Mixed Signals

Radio, digital or analog, is all about mixed signals. There is a popular saying, "I'm getting mixed signals", which implies confusion. But in radio, mixing is everything. Without it we cannot send or receive audio signals over radio frequency connections that use space itself as the connecting "wire".

Audio signals can be electronic, meaning they are represented by electrical signals flowing in wires. They can also be mechanical as in solids, liquid or air when we hear a sound or make a sound by tapping the table. My wife is tapping the table right now because she wants to go somewhere, but I'm hoping to finish this before she leaves me. Anyway:

Radio signals can also be represented by electrical signals flowing in a wire, or by photons of long wave light shining through the air and transiting the atmosphere, the ionosphere and ultimately empty space.

To make any kind of a useful radio we have to combine an audio signal - or a digital signal, as in where are my internet packets - anyway I was saying, we have to combine an audio frequency signal with a radio frequency signal prior to sending it out on the airwaves. Exactly the opposite occurs in the receiver:

goo.gl/09wN6m

To conclude this preamble, make the following mental note: When we mix one audio signal (the drums) with another audio signal (the guitar) on a mixing console in a recording studio, we are ADDING the signals together.

When we mix an audio signal with a radio signal in a radio prior to transmitting them, we are MULTIPLYING the signals together. This is called MODULATION. It comes in various flavors, AM, FM, PSK, but in all of these, the signals get multiplied to get on the air. When the signals encounter a receiver they are DEMODULATED, also by MULTIPLYING them with a radio frequency signal.

Mixers in Recording Studios Add Their Inputs

Now here's the bizarre and very cool thing that makes radio possible. When you mix two audio signals by adding them, the resulting signal is just the sum of the original signals, drums and guitar or what have you. Run with it. But when you mix two radio frequency signals by multiplying them the result is TWO signals. 

Here comes the good part. The product of two signals is two new signals - one at the sum of the original frequencies and one at the difference. So its like you can't get away from the sum thing. Multiplying them produces a sum (and  a difference which is just adding the negative). These sum and difference frequencies are called intermediate frequencies - IF for short - and they can be filtered and demodulated to discover the original signal be it audio, be it drums or guitar, or even my missing internet packets.

Since I am very interested in radio I was curious when mixing two signals what the issues were with regard to amplitude, frequency and phase.

Primarily I was concerned with the following. When we are receiving very faint radio signals from distant places like quasars or galaxies we have a very faint signal that is being mixed with a very powerful frequency produced by a local oscillator that enables us to move the sum or difference frequency to an intermediate frequency where we can grab it for demodulation (AM, FM, PSK or other). The whole mixing and unmixing thing is separate from the demodulation thing. We just have to agree before modulating what the demodulation scheme will be, so we don't even have to talk about that for this concern.

Long story short, I threw a couple of signals into my favorite geometric analysis program - Geometry Expressions™ - GX for short - written by the gang at Saltire Software - an AMAZING shop. Anyway here is what I found. Let's say the red signal is the local oscillator that you are tuning the signal in with. It can be as powerful as you want since you have control of it. Let's say the green signal (for little green men) is the signal that you are trying to pick out of the cosmic dust, litter, flotsam and jetsam. The blue signal is the mix of the two, and for this example we can see that it has about the same amplitude  as the little green men signal. 

From noise considerations, we don't want our red local oscillator to be any "louder" than the green signal, because we don't want any noise that may be in the oscillator to swamp out our fragile tiny signal in green.

From this we posit that the magnitude or strength or amplitude (however you want to say it) of the mixed signals is on the order of the strength of the LESSER of the two signal magnitudes. So if you want to pull in galaxy X, you better amplify it before you mix it, because its signal is only going to emerge from the mix as strong as it went in. The trouble with amplifying it before you mix it is that you amplify the noise too and one would like to avoid that. So you have to filter the INCOMING signal to only be in a band where you think useful information will be. This can be done starting with the antenna, if you know what frequency your information is going to be found on. This works fine for 89.1 FM because you know where the information will be. Bad for Galaxy X and the little green men.

One other thing if both signals are the same frequency (idealized case) and they differ by nothing but the phase of the signal (where in the clock cycle we started), then we get a DC offset in the resulting signal. This is usually blocked by a filter capacitor. It is an issue that must be addressed. Here is how it looks in GX:

Note that the signal strength in this case is half the strength of either signal. Making the case that when looking for little green men, its best to be as quiet as possible...