A Crystal FM Radio

David Wagner 2008/02/20 00:06

The FM broadcast band is about 87.5 to 108.0 MHz (550-680 Mrad/s), with a geometric mean of 97.2 MHz (610 Mrad/s)1), and 200 kHz channel spacing.

FrequencyWavelengthλ/2
(MHz) (rad/sec) (m) (in)
87.5 550,000 3.426 67.4
89.8 564,000 3.337 65.7
92.2 579,000 3.251 64.0
94.7 595,000 3.166 62.3
97.2 611,000 3.084 60.7
99.8 627,000 3.004 59.1
102.5 644,000 2.926 57.6
105.2 661,000 2.850 56.1
108.0 679,000 2.776 54.6

An AM broadcast band crystal radio presents a high-impedance load and seems to work best with a high-impedance antenna, usually a simple random wire antenna. This wire is usually shorter than half the wavelength (about 300-900', 100-300 m) and provides a source impedance of several thousand ohms at the end. This is good, since the off-resonance impedance of the typical crystal radio tank circuit load is also in this range and the tank elements need to pass all but the tuned frequency efficiently.2) Since the antenna is too short anyway, feeding the tank is a simple matter of extending the antenna wire into the radio.

On the other hand, FM wavelengths are much shorter, and getting enough metal into the air to gather a decent amount of radiated signal is no longer the simple case of longer is better. After one-half wavelength (about 5'), things can get complicated. High-impedance is still necessary to minimize tank loading, but getting a strong high-impedance signal from an antenna and into the crystal set requires different principles.

Antenna

An end-fed, half-wavelength antenna has an impedance of several thousand (1,800-5,000) ohms, but it is difficult to get a transmission line to efficiently conduct this level of RF. It's even difficult to make a parallel transmission line with 1000 Ohms characteristic impedance. 3)

But FM broadcast frequencies have much shorter wavelengths, with half-wavelengths of about 52-64”4) in copper wire. The short wavelength his may not be long enough to develop the voltage needed for all but exposure to the fields of the strongest nearby stations. Perhaps an end-fed collinear array would work.

   .47     .50     .50     .50     .50
 |-------|-------|-------|-------|------|  
 
  ------+ +-----+ +-----+ +-----+ +-----
        | |     | |     | |     | |
        | |     +-+     +-+     +-+
        | |
        | |
        +U+----+--->|---
        |    / |
        +--||--+
        | /
        |
       ---
        -

[How about a λ/2 collinear with 300 ohm impedance?]

Folded Dipole

Use 4'9” total length for the center of the FM broadcast band, or 468/MHz for the length (in feet) for a specific frequency.5) By this, 63” (5'3”) should be best for 89.1 MHz.

A crystal radio normally works from an unbalanced (one-wire) antenna-feedline. See A Simple 75-ohm Coax Balun for 88-108 MHz for how to make an FM balun.

 |--------- ½λ ----------|
                    
 +-----------------------+    
 +----------+ +----------+    ---
+V          | |          -V    |
            | |                |
            | |                |¼λ
            | |                |
         -V | | +V             |
            + +-----------+   ---
            |             |                 \  /
            +-UUUUU+U-----+--|<--UUU--+--||--[]--+
              :::::|:     |      = =  |          |
                   |    / |           +--VV--UUU-+
                   +--||--+                  === |
                   | /                           |
                   |                             |
                   +--UUU------------------------+
                      = =?

Resonant Circuit

The reactances of typical FM tuning elements are much smaller than their AM counterparts. The reactance of a 0.2 µH inductor ranges from 110 to 136 Ohms across the FM broadcast range, for a parallel tank off-resonance impedance of around 50 Ohms. This is only slightly lower for a 0.13 µH inductor, and can be raised back to around 50 by using a fixed capacitor in series with the tank of around 220 pF (100-500 should work fine).

Detector

Audio Circuit

1) sqrt{87500000*108000000}=97211000
2) A typical inductor for the tank is 262 µH (so it resonates across the AM broadcast range with a variable capacitance from 30-365 pF.) The reactance of these resonant elements ranges from about 850 to 3000 ohms across the band, so the parallel impedance of the tank is about 425-1500 Ohms off-resonance.
3) 28 gauge at 12”: Z=276 log_10 {2S/d} = 276 log_10 {2*12/0.0126}=905 Ohm.
4) 468/MHz

Personal Tools