Intermodulation Distortion
You connect a two-tone test signal to an amplifier and look at its output on a spectrum analyzer. Besides the two tones you put in, small extra signals appear just beside them, evenly spaced on either side. Turn the input down by 1 dB and the extra signals drop by 3 dB. Or you are listening to a radio receiver and hear a signal where nothing should be transmitting — and it vanishes when one of two strong nearby transmitters goes off the air. Both are intermodulation distortion: new signals created inside a nonlinear circuit by two real signals mixing together.
Intermodulation distortion (IMD) is one of the most important and most misunderstood phenomena in electronics. It explains why some receivers that look impressive on paper fall apart when strong signals are present, why a spectrum analyzer can show spurious products that are not really there, why audio amplifiers are tested with two tones as well as one, and why RF power amplifiers must stay linear to avoid interfering with neighboring channels. This lesson explains exactly how IMD occurs, which products matter and why, and how to recognize and measure it.
Spectrum showing two signals at 7.020 and 7.025 MHz and their IMD products. Second-order products fall far from the originals (at 5 kHz and 14.045 MHz), but third-order products at 7.015 and 7.030 MHz land right beside the original signals and cannot be filtered.
View LargerWhat is Intermodulation Distortion?
To understand IMD, you first need to understand the difference between an ideal linear device and a real-world nonlinear one. An ideal amplifier or mixer has a perfectly linear transfer function: output = gain × input. Double the input, double the output. This ideal device produces no new frequencies — its output contains only what was present at the input.
Every real electronic device — transistors, diodes, FETs, mixers — departs from this ideal. The relationship between input and output can be modeled mathematically as a power series:
Where:
• a1 is the linear gain term (wanted)
• a2 is the second-order nonlinearity coefficient
• a3 is the third-order nonlinearity coefficient
• Higher-order terms are usually small and often ignored for moderate signal levels
For a single input signal, the nonlinear terms generate harmonics: the second-order term creates a signal at twice the input frequency (2f), the third-order term creates a signal at three times the input frequency (3f), and so on. These are the harmonics you are already familiar with from earlier lessons.
But what happens when two signals are present simultaneously? This is where intermodulation occurs. When two signals at frequencies f1 and f2 are present, the nonlinear terms in the transfer function generate not just harmonics of each individual signal, but also sum and difference frequencies at combinations of f1 and f2. These combination frequencies are the intermodulation products, and the crucial problem is that some of them fall very close to — or directly on — the original signal frequencies, making them impossible to filter without also removing the desired signal.
The magnitude of these IMD products depends on how large the second- and third-order nonlinearity coefficients are (a device property fixed once the circuit is designed) and on the input signal levels (something you can influence by controlling how much signal reaches the nonlinear stage).
Second-Order IMD Products
When two signals at f1 and f2 pass through a device with second-order nonlinearity (the a2 × input² term), the following products are generated:
- f2 − f1 (difference frequency)
- f1 + f2 (sum frequency)
- 2f1 (second harmonic of f1)
- 2f2 (second harmonic of f2)
- DC component (zero frequency)
Two signals: f1 = 7.020 MHz, f2 = 7.025 MHz
• f2 − f1 = 7.025 − 7.020 = 0.005 MHz = 5 kHz (audio frequency!)
• f1 + f2 = 7.020 + 7.025 = 14.045 MHz (twice the frequency)
• 2f1 = 14.040 MHz (harmonic)
• 2f2 = 14.050 MHz (harmonic)
Notice that the second-order products land in very different frequency regions: 5 kHz (audio) and around 14 MHz, twice the original frequency. None of these fall within the passband of a front-end filter tuned around 7 MHz. This is why second-order IMD is generally not a problem in narrow-band receivers and amplifiers with a band-pass filter at the input: the filter easily rejects products outside the wanted band.
Second-order IMD becomes a significant problem in two specific situations:
- Direct-conversion (zero-IF) receivers: In a direct-conversion architecture, the mixer outputs baseband (audio frequency) signals. The difference product f2 − f1 = 5 kHz lands directly in the audio passband and cannot be filtered without also filtering the desired audio. This is why second-order intercept point (IIP2) is critical for direct-conversion receivers like those used in many modern wireless chips.
- Wideband receivers: If the receiver lacks a narrow front-end band-pass filter — as is the case with very wideband spectrum monitoring receivers — then the sum frequency f1 + f2 can fall on another receive frequency of interest.
The second-order intercept point (IP2) is the theoretical signal level at which second-order products would equal the fundamental signals. A high IP2 is most important for direct-conversion and wideband designs. For narrow-band superheterodyne receivers, IP2 is not the critical specification — third-order products are.
Third-Order IMD Products — The Most Important
Third-order nonlinearity (the a3 × input³ term) is the most troublesome in most receivers, amplifiers and instruments. When two signals at f1 and f2 pass through a device with third-order nonlinearity, numerous products are generated, but the ones that matter most are:
• 2f1 − f2
• 2f2 − f1
These are the near-in products that fall close to the original signals.
Two signals: f1 = 7.020 MHz, f2 = 7.025 MHz (5 kHz apart)
• 2f1 − f2 = 2(7.020) − 7.025 = 14.040 − 7.025 = 7.015 MHz
• 2f2 − f1 = 2(7.025) − 7.020 = 14.050 − 7.020 = 7.030 MHz
Both products land 5 kHz outside the original pair — but right beside it. They cannot be filtered without also removing the original signals. If the original signals are strong enough, these products look exactly like real signals at 7.015 and 7.030 MHz.
The pattern is clear from this example: the third-order products appear at equal spacing on the other side of each original signal. If two signals are 5 kHz apart, the third-order products appear 5 kHz beyond each signal — one on each side of the pair. The spacing between the products and the nearest original signal is always equal to the spacing between the two original signals. This means:
- Two signals 2 kHz apart generate third-order products 2 kHz away
- Two signals 10 kHz apart generate third-order products 10 kHz away
- Two signals 100 kHz apart generate third-order products 100 kHz away — but these are easier to filter or may be outside the wanted band
The closer together the two strong signals, the closer the IMD products land to them, and the more likely a third-order product is to fall on the exact frequency of a weak signal you are trying to receive or measure. This is why crowded bands are so much worse for IMD than quiet ones: with many strong signals packed closely together, the probability of two of them producing a product on any given frequency is very high.
Why third-order products cannot be filtered
Second-order products land far from the original signals and can be rejected by a simple band-pass filter. Third-order products land at 2f1−f2 and 2f2−f1, which are within the band formed by the two original signals extended by one spacing on each side. Any filter that passes f1 and f2 will also pass the third-order products, because the products are too close to the originals for any practical filter to discriminate between them. The only solutions are:
- Reduce the level of the interfering signals before they reach the nonlinear device (attenuation, better front-end filtering, notch filters)
- Use a more linear device (higher IP3 mixer or amplifier)
- Work around the interference: choose a different frequency or measurement setting
IMD Product Level Calculator
Given two equal-level tones and the system IIP3, calculate the third-order IMD product level and how far it is below the original signals (in dBc). Formula: IMD3 (input-referred) = 3×Pin − 2×IIP3
Higher-Order IMD Products
Third-order products are the most troublesome, but they are not the only near-in products. Fifth-order, seventh-order and higher odd-order products also land close to the original signals. The general formula for the frequency of nth-order intermodulation products from two signals at f1 and f2 is:
5th order: 3f1 − 2f2 and 3f2 − 2f1
7th order: 4f1 − 3f2 and 4f2 − 3f1
Each nth-order product falls (n−1)/2 × (f2 − f1) from the outer signal
• 3f1 − 2f2 = 3(7.020) − 2(7.025) = 21.060 − 14.050 = 7.010 MHz
• 3f2 − 2f1 = 3(7.025) − 2(7.020) = 21.075 − 14.040 = 7.035 MHz
The fifth-order products fall 10 kHz from the pair center — twice as far as the third-order products (5 kHz). They are generally lower in amplitude than third-order products and are only significant in heavily overdriven circuits or very high-performance systems where third-order products have been suppressed.
In most practical situations, if a receiver, amplifier or instrument has good third-order performance, fifth- and higher-order products will be negligible. The exception is a power amplifier driven into saturation, whose spectrum shows a whole series of odd-order products spreading out on each side. The rule of thumb: fix the third-order problem first, and higher-order products usually take care of themselves.
The order of IMD products and their amplitudes
| IMD order | Product frequencies | Rise rate (dB per dB input) | Typical level vs. 3rd order |
|---|---|---|---|
| 2nd order | f1±f2, 2f1, 2f2 | 2 dB/dB | Falls far from f1, f2 |
| 3rd order | 2f1−f2, 2f2−f1 | 3 dB/dB | Reference (most important) |
| 5th order | 3f1−2f2, 3f2−2f1 | 5 dB/dB | Typically 10–30 dB below 3rd |
| 7th order | 4f1−3f2, 4f2−3f1 | 7 dB/dB | Typically 20–50 dB below 3rd |
The 3:1 Slope — Why IMD is So Input-Level Sensitive
The 3:1 rise rate of third-order IMD products is the most important characteristic to understand about IMD behavior. It is what makes IMD unpredictable and operationally significant: a modest increase in the level of interfering signals can cause a dramatic increase in IMD interference.
Consider what happens as you increase the level of two input signals simultaneously, one decibel at a time:
| Input signal level (dBm) | Signal level change | Third-order IMD level (dBm) | IMD change |
|---|---|---|---|
| −80 | — | −220 | — |
| −70 | +10 dB | −190 | +30 dB |
| −60 | +10 dB | −160 | +30 dB |
| −50 | +10 dB | −130 | +30 dB |
| −40 | +10 dB | −100 | +30 dB |
| −30 | +10 dB | −70 | +30 dB |
(Assuming IIP3 = +10 dBm; IMD3 = 3×Pin − 2×IIP3)
The dramatic implication: when the two input signals are at −80 dBm, the third-order IMD level is −220 dBm — hopelessly below any noise floor, totally invisible. As the signals strengthen to −30 dBm (a 50 dB increase), the IMD products rise by 150 dB to −70 dBm. At this level, the IMD products are stronger than many real signals.
This rapid rise explains several practical observations:
- Problems seem to appear suddenly as signal levels rise past a threshold
- Moving an antenna or cable, or adding shielding, can eliminate interference that seemed intractable, by reducing one strong signal
- Adding 10 dB of attenuation reduces IMD products by 30 dB, often eliminating the false signals completely
- The interference appears and disappears as the two strong signals come and go — it is not a constant problem
The theoretical IP3 intercept point
The third-order intercept point (IP3) is defined graphically: if you plot signal output power and third-order IMD output power versus input power on a log-log scale, you get two straight lines. The signal line has a 1:1 slope; the IMD line has a 3:1 slope. These lines, extrapolated, cross at a point called the intercept point. At the input level corresponding to IP3, the IMD products theoretically would equal the signal. In practice, the receiver saturates long before this point, so IP3 is always an extrapolated value, not a directly measurable one under normal conditions.
The higher the IP3, the better the large-signal performance. IP3 is the subject of the next lesson. The key relationship to remember here is:
• Pin = level of each input tone (dBm)
• IIP3 = input third-order intercept point (dBm)
• IMD3 level relative to input signals = 2 × (Pin − IIP3) dBc
Recognizing IMD in Practice
When IMD is creating false signals in a receiver or on a spectrum analyzer, several reliable signs distinguish it from a real signal. Knowing them saves a lot of time chasing signals that do not exist.
The characteristic symptoms
1. The false signal follows the strong signals: When either of the two strong signals causing the IMD changes frequency slightly or switches off, the false signal immediately moves or disappears. A real signal would not disappear just because a transmitter on a different frequency stopped.
2. It moves by the wrong amount: If you can shift one of the two signals — for example on a bench test with two generators — a third-order product at 2f1−f2 moves by twice the shift of f1, or by the same amount in the opposite direction when f2 moves. Real signals do not behave this way.
3. The 3-to-1 attenuator test: This is the definitive diagnostic. Insert a calibrated attenuator ahead of the receiver or amplifier (or use a spectrum analyzer's input attenuator) and watch both the strong signals and the suspect signal. If 10 dB of attenuation reduces the suspect signal by about 30 dB while the strong signals drop by only 10 dB, the suspect signal is third-order IMD generated after the attenuator. If it drops by the same 10 dB, it is a real signal arriving at the input. The 3:1 ratio is the fingerprint of third-order IMD.
4. Frequency relationship test: Calculate where third-order products would fall for any two strong signals present. If the suspect signal is at exactly 2f1−f2 or 2f2−f1, it is almost certainly IMD. A spectrum analyzer makes these relationships easy to see.
A spectrum analyzer shows an unexpected signal at 7.018 MHz, about 40 dB below two strong signals at 7.020 MHz (−20 dBm) and 7.022 MHz (−20 dBm).
Third-order product from the two signals:
2fA − fB = 2(7.020) − 7.022 = 14.040 − 7.022 = 7.018 MHz
The frequency matches. You add 10 dB of input attenuation. The analyzer compensates its display, so the two strong signals still read −20 dBm — but the signal at 7.018 MHz drops by about 20 dB. Because the analyzer added 10 dB back to every reading, a 30 dB fall at the mixer shows as a 20 dB fall on the screen. Confirmed: third-order IMD generated inside the analyzer, not a real signal.
Practical remedies
Once you have confirmed IMD, your options are:
- Reduce the input level: 10 dB of attenuation reduces third-order IMD by 30 dB. This is effective when the noise floor is set by noise arriving with the signal, or when there is plenty of signal to spare — as there usually is when a spectrum analyzer is overloaded.
- Filter out the strong signals: If one or both of the strong signals is outside the band you care about — a nearby broadcast station, for example — a band-pass or high-pass filter ahead of the first nonlinear stage removes it and eliminates the problem.
- Use a notch filter: If one strong signal is the dominant cause, a narrow notch filter tuned to it reduces its contribution to IMD significantly.
- Use a more linear device: An amplifier or mixer with a higher IIP3 creates far fewer IMD products at the same input levels. In an environment full of strong signals, a high-IP3 front end is a genuine solution.
IMD in Amplifiers and Audio Equipment
IMD is not only a receiving problem. Every amplifier produces some, and the two-tone test is the standard way to measure it.
The two-tone test for RF power amplifiers
An RF power amplifier carrying a signal with varying amplitude — voice, or a modern digital signal such as an OFDM or QAM transmission — must be linear, or its IMD products spread into neighboring channels. The test feeds the amplifier two equal-level tones a few kilohertz apart and measures the output on a spectrum analyzer through a suitable attenuator. The third-order products appear at 2f1−f2 and 2f2−f1, and their level is quoted in dB relative to one of the tones (dBc) or to the peak envelope power.
| Third-order IMD | Quality | Typical result |
|---|---|---|
| −25 dBc | Poor | Amplifier overdriven or poorly biased; strong adjacent-channel products |
| −30 dBc | Acceptable | Typical of a Class AB amplifier near full power |
| −35 dBc | Good | Well-designed Class AB amplifier at moderate power |
| −45 dBc or better | Excellent | Class A operation, heavy feedback or digital predistortion |
Power amplifier IMD rises steeply as the output approaches saturation. Backing the drive off by a few decibels usually improves IMD considerably — which is why cellular base stations and Wi-Fi transmitters run their amplifiers well below peak power, or use digital predistortion, which deliberately distorts the drive signal in the opposite direction so that the amplifier's own distortion cancels it.
Audio IMD tests
Audio amplifiers are tested for IMD as well as harmonic distortion, because IMD products are not musically related to the original sounds and are more objectionable to the ear. Two standard methods are used:
- SMPTE method: A 60 Hz tone and a 7 kHz tone mixed in a 4:1 amplitude ratio. Nonlinearity makes the low-frequency tone modulate the high one, producing sidebands at 7 kHz ± 60 Hz, ± 120 Hz and so on. The result is quoted as a percentage of the 7 kHz tone.
- CCIF (twin-tone) method: Two equal high-frequency tones, typically 19 kHz and 20 kHz. Second-order distortion produces a 1 kHz difference product right in the most sensitive part of the audible range, and third-order products appear at 18 kHz and 21 kHz.
A good audio amplifier has IMD below 0.01% (−80 dB) at normal power levels. Both tests can be run with a two-channel function generator or a computer sound card, with the output examined on an FFT display.
How to check an amplifier for IMD
For an audio amplifier, feed it a twin-tone signal from a sound card or generator, connect the output through a load resistor and a suitable attenuator to an audio interface, and look for the products on an FFT. For an RF amplifier, combine two signal generators through a hybrid combiner or resistive splitter (so the generators do not intermodulate each other), feed the amplifier, and view the output on a spectrum analyzer through an attenuator. In both cases, step the input level up and down: genuine third-order products change by 3 dB for every 1 dB of input, and products that do not follow that rule are coming from somewhere else in the test setup.
Frequently Asked Questions
I see an unexpected signal near two strong ones — is it IMD?
Very likely, especially if its frequency matches 2f1−f2 or 2f2−f1 for the two strong signals. To confirm, add 10 dB of attenuation at the input. If the suspect signal falls by about 30 dB while the strong signals fall by 10 dB, it is third-order IMD generated in your equipment. If it falls by 10 dB, it is a real signal arriving at the input.
Why is third-order IMD usually worse than second-order?
Second-order products land at f1+f2 and f2−f1. For two RF signals close together, these fall either at about twice the frequency or at a low difference frequency, far from the wanted band, where an ordinary band-pass filter removes them. Third-order products land at 2f1−f2 and 2f2−f1, right beside the original signals, where no practical filter can separate them. The exceptions are direct-conversion receivers and wideband or audio systems, where second-order products can land in the wanted band.
Can a nearby transmitter cause IMD in my equipment even if it is perfectly clean?
Yes. The IMD is generated by the nonlinearity of the equipment receiving the signals, not by the transmitters. Two perfectly clean, strong signals reaching the same nonlinear stage will produce IMD products in that stage. The cure is in the receiving equipment: filtering, attenuation, or a more linear front end.
Test Your Knowledge
Answer the questions below to check your understanding of this lesson. Every answer can be found in the lesson above.