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Smith chart & Constellations

Hey folks – summer is upon us here in the great green North… the past few days we have been under a heat warning, which happens here any time the mercury climbs above 30 degrees Celsius, or about 85° F. That ended this morning with a midwestern U.S. caliber lightning storm, a very rare event in this part of the world! Fortunately, other than some temperature issues at the station I assist with and an internet outage periodically during the storm, we made it through just fine – we certainly saw record-breaking numbers for this time of year, though!

As part of the event, I ended up spending a bit of time looking at the AUI for the VS1 at our local station and it reminded me of a couple of requests that have come in over the past few months, so this issue, we are going to talk about those things.

Thank you, Mr Smith!

First, I got a request to make a bit of a dive into what we’re looking at when we view a Smith chart. The Smith chart is one of the easiest ways to get an “at a glance” characterization of a complex impedance across a range of frequencies, once you have a basic understanding of what it is measuring. Let’s look at one, here:

Image credit: By Wdwd – Own work, CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curid=11539005

It is essentially a logarithmic scale, where resistance, normalized to a reference, is plotted on the X (horizontal) axis and reactance expressed as phase, also normalized, is plotted around the circles. Because it is logarithmic, inductive reactance from zero (pure resistance) to 90 degrees of phase shift (pure inductance) covers the top half of the circle and capacitive reactance from zero to -90 (pure capacitance) covers the bottom half. For our purposes, the 1.0 mark on the horizontal axis represents 50 ohms with zero degrees phase shift (no reactance). In that mythical perfect world, this would be what you saw if you did a frequency sweep on a resistor.

In the real world, loads are very rarely 50 ohms and j0 across the operating range of a piece of equipment. So, when you do a sweep, you will see a variation, such as the one shown below:

Photo courtesy of Pierre Lonewolf, KOTZ Kotzbue, AK

In this case, we can see that at the lower end, the impedance is roughly 50.05 -j1, passing through nearly 50 ohms at the midpoint, and approaching roughly 50.05 +j1 at the upper end. With the Smith chart reading provided in the AUI of our NX series AM transmitters, you can click on the sweep (the red arc) at any point and the reading in the upper corner of the screen will show you the frequency offset from carrier, as well as the deviation from 50, j0.

So, for example, on the picture shown above, if we were to click on the lower end of the arc, it might say, “Impedance: 1.05 – j1, Frequency: -15kHz”, representing the deviation from normalized 50, j0 impedance and carrier frequency. We can then use the blue left and right arrows at the right of the title bar to step through the frequencies that were swept. Since the AUI sweeps from -15kHz to +15kHz from carrier, we’d only be able to step right from -15kHz, as that’s an end point.

What’s shown in the example above, courtesy of our friends at KOTZ (thanks, Pierre!) is a good example of what’s called Hermitian symmetry – the reactance above carrier is equal and opposite to the reactance the same spacing below carrier. This provides the most balanced load and is probably more critical to proper signal transmission, whether analog or digital, than the actual carrier frequency load impedance. It means that your signal will behave similarly both above and below carrier, so the sidebands are well matched – leading to improved signal quality and typically better coverage.

The corollary I use is that the antenna is to the RF transmission facility what the speakers are to a hi-fi system… the best amplifier (transmitter) in the world isn’t going to perform well into a bad speaker (antenna) system. This is a lesson we learned way back when directional antenna systems were first developed, it was reinforced in the days of AM stereo and it’s equally important for HD Radio technology – but it also applies to non-directional analog mono signals. The better the antenna system is set up, the further and cleaner the signal will be. In these days of increased noise floor with interference from power company insulators, LED lights, switching power supplies in almost every electronic device, it’s probably more critical than ever when it comes to operating an AM station.

This was a highly simplified description, to give an operational understanding of how plotting your measured impedances on a Smith chart can give a great visual of how well the antenna system is tuned. For a much more in-depth description, here’s a great Wikipedia article on it (and yes, I’m aware of the risks of using Wikipedia as a resource!), but I hope this helped to provide at least an entry level view of how the Smith chart works! If you have any ideas or suggestions for future topics, let me know and we’ll shoot you one of these, so you can literally say you’ve got the t-shirt!

Stars in the Sky? No, a different type of constellation…

Another thing I get asked about quite often is from our customers running FM+HD systems. For the AUI on the FM transmitters, there’s a constellation diagram on the screen that looks like a bunch of dots.

Depending on the software revision you have installed, your display may look different, but this is the current rendition. What you’re looking at here is the references – the ideal points for each of the digital carriers to land, with respect to phase and magnitude, as plotted on a cartesian graph. When you’re modulating, it will show the each of the digital carriers with respect to these ideal points, so there will be several dots scattered around the ideal points. In the mythical perfect world, they’ll be as close as possible to the ideal. However, just like the AM systems, in the real world, they will be scattered around a fair bit – how much is a function of many things, such as system linearity (including any combiners and the antenna system), along with noise throughout the modulation system or virtually any other kind of distortion.

The deviation between the ideal and the actual is known as the MER – Modulation Error Ratio. A higher MER indicates a smaller deviation from ideal. The NRSC specification for HD Radio signals is 14dB. This is important because, as with the Smith chart and hermitian asymmetry, the MER is very much an indicator of expected performance – the higher the MER, the more ideal the system performance, the better the coverage. It has been well known to TV engineering staff for years now, but has not typically been common knowledge in the radio world. Several manufacturers provide constellation diagrams, or at least MER measurement, as part of their instrumentation suites now, and it is a good tool to get familiar with, if you are running an OFDM type of digital modulation.

Again, this is just meant to be a 20 thousand foot overview – for MER and signal constellations, there is a fairly good description in the operations manual for any of our current GV series transmitters, just download the PDF from the NUG section of the website and F to search for “constellation”. You might need to click a few times to get there, but it will work. If you don’t want to go through that many steps, there is also a good description here.

On that note, folks, let’s all take care out there and I’ll see you next time – until then, be safe and happy engineering!


Jeff Welton, has worked with Nautel for 30+ years. He is currently the Nautel Sales Manager for U.S. Central Region but previously he spent 16.5 years as a Nautel Customer Service Technician. A regular speaker and contributor on broadcast engineering, Jeff has been recognized with the following awards: 2020 NAB Radio Engineering Achievement Award; 2019 APRE Engineering Achievement Award; and 2018 SBE Educator of the Year Award.

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