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Consumers and industrial users are demanding higher rates of wireless connectivity and uninterrupted connections. This would imply the need for a very complex system of transmitters and receivers distributed throughout common environments and in industrial facilities. Such demands require transceiver systems with very high throughput capability across many different frequency bands. The latest modulation standards, such as LTE-Advanced (LTE-A) and WiGig, are designed to meet these demands in the busiest of thoroughfares or facilities.

In the meantime, however, the legacy challenge of dealing with modulation distortions caused by passive components has increased wireless system costs, decreased system performance, and raised the standards of component construction. Passive-intermodulation (PIM) distortions decay data rates, block frequency bands, and are highly costly to pinpoint and repair. Distributed antenna systems (DAS) and small cells are more susceptible to PIM interference that large stand-alone antenna systems. Understanding PIM’s broad-spectrum effects and developing best practices to guard against, may become a necessity for complex antenna systems.

By definition, passive-intermodulation distortion is a complex frequency response that occurs when multiple frequency tones exist along the same signal path and encounter nonlinear junctions. PIM differs from the harmonic products of mixing, as they are usually closer to the frequency band of reception. Modulation-distortion products are a known problem with active nonlinear devices like mixers, circulators, and amplifiers. These components are rigorously designed to limit their distortion products.

The material properties of structures used in the construction of RF/microwave components also can produce nonlinear effects at certain frequencies and under certain conditions. When these nonlinear junctions are present in the signal path of an RF/microwave signal, the signals combine and produce PIM. Mathematically, PIM can be explained using a power series with sinusoidal signals. Eq. 1 is a power series of an amplitude product and an electric signal.

New Modulation Schemes Raise PIM, Eq. 1

The output of such a power series is a simple solution, as indicated in Eq. 2.

New Modulation Schemes Raise PIM, Eq. 2

When a single sinusoidal signal is added to the input of the system, more complex products are produced. The expansion in Eq. 3 demonstrates a harmonic response that grows in frequency as integer multiples of the input sinusoidal signal frequency.

New Modulation Schemes Raise PIM, Eq. 3

The input signal in Eq. 4 is a compound signal of two sinusoidal tones.

New Modulation Schemes Raise PIM, Eq. 4

When two tones are input into a power series, the response is a progression of multiple-order products. This progression is shown in Eq. 5 with only the odd-order products up to the ninth order. The order is determined by the addition of the integers multiplied by the frequency. The amplitude of the signal also is a function of the progression, and decreases as the order increases.

New Modulation Schemes Raise PIM, Eq. 5

In Eq. 5, for example, the integer multiplied by frequency one is 2. The integer multiplied by frequency two is 1. The combination of these two integers is the designation for the third-order intermodulation distortion . These products occur at the combination frequencies and at various power levels. For two tones, the frequencies at which these products occur is dictated by Eq. 6, where m is 1 less than n (Table 1).

New Modulation Schemes Raise PIM, Eq. 6

New Modulation Schemes Raise PIM, Table 1

The power of these unintended signals decreases as the order of the product increases. This is represented mathematically in Eq. 7.

New Modulation Schemes Raise PIM, Eq. 7

Graphically, this appears as a series of impulses at the frequency combinations (Fig. 1). The third-order product is often the product of concern, as it could potentially be of high enough power and within the reception band. This product also could increase the noise floor in the reception band and lower the signal-to-noise ratio (SNR). In doing so, it will directly degrade the throughput performance of high-speed data lines.

New Modulation Schemes Raise PIM, Fig. 1

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