**Elementary Analysis of Distortion in Diode
Detection of Amplitude Modulation
**

**Introduction
T**his analysis considers the distortion produced
by diode detection of amplitude modulation. A typical detector consisting
of series diode followed by a simple RC lowpass filter is analyzed.

The diode characteristic is given by the Shockley equation:

(1) I

The exponential power series is given by:

(2) e

where, in the case of a diode, x=

Examining the x

Let w

The input to the diode is given by:

(3) cos w

The diode output is given by:

(4) d(t) = [phi(t)]

(5) d(t) = cos

(6) d(t) = cos

(7) d(t) = cos

(8) d(t) = cos

(9) d(t) = cos

The typical diode detector is followed by a lowpass filter (typically an RC type, that passes only the audio frequencies). Thus, all w

(10) m(t) = m

Here, the m

Total Harmonic Distortion (THD) expressed as a percentage is given by:

(11) THD (%) = (P

Thus, the diode detector THD is given by:

(12) THD (%) = (m

Calculating the THD for various modulation indices gives:

ModulationIndex (%) |
THD(%) |

10 | 0.015625 |

20 | 0.0625 |

30 | 0.140625 |

40 | 0.25 |

50 | 0.390625 |

60 | 0.5625 |

70 | 0.765625 |

80 | 1.0 |

90 | 1.265625 |

100 | 1.5625 |

150 | 3.515625 |

200 | 6.25 |

Harmonic Distortion Versus

Modulation Index

The typical diode detector consisting of series diode followed by a simple
RC lowpass filter will produce a distorted output due to the inherent non-linearities
of the diode. The distortion increases exponentially with the modulation
index.

To verify the theoretical analysis, the diode detector circuit shown in Figure 1 was constructed. An AM signal with various modulation indices was input and the THD on the output was measured. The test equipment configuration is shown in Figure 2. The results are shown in Table 2.

**Figure 2 - Test Equipment Configuration**

ModulationIndex (%) |
THD(%) |

10 | 1.02 |

25 | 0.08 |

50 | 0.32 |

100 | 2.0 |

150 | 6.3 |

Harmonic Distortion Versus

Modulation Index

The THD measurements were made with the HP 3562A Dynamic Signal Analyzer.
The 3562A is a two channel Fast Fourier Transform (FFT) based analyzer.
It has a built in THD measurement function.

The measured THD values in Table 2 track closely with the calculated values
in Table 1. The value for 10 percent modulation appears to be erroneous,
as it is much greater than calculated. Also note that the THD values for
100 and 150 percent modulation are higher than the calculated values. This
could be due to the contribution of the higher order harmonics in the measured
values. These higher order components were not considered in the theoretical
analysis. It is clear, though that distortion increases exponentially with
modulation index or percentage. The distortion becomes problematic at indices
of approaching 100 percent and severe at percentages greater than 100 percent.

**Conclusion**

Both theoretical and empirical analysis shows that the typical diode detector
consisting of a series diode followed by a simple RC lowpass filter will
produce a distorted output due to the inherent non-linearities of the diode.
The distortion increases exponentially with the modulation index. The amount
of distortion is most significant at modulation indices approaching and
exceeding one.