13 Jul 2026

Determination of Modulation Index of an AM Wave Using CRO

practical pg-iii communication amplitude-modulation modulation-index

Aim

To generate an amplitude-modulated wave and determine its modulation index from the envelope observed on a CRO.

Apparatus

AM trainer or function generators, carrier oscillator, audio-frequency oscillator, modulator circuit, CRO, frequency counter, and connecting leads.

Experimental arrangement

The message and carrier signals are applied to the AM modulator; the modulated envelope is observed on the CRO.

Theory

An information or message signal is usually a low-frequency signal, while an antenna radiates efficiently at a much higher carrier frequency. In amplitude modulation the carrier amplitude is varied in proportion to the instantaneous message voltage, while the carrier frequency remains constant.

For a sinusoidal message,

\[s(t)=A_c[1+m\cos(\omega_m t)]\cos(\omega_c t),\]

where $m$ is the modulation index. The envelope has maximum and minimum amplitudes

\[V_{max}=A_c(1+m),\qquad V_{min}=A_c(1-m).\]

Hence the modulation index obtained from the CRO envelope is

\[m=\frac{V_{max}-V_{min}}{V_{max}+V_{min}}.\]

For $m\leq1$ the envelope does not cross zero. If $m>1$, overmodulation causes envelope distortion.

Observations

Carrier frequency: $100$ kHz; message frequency: $1$ kHz.

Message amplitude (V)	$V_{max}$ (V)	$V_{min}$ (V)	Modulation index $m$
0.50	3.00	2.00	0.20
1.00	4.00	1.00	0.60
1.50	5.00	0.00	1.00

Graph

The upper and lower envelope amplitudes are used to determine the modulation index.

Calculation

For the middle reading,

\[m=\frac{4.00-1.00}{4.00+1.00}=0.60.\]

Thus the percentage modulation is $60\%$.

Result

The modulation index of the AM wave for the selected message amplitude is

\[\boxed{m=0.60\ \text{or}\ 60\%}.\]

Viva Questions

1. What is modulation? It is the controlled variation of a carrier by an information signal.
2. What does $m=1$ mean? The carrier is 100 percent modulated and the envelope just reaches zero.
3. What happens for $m>1$? The envelope is overmodulated and the recovered signal is distorted.