Smith, the chart to end all charts ...

Foundations of Amateur Radio

In the time that I've been a radio amateur not a day has gone by without learning something new. Today was no different and this time learning took me both by surprise and delight. I realise that being delighted by charts, since that's what we're talking about, might not be something that comes naturally, but I can highly recommend that you use this as an opportunity to explore.

So, which specific chart am I referring to?

The venerable Smith Chart, something which I've seen from a distance many times in the past decade, but never actually understood, or to be honest, even looked at with anything more than a glance and a shudder.

My first exploration started with a book published in 1969 by the person who developed the chart, Phillip Hagar Smith, an electronics engineer. The book, over 250 pages, is dense and frankly my reading of the first part of the book did not fill me with delight, but based on what I discovered afterwards, I might revisit it.

The purpose of the Smith chart is to visualise complex mathematical relationships. Instead of filling your worksheet with a litany of calculations, you can draw lines, circles and read the answer straight off the chart.

For example, given the impedance of an antenna system, determining the standing wave ratio becomes a case of putting a dot on a chart, drawing a circle through the dot and reading the VSWR straight off the chart.

It gets better.

If you have a digital Smith chart, like the one shown on a NanoVNA or a RigExpert antenna analyser, you can read the antenna impedance in relation to frequency, use a tuner to change it and see the chart update in real-time in direct response to you changing inductance or capacitance by twiddling the knobs on the tuner.

One of the main things that a Smith chart solves is to visualise a chart with infinity on it, twice. In radio a short-circuit is one extreme and an open-circuit is another. Coming up with a way to show both those conditions on the same chart is a stroke of genius.

The chart has evolved over time, but in essence it's a circle with an amazing set of arcs drawn throughout. The very centre of the chart has the number 1.0 next to it. That's the point at which the VSWR is 1:1, the reactance is zero and it's called the prime centre. A dummy load should show up as a dot in that spot, regardless of frequency.

The Smith chart is normalised. It doesn't matter if you're using a 50 Ohm or a 75 Ohm antenna network system, the middle of the chart is 1.0. Follow the horizontal axis to the right and you'll discover 2.0, that represents twice the resistance. If you're using a 50 Ohm system, 2.0 represents twice that, or 100 Ohm. Go to the left, find 0.5 and that represents half, or 25 Ohm. The far left point on the horizontal axis represents zero Ohm, or a short circuit, the far right represents infinite resistance, or an open circuit.

Positive reactance, or inductance is shown above the horizontal line, negative reactance, or capacitance is shown below the line.

Going back to the middle of the chart, you'll discover a circle. All along that circle the resistance is the same, that is, on a 50 Ohm system, all of that circle represents 50 Ohm. If you look directly above the prime centre, you'll discover another 1.0 on the edge of the chart. The arc coming from that point represents an inductive reactance of 50 Ohm all along its path. Similarly, at the bottom of the chart you'll see an arc coming from a 1.0, representing the capacitive reactance.

Before you pack it in with all this inductive and capacitive reactance, think of it as another attribute of your 50 Ohm antenna system. You don't need to precisely know how it works in order to use it.

Remember how I mentioned that you could just read off the VSWR from the chart?

Drop a point on the chart, anywhere is fine. You can read off both the resistance and reactance following the two arcs through that point. If you draw a circle through the same point with the centre at the middle of the chart, the VSWR of that system is the number that you can read, where your circle crosses the horizontal axis.

Before I go, there are plenty of YouTube videos on the topic, but there are a few that I'd recommend you explore. Among an amazing array of RF educational videos, Rhode and Schwartz made a ten minute presentation called "Understanding the Smith Chart" which walks you through how to read the chart and you don't need the prerequisites to follow along. In Part two of his "Smith Chart Basics" series, Carl Oliver shows how to look up the VSWR in three easy steps and Alan W2AEW has several videos showing the chart in action with several vector network analysers or VNAs and I'd recommend that you look at videos 264 and 314 to get started, but there's plenty more of his handy work to explore.

If you take away anything from this, it should be that the Smith Chart isn't scary, there's just lots of stuff there, but spend a few minutes looking at it and you'll discover just how useful it can be in your day to day amateur antenna tuning adventures.

If you've come across other interesting resources on the topic, don't hesitate to get in touch.

I'm Onno VK6FLAB