Jack-and-Jill went up the hill
A tale about multi-carrier back off, saturation, and little brothers and sisters
In order to be heard in a communication, you need power. You need power in order to overcome the carrier-to-noise problem. Now power is expressed in Watts or dBW but another important metric is the cost to make that power (or as some CTOs like to express it, the number of dB$ it takes to make that power). How do we make power? Well, the question should be “how do we increase power?” because we start of with a tiny amount of power out of the modulator for example say -30 dBm (for those that still think linear that’s a 1/1000th of a mW or 1 nW! ). You might have heard the term EIRP of a carrier. That’s just a complicated term to express with how much power a carrier is radiated to the satellite. A classical EIRP is 70 dBW, again, thinking linear this is 10 Million Watt (beware: the reference is not mW but W, expressed in dBm this EIRP would be 100 dBm). So you see, needing to go from 1 nW to 10 MW, you need a serious amount of amplification, a serious “hill to climb”.
Probably you are wondering about the little brothers and sisters in the title. Well let me explain you how brothers and sisters are created. It’s all about linearity: if you want to amplify something then it needs to pass an amplifier. Now that amplifier has a certain transfer characteristic, a definition of how signals will exit the amplifier. You could make a graph with the input power at the x-axis and the resulting output power on the y-axis. Now you’d expect this to be a nice straight line. Let’s assume an amplifier with a gain of 10 times then a power of 1 W at the input will result in a power of 10 W and a power of 2 W at the input would result in a power of 20 W. As simple as that, a nice straight line. Now one of the specification of an amplifier is its maximum output power. This depends on the type of amplifier and the size of it’s power supply (of course, the added power has to come from somewhere!). Assume that our amplifier has a maximum output power of 100 W. So if you input 10 W, a power of 100 W will come out of the amplifier. But what happens if we input 11 W? Well, the maximum power is 100 W so even in this case the output will be 100W. We call this point saturation, we have driven the amplifier to its maximum. So here’s the hill: you can climb and climb but at certain point you reach the top and you can’t go any further up. The top is flat and stays at the same height. But wait. You can also go over the hill and go down-hill on the other side (you know there where the grass is always greener). That’s exactly what happens within an amplifier too: if you push it over saturation, the output power will gradually decrease.
The transfer curve of an amplifier is not a straight line. At low input powers it is nice and straight, we call this the linear region. But the closer you get to the top (the saturation point) the curve becomes rounded until it peaks and then falls of again down-hill. The region where the curve is not linear is called…. the non-linear region (and who said that engineering was difficult!). Assume that we input a power of 9 W in our amplifier, out comes 90 W. But we are close to the maximum (in the non-linear region) and if we in-crease the power to 9.5 W the output power will not be the expected 95 W but only 94 W. You see, the linear relationship between in and output is gone. We get less power out of the amplifier than we expected, we also call this compression.
So what, you might think. If you need a higher output power you just push a little harder and you’ll eventually reach the desired maximum output power (remember if you push it over the hill, the power will decrease again. But let me explain you a bit more about this non-linear region. A funny thing happens when you pass 2 signals through a non-linear device. Mixing will occur. I guess I could show you this with a lot of mathematical wizardry but you’ll have to believe me on this one (or else you know where to find it on the wikipedia). What will happens is that when you present 2 signals of different frequency at the input, you will get those 2 frequencies at the output but also some mixing products on other frequencies. You will find them at the sum and the difference of these frequencies (so at f1 + f2 and f1 - f2 ). In fact that is something that is used in mixer and up converters. You come in with one frequency, you mix it with another frequency (called a local oscillator) and the output contains both the sum and difference frequencies. You only need to filter out the sum and you have up converted the input frequency (say L-band) to another frequency (for example C or Ku band). We want this to happen in an up converter for sure but do we want this in an amplifier? I guess not, the amplifier basically needs to amplify what is at the input and present it at the output without the presence of any unwanted by-products. When this does happen, some refer to this as creating brothers and sisters at the output. You get it?
Hmm, so Jack and Jill (let’s name our 2 carriers like that for a while) must go up the hill but don’t want to create any brothers and sisters on their way to the top. So what do they have to do? Well they have to stay away from the top; they need to back-off. Et voila, there you have it, the infamous need for “multi-carrier input back-off” from the “saturation point”.
And why is there speak of a saturated transponder then? Well that is just a big fat boy (a carrier so wide that it fills up the entire bandwidth of a transponder) that goes up alone. He has no other carriers around so no chance that there will be brothers and sisters created. This carrier simply cannot mix with any other carrier because he is the only one around. Guess what, this big boy can go much higher up the hil. He can get much closer to the top (get closer to saturation) than in the case of multi-carrier operation. The big carrier can saturate the transponder, meaning that he can use the maximum available power of that amplifier in the satellite. If we were to transmit the same data into 2 separate carriers we would need to back off resulting in a lower output power in the output so you’d need bigger ears (antennas) to be able to receive and decently decode the transmission.
There’s plenty more things to tell about that “receiver and amplifier in the sky” that we call a satellite but that’s all for now folks.
See you later,
Your humble servant, Dave