RF Theory › Intermodulation & IP3

Third-Order Intercept (IP3)

Two tones into any real amplifier or mixer create unwanted third-order products right next to the originals — products that can't be filtered out. IP3 is the single number that predicts how bad they'll get at any input power. This page builds the classic log-log construction from scratch and lets you sweep it live.

01 — Definition

What Is Intermodulation?

Feed any real (non-ideal) amplifier or mixer two tones at f₁ and f₂, and its output isn't just those two tones amplified — the device's nonlinearity mixes them together, generating energy at new frequencies m·f₁ ± n·f₂ for every integer m,n. These are intermodulation products. The order of a product is |m|+|n|.

Why IM3 Is the Dangerous One

Second-order products (2f₁, 2f₂, f₁±f₂) usually land far from the tones and get filtered out. But the third-order products 2f₁−f₂ and 2f₂−f₁ land just outside the original tones — inside the same passband, inside the same channel, impossible to filter. This is the classic two-tone test used to characterise every RF amplifier, mixer and receiver front end.

Third-Order Products
Input: two equal-power tones at f₁, f₂ (close together, Δf = f₂−f₁)
Third-order products: 2f₁−f₂ and 2f₂−f₁ — offset by only Δf from the tones
Product power grows 3 dB for every 1 dB of input power increase (cubic nonlinearity)
Rule of thumb: the fundamental tones grow 1 dB out for every 1 dB in (slope 1). The IM3 products grow 3 dB out for every 1 dB in (slope 3) — until compression takes over. That slope difference is the entire reason IP3 exists as a concept.
02 — The Intercept Construction

The Intercept Point Construction

Plot output power vs. input power on log-log (dBm vs dBm) axes. The fundamental line has slope 1; the IM3 line has slope 3. Neither line is real at high power — both amplifiers compress and IM3 products stop growing cleanly — but if you extrapolate both ideal straight lines, they cross at a single fictitious point: the third-order intercept point.

IP3 Definitions & Construction Lines
IIP3 = input power at the extrapolated intercept  ·  OIP3 = IIP3 + Gain
Fundamental (dBm): Pout,fund = Pin + Gain
IM3 product (dBm): Pout,IM3 = 3·Pin + Gain − 2·IIP3
IM3 suppression below fundamental: ΔdBc = 2·(IIP3 − Pin)
Why this is useful even though it's fictitious: IP3 is never actually reached — the amplifier saturates and dies long before its output could get there. But because it's defined by two straight lines with known fixed slopes (1 and 3), knowing IIP3 alone lets you predict the exact IM3 level at any input power, as long as you're still in the small-signal (uncompressed) region.

Live Two-Tone Sweep

Drag Gain, IIP3 and P1dB, then slide the input power marker — watch the fundamental compress near P1dB while the extrapolated IM3 line keeps its ideal 3:1 slope until it too is pulled toward saturation.

15 dB
20 dBm
10 dBm
−10 dBm
OIP3 = 35.0 dBm Pout,fund = 5.0 dBm Pout,IM3 = −55.0 dBm IM3 suppression = 60.0 dBc
Cyan = fundamental output (solid = real compressing response, dashed = ideal slope-1 extrapolation). Red = IM3 product (solid = realistic response pulled toward saturation near P1dB, dashed = ideal slope-3 extrapolation). They cross at (IIP3, OIP3) — the white marker is your current Pin.
Two-tone spectrum at the current Pin — tall bars are the fundamentals f₁, f₂; short bars are the IM3 products 2f₁−f₂ and 2f₂−f₁, sitting just outside the passband edge.

Worked Example — Driver Amplifier

Example — Gain=15 dB, IIP3=+20 dBm, two tones at Pin=−10 dBm each
1
OIP3 = IIP3 + Gain = 20+15 = 35 dBm
2
Pout,fund = Pin+Gain = −10+15 = 5 dBm
3
Pout,IM3 = 3×(−10)+15−2×20 = −30+15−40 = −55 dBm
4
IM3 suppression = 2×(IIP3−Pin) = 2×(20−(−10)) = 60 dBc below the fundamental
✓ Back off Pin by 10 dB (to −20 dBm) and IM3 suppression improves by 20 dB (to 80 dBc) — that ×2 relationship is the signature of a third-order process.
03 — IP3 vs P1dB

IP3 vs. P1dB

The 1 dB compression point (P1dB) is where the real fundamental output has fallen 1 dB below the ideal straight line — the point where the device visibly starts to saturate. IP3 is always well above P1dB, because the intercept is extrapolated far past where the device could ever actually operate.

Rule-of-Thumb Relationship
IIP3 ≈ P1dB(in) + 10 dB    (for a classic soft-limiting, memoryless nonlinearity)
Equivalently: OIP3 ≈ P1dB(out) + 10 dB
It's an approximation, not a law: the exact gap between P1dB and IP3 depends on the device's specific nonlinearity — it can be anywhere from 6–15 dB in real amplifiers. Always use a measured or datasheet IP3 for real designs; the +10 dB rule is only for quick sanity checks.
04 — Cascaded Systems

Cascaded IIP3

In a chain of stages, IIP3 combines the opposite way from noise figure: the last stage usually dominates, because its input signal has already been amplified by every stage before it and is closest to that stage's own compression.

Cascaded IIP3 (linear power ratios, referenced to system input)
1/IIP3total = 1/IIP3₁ + G₁/IIP3₂ + G₁G₂/IIP3₃ + ⋯   (linear power, G = linear gain)
Opposite of the NF cascade: for noise figure, the first stage dominates (Friis' equation) — so you put your lowest-noise, lowest-gain stage first. For IIP3, later stages dominate — so linearity requirements tighten as you move toward the chain's output. This tension between "low NF wants gain early" and "good IIP3 wants gain late" is the central RX chain design trade-off. The RX Chain Designer computes this automatically for a full multi-stage chain.
05 — Dynamic Range

Spurious-Free Dynamic Range

SFDR is the input power range over which a signal is both above the noise floor and its IM3 products are still below the noise floor. It's the practical, usable dynamic range of a receiver — bounded on the low end by noise and on the high end by IP3.

SFDR (Two-Tone)
SFDR = (2/3)·(IIP3 − Nin)   [dB], where Nin = input-referred noise floor = −174 + 10·log₁₀(BW) + NF   [dBm]
Both terms matter equally: a higher IIP3 widens SFDR from the top; a lower noise figure (or narrower bandwidth) widens it from the bottom. Improving either helps — but SFDR only scales as ⅔ of whichever you improve, since the IM3 line has a 3:1 slope.
06 — Design Rules

IP3 Design Rules

Rule 01
Back off 1 dB → IM3 improves 2 dB
Third-order products fall twice as fast as the fundamental when you reduce input power.
Rule 02
IIP3 ≈ P1dB + 10 dB (rough)
Quick sanity check only — always use measured/datasheet IIP3 for real link budgets.
Rule 03
Later stages dominate cascaded IIP3
Opposite of noise figure — linearity gets harder to hold as gain accumulates through the chain.
Rule 04
OIP3 = IIP3 + Gain
Always state which reference (input or output) a datasheet IP3 number uses — mixing them is a common error.
Rule 05
SFDR scales at ⅔ rate
A 3 dB IIP3 improvement only buys 2 dB more spurious-free dynamic range.
Rule 06
Two-tone test ≠ single-tone P1dB
Always specify which test produced a linearity number — they characterise different things.

Third-Order Intercept Point and Intermodulation Distortion

The third-order intercept point (IP3) is the standard figure of merit for RF amplifier and mixer linearity. It is measured with a two-tone test: two equal-amplitude tones close in frequency are applied, and the power of the third-order intermodulation products (2f₁−f₂, 2f₂−f₁) is measured relative to the fundamental tones as input power is swept.

Why IP3 Matters for Receiver Design

In a crowded RF environment, two strong out-of-band interferers can intermodulate inside an LNA or mixer and produce a third-order product that lands directly on the desired channel — a problem no filter downstream can remove, since filtering happens before the nonlinearity that created the product. This is why IIP3 is specified for every LNA, mixer, and receiver front end.

IIP3 vs OIP3

IIP3 (input-referred) and OIP3 (output-referred) differ by exactly the stage gain: OIP3 = IIP3 + Gain. Datasheets are inconsistent about which they report — always check which reference point a quoted IP3 number uses before comparing components.