How do you calculate IP3 from a two-tone test?

A two-tone test drives the device with two equal-power tones at frequencies f1 and f2 (closely spaced). The output contains the fundamentals (f1, f2) and IMD3 products (2*f1-f2, 2*f2-f1). OIP3 = P_out_fundamental + delta/2, where delta is the dB difference between the fundamental and IMD3 output power. IIP3 = P_in + delta/2, or IIP3 = OIP3 - Gain. Example: two tones at -20 dBm each, LNA with 15 dB gain. Output fundamentals at -5 dBm. IMD3 products at -65 dBm. delta = 60 dB. OIP3 = -5 + 30 = +25 dBm. IIP3 = +25 - 15 = +10 dBm. The IMD3 products grow 3 dB for every 1 dB increase in input power (3:1 slope on a log plot), which is why the intercept point is theoretical and never actually reached (the device compresses first).

What is SFDR and how does it relate to IP3?

Spurious-Free Dynamic Range (SFDR) is the range of input power levels where the signal is above the noise floor and the IMD3 products are below the noise floor. SFDR = 2/3 * (IIP3 - noise_floor), where noise_floor = -174 + NF + 10*log10(BW). Example: IIP3 = +10 dBm, NF = 3 dB, BW = 1 MHz. Noise floor = -174 + 3 + 60 = -111 dBm. SFDR = 2/3 * (10 - (-111)) = 2/3 * 121 = 80.7 dB. This means you can handle signals from -111 dBm (noise floor) to -111 + 80.7 = -30.3 dBm without IMD3 products exceeding the noise floor. SFDR is the most comprehensive single metric for receiver dynamic range because it combines both noise and linearity performance.

How does IP3 cascade through a receiver chain?

For a cascade of stages, the overall IIP3 can be approximated: 1/IIP3_total = 1/IIP3_1 + G_1/IIP3_2 + (G_1*G_2)/IIP3_3 + ... (all in linear power, not dB). Key insight: unlike noise figure (where the first stage dominates), for IP3 the LAST stages tend to dominate because their distortion products see the full cumulative gain. This is why the mixer and IF amplifier in a receiver typically limit the system IP3, not the LNA. Design tradeoff: the LNA needs enough gain to overcome the mixer's noise contribution (Friis), but not so much gain that it drives the mixer into nonlinearity (IP3 cascade). The optimal LNA gain balances these competing requirements.

Linearity

IP3 (Third-Order Intercept Point)

/eye-pee-three/ (IIP3, OIP3)

IP3 is the theoretical power where fundamental and IMD3 products are equal. OIP3 = P_out + Δ/2. IIP3 = OIP3 - Gain. IMD3 products (2f₁-f₂, 2f₂-f₁) fall near the desired signal and cannot be filtered. SFDR = 2/3×(IIP3 - noise floor). In cascade, later stages dominate (unlike NF where first stage dominates).

OIP3: P_out+Δ/2

IMD3 slope: 3:1

SFDR: 2/3×(IIP3-NF)

Understanding IP3

IP3 characterizes how well a component handles multiple signals without creating unwanted intermodulation products. When two signals pass through a nonlinear device, the third-order products (2f1-f2, 2f2-f1) are especially problematic because they fall close to the original frequencies and cannot be removed by filtering. Higher IP3 means the component can handle stronger interfering signals without corrupting the desired signal. IP3 is the most important linearity metric for receiver design.

IP3 Formulas

Third-order intercept point:
OIP3 = P_out+ΔP/2 dBm
ΔP = P_fund−P_IM3 (dB)
IIP3 = OIP3−Gain

IM3 products:
f_IM3 = 2f₁−f₂, 2f₂−f₁
P_IM3 grows at 3 dB/dB input

SFDR:
SFDR = (2/3)(IIP3−NF−10log(kTB)) dB

IP3 by Component

Component	IIP3	Gain	OIP3	Notes
GaAs pHEMT LNA	-10 to +5 dBm	15-20 dB	+10 to +25 dBm	Low NF priority
SiGe LNA	-5 to +15 dBm	12-18 dB	+10 to +30 dBm	Linearity priority
DB mixer	+5 to +25 dBm	-6 to -8 dB	0 to +18 dBm	Passive, high linearity
Active mixer	-5 to +10 dBm	+5 to +15 dB	+5 to +20 dBm	Gain but lower IIP3
IF amplifier	+10 to +30 dBm	15-25 dB	+25 to +45 dBm	High linearity

Key Equations

Decibel conversion:
Power: dB = 10log(P₂/P₁)
Voltage: dB = 20log(V₂/V₁)

dBm to watts:
P(W) = 10^{(dBm−30)/10}
0 dBm = 1 mW, +30 dBm = 1 W

Wavelength:
λ = c/f = 300/f(MHz) meters

Comparison

Component	IIP3	Gain	NF	Application
LNA (low noise)	+5 to +15 dBm	15–25 dB	0.5–2 dB	Receiver front-end
Mixer (passive)	+15 to +25 dBm	−6 dB	6–8 dB	Frequency conversion
PA (linear)	+30 to +45 dBm	10–30 dB	3–5 dB	Transmitter
Filter (passive)	Very high	~0 dB (loss)	= IL	Selectivity
Rx chain	+0 to +10 dBm	60–90 dB	3–8 dB	System level

Common Questions

Frequently Asked Questions

Two-tone test?

Drive with two equal tones. Measure fundamental and IMD3 at output. OIP3 = P_fund + delta/2. IMD3 grows 3 dB per 1 dB input increase. IP3 is theoretical; device compresses before reaching it.

SFDR?

SFDR = 2/3*(IIP3 - noise floor). Combines NF and linearity. IIP3=10dBm, NF=3dB, 1MHz BW: SFDR = 80.7 dB. Most comprehensive single metric for receiver dynamic range.

IP3 cascade?

1/IIP3_total = 1/IIP3_1 + G1/IIP3_2 + ... Later stages dominate (opposite of Friis NF). LNA gain must balance NF cascade vs. IP3 cascade. Too much gain degrades linearity.

Related Terms

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