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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.

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.

In the frequency domain, the carrier frequency is flanked on both sides by mirror image copies of the modulating signal.

Ω_M1 = Ω_c ± ω_m1, Ω_M2 = Ω_c ± Ω_m2

Frequency modulation (FM) spectrum - RF Cafe

AM General Equation

Let the carrier be x_c(t) = X_c·sin (Ω_ct),
and the modulating signal be x_m(t) = X_m·sin (ω_mt)

Then x(t) = X_c·[1+m·sin (Ω_mt)]·sin (Ω_ct)

Modulation Index

m =

Vmax - Vmin
Vmax + Vmin

In the following examples, the carrier frequency is nine times the modulation frequency. Red (dashed) lines represent the modulation envelope. Blue (solid) lines represent the modulated carrier.

100% Modulation

100% amplitude modulation (AM) graph - RF Cafe

Here, the maximum voltage (Vmax) is 2 V and the minimum (Vmin) is 0 V. From the modulation index formula:

m =

2 - 0
2 + 0

= 1.0

50% Modulation

50% amplitude modulation (AM) graph - RF Cafe

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

m =

3 - 1
3 + 1

= 0.5

25% Modulation

25% amplitude modulation (AM) graph - RF Cafe

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

150% amplitude modulation (AM) graph - RF Cafe

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.

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