Smith Chart for Ham Radio: Reading Impedance, SWR and Matching

Open the display of a modern antenna analyzer and you will often see a round grid covered in circles and arcs, with a thin line wandering across it. For many amateurs, this is the part of the instrument they skip. Yet the Smith chart carries more information than any SWR number: it tells you the resistance and the reactance of the antenna, whether the antenna is too long or too short, how the match will change if you add a coil or a capacitor and how the cable between the analyzer and the antenna affects what you see. This guide explains the chart in plain language, with worked examples that need nothing more than the numbers on the screen.

What the Smith Chart Is

The Smith chart is, in the words of the reference article, a circular nomogram used in radio frequency engineering to solve transmission line and impedance matching problems. It plots a complex reflection coefficient on a grid of normalized electrical impedance. It emerged in the late 1930s, from the independent work of several engineers including Phillip Smith, whose name is the one that stuck. Although paper charts have largely been replaced by software for calculation, the format remains the standard display of vector network analyzers and RF simulation programs, so it is useful to know how to read it. The Smith chart article gives the history and the mathematics, and our guide here concentrates on practical use.

The idea is to take the impedance of a load, which has a resistance and a reactance, and turn it into a single point on a map. Impedance is written as R plus jX, where R is resistance in ohms and X is reactance, positive for an inductive load and negative for a capacitive one. Because impedance is a two-part number, it needs a two-dimensional picture, and the chart provides it.

Normalizing: Why the Centre Is a Perfect Match

The chart does not plot ohms directly. It divides every impedance by the characteristic impedance of the system, which for amateur radio is almost always 50 ohms. The result is called normalized impedance, written as a small z. A load of 50 ohms resistive becomes 1 plus j0. That point sits exactly at the centre of the chart, and it represents a perfect match, with no reflected power and an SWR of 1:1.

The advantage of normalizing is that the same chart works for any system. A 75 ohm cable system uses the same picture with a different reference number. Most instruments let you set the reference impedance, and the NanoVNA and similar analyzers default to 50 ohms.

The Grid: Circles and Arcs

The grid consists of two families of curves.

• Circles of constant resistance. All of them touch the right-hand edge of the chart. The circle that passes through the centre is the one for a normalized resistance of 1, or 50 ohms. Circles to the left correspond to lower resistance, and circles to the right to higher resistance.
• Arcs of constant reactance. These curve out from the right-hand edge. The arcs in the upper half of the chart represent positive, or inductive, reactance. The arcs in the lower half represent negative, or capacitive, reactance. The straight horizontal line through the centre is zero reactance, a purely resistive load.

The left-hand edge of the chart is zero resistance, which is a short circuit. The right-hand edge is infinite resistance, an open circuit. The outer rim of the chart is a pure reactance with no resistance, in which all the power would be reflected. Real antennas are always inside the rim, since they radiate and lose some power.

From Position to SWR

The distance of a point from the centre tells you how bad the mismatch is. That distance is the magnitude of the reflection coefficient, which is written as gamma. It is found with a simple formula: gamma equals the load impedance minus the reference impedance, divided by the load impedance plus the reference impedance. The SWR follows from it: SWR equals one plus the magnitude of gamma, divided by one minus the magnitude of gamma. The centre has a gamma of zero and an SWR of 1. The rim has a gamma of 1 and an infinite SWR.

If you draw a circle centred on the middle of the chart that passes through your point, every point on that circle has the same SWR. That is why it is called the SWR circle. Where the circle crosses the horizontal line on the right-hand side, the normalized resistance is numerically equal to the SWR. This gives you a quick way of reading the number from the chart. Our guide to what an SWR meter tells you and what it hides explains why this number alone does not say what to do, while the chart does.

Take a few examples with a 50 ohm system.

• A 100 ohm resistive load. The normalized impedance is 2 plus j0, on the horizontal line right of centre. Gamma is 50 divided by 150, or one third. The SWR is (1 plus 1/3) divided by (1 minus 1/3), which is 2.
• A 25 ohm resistive load. The normalized value is 0.5, left of centre. Gamma is minus one third in magnitude, and the SWR is again 2. The same SWR circle passes through both points, one on each side of the centre.
• A load of 50 plus j50 ohms. Normalized, it is 1 plus j1, above the line. The reflection coefficient works out to 0.2 plus j0.4, with a magnitude of about 0.447. The SWR is about 2.6. The load is inductive.

Using the Chart to Plan a Match

The last example shows the power of the chart. The load of 50 plus j50 ohms has the right resistance, and the problem is only reactance. To cancel a positive 50 ohms of reactance, you add a negative 50 ohms in series, which is a capacitor. At 14.2 MHz the reactance of a capacitor is 1 divided by 2 pi times the frequency times the capacitance, so a reactance of minus 50 ohms needs a capacitance of about 224 picofarads. Adding it moves the point straight down along the constant resistance circle to the centre of the chart. A single component has solved the problem.

That is the general method. A series element moves the point along a circle of constant resistance. A shunt element moves it along a circle of constant conductance, which is the same chart rotated by 180 degrees. Practical matching networks, such as the L network used in many antenna tuners, combine one series and one shunt element to bring any point into the centre. Software and many analyzers can suggest the values, but it helps to understand the moves. For a broader view, see the impedance matching overview, and our guide to baluns and ununs for the transformer type of match.

Moving Along a Transmission Line

When you look into a length of cable, the impedance you see changes with the length of the line. On the chart this is a rotation about the centre at a constant SWR circle. Moving toward the generator, away from the load, is a clockwise rotation. One complete turn of the chart corresponds to half a wavelength of cable, so a quarter wavelength is half a turn, which flips the impedance to the opposite side of the circle. This is how a quarter-wave line works as an impedance transformer: the impedance seen at its input equals the square of the line impedance divided by the load impedance. To match a 100 ohm load to a 50 ohm line, for example, you need a quarter-wave section with an impedance of about 70.7 ohms, which is the square root of 50 times 100.

The physical length of such a section is shortened by the velocity factor of the cable, as explained in our article on velocity factor. The same rotation explains something that confuses many beginners: the impedance measured at the analyzer is not the impedance of the antenna unless the cable is very short or the analyzer is calibrated at the antenna end. A cable of any length turns the plot around the chart. That is why you should use a short, known jumper and calibrate at the connector when you want a true reading, or compensate for the cable using the analyzer’s port extension function.

Reading a Sweep on a NanoVNA

An analyzer does not show a single point but a trace, one point for each frequency in the sweep. The trace tells a story.

• Resonance is where the trace crosses the horizontal line. At that point the reactance is zero. If it crosses to the right of the centre, the resistance is above 50 ohms. If it crosses on the left, it is below 50 ohms.
• The direction of travel. As the frequency rises, the trace moves clockwise on the chart in most cases. A trace that circles the centre in a small loop indicates a narrow resonance with a good match, and one that stays near the rim indicates a poor match.
• Bandwidth. Draw an SWR circle for 2:1 or 3:1. The part of the trace inside the circle is the usable range of the antenna, and the frequencies at its ends mark the edges of that range.
• Multiple loops. A trace that makes several loops over a wide sweep may mean that the antenna has harmonic resonances, or that the cable is long enough to rotate the plot more than once.
• Noise and spikes. A jagged trace usually points to a poor connection, a common mode current on the cable or a pickup of a strong nearby transmitter. Try a ferrite choke on the cable and a different position.

Our guide to the NanoVNA antenna analyzer covers the calibration and sweep settings in detail. Calibration comes first, because an uncalibrated chart is a decoration.

Common Mistakes

The most frequent mistake is to look at the chart without checking the reference plane. The point you see belongs to the place where the analyzer was calibrated, not to the antenna. The second is to read the SWR circle on the wrong side of the centre. The SWR is given by the crossing on the right-hand side. The third is to apply a match that works at one frequency and then expect it to work across the whole band, since the reactance changes with frequency. The fourth is to forget that real components have losses, so a matching network adds some loss, especially when the point starts near the rim. And the last is to trust a perfect centre dot without asking how much of the power is lost in the cable or the antenna. Matching moves power around, it does not create it. If you want to see how the impedance of a design relates to its efficiency before you build it, our beginner walkthrough of antenna modelling with EZNEC and 4nec2 is a good place to start.

The Bottom Line

The Smith chart looks forbidding but follows a few simple rules. The centre is a perfect 50 ohm match, the horizontal line is zero reactance, the upper half is inductive and the lower half is capacitive. The distance from the centre gives the SWR, a clockwise turn moves you toward the generator along the cable, and a series or shunt component moves you along a circle towards the centre. Use it to see why an antenna is mismatched, not just that it is. Calibrate at the right plane, read the trace with a calm eye, and the chart will repay the effort every time you tune an antenna.

Frequently Asked Questions

What does the centre of a Smith chart mean?

It is the point of normalized impedance 1 plus j0, which is the reference impedance, usually 50 ohms. At that point there is no reflection and the SWR is 1:1.

How do I read SWR from a Smith chart?

Draw a circle centred on the middle through your point. Where it crosses the horizontal line to the right of the centre, the normalized resistance equals the SWR.

What do the upper and lower halves of the chart show?

The upper half is inductive reactance and the lower half is capacitive reactance. An antenna that is too long shows up in the upper half, and one that is too short in the lower half.

Why does a longer cable change my reading?

Cable rotates the impedance around the centre at constant SWR. One full turn is half a wavelength of cable, so you must calibrate at the antenna end or compensate for the cable.

Do I need the Smith chart if I have an SWR meter?

No, but the chart tells you much more. It shows resistance and reactance, so it tells you how to fix the mismatch, not just how big it is.

Can I use the Smith chart with a 75 ohm system?

Yes. Normalize to 75 ohms, or set the analyzer reference to 75 ohms, and the chart works in the same way.