How much is a bit worth?

Foundations of Amateur Radio During the week I finally made the decision to purchase my first software defined transmit capable radio. It wasn't an easy choice for me, given that the range of options vary in price from "not much" to "more than my car is worth" and an infinite number of choices between those. One of the considerations, other than price, was a thing called bit-depth. In the past I've spoken about how an analogue to digital converter or ADC uses bits to represent a radio signal. In short, a voltage coming from an antenna is represented as a digital value inside the radio. No signal represents a value of zero and maximum signal represents the maximum value that fits into the decoder. A concrete example might be an 8-bit ADC which can represent 256 different values. If you look at the choices available to you, you'll see that there are 8-bit radios, 12-bit ones, 16-bit, 18-bit and 24-bit radios. On the face of it you could just say, more bits is better, but how much better? For example, an ANAN-10 and a FLEX-3000 radio, both costing about the same, have a different ADC. The ANAN is a 16-bit device and the FLEX is a 24-bit device. At the other end, a HackRF One is an 8-bit device and costs twice as much as an ADALM Pluto that's a 12-bit device. How do you choose and what are you choosing? Essentially you're choosing something called dynamic range. Think of it as the range of signal strengths that you can represent using a number of bits. As it happens there's a formula for that. It's 20 times the log 10 of 2 to the power of the number of bits times the square root of 3 divided by 2 and it represents decibels relative to full scale or dBFS. In more recognisable terms, it comes down to a bit being worth 6 dB of range. A good approximation is the number of bits times six plus two. For example, a 6-bit SDR will have a dynamic range of 6 times 6 bits is 36, plus 2 makes 38 dB of range. An 8-bit SDR has 6 times 8 bits is 48 plus 2 makes 50 dB of dynamic range. I'm using rounded off numbers here but it gives you a pretty accurate sense of scale. Six times the bits plus 2 works until about 36-bits and then it's off by one dB, until we hit 85-bits - which we won't likely be able to buy at the local ham store for a little while yet - and then it'll be off by 2 dB. Another way to think of dynamic range is to think of it as the difference between the weakest signal you can measure and the strongest signal. Given your SDR is going to be using a whole chunk of radio spectrum, you likely will have to deal with your local broadcast stations as well as that QRP signal you want to decipher, so more dynamic range is better. Let's give this some context. The Australian Broadcasting Corporation, the ABC, has a local AM station on 720 kHz that has a transmitter with an EIRP of just under 155 kilowatts. My QRP station uses 5 watts. My signal is 45 dB weaker than that local transmitter. This means that in order for an SDR to be able detect my signal in comparison to the broadcast station, it would need to have a range of 45 dB or 45 less 2 is 43 divided by 6 is 8 bits range at a minimum. Now this isn't precise or complete, but it should give you some sense of scale. In this example, the amplitude range of my 5 watt signal is represented by a digital range of 1 and the broadcast transmitter is represented by a range of 255 values. That means that the best you could hope for in decoding my signal would be if I was transmitting Morse, the absence or presence of my signal would make the value representing my signal go from 0 to 1. As you might imagine, this is not suitable to decode something more complex like SSB. My Morse signal is also right at the noise floor, so it might not even be detectable at all. Similarly, in the absence of a 150 kilowatt station, but say a 1500 watt station, you'd need just under 25 dB range, or 4-bits. Now before you start pointing out that there are other issues, yes, there are, sample rate, clock stability to name two. We'll get to those. I should also point out that normally you'd represent the voltage range using both positive and negative values and I didn't mention that the maximum is calculated using RMS. In the meantime, I'm getting excited to see my new toy arrive. I'll let you know how it goes. I'm Onno VK6FLAB