A single-phase, full-bridge diode rectifier fed from a 230 V, 50 Hz sinusoidal source supplies a series combination of finite resistance, R, and a very large inductance, L. The two most dominant frequency components in the source current are

Correct Answer: 50 Hz, 150 Hz

Step-by-step Explanation:

1. Analysis of the Load and Current Behavior:
The rectifier is a single-phase full-bridge diode rectifier connected to a source with a frequency of:
$f=50\text{ Hz}$
The load consists of a series combination of a finite resistance, $R$, and a very large inductance, $L$. Because the inductance is very large ($L\to \infty$), it acts as a constant current source that filters out all AC ripple. Thus, the load current (DC output current) is smooth and constant, represented as $I_d$.

2. Deriving the Source Current Waveform:
During the positive half-cycle of the AC source voltage, diodes $D_1$ and $D_2$ conduct, causing the source current $i_s\left(t\right)$ to be equal to $+I_d$.
During the negative half-cycle of the AC source voltage, diodes $D_3$ and $D_4$ conduct, causing the source current $i_s\left(t\right)$ to be equal to $-I_d$.
As a result, the source current $i_s\left(t\right)$ is a symmetrical square wave with an amplitude of $I_d$ and a time period equal to the source voltage period.

3. Fourier Series Analysis of the Source Current:
A symmetrical square wave can be expressed in terms of its Fourier series expansion as:
$$i_s\left(t\right)=\frac{4I_d}{\pi }(sin(\omega t)+\frac{1}{3}sin(3\omega t)+\frac{1}{5}sin(5\omega t)+...)$$
Here, the angular frequency of the source is $\omega =2\pi f$.

4. Identifying the Dominant Frequencies:
The Fourier series shows that the source current contains only odd harmonic components:
$$f_n=nf\text{ where }n=1,3,5,7,...$$
The amplitude of each harmonic component is inversely proportional to its order ($1/n$). The two components with the largest amplitudes (the most dominant components) are:
- The fundamental component ($n=1$): $f_1=1\times 50\text{ Hz}=50\text{ Hz}$
- The third harmonic component ($n=3$): $f_3=3\times 50\text{ Hz}=150\text{ Hz}$

Therefore, the two most dominant frequency components in the source current are 50 Hz and 150 Hz.