Power, Linearity, and Distortion Compression and Intercept Points Informational

How do I calculate intermodulation product levels from two tone measurements?

Intermodulation product levels are calculated from a two-tone test, which is the standard method for characterizing the linearity of RF components: (1) Two-tone test setup: apply two equal-amplitude signals (tones) at frequencies f1 and f2 (closely spaced, e.g., f1 = 1000 MHz, f2 = 1001 MHz). The device nonlinearity generates intermodulation products at: 2×f1 - f2 = 999 MHz (IM3 low). 2×f2 - f1 = 1002 MHz (IM3 high). 3×f1 - 2×f2, 3×f2 - 2×f1 (IM5 products). And many others (IM2 at f1+f2 and f2-f1, higher orders). (2) Calculating IM3 levels from IP3: if you know the IIP3 of the device and the input power per tone (P_in): IM3 level (dBm) = 3 × P_in - 2 × IIP3. Example: IIP3 = +10 dBm, P_in = -20 dBm per tone. IM3 = 3 × (-20) - 2 × (+10) = -60 - 20 = -80 dBm. The IM3 products are at -80 dBm. The fundamental tones are at P_out = P_in + Gain. If gain = 15 dB: P_out = -20 + 15 = -5 dBm. IM3 relative to fundamental: -80 - (-5) = -75 dBc. (3) Conversely (calculating IP3 from measured IM3): measure the fundamental output power (P_f) and the IM3 output power (P_IM3). OIP3 = P_f + (P_f - P_IM3)/2 = P_f + delta/2. Where delta = P_f - P_IM3 (in dB). Example: P_f = +10 dBm, P_IM3 = -50 dBm. Delta = 60 dB. OIP3 = 10 + 60/2 = +40 dBm. IIP3 = OIP3 - Gain. (4) IM3 vs input power: IM3 rises 3 dB for every 1 dB increase in input power (as long as the device is in the small-signal regime). The delta between the fundamental and IM3 decreases by 2 dB for every 1 dB increase. At the IP3 point: delta = 0 (IM3 = fundamental, but this is extrapolated; the device compresses before reaching this point).

Category: Power, Linearity, and Distortion

Updated: April 2026

Product Tie-In: Amplifiers, Mixers, Attenuators

Two-Tone IM3 Calculation

The two-tone test is the cornerstone of RF linearity characterization, providing the data needed to predict intermodulation performance in multi-signal environments.

Measurement Setup

(1) Two signal generators: each set to a different frequency (spacing depends on the application; typically 1-10 MHz for narrowband devices, 20-100 MHz for wideband). Both generators at the same output power. A combiner (resistive or hybrid) combines the two signals and presents them to the DUT input. (2) Output measurement: a spectrum analyzer measures the output spectrum. The fundamental tones and IM3 products are visible on the display. Read the power levels of the fundamentals and the IM3 products. Calculate OIP3 from the measured data. (3) Precautions: ensure the signal generators are clean (their own IM3 must be much lower than the DUT IM3). Use isolation between the generators (to prevent one generator from modulating the other). Verify the spectrum analyzer dynamic range is sufficient (the IM3 products may be 60-80 dB below the fundamentals).

IM3 Calculation

IM3 = 3×P_in - 2×IIP3 (dBm)
OIP3 = P_fund + (P_fund - P_IM3)/2
IM3 rises 3 dB per 1 dB input increase
ΔP = P_fund - P_IM3 (dBc)
f_IM3 = 2f₁-f₂ and 2f₂-f₁

Common Questions

Frequently Asked Questions

What tone spacing should I use?

The tone spacing depends on the application: for amplifiers: 1-10 MHz spacing (close enough to be in the same gain band). For mixers: the spacing should be within the IF bandwidth. For PAs with DPD: the spacing should cover the correction bandwidth (typically 5× the signal bandwidth). The IM3 level can vary with tone spacing due to memory effects (thermal and electrical). For a complete characterization: sweep the tone spacing.

Do IM3 and IM5 have different slopes?

Yes. IM3 rises at 3 dB/dB (3:1 slope on a dBm vs dBm plot). IM5 rises at 5 dB/dB (5:1 slope). IM7 rises at 7 dB/dB. Higher-order products rise faster, so at high signal levels they can exceed the IM3 level. But at typical operating levels: IM3 dominates (IM5 and higher are much lower).

What if the two IM3 products are not equal?

In an ideal memoryless nonlinearity: the upper and lower IM3 products are equal. Asymmetry indicates: memory effects (the device response depends on the recent signal history due to thermal or bias circuit time constants), second-order nonlinearity contributing to the IM3 through a cross-product with the fundamental, or frequency-dependent nonlinearity. Report both IM3 levels and use the worse (higher) one for the IP3 calculation.

Keep Reading