Radio circuits built by Don Cross

Reflex AM receiver – August 2009

I am very pleased to report that I have finally built a radio receiver that is good enough that I can enjoyably use it!

This receiver is a modification of Charles Wenzel's Two Transistor Reflex Radio. Instead of a ferrite AM loopstick antenna, I use a magnetic loop antenna, and I added an LM386 amplifier stage to drive an 8-ohm speaker. There is a switch to select whether this amplifier should be used to power the speaker or whether crystal earphone listening is desired. I use six AA rechargeable NiMH batteries to provide the 8V power supply, but a 9V alkaline battery or a 6V lantern battery work just fine. I think even a small solar cell array would suffice to power this thing if you were camping on a sunny enough day!

receiver prototype
Prototype receiver on breadboard. I will soon move all parts currently mounted on the breadboard to a soldered circuit board. I will also add interface connections with screws on the wood base, so that I can swap out other receiver modules to the same wooden box.
finished receiver
Update – 25 August 2009. The finished AM receiver. The detector and audio amplifier circuitry is now soldered to a permanent circuit board. I added a handle to make it easy to carry the radio around.
finished receiver, inside view
Close up view of the inside of the finished receiver. I have the schematics folded up inside a small zipper-style plastic bag, attached to the inside of the wood frame using Velcro. The screw connections facilitate removing the circuit board and replacing it with other experimental designs.

receiver schematic

Notes about this circuit

Experimental determination of inductance L and parasitic capacitance Cx

Tonight (28 August 2009) I had fun with an experiment to figure out the inductance of the tuning coil (the 20 turns of magnet wire), along with its so-called "parasitic" capacitance. I tuned the receiver to 6 different radio stations. For each radio station, I turned the receiver off, disconnected one of the tuning capacitor wires, and measured the tuning capacitor with my capacitance meter.

Now in each case, I know both the frequency of the radio station f and the tuning capacitance Ct. If you look at the schematic above, you will note that the 220pF capacitor labeled C1 (which I will call Cf here) can be included or excluded from the tuning circuit, using the "band" switch. I was able to tune two of the radio stations (WDBO and WORL) with either band switch setting, because they broadcast on frequencies included in the overlap of both bands. I recorded the band switch setting in all measurements. Overall, I took a total of 8 measurements of the 6 stations, with WDBO and WORL having 2 measurements each (one for each band switch position).

My goal was to solve for two unknowns: inductance L and parasitic capacitance Cx. The total capacitance of the tank circuit is

C = Ct + BCf + Cx
where B indicates the state of the band switch: when that switch is closed, the capacitor Cf is included and B=1. When the switch is open, Cf is excluded and B=0.

The relationship between frequency, total capacitance, and inductance is

LC = 1012 / (2πf)2
The factor of 1012 is needed to correct for the fact that f is expressed in kHz and LC is expressed in pF*μH. If "pure" units of Hz, F, and H were used, this numerator would simply be 1. The squared reciprocal of kHz makes the answer 106 times bigger than it would have been with Hz, because now we are dividing by a number that is a million times smaller (a thousand squared). By definition, there are 1012 pF in one farad, and 106 μH in one henry. Putting all of this together, we get a correction factor of 10(12 + 6 − 6) = 1012.

I made a spreadsheet that used this formula to calculate the value of LC for each station frequency f, recorded the tuning capacitor Ct measurements, and had a box where I could modify my guess for the value of Cx. When I divide the calculated value of the product LC by the total capacitance C, I get a theoretical value for the inductance L. By trial and error, I settled on an optimal value for Cx = 38.5pF, and modified the nominal value of Cf to be 223pF to make all the L values as close together as possible. Here is table that shows what my spreadsheet looks like:

station f [kHz] LC [pF*μH] Ct [pF] B C [pF] L [μH]
WFLF 540 86867 218 1 479.5 181.16
WDBO 580 75298 155 1 416.5 180.79
WDBO 580 75298 378 0 416.5 180.79
WORL 660 58150 65 1 326.5 178.10
WORL 660 58150 288 0 326.5 178.10
WYGM 740 46257 221 0 259.5 178.25
WONQ 1030 23876 91 0 129.5 184.37
WSDO 1400 12924 33 0 71.5 180.75

Based on these data, I have the following estimates:

L = (180.2 ± 4.6) μH

Cx ≈ 38.5 pF

I used two standard deviations around the mean value for the uncertainty of L.

(Update: 9 September 2009) I realized I should go back and measure the resistance of the magnetic loop antenna. It turns out to be 3.0 Ω.

This kind of analysis should help me design better hand-wound magnetic loop antennas in the future. Ideally, I may be able to design a tuner that doesn't need a band switch to cover the entire AM band. Another possibility is that I may be able to design a tuner that uses a variable inductor instead of a variable capacitor to tune to various stations. In general, it will be interesting to compare experimentally determined coil behavior with the values I get from the various formulas for estimating inductance based on coil geometry.