The Ham Radio Series 36 - What Are S-Parameters and Why Should I Care?

I mentioned in February of ‘22 that I had bought a NanoVNA.  If you’re unfamiliar with the term, VNA is short for a Vector Network Analyzer, a test instrument that can measure the complex impedance of something, and a handful of different NanoVNA models have hit the amateur market in the last few years.  In particular, I bought the H4 model for a couple of reasons; the fact that it has a larger LCD than most of the other models and that I’ve heard good things about its ability to work to 1.5 GHz out of the box.  

It’s hard to convey just how big a deal these things are to people who are new to the game, but through some clever tricks in digital design, they’ve absolutely crushed the price of test equipment.  The first 1.5 GHz vector network analyzer I ever touched, back in about ‘84, was an exquisite piece of lab equipment from HP – who was just the test equipment giant in those days – that cost over $100,000.  The NanoVNA H4 today is under $100, or right around there.  That’s far less than 1/1000 of the cost of that HP, partly because of the constant depreciation of the dollar by the Federal Reserve.  Sure, the $100 Chinesium (almost always) NanoVNA doesn’t have as good specifications as the HP did, but a close approximation to the value is better than a guess or assuming “it should be good.” 

The default display that my NanoVNA starts up with is might be unique to this software, but from reading a NanoVNA users’ group for a few years, I think it’s pretty common.  It overlays four channels of information: three different rectangular plots of one S-parameter per plot and a Smith chart of one those S-parameters.  Since I’ve been working almost exclusively with S-parameters since the early 1980s, I’m at home with them, but questions about what those things mean are rather common. 

You can see a four trace display on this sample NanoVNA; I couldn't begin to guess what kind of thing it's sweeping from 50 kHz to 900 MHz.  (Image clearly from DX Zone; they don't sell these (or anything that I know of) but are an information aggregator.)

So what’s an S-parameter?  The S stands for scattering, but what does that mean?  Ever seen the “one way glass” that’s used for security (or used to be)?  The light is scattered in the favored direction to get it to work the way they want.  If you look at the glass from the outside, you see your reflection; the security guy inside sees you plainly but doesn’t see his reflection as clearly as you see yours.  If there’s a poorly placed light on his side of the glass, you may be able to see him as well.

In RF circuits, when you input a signal into an amplifier, filter or really anything, a (hopefully) tiny amount is reflected back.  Most goes through the network, exactly how the input changes to the output is what’s being measured.  Some of the output maybe reflected back to the input because the Device Under Test’s output impedance doesn’t match the circuit it’s connected to. 

While S-parameters can be measured and calculated for three, four, or any number of ports, the most widely used are for two port networks.  The four parameters are S11, S21, S12 and S22; you’ll see those written that way or as subscripts: S₁₁, S₂₁, S₁₂ and S₂₂.  If you want to be published, subscripts are probably the way to go; since it’s a bunch of extra work to use subscripts in Blogger’s editor, please forgive me for using plain script.  In real life, you’ll see both formats used.  In all cases the format is S (port measured at, port measured with respect to); in other words, S11 is the signal measured at port 1 with respect to port 1; S21 is the signal at port 2 with respect to port 1.  

Direction is all important;  S21 is the signal at port 2 with respect to the input at port 1; if it’s bigger than the input, the thing being tested has gain.  S12 is the signal at port 1 with respect to port 2; usually called reverse isolation.  While a passive network, like an attenuator, will have S12 = -S21, an amplifier won’t resemble the inverse of the gain (unless it was designed to be, amplifiers don’t work like that).  For example, the typical one or two transistor amplifier ICs you’ll buy might have an S21 of 10 or 15 db, but an S12 of 6 dB.  

In the case of S11, the input impedance, a signal from the VNA is applied to port 1 and the amount reflected to port 1 is used to calculate Return Loss – a single number for the input impedance in dB; the direction separates the signal going to the input and the (expected to be) much smaller signal returning to the VNA port 1 determines the value of S11.  It’s the same basic description for the output Return Loss; the VNA measures the signals going both directions on the output pin.  Return loss is expressed in decibels by the VNA, but since it’s a measurement of reflected signal, it’s conceptually the same as the Standing Wave Ratio, or Voltage Standing Wave Ratio (SWR or VSWR) you’ve seen before.  

When measuring S11, port 2 is grounded and for S22, port 1 is grounded.  Mathematically:

The value the VNA displays it 20*log of these calculated values. 

So what are these S-parameters and the NanoVNAs good for?  To begin with, they’re entirely a tool for people who build things, whether antennas, passive circuits like filters or RF switching networks, and active circuits like amplifiers. They’ll test a length of coax for loss and other things you’ll want to know.  If you’re not a “home brewer” no test equipment is useful.  Exactly how useful depends on what you’re measuring.  If you’re working on something like a lowpass or bandpass filter, they’ll tell you everything there is to know.  If you’re working on an amplifier, they’ll tell you gain, and input and output matches.  Those are the big characteristics for an RF amplifier but they won’t tell you noise figure, linearity, intercept points or other things you need to know – depending on the application for the amplifier.

One thing that I’ve used the NanoVNA for several times, as well as my first, one port, VNA, my antenna analyzer, was to export a file of S-parameters of an antenna scan into a Smith chart to design a matching network.  Coming soon will be an introduction to the Smith Chart.