Crystal Radio Impedance Matching

David Wagner 2008/04/20 01:48

Efficient energy transfer requires matching the source to the load. For the crystal radio builder, and especially for those pursuing DX signals, this is not a trivial task. Each of the four main subsystems in a set, antenna-ground, resonant tank, detector, and acoustic transducer, has a characteristic impedance different from the next in line. Complicating the problem is how component impedance varies with the frequency and even the type of audio content being received. Much of the art of crystal radio design is in how seemingly incompatible components are coupled to one another efficiently enough to transfer the faint power of a distant signal directly into sound loud enough to hear clearly.

The usual solution to this problem involves loosely (and variably) coupling air-core inductors to match the radio frequency components, and using one or more specialized audio transformers to match the detector to the headphones or speaker in use. This analysis takes a slightly different approach and considers the design of matching transformers for each stage. Though this design can be used with traditional air-cored coils, it may prove more useful for coupling closed-field toroidal inductors which are more compact and less sensitive to their environment than traditional inductors.

  • Antenna-ground
  • Tank
  • Detector
  • Transducer

The fundamental difficulty arises in transferring energy efficiently past the parallel resonant tank circuit. To maintain its selectivity, the LC tank must not be heavily loaded; the signal passing across it must have a very high impedance. But the impedance cannot be so high that the tank itself loses too much of the signal.

Assuming the use of an appropriate detector and efficient transformers and headphones, the quality of the resonant tank (or tanks) limits the performance of and determines the optimum signal impedance of a crystal set. To understand why, it helps to understand the signal path from antenna to eardrum. FIXME

Antenna-ground Impedance

Unless you are lucky enough to be able to use a truly enormous antenna, or are interested in higher frequencies, an AM broadcast band antenna will typically have a fairly low resistive impedance and a relatively high capacitive reactance that varies significantly across the band.

It is useful to consider the standard dummy broadcast band antenna, which appears to be similar to what one can expect from a 100' vertical wire. Other random wires will behave similarly though it will usually be necessary to adjust component values to effect a good match.

FIXME

Once the capacitive reactance is tuned out, the signal has a very low resistive impedance, usually in the tens of ohms.

Tank Coupling

Loosely coupling air-core inductors through mutual inductance when separated by a coil diameter or so is the standard means to transfer RF energy to the detector tank, and will not be covered in detail here. An alternative means is needed to transfer energy between closed-field inductors. Both inductive and capacitive coupling can be used.

Inductive coupling seems to be more common, and involves placing the primary winding of a small RF transformer in series with the antenna tank coil, and the secondary in series with the detector tank coil. For efficient energy transfer, the primary winding should have an inductive reactance approximately equal to the antenna-ground resistance, and a secondary winding reactance equivalent to the detector tank loading. For example, a transformer may have primary and secondary windings on an FT50-61 tapped from 2-9 turns, resulting in 0.3-5.6 µH, about 2-35 Ω inductive reactance at 1 MHz.

A simpler and more adjustable coupling uses a small variable capacitor. A 10pF trimmer can be used to couple directly between the tanks, or a larger 50-100 pF variable capacitor may be used with an RF transformer to step up the impedance. In either case, a larger variable capacitor may be placed in series with a fixed capacitor.

FIXME

When an electrically short antenna is made resonant, its impedance is a few ohms greater than the ground resistance. For efficient energy transfer, the capacitor should have an impedance at the frequency of interest equivalent to twice the equivalent parallel tank loading resistance caused by a circulating current resistance equal to the antenna resistance.

  • R_P = {(2 pi f L_tank)^2}/{R_circ}

The antenna-ground resistance of the standard dummy antenna is 25 Ω.

  1. X_couple = 2 R_P = {2*(2*pi*1*10^6*90*10^{-6})^2}/{25}=25556
  2. C_couple=6.2 pF

FIXME Twice? Coupling impedance should be equal to source impedance: 2.4-88 pF @1720-520 kHz.

Tank Impedance

Detector Impedance

The detector is a nonlinear device and its impedance varies with signal strength. For very small-signal detection, it approaches the zero-crossing impedance, a large value that can often be estimated from diode parameters or assumed for the device in use. For efficient energy transfer, the audio impedance should match the detector's impedance at the signal level being detected. This value will be somewhat less than the zero-crossing impedance since the current of the smallest audible signal is somewhat greater than zero, but the zero-crossing impedance provides an upper bound.

For moderate to high signal strength reception…FIXME

Transducer Impedance

FIXME


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