1. General Non-linearityx
f( )
y = f(x)
Any f(x) can be represented as a Taylor series expansion:
a0 represents a DC offset
a1 represents the linear gain
a2 represents the 2nd order response
a3 represents the 3rd order response
etc
We model devices as linear, but no practical devices are perfectly linear, so the Taylor coefficients ai are small, but not zero for i ≠ 1 .
We are going to examine the third order response when the input, x, is the sum of two sinusoids having equal amplitudes but different frequencies:

2. Then wX = 2w1 –(w1 + Dw) = w1 - Dw
The amplitude of Third Order Responses are proportional to the third power of the amplitudes of the generating signals.
The “Culprit”
The Other “Culprit”
wX = 2w1 - w2
Let w2 = w1 + Dw.
Then wX = 2w1 –(w1 + Dw) = w1 - Dw
A 1 dB increase in the amplitude of the interfering signals creates a 3 dB increase in the third order interference. Dw Dw Dw wX w1 w2 wY

3. Intermodulation Characteristics
Po(dBm)
3rd Order Intercept Point
PIP,o = PIP,i + G
PIP,o
Linear Response to Desired Signal
3rd order Response to Interference 1 3 1
Ps,o
SNR 1
Pd,o
IMDR =
Pd,i – Ps,i
PN,o
Pi(dBm)
PN,i
Ps,i
PSF
Pd,i
PIP,i
“Spurious Free”

4. Example
An amplifier has a gain of 22 dB and a 3rd order output intercept point of 27 dBm. Assume the effective noise input power is PN,i = -130 dBm.
Determine Spurious Free Range
PN,i + G = PN,o = Pd,o = 3(PSF + G) – 2PIP,o
PSF = (PN,i + 2PIP,o -2G)/3 = (– 130 dBm + 54 dB – 44 dB)/3
= – 40 dBm
Determine IMDR for an input signal level of -80 dBm and SNR = 15 dB.
Pd,i = (Ps,i + 2(PIP,o -G)– SNR )/3
= (– 80 dBm + 2(27 dBm – 22 dB)) – 15 dB )/3
= – 28.3 dBm
IMDR = Pd,i - Ps,i = – 28.3dBm – (– 80 dBm) = 51.7 dB

5. PIP,o
Ps,o
S/N
Pd,o
PN,o
IMDR
Ps,i
PN,i
PSF
Pd,i