# Definition of Modulation index

In order for proper AM to occur, the modulating signal voltage Vm must be less than the carrier voltage Vc.  Therefore, the relationship between the amplitudes of the modulating signal and carrier is important.  This relationship is expressed I the terms of a ratio known a the modulation index m. Modulation index is also called modulation factor, modulation coefficient , or the degree of modulation.

Modulation index is simply the ratio of the modulated signal voltage to the carrier voltage.

m = Vm / Vc

## Explanation:

The modulation index should be a number between 0 and 1.  If the amplitude of the modulating voltage is higher than the carrier voltage, m will be greater than 1. This will cause sever distortion of the modulated waveform.  This is shown in below figure. Here a sine have information signal modulates a sine wave carrier, but the modulating voltage is much greater than the carrier voltage.  This condition is called over modulation. As you can see, the waveform is flattened near the zero line.  The received signal will produce an output waveform in the shape of the envelope, which in this case is a sine wave whose negative peaks have been clipped off.  By keeping the amplitude of the modulating signal less than the carrier amplitude, no distortion will occur.  The ideal condition for AM is where Vm = Vc or m = 1, since, this will produce the greatest output at the receiver with no distortion.

(a) Distortion of the envelop caused by over modulation where the modulating signal amplitude Vm is greater than the carrier signal Vc

The modulation index can be determined by measuring the actual values of the modulation voltage and the carrier voltage and computing the ratio.  However, it is more common to compute the modulation index from measurements taken of the composite modulated wave itself.  Whenever the AM signal is displayed on an oscilloscope, the modulation index can be computed from Vmax and Vmin as shown in figure (b).

(b) An AM wave showing peaks (Vmax) and troughs (Vmi)

The peak value of the modulating signal Vm is one-half the difference of the peak and trough values and is computed with the expression.

Vm = Vmax – Vmin / 2

By observing the figure (b), you can see Vmax is the peak value of the signal during modulation, while Vmin is the lowest value, or trough, of the modulated wave.  The Vmax is one-half the peak-to-peak value of the modulating signal.  One half of that, of course, is simply the peak value.

The peak value of the carrier signal Vc is the average of the Vmax and Vmin values and is computed with the expression.

Vc = Vmax + Vmin /2

Substituting these values in our original formula for the modulation index produces the result

m=Vmax-Vmin / Vmax+Vmin

The values for Vmax and Vmin can be read directly from an oscilloscope screen and plugged into the formula to compute the modulation index.

For example, suppose that the Vmax value read from the graticule on the oscilloscope screen is 4.6 divisions and Vmin is 0.7 divisions.  The modulation index is then

m= 4.6-0.7 / 4.6+0.7

=3.9 / 5.3

=0.736