What Is Intermodulation (IM3)? Third-Order Products, IP3 and How to Avoid It

The Short Answer

Intermodulation, often shortened to IM or IMD, is the interference a system creates when two or more signals mix in a device that is not perfectly linear. Instead of passing the signals through unchanged, the device combines them and produces new signals at the sums and differences of the original frequencies.

For two carriers at frequencies f₁ and f₂, the products appear at every combination of:

Intermodulation product = m · f₁ ± n · f₂

The order of a product is m + n. The third-order products, 2·f₁ − f₂ and 2·f₂ − f₁, are the ones that cause most of the trouble, because they land closest to the original carriers and often fall straight onto a working channel. Once a product sits inside the wanted channel it cannot be filtered away, because filtering it would remove the signal you are trying to hear. So intermodulation, like the noise floor it raises, has to be stopped where it is made.

Where Intermodulation Comes From

A perfectly linear device produces an output that is simply a scaled copy of its input. Real devices are never quite linear. At high signal levels an amplifier compresses, a mixer has curvature by design, and even a metal joint can behave non-linearly. Any of these can act as a weak mixer.

When a single signal passes through a non-linear device you get harmonics, at two, three and more times the original frequency. Those are usually easy to filter, because they sit far from the wanted band. Intermodulation is worse, because with two or more signals present the device produces sums and differences as well, and some of those fall right next to, or on top of, the original carriers.

The Non-Linear Polynomial: Where the Orders Come From

If you want the single line of maths behind it, the output of a real device can be approximated as a power series of its input:

V_out = a₁·x + a₂·x² + a₃·x³ + …

The first term is the linear gain you actually want. Everything after it is distortion. Feed in two tones and each term produces its own family of products. The squared term generates the second-order sums and differences, the cubed term generates the third-order products, and higher terms carry on up the series. The third-order term is the one that yields 2·f₁ − f₂ and 2·f₂ − f₁, and because it multiplies three copies of the input it grows on a 3 to 1 slope with drive level.

Junior engineers can take that result on trust and skip ahead. The idea to carry forward is that the order of a product tells you which term in the device’s non-linearity created it, and how quickly it grows as the signals get stronger.

Active and Passive Intermodulation

Intermodulation splits into two families, and the distinction matters because the fixes differ.

• Active intermodulation happens in powered devices driven beyond their linear range. Transmitter power amplifiers fed by more than one carrier, and receiver front ends hit by strong off channel signals, are the classic sources. This article focuses on active IM and the third-order intercept point that describes it.
• Passive intermodulation, or PIM, happens in unpowered parts such as connectors, cable joints and antennas, where a loose, corroded or magnetic junction behaves like a tiny mixer. It follows the same frequency maths but has different causes and cures, covered in detail in what is passive intermodulation and how to prevent it.

Both belong to the wider picture of why sites are getting noisier, set out in what is RF interference and why it is getting worse.

Where the Products Land: The Formula

Two carriers at f₁ and f₂ create products at every m · f₁ ± n · f₂, with the order equal to m + n. Even-order products, such as the second order f₁ + f₂ and f₂ − f₁, usually fall well away from the carriers and are easy to filter in a narrowband system. The odd-order products are the problem, and the third order most of all:

2·f₁ − f₂ and 2·f₂ − f₁

Here is a concrete case. A shared UHF site runs two transmitters at f₁ of 450.000 MHz and f₂ of 450.025 MHz. The third-order products are:

2 × 450.000 − 450.025 = 449.975 MHz 2 × 450.025 − 450.000 = 450.050 MHz

The products land exactly 25 kHz either side of the pair, on the adjacent channels. If a co-sited receiver is tuned to 449.975 MHz, it is now hearing interference the site made for itself.

   2f1 - f2      Carrier 1      Carrier 2      2f2 - f1
   449.975       450.000        450.025        450.050
      |             |              |              |
  ----+-------------+--------------+--------------+----> MHz
      |             |              |              |
   IM3 product    wanted         wanted       IM3 product
   (channel       carrier        carrier      (channel
    below)                                     above)

      <-- 25 kHz --><-- 25 kHz --><-- 25 kHz -->

Add a third transmitter and the three-signal products, such as f₁ + f₂ − f₃, multiply the combinations quickly, which is why busy sites need every carrier checked against every other.

Warning: the higher orders still bite

Each step up in order produces a weaker product, so it is tempting to plan around the third order alone. On a high power site with many carriers, fifth-order products can still sit well above the noise floor, and more carriers mean far more combinations that can reach a receive channel. Check the orders your real band plan allows, not just the third.

Third-Order Products Are the Problem

Third-order intermodulation earns its reputation for two reasons. The first is placement. The products at 2·f₁ − f₂ and 2·f₂ − f₁ sit just outside the pair of carriers, so on a site where channels are packed close together they land on real working frequencies rather than in empty guard band.

The arithmetic makes this exact. If the two carriers are one channel spacing apart, so that f₂ = f₁ + Δ, then 2·f₁ − f₂ works out to f₁ − Δ and 2·f₂ − f₁ works out to f₂ + Δ. Each product therefore falls precisely one channel spacing beyond the pair, which on an evenly spaced band plan is the next licensed channel along. Equal channel spacing, the very thing that makes a band plan tidy, is exactly what drops IM3 onto a working frequency.

The second is how fast they grow. A third-order product rises about three times as fast as the signals that create it. Lift the input level by 1 dB and the product lifts by roughly 3 dB. That non-linear scaling is why intermodulation can stay hidden during a quiet, low power test and then become severe once the site runs at full power or a second strong signal appears.

The Third-Order Intercept Point (IP3) and the 3 to 1 Rule

The linearity of an active device is summed up in one figure, the third-order intercept point, written IP3 or TOI. It is the theoretical level at which the third-order product would rise to equal the wanted signal. No real device ever reaches it, because it compresses first, but the extrapolated point is a clean way to compare devices. A higher IP3 means a more linear device that makes less intermodulation at a given signal level.

IP3 is quoted at the input as IIP3 or at the output as OIP3. The useful working relationship is that the third-order products sit below each carrier by:

IM3 suppression (dBc) = 2 × (IIP3 − Pin)

where Pin is the level of each of the two tones at the input. This is the 3 to 1 rule in practice. Because the product grows on a 3 to 1 slope against the carriers, every 1 dB you take off the input level buys 2 dB more suppression in dBc.

Worked Example: A Multi-Carrier Site

Take a receiver whose low noise amplifier has an IIP3 of −5 dBm. Two strong off channel signals, from nearby transmitters, each reach the amplifier input at −30 dBm.

The third-order suppression is:

2 × (−5 − (−30)) = 2 × 25 = 50 dB

So the intermodulation product sits 50 dB below each −30 dBm tone, at −80 dBm. If the receiver noise floor is around −110 dBm, that product is 30 dB above the floor, sitting on the wanted channel and burying any weak signal underneath it. The receiver is desensitised even though nothing is wrong with the radio or the frequency plan on paper.

Now apply the 3 to 1 rule. Cut the two interfering signals by 10 dB before they reach the amplifier, ideally with selective filtering that rejects the off channel energy rather than broadband attenuation that also weakens the wanted signal. Each tone drops to −40 dBm, the suppression becomes 2 × (−5 − (−40)) = 70 dB, and the product falls to −110 dBm, back at the noise floor. Ten decibels less drive has bought a 20 dB improvement, which is the whole reason filtering and isolation are the primary tools against intermodulation.

Transmitter IM and Receiver IM

Intermodulation on a site shows up in two directions, and it helps to name them.

• Transmitter IM is created when the output of one transmitter reaches the non-linear final stage of another and mixes with its carrier. The products radiate from the antenna as spurious emissions. The cures are isolation between transmitters, using isolators or circulators, and cavity filters on each output.
• Receiver IM is created inside the receiver front end when two or more strong external signals drive the low noise amplifier or mixer into its non-linear region, producing a product on the wanted channel. The cures are front end selectivity, a higher IP3 front end, and enough filtering to keep the strong signals out.

The frequency maths is identical for both. What differs is where the mixing happens and therefore where you place the fix.

What Is Receiver Desensitisation?

Receiver desensitisation, usually shortened to desense, is any loss of receiver sensitivity caused by an unwanted signal. The symptom is always the same. The weakest signal the receiver can still decode has to be stronger than it should be, so the usable range shrinks even though the radio itself is working to specification.

Intermodulation is one cause of desense, but not the only one, and the three main mechanisms are easy to confuse. It is worth keeping them apart, because each points at a different fix.

All three raise the effective noise floor and shrink the cell, which is why they get lumped together as desense in the field. Telling them apart is what points you at the right cure: coordination and filtering for intermodulation, a stronger front end for blocking, and a cleaner local oscillator for reciprocal mixing.

Surface and Underground Behaviour

The intermodulation environment is not the same everywhere. In open air surface deployments, the full set of second, third and fifth-order products matters, because higher-order products can still propagate and reach a receiver.

In many underground systems, such as mines, tunnels and metro, the third-order products are typically the dominant concern. Higher-order products are usually generated at much lower levels to begin with, and the propagation environment, coupling and system architecture often leave them contributing far less to the interference budget. Both the two-signal product, 2·f₁ − f₂, and the three-signal product, f₁ + f₂ − f₃, tend to drive the budget in these environments, and closely spaced carriers interact more than they would in the open. Analysing a plan in the right mode, surface or underground, keeps the effort on the products that actually matter rather than ones the environment leaves insignificant.

How to Prevent Intermodulation

Intermodulation is far cheaper to design out than to chase after commissioning. Work down this checklist, roughly in order of return:

• ✔ Optimise the channel assignments. The best defence is arithmetic. Choose channels so that the third-order products of any carrier pair do not fall on a working frequency, and check every combination before anything is built.
• ✔ Fit cavity filters and duplexers. Sharp cavity filters and duplexers on transmitters and receivers keep strong signals away from the non-linear stages where they would mix.
• ✔ Use combiners built for the job. A proper transmitter combiner adds isolation between outputs rather than simply tying them together, which keeps one carrier out of another’s final stage.
• ✔ Isolate the transmitters. Isolators and circulators stop one transmitter’s output from reaching another’s final amplifier, removing a large share of transmitter IM.
• ✔ Increase antenna isolation. Physical separation and vertical stacking raise the isolation between systems and cut the coupling that feeds intermodulation.
• ✔ Improve the receiver IP3. For front ends exposed to strong signals, a higher IIP3 device makes less intermodulation at the same input level.
• ✔ Reduce transmitter power where you can. Because of the 3 to 1 slope, a small drop in the level reaching a non-linear stage produces a large drop in the product.
• ✔ Remove passive junctions. Clean, torque and minimise connectors so the passive path does not add PIM on top of the active intermodulation.

Common Intermodulation Mistakes

• Checking only the third order. Fifth-order products can sit above the noise floor on busy, high power sites. Check the orders your band plan actually allows.
• Assuming a clean spectrum analyser trace means a clean site. Intermodulation can hide at low power and appear only when a second strong signal or full power arrives.
• Blaming the radio for a coordination problem. A product landing on the wanted channel is a frequency plan issue, not a faulty receiver.
• Adding transmit power to fix coverage. More power lifts the intermodulation products faster than the wanted signal, so it can deepen a desense problem.
• Ignoring the passive path. A perfectly linear active chain can still suffer passive intermodulation from a loose or corroded connector, which is a separate check.

Frequently Asked Questions

What is intermodulation in simple terms? Intermodulation is interference made when two or more signals mix in a device that is not perfectly linear, such as an overdriven amplifier or a mixer. The device creates new signals at the sums and differences of the original frequencies, and some of those fall on working channels.

What is third-order intermodulation? Third-order intermodulation refers to the products at 2·f₁ − f₂ and 2·f₂ − f₁, where the multipliers add up to three. They matter most because they land closest to the original carriers and grow three times as fast as the signals that create them.

What is IP3 or the third-order intercept point? IP3 is the extrapolated signal level at which the third-order product would rise to equal the wanted signal. It is a single figure of merit for linearity. A higher IP3 means a more linear device that produces less intermodulation at a given level.

What is the difference between intermodulation and passive intermodulation? Intermodulation covers any non-linear mixing, including active devices such as amplifiers and mixers. Passive intermodulation, or PIM, is the special case that occurs in unpowered parts such as connectors and antennas. The frequency maths is the same, but the causes and cures differ.

How do you prevent intermodulation? Coordinate the frequency plan so products miss working channels, filter with cavities and duplexers, isolate transmitters with isolators or circulators, specify a high enough IP3 for exposed receivers, and keep strong signals out of non-linear stages.

Why does third-order intermodulation grow so fast? Because the product rises on a 3 to 1 slope against the carriers. A 1 dB rise in the input level lifts the third-order product by about 3 dB, so it can jump from harmless to severe over a small change in signal strength.

Build it in noIM₃

The intermodulation calculator computes the second, third and fifth-order products for any list of carriers, in surface or underground mode, and flags the products that fall too close to a working channel. When the mixing is in the passive path rather than an active device, the PIM calculator covers the connector and antenna side. The frequency plan optimiser and frequency coordination tool then help choose channels whose products miss every receiver on the site.

Key Takeaway

Intermodulation is the interference a site makes for itself when two or more signals mix in a stage that should be linear but is not. The third-order products at 2·f₁ − f₂ and 2·f₂ − f₁ land closest to the carriers, grow three times as fast as the signals that create them, and cannot be filtered once they sit on the wanted channel. The linearity of a device is captured by its IP3, and the 3 to 1 rule means a small cut in the signal reaching a non-linear stage buys a large cut in the product. Stop intermodulation with a coordinated frequency plan, hard filtering and good isolation, and it never reaches the receiver in the first place.