Smith Chart Tutorial for Ham Radio: Building Impedance Matching Networks with DIY Inductors

Today finds the unsuspecting ham radio op perusing YouTube for something new to learn as it is really cold outside. He stumbles across a video about using a Smith Chart to match impedance and is intrigued…

What happens next is kinda terrifying…lol

Well to be honest, it is really kinda boring till you see how a smith chart sort of works and you start to learn how to use it to some degree. I have known about them for years, but have never understood how they work or even how to read them. The other day though I landed on a video. This one shown below to be exact and I was hooked.

As you can see, if you watch this video, (maybe a couple of times), he explains it in simple enough terms that I actually understood what was going on finally! I did come into it with the understanding that the upper half was inductive and the lower half was capacitive from tuning my antennas with the nanoVNA. I would leave the smith chart on out of laziness and simply used the SWR graph to move the null to the operating frequency. But during this time, I started looking at the information presented on the display and noticed at times it would show capacitance and sometimes it would be inductance and also where the marker was sitting. This gave me the clue about what it was sharing with me. That was the extent of my smith chart knowledge though. At least it made sense to me. So the next logical thing to do was to order some smith chart notebooks from Amazon and a drawing compass so I could use said charts. While I was anxiously awaiting the new goodies to arrive, I started binge watching videos on smith chart use and taking away what I could from each video to add to what I already knew. By the time the paper arrived (I know I could have printed them off the web but the notebook format is really nice to be honest) {sarcasm}I was already a “master” at these “simple” charts… haha. {/sarcasm}

I will be honest with you. There is so much about these charts that I still don’t understand that it boggles the mind, but I have figured out how to use them for impedance matching and it is kinda awesome. I actually made the last few pages in my new notebook a cheat sheet based on the above video so I could reference it easily without having to watch the video over and over. I am absolutely going to build one of these fixtures when I get back home too. I would already have done it but I am not able to access my bench to put it together… So what follows is what you do when you don’t have that gear handy.

First things first, I bought a new toy. This is a 200 mhz “scope meter” but this one has another trick it can exploit. This is a actual dual channel oscilloscope AND it also has a arbitrary waveform generator as well! On top of the usual multi-meter functions as well. This thing has a lot to offer…till it doesn’t. It didn’t take long to figure out that the waveform generator doesn’t have the sweep function in it, this would have been nice to play with things. I can’t find FFT modes anywhere in it either so it can’t be a “poor man’s spectrum analyzer”. The little meter does have enough options to be really useful for what I was doing anyway so let’s get started… oh, it doesn’t come in this nice hardshell case. This is an Apache case from Harbor Freight. It is the perfect storage container in my opinion and I am happy to have it trimmed out like this. It didn’t take too long to figure out how to use the oscilloscope and I made a cheat sheet for it too so I can access useful features more easily in the future since a lot of it is hidden in menus due to the diminutive size.

What you see here is pure desperation to see if I can make this smith chart stuff work for me. I am literally about to start making capacitors out of aluminum foil, a sheet of notebook paper and painters tape… Spoiler alert, it worked… You see, in another video I found on YouTube, there was this idea that you don’t need a LCR meter to measure your components as long as you have a known value device, a battery and some ingenuity. I also had a lot of time to play with this concept so here we are… I started by making a really big capacitor to start with to do a proof of concept and to see if there was enough capacitance to make this project work. Turns out there was way more than needed with the initial design, WAY more. So with the proof of concept made from three full size sheets of paper laminated with aluminum foil on one side of each one and then stacked so that the center sheet was one plate and the top and bottom were the opposite plate, I found I had made a .0034uF capacitor! This was more than enough to play with HF radio RF frequencies!!! Woohoo! Now this is all based on me being able to believe my new meter and later I find out that there is 17pf of stray capacitance in my meter and leads. Once I figure this out, and factor it into my math, it is all good but for now with this thing being 3408pf, I don’t think it is really a problem. The cigar box is there to use gravity to apply an even pressure to the “plates” and hold them at a consistent spacing as at this point, these were just three sheets stacked up. The top and bottom are connected to the black lead and the middle one is connected to the red lead. Also tested it with just on plate on the black lead and yep… capacitance went WAY down, so this style of capacitor worked pretty well to be honest. I could make it go up a good bit more by pressing on the cigar box too, I saw 5.0nF at one point while playing with it, that is crazy to me…

I had read somewhere about this idea to be honest. Well a cruder version of it actually. They made an impromptu antenna L network with two sheets of aluminum foil and a sheet of news paper or something like that. That made the capacitor and the inductor was wound on something found commonly in the house in the 1960s or 70s as well. They just used regular old romex house wire to make the inductor and it also worked just fine. Sometimes you just really need to have some “want to” and it can be done. I was a little more superfluous with my build as I didn’t need it to get on the air but rather as an experiment to see what I could learn.I honestly was really surprised to see how much capacitance I could get out of notebook paper and aluminum foil from the grocery store. This tells me that literally anyone that needs an antenna tuner, has one if they want it bad enough. You don’t have to have a Ten Tec 238 to be able to tune that random wire, you just need to gather some stuff you probably already have in the house…

Side note, I also finally acquired a new case for my POTA Scout 555 radio. I still need to finish the pockets for the band modules when I get home, but I now have it in a proper case and not just sitting in a cardboard box in the back of the truck! Also, I made another 60 meter contact today… to the same exact person that I made the first one with a couple weeks back! HAHA! I think we are the only two people on 60 meters CW in the mornings ever…

Here we see what I measured the other day while at a POTA park. What these numbers show is the antenna measurements for the band at the base of the antenna. I literally took the nanoVNA and adapted it to the antenna socket directly to eliminate the 50 ohm feedline from interacting with the measurement. As we will learn soon enough that you can use a piece of feedline (coax in particular) to move the base value around the smith chart should you need the starting point to be somewhere else. But I also learned something else about these starting point numbers below that I will share with you in a little bit.

At the top of the page, right next to the “40m” is what the nanoVNA reported that day at the park. (15.4 ohms and 87.3pf) you have to have two coordinates to plot anything on a chart so these are the two numbers you need to plot your starting point. Ignore the other notes as I am probably wrong on some of it and it actually makes more sense later. But the first thing I had to do was to turn these numbers into the proper numbers that the smith chart uses. This is called normalizing them. You see the chart is relative, you can assign whatever value you want to the center point on the chart and the rest of the chart is “relative” to this value. So if you were to work with 75 ohm coax and wanted to make an impedance matching network to work with it and having minimal losses, then you would assign 75 ohms to the center point. Since we use 50 ohms in almost all amateur radio (if not all) then our value is 50 ohms at the center point.

So here is my 80 meter plot (below) to get to a 50 ohm impedance from where it started at… yes… 1 ohm and 79.7pf capacitive! You see I am designing a matching network to couple my 50 ohm coax to a 18.4 feet tall telescoping vertical with a couple of radials thrown out on the ground. This is not even close to a matching antenna for the 80 meter band at all. Hence the terrible numbers to start with. Well, this was like those jokes you here from high school where you get something simple in the lecture in class about a subject then in the book it might show it with one more complication but the exam shows the Drake equation for the problem on the test! Well this is what happened to me as in the video above, the number in the video was closer to the middle of the lower half of the chart making for a more straight forward solution to the problem. I also did my admittance math wrong too if I am right…lol… since it is all inverted, but this doesn’t matter at this time. What you need to know at this point is that my problem lies outside the unity circle (that is the one I drew on the chart) and I need my “arc of movement” to cross this circle… it does but nearly at the infinity point (on the right side of the chart) which makes the math almost worthless… The reason the math gets pretty inaccurate is the numbers on the chart start getting logarithmic is value and so a small movement on the chart in this area makes huge changes in the values. You want your plot point anywhere else but here, yet this is where I am at in this blog post… haha

Knowing all this, I start this complicated, 3 position move to get me to the center of the chart. Mind you, I think this would actually work, but I am not sure if the math is mathing right at this time. (I am thinking the first move is a piece of transmission line to move the start point around the circle instead of an inductor and the second movement is also not a capacitor either so basically this whole thing is drawn wrong…lol) You will see why in a minute too as to why I dont know. The schematic for this movement is scrawled in the upper left hand corner of the notebook page if you wondered what it would look like to make this circuit. Two inductors and a capacitor to get to 50 ohms… how many antenna tuners have TWO inductors in them? I will help you out here… not many, if any. The number of inductors alone would make this a no go design for the most part unless is was going to be a one band wonder. Just remember I am pretty sure the math on this is wrong, the plot directions are correct, but I am thinking that the suseptance values are needing to be inverted to calculate the impedance for the two movements on the blue lines. Anyway, the point of this blog post is to show what is possible if you want to learn something new and it is not about the math around a smith chart…yet…lol I am diving back into the tutorials to figure out the blue part of the chart next.

After I pulled my hair out for a while…wait, that don’t apply to me…I’m bald already… After getting over the frustration of trying to solve this problem, I redrew it on a fresh page and looked hard at it for a minute and had an epiphany… The plot point is not INSIDE the circle, or even anywhere closer to the middle of the chart at all, which would have been ideal, BUT it is really close to the unity line already. I mean REALLY close, so close in fact, I bet you could simply run around the unity line clockwise to the center point and just “eat” the misalignment on the horizontal resistance line of such a tiny amount and no one would even notice in the real world. You know what this matching network now looks like? A huge by large inductor is what, just a plain ole gigantic coil… Moving clockwise around the impedance lines (the red ones) indicates adding inductance to solve the problem. This is what all the antenna companies use when you buy a mobile 80 meter whip antenna if you think about it, just a huge load coil and nothing more. If you were to zoom in on this, I am guessing the resistive value when you get to the end of the arc, at the horizontal center line (which is the pure resistance line) would be something like 49.2 ohms or something close to that, literally less than 1.1 : 1 SWR maybe less to be honest.

Armed with this knowledge, I wanted to test this theory. So I now needed a way to make a coil to insert between the feedline and the base of the vertical to see if I had learned anything. Well I had this new scope / meter / signal generator widget and I had a way to make a capacitor, I then remembered a video where I guy showed how to measure inductors and capacitors with only a oscilloscope if you have one known device. Well, I have a capacitor that I made and I can measure it with the new meter, so that will give me the “known”.

So I fire up the new meter and plug in the leads and find this. There is no way to “tare” out this number either so you simply have to subtract it from what ever you measure. I figured this would be pretty easy so I just went with it. Below is a photo while I was trimming the capacitor to a size I wanted. I was looking for 100pf and as you can see below on the meter, I was getting close. This is measuring right at 121pf in the photo. I would trim off the edge of the sheet and then check it again, rinse and repeat till it was close to what I wanted.

Once I had my brand spanking new capacitor made and trimmed to size (105pf), I setup a test fixture to do my test with. The test fixture is also expedient since it is all that I had was one of those “BNC to binding post” adapters and just used it as a sort of bread board to attach all the parts to the system. It worked, it was pretty janky, but it worked. All that we have here in reality is a parallel tank circuit. It will resonate at one frequency natively and I can measure that and then use a simple online calculator to see what the inductance is based on my capacitor value and the frequency of the tank circuit. How do I get it to resonate then? Simple, use a battery…

In the other video I had recently watched he showed simply setting the scope to trigger off of a voltage level close to the value of the battery which will allow the scope to capture the ringing of the tank circuit if you pulse it with a battery. I just took a AA out of my pocket flashlight and used it, set the trigger to normal and set the trigger level to about 1 volt and started touching the battery to the two red wires going out to the left in this photo below. This biased the tank circuit (simply applying a dc voltage across the capacitor and charging it) and I was rewarded with what you see below on the scope in the below photo. To be perfectly honest with you, I had done so much wrong in this process that I was honestly surprised that it worked. I even had to show it to Teresa and she had literally zero idea about what she was seeing here, but I had to show SOMEONE that it has actually worked!

The ringing the scope captured is nice and clean and I was able to measure the period of the sine wave at 172 nanoseconds. Transforming the time into a frequency is easy, you simply invert the number or divide 1 by .000000172 and you get 5,813,953 hz. This frequency is not relevant to the ham bands but is only useful in telling us what the value of the inductor is, which is what we want anyway. As you can see from the screen shot below, this inductor is 6.245 uH (micro henrys). I did the plot on the smith chart for 40 meters for this antenna and came up with almost exactly this number, I came up with 6.62uH on the math. This also makes sense as I did this physical coil for the 213” (17.75’) WRC vertical and not this one that is longer that I am using now 221” (18.4’). Another possible reason for the variation from the measured and the plotted values is that my capacitor value could be slightly different from being moved around or being in proximity to metal or some such. You could touch the capacitor with your finger tip and the value would change so this is probably part of the variation…

I made this actual load coil by guessing to be honest, I did use the nanoVNA as a SWR meter when I made it and I would take off a coil or two and measure it and I simply walked the null in on the antenna for 40 meters that day. Now I know how to use a smith chart to do that math ahead of time. That is pretty cool.

Literally using trash to resonate as a tank circuit is kinda cool to be honest with you. The wires for the capacitor are simply taped to the aluminum foil, nothing more as I didn’t have a way to solder them together or anything like that. This was truly a temporary test fixture for experimentation.

The next logical step was to make an inductor for 60 meters and to hook it up to the antenna and measure it with the nanoVNA to see how close I could get it. This is where things started to go south…

First of all, I had problems replicating the same resistance and capacitance from that day at the POTA park. The photo of the VNA above shows what I am talking about. Now it is 1 ohm… yeah basically a dead short for the RF. But more importantly it is different from the day of my test which was about 10 ohms (if memory serves me) but basically this doesn’t matter when you get to the region of the smith chart that this plot is landing in. The capacitance is what really drives this position between these two numbers and it was virtually the same. The amount of inductance will be more for 1 ohm but not a whole lot more.

Well what happened when I hooked up the coil and the vertical and stuff in the driveway was a whole bunch of nothing! It just made a circle around the outside of the smith chart, which is bad if you don’t know. You want your line to go through the center of the chart at the frequency you want to use and if it goes around the outside it ain’t going through the middle!

Deflated that I had probably done all that math wrong…again… I was about to throw in the towel when the wind blew and the plot on the nanoVNA moved towards the center! What just happened??? I start messing with this and that, as you can see in the photo above that the coil output wire is just poked into the coax port on the antenna. This has to be the worst way to make this connection, but if this is all you have, then this is what you do…

I could grab the vertical and that would make drastic changes to the smith plot, so I thought about moving the antenna without touching it and I found a roll of electrical tape and used that to tug on the vertical as it is in a QD mount (which is not a great connection to be honest that I have found). I even cleaned some stuff to no avail, but when I put the tape on the antenna and pulled it in certain directions, I would get the plot you see below. Notice the marker is at 5.340 mhz and at 55.2 ohms and just 1.49nf capacitive. This is less than 1.2 : 1 SWR and I am sure that it is off a little because of the system losses at this point. All the loose and dirty connections along with the random radial placement (I find this makes a pretty large difference with my systems) made getting repeatable results almost impossible. This told me that the coil worked though and that my math was not wrong! I had actually learned something here!

Once I figured this out and took a couple of photos for the blog, I tore the system back down and put it all away so I could get started on this write up about it. This has been an amazing process to do this and I learned way more than just how to do impedance matching with a smith chart. I learned that my system is way too inconsistent to simply make a coil and expect it to work in the system. If I had all the parts hard mounted in place with corrosion inhibiting paste on the connections then I could calculate this coil and it would drop right in. I was blown away by this and cant wait to find another use for my smith chart notebook. I hope this has helped you in some way either by simple entertainment or by learning something about smith charts and antennas, or maybe that there are YouTube videos about how to do this sort of stuff, either way, thank you for reading to here and I hope you come back for more of my ramblings in the future!

73

WK4DS - David