# Understanding Intermodulation Distortion in Broadband Signals

### Key Takeaways

• Intermodulation distortion occurs in nonlinear circuits being sourced with broadband signals.

• Intermodulation distortion arises due to a similar mechanism as harmonic distortion.

• Active and passive circuits can produce intermodulation distortion, and designers should know the input signal limits at which intermodulation distortion becomes too strong.

Intermodulation distortion occurs in high-frequency amplifier systems with modulated signals, and this distortion can reduce download rates significantly.

Nonlinear components and circuits often need to interact with broadband signals without producing distortion. When viewed in the frequency domain, intermodulation distortion can arise when any broadband signal interacts with a nonlinear system, and it’s important to understand how strong distortion peaks can get for a given input signal level. In this article, we’ll present a clear explanation of intermodulation distortion in passive and active systems and an example of what you’ll see in a spectrum analyzer.

## What Is Intermodulation Distortion?

Intermodulation distortion occurs when a broadband signal interacts with a nonlinear system. When a broadband signal is sent into a component with nonlinear impedance, harmonic generation and frequency mixing will occur simultaneously which creates additional peaks in the signal’s power spectrum. These generated peaks are mathematically related to the input signal’s power spectrum, and the additional peaks in the frequency domain produce a distorted signal in the time domain.

### Systems Exhibiting Intermodulation Distortion

A nonlinear system that generates intermodulation distortion could be active or passive. By “nonlinear system,” we could refer to any of the following cases:

• General nonlinear circuits: This includes amplifiers near saturation, diodes and transistors operating near saturation, ferrites exhibiting hysteresis, and photodiodes in photovoltaic mode

• Nonlinear materials: Although normally considered in lasers and optics, unique electronic materials with nonlinear responses will generate intermodulation distortion.

• Rusty bolt effect: Passive components that are normally linear but that have some manufacturing imperfections can create intermodulation distortion (called passive intermodulation) via the “rusty bolt effect.”

RF power amplifiers and precision high-power audio amplifiers are the most common active circuits that generate intermodulation distortion. For passive components and systems, the 3GPP performance standards for 5G electronics set limits on passive intermodulation generated by passive components in base stations.

### Example of Intermodulation Distortion

An example of intermodulation distortion in an FM signal is shown below. Here, the two primary peaks mix in the nonlinear component to produce additional peaks in the frequency domain. In general, an infinite number of additional peaks are generated. Intermodulation peaks are formed through sums and differences of the two primary peaks in the FM signal (shown in red). The most prominent peaks are the third-order intermodulation peaks, which lie closest to the two source peaks in the FM signal.

Intermodulation peaks in FM signal.

In the above graph, the red peaks are the two sidebands for the input FM signal. The orange peaks are called harmonics because they are simple integer multiples of the input sidebands. The blue peaks are the intermodulation peaks. When viewed on a spectrum analyzer, the readout would show a broad band around each peak frequency. The above power spectrum can then be converted back to the time domain with an inverse Fourier transform.

While the above example shows an FM signal (sum of two harmonic signals with matched phase), a similar effect occurs with broadband signals that are continuously distributed in the frequency domain. In this case, we have a much more complex power spectrum that is not composed of discrete peaks.

### Intermodulation Distortion vs. Harmonic Distortion

Intermodulation distortion and harmonic distortion are similar in that they arise due to nonlinear harmonic generation and frequency mixing. They also both produce distortion in the time domain; harmonic distortion is normally seen as clipping, while intermodulation distortion is seen as undesired modulation. Harmonic distortion occurs when a signal is being mixed with itself, and one can imagine the two peaks in the above example being the same frequency. Intermodulation distortion involves mixing among different frequencies, leading to the even and odd set of symmetric peaks shown above.

## Describing Intermodulation Distortion

In general, we can describe intermodulation distortion in terms of an arbitrary nonlinear transfer curve relating the input voltage and output current for a broadband signal. If we define I(V) to be the current as a function of the input signal’s voltage, then its Taylor expansion is:

Nonlinear current vs. voltage relationship expanded as a Taylor series.

If we expand the voltage of the input signal in terms of a set of discrete frequencies (e.g., as the DFT of a discrete temporal signal), we have:

Once the polynomial terms are expanded, we can see how frequencies combine to produce the peaks responsible for intermodulation distortion.

Intermodulation distortion and its generated frequency peaks arise from expanding the polynomial terms in the above equation. Depending on the value of the derivative terms, various sets of intermodulation peaks will have different magnitudes. However, it is generally difficult to eliminate a specific set of intermodulation peaks at all input powers when designing a circuit. SPICE simulation tools can help you visualize signal behavior and quantify intermodulation distortion.

## Simulating and Modeling Intermodulation Distortion

Intermodulation distortion is a nonlinear frequency domain effect, so you can’t spot it simply using transfer functions in a SPICE simulator. Instead, you need to work in the time domain at various signal levels. This can be done with a nonlinear circuit schematic or a general model for a nonlinear current-voltage relationship at the system level. You can use the following process to determine intermodulation distortion from a SPICE simulation:

• Run a transient analysis with an arbitrary broadband input signal source.

• Measure the transformed output voltage/current in the time domain.

• Calculate the Fourier transform of the voltage/current to get a power spectrum.

• Compare the output.

Finally, as the input signal level is swept to higher values, it becomes clear when the third-order intermodulation products are the same intensity as the input signal spectrum (IOP3 point in power amplifiers). Looking at this comparison vs. frequency can help you determine an acceptable maximum input signal level for your nonlinear circuit to ensure intermodulation distortion is minimized.