Half Wave Rectifier : Part2

1.6 D.C. Power Output (P_DC)

       The d.c. power output can be obtained as,

1.7  A.C. Power Input (P_AC)

       The power input taken from the secondary of transformer is the power supplied to three resistances namely load resistance R_L, the diode resistance R_f and winding resistance R_s. The a.c. power is given by,

1.8 Rectifier Efficiency (η)

       The rectifier efficiency is defined as the ratio of output d.c. power to input a.c. power.

       If (R_f  + R_s) << R_L as mentioned earlier, we get the maximum theoretical efficiency of half wave rectifier as,

       Thus in have wave rectifier, maximum 40.6 % a.c. power gets converted to d.c. power in the load. If the efficiency of rectifier is 40% then what happens to the remaining 60% power. It is present interms of ripples in the output which is fluctuating component present in the output.

Note : Thus more the rectifier efficiency, less are the ripple contents in the output.

1.9 Ripple Factor (γ)

       It is seen that the output  of half wave rectifier is not pure d.c. but a pulsating d.c. The output contains pulsating components called ripples. Ideally there should not be any ripples in the rectifier output. The measure of such ripples present in the output is with the help of a factor called ripple factor denoted by γ. It tells how smooth is the output.

Note : Smaller the ripple factor closer is the output to a pure d.c.

       The ripple factor expresses how much successful the circuit is, in obtaining pure d.c. from a.c. input.

Definition :

       Mathematically ripple factor is defined as the ratio of R.M.S. value of the a.c. components in the output to the average or d.c. components present in the output.

       Now the output current is is composed of a.c. component as well as d.c. component.

       Let             I_ac = R.M.S. value of a.c. component present in output
                         I_DC = D.C. component present in output
                         I_RMS = R.M.S. value of total output current
.^..                      I_RMS  = √ (I_AC² +I_DC²)
.^..                      I_ac = √ (I_RMS² +I_DC²)

       This is the general expression for ripple factor and can be used for any rectifier circuit.
       Now for a half wave circuit,

       This indicates that the ripple contents in the output are 1.211 times d.c. component i.e. 121.1% of d.c. component.

Note : The ripple factor for half wave is very high which indicates that the half wave circuit is a poor converter of a.c. to d.c.

       The ripple factor is minimized using filter circuits along with the rectifiers.

1.10 Load Current

       The load current I_L which is composed of a.c. and d.c. component can be expressed using Fourier series as,

       This expression shows that the current may be considered to be the sum of an infinite number of current components, according to Fourier series.

       The first term of the series is the average or d.c. value of the load current. The second term is a varying component having frequency same as that of ac.c supply voltage. This is called fundamental component of the current having frequency same as the supply. The third term is again a varying component having frequency twice the frequency of supply voltage. This is called second harmonic component. Similarly all the other terms represent the a.c. components and are called harmonics.

       Thus ripple in the output is due to the fundamental component along with the various harmonic components. And the average value of the total pulsating d.c. is the d.c. value of the load current, given by the constant term in the series, I_m/π.