Intermodulation distortion (IMD) can wreak havoc in modern wireless-communications systems. The better it is understood, the better its effects can be minimized. IMD can be described by examining the linearity of a two-port network. This study of IMD will explore the relationship between the intercept points and the coefficients of the polynomial that is used to model the transfer function of an amplifier.

Increasingly crowded spectrum brings with it greater possibility of interference. As a result, system designers are striving to reduce interference susceptibility, for example, through improved linearity. A system's linearity governs how much IMD will occur within it, which in turn can create interference. Through improved linearity of the system building blocks, the overall susceptibility of a system to interference can be decreased.

IMD occurs as two or more signals pass through a two-port network with a nonlinear transfer function. The spectrum at the output of the device is comprised of the original signals and additional spurious signals. The additional spurious signals can cause interference within the original system or in other systems. When the spurious signals are of sufficient amplitude, they can overpower the signal of interest, resulting in interference and, in extreme cases, loss of transmitted information, such as voice, data, or video. The undesirable effects of IMD can be mitigated, by improving the linearity of system components (amplifiers, other semiconductors, and even passive elements), which cause IMD.

To understand IMD, consider a two-port network, such as an amplifier, with the nonlinear transfer function as shown in Fig. 1:

where:
c₀ = the DC offset;
c₁ = the voltage gain; and
{c₂,c₃,...c_n} = the nonlinear distortion coefficients.

This article will focus on linear, second-order and third-order terms, although the analysis is similar for higher-order terms.

Let a test signal, v_in, be the superposition of two sinusoids of unequal frequency, that is:

where s₁(t) and s₂(t) are signals in a different system, or they may originate from other sources within the same system. This analysis assumes un-modulated test tones for simplicity, although the same processes occur when modulated signals pass through nonlinear circuitry.

If the test signal s(t) is applied to the nonlinear two-port network, the result is:

Using the trigonometric identity,

The second-order term can be expanded as:

Notice that the output consists of frequency components that were not present in the input. The second-order term in the power series produces harmonic distortion of both input sinusoids. It also produces mixing terms. Note that the mixing terms simply represent upconversion and downconversion processes. Additionally, a DC offset is produced. The down-conversion term can pose problems in heterodyne receivers because it can interfere with the desired signal at the intermediate frequency (IF). In a transmitter, the mixing terms and the harmonic distortion terms can be problematic in that they may cause it to transmit energy within other portions of the spectrum, blocking or interfering with desired signals at those other frequencies. DC terms can cause problems in homodyne receivers by saturating the DC-coupled baseband amplifiers.

The same trigonometric identity can be used to expand the third-order terms yielding:

Like the second-order term, the third-order term produces spurious signals in the output that were not present in the input. The third-order term produces scaled copies of the original signal (amplitude distortion), harmonic distortion, and mixing terms. The difference mixing terms form new signals that are spectrally close to the original signals, making them difficult to remove with filters. In fact, they may fall within the passband of the system and cause interference. Here again, the sum mixing terms and the harmonic distortion terms may cause a transmitter to transmit in adjacent bands inadvertently. The amplitude distortion is unacceptable in systems that use higher-order modulation schemes such as 16-state quadrature amplitude modulation (16QAM), because the distortion results in an error component in the received vector, degrading the receiver's bit-error rate (BER). A spectral plot of the output that might be seen on a spectrum analyzer is shown in Fig. 2.

In order to further simplify the analysis, it is customary (though not necessary) to make the amplitude of the input sinusoids equivalent, that is a₁ = a₂ = a. The coefficients of the linear, second-order IMD, and third-order IMD terms become:

respectively.

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