What are the frequencies of the second-order and third-order distortion tones given two frequency peaks?

In general, the third order distortion tones are understood to exist as in-band distortion at frequencies 2ω21 and 2ω12 in a two tone intermodulation test. Third order distortion also exists at frequencies ω1 and ω2. Second order distortion tones are found outside of a narrowband system at 2ω2, 2ω1, and ω12.  

Consider the two-tone input of a non-linear system with frequencies ω1 and ω2:

Vin = A[cos(ω1t)+cos(ω2t)]

The second order and third order distortion tones are calculated on the following page. In summary, the tones are shown in the table below. This shows that third order distortion tones are found not only in the positions mentioned above, but also contribute to the fundamental tone frequencies.  In a spurious-free system, all third order tones will be below the noise floor. This is verified in MATLAB with ω1, ω2 at 500kHz, 501kHz.

FrequencyComponents
DCa0+A2a2
ω1Aa1+2A3a3
ω2Aa1+2A3a3
2 ω1A2a2/2
2 ω2A2a2/2
ω1+ ω2A2a2
ω1 – ω2A2a2/2
ω2– ω1A2a2/2
3 ω1A3a3/4
3 ω2A3a3/4
2 ω1+ ω23A3a3/4
2 ω1– ω2A3a3/2
2 ω2+ ω13A3a3/4
2 ω2– ω1A3a3/2
– ω2A3a3/4
– ω1A3a3/4
ω1-2 ω2A3a3/4
ω2-2 ω1A3a3/4

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