6.3.1 Modulation Factor

When we consider the performance of AM systems, we use a parameter called the modulation factor (m), defined as:

m = \frac{maximum amplitude - minimum amplitude}{maximum amplitude + minimum amplitude}

(6.9)

The modulation can be expressed as a percentage, when it is known as the percentage modulation or the depth of modulation. For sinusoidal modulation the maximum amplitude of the modulation envelope is, from Equation (6.5) and Figure 6.1, V_c+V_m and the minimum amplitude is V_c–V_m so that Equation (6.9) becomes:

m = \frac{(V_{c} + V_{m}) - (V_{c} - V_{m})}{(V_{c} + V_{m}) + (V_{c} - V_{m})} = \frac{V_{m}}{V_{c}}

(6.10)

For envelope detection (Section 6.1.2.3.2), the maximum value of the modulation factor is unity (1) since this gives a minimum value of zero to the envelope. If a larger modulation factor is used, the envelope no longer resembles the modulating waveform. Figure 6.4(a) shows the effect of even a small amount of over-modulation with m=1.2. Figure 6.4(b) shows the resulting distortion once the waveform has been demodulated using envelope detection. For telephone-quality speech the average modulation depth is approximately 50%.

Figure 6.4. Over-modulation of a sinusoidally modulated AM wave with a) the overmodulated carrier and b) the distortion in the demodulated signal.

Since the modulation factor is an important design consideration for a system, the equation for AM, Equation (6.5), is commonly rewritten as:

υ (t) = (1 + m \sin (ω_{m} t)) V_{c} \sin (ω_{c} t)

(6.11)