Question E4D10:
What does a third-order intercept level of 40 dBm mean with respect to receiver performance?  

Choices:  
A: Signals less than 40 dBm will not generate audible third-order intermodulation products  
B: The receiver can tolerate signals up to 40 dB above the noise floor without producing third-order intermodulation products  
C: A pair of 40 dBm input signals will theoretically generate a third-order intermodulation product that has the same output amplitude as either of the input signals  
D: A pair of 1 mW input signals will produce a third-order intermodulation product that is 40 dB stronger than the input signal    

Correct Answer is  C: A pair of 40 dBm input signals will theoretically generate a third-order intermodulation product that has the same output amplitude as either of the input signals  

To understand IP3 (third-order intercept), remember it’s a theoretical point from a two-tone test where the extrapolated third-order intermodulation (IM3) products would equal the fundamental tones.

Why the correct answer is correct (Choice C)
- A “third-order intercept level of 40 dBm” means the input-referred IP3 (IIP3) is +40 dBm.
- By definition, if two equal input tones were each at $P_{in} = +40\ \text{dBm}$, the extrapolated third-order IM product would have the same output amplitude as either tone. Real receivers compress before that point, so it’s a theoretical construct.

Why the other choices are incorrect
- A: “Signals less than 40 dBm will not generate audible third-order IM products”  
  Incorrect. IM3 products are generated at any nonzero level; whether they’re audible depends on how far below the desired signals they are, not on a hard threshold at 40 dBm.
- B: “The receiver can tolerate signals up to 40 dB above the noise floor...”  
  Incorrect. IP3 is referenced to absolute input power (dBm), not to the noise floor. It’s about nonlinearity, not sensitivity.
- D: “A pair of 1 mW input signals will produce an IM3 product 40 dB stronger than the input signal”  
  Incorrect. With $P_{in}=0\ \text{dBm}$ and IIP3 = +40 dBm, the IM3 product is far below the tones, not stronger.

Useful formulas and rules of thumb
- Two-tone IM3 spacing (input-referred):
  $$\text{IM3 (dBc)} = 2\,(IIP3 - P_{in})$$
  Example: $IIP3=+40\ \text{dBm}$, $P_{in}=0\ \text{dBm}$ → IM3 is $2\times(40-0)=80$ dB below each tone.
- Equivalent form (output-referred):
  $$\text{IM3 (dBc)} = 2\,(OIP3 - P_{out})$$
- Absolute levels:
  $$P_{\text{IM3}} = 3P_{in} - 2\,IIP3 \quad\text{(in dBm)}$$
  or
  $$P_{\text{IM3,out}} = 3P_{out} - 2\,OIP3 \quad\text{(in dBm)}$$
- Rule of thumb: Increasing each tone by 1 dB raises IM3 by 3 dB, so the IM3-to-tone spacing shrinks by 2 dB per dB.