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I am an RF noob and am trying to understand if optimizing an AM crystal radio antenna (maximizing the signal transmission from the antenna to the LC tank) is practical, or even makes sense. Here is a schematic of the circuit I am working with:

Simple Crystal Radio

My approach so far has been to treat my (theoretical) antenna (long wire) as a transmission line, and treating the LC tank as the load of the transmission line. In order to keep things simple, I have not considered loading by the diode. I reviewed a little literature about transmission line termination/impedance matching, and it seems that there would be some impedance value (implemented as a resistor between the antenna and the tank) which would maximize signal transmission at a given frequency.

Here are my questions:

  1. Does treating the antenna as a transmission line make sense?
  2. If so, how is the characteristic impedance of the antenna calculated?
  3. In adding a terminating resistor between the antenna and the tank, I would be making a voltage divider because I would 'read' the voltage between the tank and resistor i.e. this is where I would connect the diode. Would this potentially offset any gains I might make by impedance matching between the antenna and the tank?
  4. It seems that optimization may only be possible for one tank impedance, and, by extension, one specific wavelength. So, any 'optimized' design would only be able to listen to one radio station, and therefore not be useful even if it did work. Is that correct?

Thanks!

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Generally we do not think of antennas as transmission lines, but rather loads. In this case, the problem is designing a matching network (LC tank) to match your antenna to the diode/envelope detector (receiver). In this case, matching means you transform the antenna's impedance to the complex conjugate of the receiver's impedance (or vice versa).

The tool you would want to use for this is a Smith Chart. I would use ADS's smith chart tool. I think you can get a free trial if you don't have access.

  1. Treat the antenna as an impedance Z = R + jX. R is a combination of the radiation resistance of the antenna and ohmic loss. In your case, X may be negative, meaning that the antenna will be capacitive.

  2. The impedance Z of the antenna is calculated just like any other network (just a bit more arcane). Practically, you can measure the complex reflection coefficient (S11) using a network analyzer and back-calculate Z.

$$ Z = \frac{1+s_{11} }{1-s_{11}}$$ If you don't have a network analyzer, some simple antennas will have analytic formulas (short dipole example).

  1. Adding a resistor is not the worst idea, but it could dramatically decrease the efficiency of the network. In this case, you would be looking at the parameter S21 of the matching network when terminated by the appropriate loads. It may offset the power gain you get from matching.

  2. Your analysis is correct, the bandwidth of the overall network would be very small (this is on purpose!) However, your figure contains the solution: changing the value of the variable capacitor will change the resonant frequency of the LC tank, which will change the frequency of the perfect match, which will change the frequency of the radio station.

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  • \$\begingroup\$ Thanks for the thorough response! I will be sure to look into Smith Charts. \$\endgroup\$ – Mason_Schellenberg Sep 12 '20 at 22:25
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Yet another method to try matching the antenna to the tuned tank circuit is to inductively couple the antenna to the inductor via a second set of windings, instead of directly connecting it to the inductor capacitor junction.

See: https://commons.wikimedia.org/wiki/File:Inductively_coupled_crystal_radio_circuit.svg

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