The basics of how to use a Smith Chart and the RF performance of a paperclip
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00:00 Getting Started
00:27 How to Plot Complex Impedances on a Smith Chart
01:30 Open and short circuits on the Smith Chart
01:40 Normalized impedances and impedance matching on the Smith Chart
02:25 Smith Charts over changing frequencies
02:47 Testing a paperclip's RF performance with a Smith Chart and VNA
04:30 Testing Mega Clippy's RF antenna performance with a Smith Chart and VNA


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Today we’re going explore Smith Chart basics, and then use that information to learn about the RF performance of a paperclip. Would this make a good antenna, at what frequencies does it resonate?
A Smith chart makes this really easy to see.

Smith Charts look scary at first, but they’re not once you know what’s going on. Let’s start with a complex impedance, say .5 + j1.1.

If you plot out this impedance on the complex plane, our X-Axis is our real component, or resistance, and the Y-Axis is our imaginary component, or inductance and capacitance. Inductors are positive, capacitors are negative. And you can plot it! We see where our real component .5 and our imaginary component, 1.1, meet, and we plot it. Simple Algebra 1 stuff.

A smith chart is basically this graph, but you curl it in on itself into a circle.

This might seem weird, because all of these axis go to infinity. It would be hard to plot infinity resistance on this, but with the Smith Chart we can. And, an open circuit is infinite resistance, infinity is not some weird edge case for electronics – open circuits are everywhere!

So to plot the same .5 + j1.1 on the Smith Chart, we do the same thing we did before, we find .5 on the real axis, and +1.1 on the imaginary axis and draw a spot where they meet. It’s Algebra 1 but it’ll impress and confuse all the business majors.

We have an open circuit – infinite impedance on the far right, and a short circuit or 0 impedance on the far left. And literally everything in between.

The Smith chart now gets more complicated for two reasons. Reason number one is that all this is normalized information.

For example, RF folks like 50 ohm systems, so if we had an impedance of 75 + j40, we’d end up with a normalized impedance of 1.5 + j.8 and we can plot it.
In an ideal world, our generator and load are impedance matched, so we end up with 1 + j0 right in the middle. We get the best transmission, the transmission coefficient is 1, the reflection coefficient is 0, and our VSWR is 1. The Smith Chart tells us that! We can also use this information to design impedance matching networks to move a point from non-ideal to ideal. This is easier with a combined smith chart that has both impedance and admittance, but we’re not going there today.

The second reason this gets complicated is that impedance is dependent on frequency. And everything is a combination of resistance, inductance, and capacitance. So, naturally, as our frequency changes so does our impedance.

So at one frequency we have one nice point, but in RF engineering we care about a range of frequencies so we often end up with some sort of curve as our frequencies change. This is really nice, though, because we get a picture of our system as frequencies change.

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