Intermodulation Distortion & IP3
When two or more signals pass through a nonlinear device (an amplifier, mixer, or any component with a nonlinear transfer function), new frequency components are created. These intermodulation (IM) products can fall within the passband of the system and cannot be removed by filtering. Third-order intermodulation (IM3) is the dominant concern in most RF receivers and transmitters.
Why Nonlinearity Matters
A perfectly linear device produces outputs only at its input frequencies. A nonlinear device with input \(x(t) = a_1\cos(\omega_1 t) + a_2\cos(\omega_2 t)\) produces output terms at frequencies \(n\omega_1 \pm m\omega_2\) for all integers n, m. The third-order products at \(2\omega_1 - \omega_2\) and \(2\omega_2 - \omega_1\) are close to the original signals and fall in-band.
Third-Order Intercept Point (IP3)
In a two-tone test, both the desired output and the IM3 products are plotted as a function of input power. On a log-log scale, the desired output has slope 1 (1 dB output per 1 dB input); the IM3 products have slope 3 (3 dB output per 1 dB input). Extrapolating these two lines, they intersect at the IP3 point.
where all powers are in dBm and G is the gain in dB. The OIP3 is typically 10–15 dB above the 1 dB compression point.
Input and Output IP3
| Parameter | Symbol | Typical values | Notes |
|---|---|---|---|
| Input IP3 | IIP3 | −10 to +40 dBm | Referred to device input |
| Output IP3 | OIP3 | 0 to +50 dBm | OIP3 = IIP3 + Gain |
| 1 dB compression | P₁dB | ≈ IIP3 − 9.6 dB | Empirical approximation |
| Low-noise amplifier | IIP3 | 0 to +15 dBm | Trades with noise figure |
| Power amplifier | OIP3 | P₁dB + 10 dB | Backed off from saturation |
| Passive mixer | IIP3 | +15 to +25 dBm | Higher than active |
IMD Ratio & Dynamic Range
The intermodulation distortion ratio (IMD) is the power difference between the desired signal and the IM3 product at the output:
The spurious-free dynamic range (SFDR) is the input power range over which the system can operate without IM3 products exceeding the noise floor:
Cascaded IP3
For a chain of stages, the cascaded IIP3 is dominated by later stages (because the signal is amplified). The reciprocal rule gives:
where all quantities are in linear (not dB) units. This is why the last high-gain stage in a receiver chain typically limits linearity.
Practical Implications
- LNA IIP3: typically +5 to +15 dBm. Must handle the full received signal range without generating IM3 products that mask weak desired signals.
- PA linearity: power amplifiers operate backed off from their P₁dB to maintain acceptable IM3. ACPR (adjacent channel power ratio) is the PA equivalent of IMD.
- Mixer IIP3: passive mixers (diode or FET ring) have higher IP3 than active mixers but higher conversion loss.