rectifier current consists of a large number of ac components (which constitute the ripple) in addition to the dc component. The first term is ILM/2 which represents the dc component IL(dc). Sin ωt has a peak value of (ILM/2). It is called the fundamental or first harmonic component and it’s rms value is
IL1 = ILM/2√2
The third term represents the second harmonic component whose frequency is doubled that of the supply frequency. The rms value is
IL2 = peak value/√2 = 2ILM/3π× √2 = √2 ILM /3π.
The fourth terms represents the third harmonics component whose frequency is four times the supply frequency. It’s rms value is
2 ILM/15π × √2 = √2× ILM / 15 π.
The rms values of other components can be similarly calculated, However, they found to be of continuously diminishing value.
The rectified output (or load ) current consist of
(i) dc component, IL(dc) = ILM/π
(ii) ac component of rms value IL1, IL2 and IL3 etc. Their combined rms is given by
IL(ac) = √IL12+ IL22 + IL32 +…………
The rms (or effective) value of the total load current is given by
IL = √IL(dc)2 + IL(ac)2
= √IL(dc)2 + (IL12 + IL22 + IL32 + ……..)
Similarly, the Fourier series of the load voltage is given by
UL = VLM (1/π + sin ωt/2 – 2cos 2 ωt/3 π – 2 cos 4 ωt/15 π……..)
It also consist of
(i) a dc component, VL(dc) = VLM/π
(ii) ac component of rms value VL1, VL2 and VL3 etc. which are given by
VL1 = VLM/2√2,
VL2 = √2.VLM/3 π,
VL3 = √2VLM/15 π etc.
Again,
VL(ac) = √VL12 + VL22 +VL32 + ……
The rms value of entire load voltage is given by
V = √VL(dc)2 + VL(ac)2 = √VL(dc) + VL12 + VL22 +VL32 + ……
Related Topic
- Single-phase half-wave rectifier
- AVERAGE AND RMS VALUE OF SINGLE-PHASE HALF-WAVE RECTIFIER
- Efficiency of single-phase half-wave rectifier
- Ripple Factor of single phase Half-Wave rectifier
- Peak Inverse Voltage (PIV) of single phase half wave rectifier
- Peak current of single phase half wave rectifier
- Transformer Utilization Factor (TUF) of single phase half wave rectifier
- Advantage and Disadvantage of single-phase half-wave rectifier