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

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.

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

Let I

I

I

This is the general expression for ripple factor and can be used for any rectifier circuit.

Now for a half wave circuit,

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

_{ac}= R.M.S. value of a.c. component present in outputI

_{DC}= D.C. component present in outputI

_{RMS}= R.M.S. value of total output current**.**I^{.}._{RMS}= √ (I_{AC}^{2}+I_{DC}^{2})**.**I^{.}._{ac}= √ (I_{RMS}^{2}+I_{DC}^{2})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.

__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.

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