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Sec. 4–9 Nonlinear Distortion 263
will subtract from the linearly amplified component at f 1 , thus producing a saturated
characteristic for the sinusoidal component at f 1 . For an amplifier that happens to have the
particular nonlinear characteristic shown in Fig. 4–6, the intercept point occurs for an RF
input level of -10 dBm. Overload characteristics of receivers, such as those used in police
walkie-talkies, are characterized by the third-order intercept-point specification. This dBm
value is the RF signal level at the antenna input that corresponds to the intercept point. When
the receiver is deployed, input signal levels need to be much lower than that value in order to
keep the undesired interfering intermodulation signals generated by the receiver circuits to an
acceptable level. For transmitter applications, the intercept-point specification is the output
signal level corresponding to the intercept point.
Other properties of an amplifier are also illustrated by Fig. 4–6. The gain of the amplifier
is 25 dB in the linear region, because a -60- dBm input produces a -35- dBm output
level. The desired output is compressed by 3 dB for an input level of -15 dBm. Consequently,
the amplifier might be considered to be linear only if the input level is less than -15 dBm.
Furthermore, if the third-order IMD products are to be down by at least 45 dBm, the input
level will have to be kept lower than -32 dBm.
Another term in the distortion products at the output of a nonlinear amplifier is called
cross-modulation. Cross-modulation terms are obtained when one examines the third-order
products resulting from a two-tone test. As shown in Eqs. (4–50) and (4–51), the terms
3
3
and
are cross-modulation terms. Let us examine the term
3
If we allow some amplitude variation in the input signal A 1 sin v 1 t, so that it
2 K 3A 2 2 K 2
2 K 3A 2 1 A 2 sinv 2 t 3A 1 A 2 sin v 1 t
1 A 2 sinv 2 t.
looks like an AM signal A 1 [1 + m 1 (t)] sin v 1 t, where m 1 (t) is the modulating signal, a thirdorder
distortion product becomes
3
2 K 3A 2 1 A 2 [1 + m 1 (t)] 2 sin v 2 t
(4–53)
Thus, the AM on the signal at the carrier frequency f 1 will produce a signal at frequency f 2
with distorted modulation. That is, if two signals are passed through an amplifier having thirdorder
distortion products in the output, and if either input signal has some AM, the amplified
output of the other signal will be amplitude modulated to some extent by a distorted version
of the modulation. This phenomenon is cross-modulation.
Passive as well as active circuits may have nonlinear characteristics and, consequently,
will produce distortion products. For example, suppose that two AM broadcast stations have
strong signals in the vicinity of a barn or house that has a metal roof with rusted joints. The roof
may act as an antenna to receive and reradiate the RF energy, and the rusted joints may act as a
diode (a nonlinear passive circuit). Signals at harmonics and intermodulation frequencies may
be radiated and interfere with other communication signals. In addition, cross-modulation
products may be radiated. That is, a distorted modulation of one station is heard on radios
(located in the vicinity of the rusted roof) that are tuned to the other station’s frequency.
When amplifiers are used to produce high-power signals, as in transmitters, it is desirable
to have amplifiers with high efficiency in order to reduce the costs of power supplies,
cooling equipment, and energy consumed. The efficiency is the ratio of the output signal
power to the DC input power. Amplifiers may be grouped into several categories, depending
on the biasing levels and circuit configurations used. Some of these are Class A, B, C, D, E, F,
G, H, and S [Krauss, Bostian, and Raab, 1980; Smith, 1998]. For Class A operation, the bias
on the amplifier stage is adjusted so that current flows during the complete cycle of an applied