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!
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. |
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. |
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. |
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 C_{t}. If you look at the schematic above, you will note that the 220pF capacitor labeled C1 (which I will call C_{f} 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 C_{x}. The total capacitance of the tank circuit is
C = C_{t} + BC_{f} + C_{x}where B indicates the state of the band switch: when that switch is closed, the capacitor C_{f} is included and B=1. When the switch is open, C_{f} is excluded and B=0.
The relationship between frequency, total capacitance, and inductance is
LC = 10^{12} / (2πf)^{2}The factor of 10^{12} 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 10^{6} 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 10^{12} pF in one farad, and 10^{6} μH in one henry. Putting all of this together, we get a correction factor of 10^{(12 + 6 − 6)} = 10^{12}.
I made a spreadsheet that used this formula to calculate the value of LC for each station frequency f, recorded the tuning capacitor C_{t} measurements, and had a box where I could modify my guess for the value of C_{x}. 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 C_{x} = 38.5pF, and modified the nominal value of C_{f} 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] C_{t [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:
I used two standard deviations around the mean value for the uncertainty of L.L = (180.2 ± 4.6) μH
C_{x} ≈ 38.5 pF
(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.