In general, the third order distortion tones are understood to exist as in-band distortion at frequencies 2ω_{2}-ω_{1} and 2ω_{1}-ω_{2} in a two tone intermodulation test. Third order distortion also exists at frequencies ω_{1} and ω_{2}. Second order distortion tones are found outside of a narrowband system at 2ω_{2}, 2ω_{1}, and ω_{1}+ω_{2}.

Consider the two-tone input of a non-linear system with frequencies ω_{1} and ω_{2}:

V_{in} = A[cos(ω_{1}t)+cos(ω_{2}t)]

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 ω_{1}, ω_{2} at 500kHz, 501kHz.

Frequency | Components |

DC | a_{0}+A^{2}a_{2} |

ω_{1} | Aa_{1}+2A^{3}a_{3} |

ω_{2} | Aa_{1}+2A^{3}a_{3} |

2 ω_{1} | A^{2}a_{2}/2 |

2 ω_{2}_{} | A^{2}a_{2}/2 |

ω_{1}+ ω_{2}_{} | A^{2}a_{2} |

ω_{1} – ω_{2} | A^{2}a_{2}/2 |

ω_{2}– ω_{1} | A^{2}a_{2}/2 |

3 ω_{1} | A^{3}a_{3}/4 |

3 ω_{2} | A^{3}a_{3}/4 |

2 ω_{1}+ ω_{2} | 3A^{3}a_{3}/4 |

2 ω_{1}– ω_{2} | A^{3}a_{3}/2 |

2 ω_{2}+ ω_{1}_{} | 3A^{3}a_{3}/4 |

2 ω_{2}– ω_{1} | A^{3}a_{3}/2 |

– ω_{2} | A^{3}a_{3}/4 |

– ω_{1} | A^{3}a_{3}/4 |

ω_{1}-2 ω_{2}_{} | A^{3}a_{3}/4 |

ω_{2}-2 ω_{1}_{} | A^{3}a_{3}/4 |