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Rusty bolt effect

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When radio waves from clean transmitters interact with dirty connections or corroded parts (which would then act as a diode) of a television, the rusty bolt effect, including the generation of harmonics and/or intermodulation in the signal, can occur. Rusty objects can re-radiate radio signals with harmonics and other unwanted signals; a television might then receive and attempt to interpret these signals.

If one experiences this problem, one should check both the transmitter and the television for dirty connections or corroded parts. One should also check for signs of corrosion in the cables which link the equipment to the antennae and for badly made joints. Beyond this, one might check any metal objects near the antenna for rust or corrosion. Any of these could be the source of the problem.

It is possible to cure this problem in several ways:

  • Remove the corroded object. This is often the best cure because if you can eliminate the object then the interference it generates will cease entirely.
  • Clean the object to allow proper electrical flow.
  • Place an insulator between the two objects which are making the rust bolt. This will stop the RF current entirely.
  • Lower the RF field strength, the math below explains how this will greatly reduce the intensity of the effect.
  • Get a better antenna which is more directional. It may be possible to point the aerial in such a direction that it does not pick up the unwanted signal coming from the rusty bolt.

Mathematics associated with the rusty bolt

The transfer characteristic of an object can be represented as a polynomial:

E o u t = ∑ n = 1 ∞ K n E i n n {\displaystyle E_{out}=\sum _{n=1}^{\infty }{K_{n}E_{in}^{n}}}

Or, taking only the first few terms (which are most relevant),

E o u t = K 1 E i n + K 2 E i n 2 + K 3 E i n 3 + K 4 E i n 4 + K 5 E i n 5 + . . . {\displaystyle E_{out}=K_{1}E_{in}+K_{2}E_{in}^{2}+K_{3}E_{in}^{3}+K_{4}E_{in}^{4}+K_{5}E_{in}^{5}+...}

For an ideal perfect linear object K2, K3, K4, K5 etc are all zero. A good connection approximates this ideal case with sufficiently small values.

For a 'rusty bolt' (or an intentionally designed frequency mixer stage), K2, K3, K4 and/or K5 etc are not zero. These higher-order terms result in generation of harmonics.

The following analysis applies the polynomial representation to an input sine-wave.

Harmonic generation

If the incoming signal is a sine wave {Ein sin(ωt)}, (and taking only first-order terms), then the output can be written:

E o u t = K 1 E i n s i n ( ω t ) + K 2 E i n 2 s i n ( 2 ω t ) + K 3 E i n 3 s i n ( 3 ω t ) + K 4 E i n 4 s i n ( 4 ω t ) + K 5 E i n 5 s i n ( 5 ω t ) + . . . {\displaystyle E_{out}=K_{1}E_{in}sin(\omega t)+K_{2}E_{in}^{2}sin(2\omega t)+K_{3}E_{in}^{3}sin(3\omega t)+K_{4}E_{in}^{4}sin(4\omega t)+K_{5}E_{in}^{5}sin(5\omega t)+...}

Clearly, the harmonic terms will be worse at high input signal amplitudes, as they increase polynomially with the amplitude of Ein.

Mixing product generation

Second order terms To understand the generation of nonharmonic terms (frequency mixing), a more complete formulation must be used, including higher-order terms. These terms, if significant, give rise to intermodulation distortion.

E f 1 + f 2 = k E f 1 × E f 2 {\displaystyle E_{f_{1}+f_{2}}=kE_{f_{1}}\times E_{f_{2}}}

E f 1 − f 2 = k E f 1 × E f 2 {\displaystyle E_{f_{1}-f_{2}}=kE_{f_{1}}\times E_{f_{2}}}


Third order terms

E f 1 + f 2 + f 3 = k E f 1 × E f 2 × E f 3 {\displaystyle E_{f_{1}+f_{2}+f_{3}}=kE_{f_{1}}\times E_{f_{2}}\times E_{f_{3}}}

E f 1 − f 2 + f 3 = k E f 1 × E f 2 × E f 3 {\displaystyle E_{f_{1}-f_{2}+f_{3}}=kE_{f_{1}}\times E_{f_{2}}\times E_{f_{3}}}

E f 1 + f 2 − f 3 = k E f 1 × E f 2 × E f 3 {\displaystyle E_{f_{1}+f_{2}-f_{3}}=kE_{f_{1}}\times E_{f_{2}}\times E_{f_{3}}}

E f 1 − f 2 − f 3 = k E f 1 × E f 2 × E f 3 {\displaystyle E_{f_{1}-f_{2}-f_{3}}=kE_{f_{1}}\times E_{f_{2}}\times E_{f_{3}}}

Hence the second order, third order and higher order mixing products can be greatly reduced by lowing the intensity of the original signals (f1, f2, f3, f4 ...... fn)

References

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