this video is simply a recording of a presentation that I delivered to a VHF amateur radio conference in October of 2018 on the basics of Smith charts so what is a Smith chart it's really a graphical tool to help you plot and compute a number of things such as complex impedance complex reflection coefficient voltage standing wave ratio and transmission line effects as well as helping you to design RF matching networks and it's certainly much much more that can be done with a Smith chart so let's break it down first thing we need to talk about is normalized impedance the complex impedance that we plot on the Smith chart is done with what we call normalized impedance normalized impedance is when we take the actual measured impedance and divide it by the system impedance in most cases that system impedance or z0 is 50 ohms so essentially going to divide all the values by 50 ohms so in the case of a complex impedance value of 37 plus J 55 we divide both of those values by 50 to get our normalized impedance and we'll call that a Z prime so in this case the Z prime would be 0.7 4 plus J 1.1 this makes the Smith chart usable for any system impedance whether may be a a 600 ohm impedance system a 75 ohm impedance system or like I said in most RF applications it's a 50 ohm impedance system and this normalized Z Prime of this normalized impedance is what we plot on the chart so let's take a look at some of the important regions on the Smith chart the center axis or prime axis is the purely resistive axis so any points lying just on that axis or where there is no reactive component at all the region above that access that hemisphere is where the reactive component is inductive and therefore the region below that is where our reactive component is negative or capacitive let's look at some key values on the Smith chart right dead center is our system impedance so in our 50 ohm system that center point represents 50 ohms all the way over to the right along that prime axis is open circuit where essentially infinity and then obviously at the other end represents a short circuit these circles on the Smith chart that are you can see are all kind of tangent to the infinity axis represent constant resistance or normalized constant resistance so the one that passes right through the center of the Smith chart is the normalized resistance a circle a value of 1 there is a lead constant normalized resistance of 3 constant normalized resistance of 0.4 and if you look carefully along the center axis the Smith chart you can actually see these values right along the circles so we can see there is 1.0 1.2 1.4 1.6 etc so that's how you can figure out the values of these constant resistance circles the arcs that are all emanating from the open circuit position are the constant reactance arcs so we've got the in this case here's our constant R conductive reaction reactance of point 1 or 2 Sydnee 1.0 and the constant capacitive reactance of minus j 1.0 and you can see here's plus 0.5 and minus 0.5 and again if you look along the axis of these labels for these arcs you can see what those values are and of course if there is no reactance at all essentially you're right back on to our constant resistance line or prime prime axis within the Smith chart so let's plot their complex impedance let's start off with complex impedance of say 25 plus J 40 so we know what's inductive we're going to be above the act they the center axis the first thing we need to do is normalize that by dividing by 50 and that gives us a normalized complex impedance of 5 plus J 0.8 so what we do is simply look for the intersection of the resist resistance circle of 0.5 and the reactance circle of 0.8 and if we follow those along and we find the point where those intersect that plots that complex impedance on the Smith chart and oftentimes when we're designing a matching Network we're going to be adding elements like resistors are assuming inductors and capacitors to create a matched circuit if we add elements in series we're going to move along the Smith chart curves in a certain way so we typically will add these components to essentially drive our complex impedance down to the desired point which is the system impedance if we add series inductors and series capacitors we're going to move along the constant resistance circles so for example if we add a series inductor we're gonna move clockwise along that constant resistance circle and we can see if we move for example from this point to this point we essentially added in this case zero point six normalized reactance to are measured impedance series capacitors move us counterclockwise along the constant resistance circles so what about admittance it's handy to think talk about admittance when we're adding elements in parallel now of course everything we've talked about thus far is constant impedance so what do we do well admittance is really just 1 over the impedance right so that's pretty easy so in a sense that you say well they're constant or the conductance or is 1 over resistance and susceptance is 1 over reactants but reality is those two equations are really only true when the real component ok the R is zero ok that's the only time we're really going to have that because otherwise we're to take this complex quantity and invert it and that's a little bit more complex math however converting to complex impedance or from complex impedance to come let's admittance on the Smith chart that's really easy it's a lot easier than doing the math let me show you how so first we start off with the impedance that we've plotted on the Smith chart okay and then we draw a circle that's centered at the system impedance right in the center that crosses through our measured impedance and then we draw a line diagonally through the circle cutting through the center of that circle and then touching the other sides or bisecting our circle and that location that we wind up with on the other side is essentially our complex admittance so when we just read the values right off the chart from the resistance and reactance lines so in this case a constant or impedance of 1 plus J 1.1 is a complex admittance of 0.45 minus J point 5 as shown here so the admittance curves where are they because we've talked about these impedance curves constant resistance and constant reactance the admittance curves are really just taking the Smith chart and rotating it 180 degrees so if we actually just turned that chart around we would actually have that so we can actually just play a trick by doing that by doing the bisecting that we just showed on the previous slide but what you'll also find is that you can pick up and find combination Smith charts in this case all of the red lines okay the red circles for constant resistance the red arcs for the are constant reactance lines and then the blue lines shown here are all for the admittance so constant conductance lines and constant susceptance lines so these combo charts are available to make your life easier and if you want to go through and manually do transmission line and penis matching network computations so again here's the constant conductance circles and the constant susceptance arcs so if we're gonna add elements in parallel we want to use those admittance curves okay so in the case of adding a shunt L or shunt C we're going to move along the constant conductance circles so here we can actually see adding a parallel inductor moves along a constant conductance circle this way adding a parallel capacitor moves along the constant conductance circle that way so this is much easy the easiest thing to do is to use a combination Smith chart to be able to go ahead and do this rather than doing the transformation that was shown a couple of slides back it can be done either way but certainly easier to do with the combo chart so here's a quick tip and to remember which direction you rotate in when you're adding inductors you elevate through the real axis so adding series inductors rotates up through the real axis this way along the constant resistance circles and then adding parallel inductors rotates on the constant conductance circles up through the real axis that we're elevating through the real axis kind of corny but it works well we can get even more corny and say well we're adding capacitors we crash down through the real axis rotate the other way down or going down through the real axis with adding series capacitors here we're rotating down on the real constant resistance circles and now we're the parallel capacitors rotate down on the constant conductance circles rotating or crashing down through the real axis so a little bit corny but it's you know easy to remember now which way we rotate along these axes when we're adding series or parallel inductors or capacitors a little bit more Smith chart magic some other detail that's on here and we'll talk about what we're called radially scaled parameters and these are the parameters that you see down along the bottom axis well talk about just a couple of them is there's a number of them there but we'll talk about the most common ones so let's say I've got a complex impedance plotted on my Smith chart here first thing let's do it's a straw like a radial line from the center to that point now if we rotate that line up to the real axis okay so we're just kind of just a little compass and draw that up here and then extend that line straight down to our radially scale parameters we can read a number of parameters right off the Smith chart first thing we can see that is for this particular complex impedance that would represent a voltage standing wave ratio of two point three two one right we're reading that right off of our SWR axis here that also corresponds to a return loss of eight point one dB also corresponds to a power reflection coefficient of 0.1 55 or a voltage or current reflection coefficient of zero point three nine so really easy to go ahead and determine those parameters now something that's interesting to note is that any impedance that is along this arc or effectively even all the way along the circle will have the same SWR so let's talk about standing wave ratio and transmission lines and how we can relate that on a Smith chart so again as I mentioned in the previous slide we draw a circle around the Smith chart centered at the center cutting through are measured impedance the this is plotting out is a whole array of different impedances that will give us the same SWR no matter where we are now one trip around that Smith chart going around the circle represents a 1/2 wavelength of transmission line length so what that tells us is that each time the transmission line length is increased by a half a wavelength we're repeating the impedance so let's say for example I've got an antenna that has a certain impedance and the transmission line without going to that antenna is a multiple of half wavelengths long that means that the impedance looking into the transmission line is equal to the actual antenna impedance okay and that will repeat itself every 1/2 wavelength of length of transmission line now of course halfway around they turn to each Smith chart then is a quarter wavelength now what's really interesting here is that you get an impedance transformation that's pretty pretty significant and unique with quarter wavelength or odd quarter wavelength multiples like a 1/4 wavelength or 3/4 wavelengths etc I get this transmission line or this impedance transformation and the most interesting one to look at is let's say the impedance were looking at was an open circuit okay if I go half if I add a transmission line that is a quarter wavelength long and that's open circuited at the end it will look like a short circuit at the quarter wave length point and vice versa if I have a quarter wavelength long transmission line that's shorted at the far end it looks like an open at the transmission at the it at the input end so let's talk a little bit more about that our practical application let's say I've measured a given impedance at my transmitter end of a transmission line so I've got a transmission line going to an antenna and I measure the impedance that's seen at the transmitter ok I can use the Smith chart to predict what the impedance is actually at the antenna so what we can do is use these scales along the outer edge here we can see their scale that says wavelengths towards generator or wavelengths towards the load so if I measure a given impedance at the transmitter and I know the length of the coax to the antenna or the length of transmission line to the antenna I can then predict what the actual antenna impedance is and once I know what that intended piece is I can then design a matching Network that can be placed at the antenna to match the 50 ohm transmission line impedance and therefore avoid transmission line losses so how do we go about designing ell networks or impedance matching networks the simplest would be an element matching Network we're simply going to be talking about adding a series or parallel inductor or capacitor to move from our load impedance or measured impedance to and there are different topologies that can be used so we could add a shunt capacitor in series inductor a shunt inductor and series capacitor and vice versa there's a number of different ways of doing that which topology you use depends on where your load impedance winds up being if your load impedance winds up in this area up here then that tells us we can use this topology we could also use one of these topologies as well similarly if my load impedance was down here I might want to use this topology okay or maybe possibly that one depending on where the load impedance is the choice of which one you use might be determined by whether we want you know say a high pass network or a low pass network or it might be based on what components you have available in terms of the selection of inductors and capacitors that you might have available or that you might have to wind or design so there may be some other practical considerations that might influence your decision on which topology to use for your matching Network when you have a choice of more than one so again sometimes more than one topology will work so let's go take a look at a practical example or two first let's look at the process what I like to do if I'm going to do this manually is start off by drawing the constant conductance circle on the Smith chart as well as the constant resistance circle for for the unity value of conductance and ruin'd resistance they're going to help me later when I design the network because what we want to do is pick a topology based on where the inductance is or the impedances in this case this topology is going to work so it start off with say a series inductor and then a shunt capacitor so the first thing we want to do is add the first element so that we rotate around until we hit either the unity resistance or unity conductance circle in this case here if we add a series inductor and rotate up until we hit our constant conductance circle now I've got the right amount of inductance for my net matching Network and then I can add a Passover to rotate down through the constant conductance circle until I reach my normalized impedance value or my system impedance value and once I know that I can figure out how far or how much inductance and how much capacitance I've added and then compute those values so let's do an example so the first step we want to do again as we let's say we're operating at 432 point one megahertz and we've measured in impedance with say an impedance analyzer or vector vector network analyzer of 75 minus J 60 ohms so first we need to normalize that and that gives me a normalized load impedance of 1.5 minus J 1.2 so we want to go and plot that value so there we have it right here now that I've got that value plotted let's pick a topology based on where that is again for my little yin-yang diagrams earlier I can see that this topology here which consists of a shunt inductor followed by a series capacitor would give us the right values or the right network to bring me from this impedance point to our system impedance or the center of the Smith chart so here's how we go about it so first thing I'll do is I'll draw in my constant resistance unity circle is what kind of help us later first thing I want to do is add a shunt inductor so we're gonna rotate a longest constant conductance line until we hit that constant conductance circle so we rotate up and we've got that all right now how far did we move if we take a look at the curves here we look at the my blue lines here that I was 0.3 there's 0.4 so we were sitting at about 0.3 two rotating up to zero so that's this segment here was adding 0.32 and then this segment here if we follow the numbers is adding point zero five so the total amount of normalized inductive susceptance that we've added is 0.82 ohms okay so if we invert that that tells us that our normalized inductive reactance is 1.2 2 ohms and we multiply that by 50 that gives us my inductive reactance of 61 ohms and then we can calculate back from our 432 megahertz operating frequency and calculate back to a inductor of 22.5 nano Henry's so now I know the inductor value for my net matching Network now the next step is we want to and our series capacitor to rotate down to the center of the Smith chart so if we add that value in there we can see that I've actually moved by a normalized capacitive reactance value of 1.2 so if we unknown got a capacitive reactance of 60 ohms and again knowing our operating frequency we can calculate a capacitor value in this case of 6 point 1 4 Pico farad's so now we've designed a matching Network that took me from my measured complex impedance that wasn't matched to 50 ohms by adding these two components to it we now have a 50 ohm input impedance looking into that Network now this was all done using a one of the combination charts which makes it really easy let me just show you the process of what you would do if you wanted to go through the pain of converting from impedance to admittance and back and forth so again we would first draw the our constant conductance circle unity circle we plot our value and the constant SWR circle because remember we the first thing we're adding was a shunt element so I need to convert to admittance so we bisect the circle we've converted to our measured admittance now that I've converted to admittance now I want to add that parallel inductor but because on route I've rotated everything 180 degrees when I add that inductor I'm rotating down along the what would be the constant resistance circles but now our constant conductance okay until we hit my constant conductance line of zero and then we want to draw another unity or she made another constant SWR circle around that bisect again so now that we're back in the impedance domain instead of admittance domain and no one can add our series capacitor to get back down so we're still got the same length of arcs that we showed earlier and then you can use that to compute the complex impedance values or complex resistance or assuming complex capacitance and inductance values and get back to that same matching network so it's a lot more complex to do it this way the combo charts make it a lot easier in fact there's automated ways of making it even easier yet but I want to show you the mechanics of how all this works so in summary a Smith chart is really a very highly useful tool and probably more so back in the days before computers and before calculators we could actually solve some of these very complex transmission line impedance matching problems graphically rather than having to run through all of the very complex math we can do the complex impedance transformations from you know capacitor capacitance and inductance from reactants to susceptance and back and forth we can do all those transformations we can do impedance transformations with transmission line lengths very easily we can determine SWR return loss and a lot more and design matching networks and a whole lot more that we haven't touched on so a pretty brilliant invention that was done that was developed here for doing these complex transmission line type of equations and that we really didn't touch on them these days a lot of this work can be done in an automated way and what I'd really suggest that you do if you're interested in playing with this is check out a pc-based tool called sim Smith it was written by another ham 80/60 Y and you can see the link here and I'll put those links in the video down the description down below where you can actually go and download this program and then also my friend Larry Banco w0q QE has done a lot of really great tutorial on sim Smith in terms of how to use it and things like that he's got some examples on his website that's shown here on the bottom link and he's also got an excellent YouTube page where he's got a couple of really great tutorial videos on using Sims myth but basically can run through everything that I showed you to do manually but do it in an automated way and it really takes using Smith's charts literally to the next level so I hope you enjoyed this this short little presentation of this of the introduction to Smith charts and you got a little bit better idea of what Smith charts are used for thanks again for watching