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260
Bandpass Signaling Principles and Circuits Chap. 4
v 0 output
Saturation
level
v i input
Figure 4–5
Nonlinear amplifier output-to-input characteristic.
Then the second-order output term is
K 2 (A 0 sin v 0 t) 2 = K 2
2A 0
(1 - cos 2v
2
0 t)
(4–45)
This indicates that the second-order distortion creates a DC level K 2 A 2 0 >2 (in addition to any
DC bias) and second harmonic distortion with amplitude K 2 A 2 0 >2. In general, for a single-tone
input, the output will be
v out (t) = V 0 + V 1 cos(v 0 t + w 1 ) + V 2 cos(2v 0 t + w 2 )
+ V 3 cos(3v 0 t + w 3 ) + Á
(4–46)
where V n is the peak value of the output at the frequency nf 0 hertz. Then, the percentage of
total harmonic distortion (THD) is defined by
THD (%) = 4 a q n=2 V n 2
V 1
* 100
(4–47)
The THD of an amplifier can be measured by using a distortion analyzer, or it can be evaluated
by Eq. (4–47), with the V n ’s obtained from a spectrum analyzer.
The intermodulation distortion (IMD) of the amplifier is obtained by using a two-tone
test. If the input (tone) signals are
v i (t) = A 1 sin v 1 t + A 2 sin v 2 t
(4–48)