Between decibels and milliwatts ...

Foundations of Amateur Radio Between decibels and milliwatts ... As you might recall, I've been working towards using a cheap $20 RTL-SDR dongle to measure the second and third harmonic of a handheld radio in an attempt to discover how realistic that is as a solution when compared to using professional equipment like a Hewlett Packard 8920A RF Communications Test Set. I spent quite some time discussing how to protect the receiver against the transmitter output and described a methodology to calculate just how much attenuation might be needed and what level of power handling. With that information in-hand, for reference, I used two 30 dB attenuators, one capable of handling 10 Watts and one capable of handling 2 Watts. In case you're wondering, it's not the dummy load with variable attenuation that I was discussing recently. I ended up using a simple command-line tool, rtl-power, something which I've discussed before. You can use it to measure power output between a set of frequencies. In my case I measured for 5 seconds each, at the base frequency on the 2m band, on the second and on the third harmonic and to be precise, I measured 100 kHz around the frequencies we're looking at. This generated a chunk of data, specifically I created just over a thousand power readings every second for 15 seconds. I then put those numbers into a spreadsheet, averaged these and then charted the result. The outcome was a chart with three lines, one for each test frequency range. As you'd expect, the line for the 2m frequency range showed a lovely peak at the centre frequency, similarly, there was a peak for the other two related frequencies. The measurement data showed that the power measurement for 146.5 MHz was nearly 7 dB, for 293 MHz it was -44 dB and for 439.5 MHz it was -31 dB. If you've been paying attention, you'll notice that I used dB, not dBm or dBW in those numbers, more on that shortly. From a measurement perspective we learnt that the second harmonic is 51 dB below the primary power output and the third harmonic was about 38 dB below the primary power output. First observation to make is that these numbers are less than shown on the HP Test Set where those numbers were 60 dB and 62 dB respectively. Second observation, potentially more significant, is that pesky dB thing I skipped over earlier. If you recall, when someone says dB, they're referring to a ratio of something. When they refer to dBm, they're referring to a ratio in relation to 1 milliwatt. This means that when I say that the power reading was 7 dB, I'm saying that it's a ratio in relation to something, but I haven't specified the relationship. As I said, that's on purpose. Let me explain. When you use an RTL-SDR dongle to read power levels, you're essentially reading numbers from a chip that is converting voltages to numbers. In this case the chip is an Analog to Digital Converter or an ADC. At no point has any one defined what the number 128 means. It could mean 1 Volt, or it could mean 1 mV, or 14.532 mV, or something completely different. In other words, we don't actually know the absolute value that we're measuring. We can only compare values. In this case we can say that when we're measuring on the 2m band we get a range of numbers that represent the voltage measured along those frequencies. When we then measure around the second harmonic, we're doing the same thing, possibly even using the same scale, so we know that if we get 128 back both times we might assume the voltage is the same in both cases, we just don't actually know how much the voltage is. We could say that there's no difference between the two, or 0 dB, but we cannot say how high or low the voltage is. This is another way of describing something I've discussed before, calibration. So, if I had a tool that could output a specific, known RF power level, and fed that into the receiver and measured, I could determine the relationship between my