Okay, after having read WB8ICN's postings on QRPedia, I decided to try to measure the impedence of both of my meters. I dug a 1.5M ohm resistor out of the pile, and hooked some jumper leads to it. I then did the following:
- Measure the resistance of the resistor, using the DVM as an ohm meter (R)
- Measure the voltage of a 9 volt battery, using the DVM as a volt meter. (V)
- Hook the resistor in series with the battery, and measure the resulting voltage. (Vm)
What we are looking for is the resistance of the meter, which we will call Rm. A little math should show that Rm = R * Vm / (V - Vm). Okay, that heavy lifting aside, let's see what we discovered about my two meters:
For my better meter, a nice Radio Shack PC interfaceable multimeter, I got the following readings:
- R = 1.496M ohms
- V = 9.24 volts
- Vm = 7.94 volts
Plugging these values into the formula, we get a value for Rm of 9.18M ohms, considerably off from the 10M ohms that we used as the "nominal" value. Later, I'll go back and work up the correction factor for the previous nights example, but for now, let's move onto my second meter, a cheapy $20 one that I've used mostly to check my car battery and continuity. I recorded the following values:
- R = 1.480M ohms
- V = 9.14 volts
- Vm = 3.68 volts
Plugging these values in, I get about .997M ohms, or about 1Mohm! No wonder my previous readings were so crazy, with the 4.4M ohm resistance of my series resistors, this thing was dividing the peak value down considerably.
Okay, let's go back to my dummy load experiment. First, on meter number one, we find that Rm of 9.18M ohms. If we go through my various calculations and correct for the measured values, we find that the output power should be around 4.71 watts. Doing the same for measurement number two, we'd get an output power of around 4.67 watts, both in excellent agreement!
(Note, I didn't measure the voltage drop of the diode, I'm assuming 0.7 v. The data sheet says the maximum drop would be 1v).
Well, I've been mucking around with my RF probe circuitry a bit tonight, and encountered something pretty strange. I have two digital multimeters lying around, and my newly rebuilt RF probe/dummy load that I described earlier. I hook one multimeter to it, and I get a reading of 14 volts. I get my other cheapie meter, and I get a reading of about four volts. Yet, both are probably "correct". How can that be?
Well, first, let's review the circuit that I have revised to:
I have used a different diode (a 1N914, which is probably better than the 1N4001 that I had in there previously, but not as good as the germanium diode you see in the schematic) and didn't have any 4.7M ohm resistors, so I hooked two 2.2M ohm resistors in series. The voltage drop for the 1N914 is probably about 0.7 volts, but haven't measured it. The purpose of the 4.7M ohm resistor is to convert the peak voltage (as gathered in the capacitor) to RMS voltage. How does this work? Well, if you imagine that the meter has some input resistance, then we basically have a voltage divider: the voltage that is measured by the voltmeter is the peak voltage, multiplied by the resistance of the meter divided by the sum of the meter resistance and the 4.7M ohm resistor. In years past, where this design was first put out, the common impedance for meters was around 11M ohms. So, the voltage we get out is the peak voltage * 11 / (11+4.7) = .7006 * the peak voltage. The peak voltage is sqrt(2) times the RMS voltage, so the RMS is the peak divided by sqrt(2). 1.0 / sqrt(2), which is .7071 or so, so the 4.7 Mohm resistor would be about right for a voltmeter with 11M ohm resistance.
Reading up on the subject, modern digital volt meters have an input impedence of 10Mohms. To figure out what size of a resistor we need for that, we solve 10 / (10 + R) = 1/sqrt(2) for R, and we end up with about 4.1M ohm resistance. I ended up approximating this by two 2.2M ohm resistors, which is closer, but still not perfect.
Okay, so that's my thinking. So, I jumper the thing to one of two meters, and get a reading of about 14 volts. This indicates an output power of 14*14/50 or 3.92 watts (this was my FT-817 in 5 watt mode). The number is small, but I expected that. I haven't accounted for two things: either the voltage drop of the diode, nor the problem with using the wrong series resistors. Instead of dividing the peak by the sqrt(2), I am multipling by about .694. Still assuming a 10M ohm resistance, my 14 volts should have been about 14.17 volts, plus the voltage drop (say .7 volts). This works out to about 4.42 watts. In the right ballpark, given that we didn't really measure the impedence of the meter.
But here's the odd thing! I hooked it to another, cheap meter of mine, and got only 3.92 volts! This is a budget DVM, which probably cost me about $10 that I have used mostly to check to see if my car battery is dead, but the difference is startling. The only conclusion I can draw is that the cheaper meter has a dramatically different impedence, probably around 0.5 Mohms. To test this idea, I measured the peak voltage at the junction between the cap and the diode, and both meters were in agreement. Interesting!
Through a coincidence, WB8ICN has been examining the same issue on QRPedia. He suggests using a potentiometer hooked to a regulated power supply, and measuring the voltage as you adjust the potentiometer until it reaches half the supply voltage, then the potentiometer is set to the impedence of your meter. Of course, with a little algebra, you don't need to do that: you can just measure the voltage drop of any resistor with a resistance of a 1M ohm or so, and work it out. I'll probably do that for both my meters, and then stick a little note on them so I remember.
Oh well, that's my electronics tinkering for the day.
My dummy load experiment still has a few unanswered questions, but I found that the ARRL Handbook has had a circuit which is basically what I built, minus the one series resistor. It looks like this:
Okay, they use a germanium diode with considerably lower voltage drop, and include a 4.7M ohm resistor in series to the DVM. This circuit also appears on the QRPEDIA posting on RF probes, and apparently is constructed as part of the assembly of the Elecraft K2.
Here's a posting talking about how the different diodes make for different performance.