## Saturday, July 18, 2020

### A Ham Radio Series 8 – The Basics of RF Design

When I started asking what you readers wanted to know, the question came up about the fundamentals of radio design.  Radio Frequency (RF) design has been around as a specialty of electrical engineering pretty much as long as engineering has been practiced.

The basics really boil down to a few things.  In order of what I think of as the importance.
Cascade design; stage by stage gain, noise figure and intercept point.
Filtering
Impedance matching
Transmission lines

This is what one of my generic receiver design sheets looks like, once it's filled in.  Each column across the top is one stage of the receiver.  This is a UHF receiver with a low noise amplifier mounted remotely and then connected by a long cable to the main receiver.  That makes the requirements for Noise Figure higher than a standalone UHF receiver.

The cascade Noise Figure can be calculated by this relationship:

This is all done in the linear domain, "Noise Factors", not Noise Figure, which is 10*log(Noise Factor) that's why a couple of lines in the spreadsheet say "Linear" and others say "dB" and in the spreadsheet, it converts back and forth between linear and dB.  The first line is an example for up to four stages.  The combined result is the noise factor of stage one plus the noise factor of stage 2 minus 1, quantity divided by the gain of the first stage.  For three stages, you add another term that's the noise factor of stage 3 minus 1, quantity divided by the product of the gains of stage 1 and stage 2.  A concise way of describing that is in the bottom equation, which is the cascade noise figure of N stages; it's the sum of the previous stage's noise factor (minus 1) divided by the product of all the stage gains up to that point.

It may not be apparent that a low noise, high gain first stage covers a multitude of sins farther down the chain and sets the system noise figure.

This topic could take another blog post by itself, while the other subjects have had books written about them.  I could do basics in a post or two each.

Filtering is indispensable and there’s a metric butt load of commercial suppliers but the exact parameters you need in your filter can sometimes vary enough to not allow an off-the-shelf product.   This is especially true when you’re designing new systems that the market hasn’t responded to, yet.  If you’re building another ham radio transceiver, there’s probably something on the market you can use.  If you’re building a system custom-designed for yourself or a niche market, you might need to design a filter.  Assuming you don’t want to pay some professionals to design it for you.

Impedance matching is honestly less important than it used to be because as the level of integration of components has gone up, there has been a tendency to standardize on certain impedance values.  When RF design was mostly discrete transistors (and tubes before that), it was common to have to tune stages to each other and match input and output impedances.  Now that the level of abstraction has gone to integrated circuit amplifiers that can be arranged in series strings, complete FM receivers on a chip, and other functions, the impedance settled on is often 50 ohms.  This makes it relatively easy to choose, for example, amplifiers, mixers, filters and whatever function you need with 50 ohm input and output so that there’s no need to match impedances.  Cable TV systems or systems that only receive tend to be 75 ohms (cable TV is by far the largest market) and there are tons of 75 ohm components available to choose from.

This is totally ignoring things like shirt pocket radios that have a builtin, telescoping antenna.  These systems tend to be more casually designed.

The reason radio systems have centered on 50 ohms since around WWII is that it’s a good compromise for both transmitting and receiving.  It can be shown that loss in coaxial cables is minimized around 75 ohms while power handling is best at lower impedance, around 35 ohms, so for systems that both transmit and receive, 50 ohms serves both well.  The range of impedances is because coaxial cable impedance depends on the geometry: the ratio of outer and inner diameters, and power handling depends on the loss in both of those – which also sets the sizes.

At this point, it’s worth mentioning that filters can also match different impedances between their input and output and can allow you to further reduce your use of parts.

Transmission lines are worth talking about because they help understanding lots of points about how to build things that work, plus they have properties that are mysterious and strange to first time learners.  Did you know that if you cut a length of coax to exactly 1/4 wavelength at some frequency and leave the end open that it behaves like a short circuit to ground for that frequency?  Not just that frequency where it's 1/4 wavelength long, but also at the odd harmonics; 3/4 wavelength, 5/4, and so on (although the behavior gets less perfect).  Unlike any other short to ground you make, the T line doesn't short out any DC you put on it.  It's only a short to RF at the frequency where the line is 1/4 wave long.  If you solder across that cable to short out the center conductor to the shield, you've made it an open circuit at that frequency.

That behavior can either be convenient or confuse the shit out of you!