AMPLITUDE MODULATION 

Amplitude modulation uses the instantaneous amplitude of a modulating signal (voice, music, data, etc.) to
directly vary the amplitude of a carrier signal. Modulation index, m, is used to describe the ratio of maximum
voltage to minimum voltage in the modulated signal. If the modulating signal is equal in magnitude to the carrier,
then m = 1 and the modulated signal varies from a scaled maximum of unity down to zero (see figure below). When
m = 0, no modulation of the carrier is performed. If m is greater than 1, the carrier is actually cut off for
some period of time, and unwanted harmonics are created at the transmitter output.
In the frequency domain, the carrier frequency is flanked on both sides by mirror image copies of the
modulating signal. w_{M1 } = w_{c}±w_{m1}, w_{M2} = w_{c}±w_{m2}

AM General Equation 
Let the carrier be x_{c}(t) = X_{c}·cos (w_{c}t),
and the modulating signal be
x_{m}(t) = X_{m}·cos (w_{m}t) 
Then x(t) = X_{c}·[1+m·cos (w_{m}t)]·cos (w_{c}t) 
Modulation Index 
m = 
Vmax  Vmin Vmax + Vmin 

In the following examples, the carrier frequency is eleven time the modulation frequency. Red (dashed)
lines represent the modulation envelope. Blue (solid) lines represent the modulated carrier. 
100% Modulation  
Here, the maximum voltage (Vmax) is 2 V and the minimum (Vmin) is 0 V. From the modulation index formula:

50% Modulation  
Here, the maximum voltage (Vmax) is 3 V and the minimum (Vmin) is 1 V. From the modulation index formula:

25% Modulation  
Here, the maximum voltage (Vmax) is 1.25 V and the minimum (Vmin) is 0.75 V. From the modulation index formula:
m = 
1.25  0.75 1.25 + 0.75 
= 0.25 

150% Modulation  
Here, the maximum voltage (Vmax) is 2.5 V and the minimum (Vmin) is 0.5 V. From the modulation index formula:
m = 
2.5  (0.5) 2.5 + (0.5) 
= 1.5 

Note: AM waveforms created with MathCAD 4.0 software.
Class 
Conduction Angle 
Maximum Efficiency 
Description 
A 
360º 
25% 
Device is biased in to conduct in the linear region all the time. 
AB 
> 180º, << 360º 
 
Two devices connected like a Class B, but biased to conduct somewhere between Class A and Class B. 
B 
180º 
78.5% 
Two devices in series with the output taken at the common junction. Both devices biased to conduct in the
linear region for opposite half a cycle, i.e., they are never on at the same time. 
C 
> 0º, < 180º 
 
Device is biased to turn on after a certain input threshold voltage is exceeded. Very efficient, but creates
distortion. 
D 

100% 
Used to switch completely on or completely off. 
E 


Used for rectangular input signals. 

