Antenna Impedance and Reactance Explained: Resonance, R and X

An antenna analyzer shows two numbers that look like a puzzle on the first day: something like “R = 62, X = 18”. The SWR meter reports one number, but the analyzer shows two, and the second one has a sign. Those numbers describe antenna impedance and reactance, and once they make sense, a great deal of antenna practice becomes simple: why a dipole is cut to a certain length, why a loading coil works, why a tuner can match almost any load and why the SWR at the end of a cable is not always the SWR at the antenna. This guide explains resistance, reactance and impedance in plain terms, shows how they produce the SWR and gives practical rules for using them with a real antenna.

Resistance, Reactance and Impedance

In a direct current circuit, only resistance matters: it is measured in ohms and it turns electrical power into heat. In an alternating current circuit there is a second effect. Coils and capacitors store energy and give it back every cycle, so they oppose the current without consuming power. This opposition is called reactance, and it is also measured in ohms. The two together form the impedance, which the Wikipedia article on electrical impedance describes as a complex quantity with a resistive part and a reactive part. The usual way to write it is Z = R + jX, where R is the resistance, X is the reactance and j marks the part that is shifted by a quarter of a cycle.

The sign of X has a direct meaning. A positive reactance is inductive: it behaves like a coil. A negative reactance is capacitive: it behaves like a capacitor. The two cancel each other, which is the key to nearly all matching.

Two formulas are worth remembering. The reactance of a coil is X = 2 times pi times f times L, and the reactance of a capacitor is X = 1 divided by 2 times pi times f times C, with a negative sign. At 7.1 MHz, a coil of 1 microhenry has a reactance of about +45 ohms, while a capacitor of 100 picofarads has about -224 ohms. A small coil is a small reactance, and a small capacitor is a large one, and both change with frequency in opposite directions: the coil rises with frequency, the capacitor falls.

What Resonance Means for an Antenna

An antenna is not a coil or a capacitor, but near its first resonance it behaves like a series circuit made of both. Below the resonant frequency, the antenna is electrically too short, and the feedpoint shows a negative, capacitive reactance. Above it, the antenna is electrically too long, and the reactance is positive and inductive. At the resonant frequency, the two cancel and X is zero. The resonance of the antenna is therefore defined as the frequency where the feedpoint reactance is zero, and the impedance is purely resistive.

That definition has a practical result. If your analyzer shows X = -30 at your operating frequency, the antenna is too short for that frequency, or the frequency is below the resonance of the antenna. If X is +30, the antenna is too long. The sign tells you which way to cut or extend the wire, and that is why a dipole is trimmed with an analyzer and not by guessing. Our guide to the velocity factor explains why the physical length of a wire is shorter than the free-space half wavelength.

The Resistance That You See at Resonance

At resonance, the remaining resistance has two parts. The first is the radiation resistance, which represents the power that leaves as radio waves; this is the useful part. The second is the loss resistance, which stands for the power lost in the wire, the ground and the nearby objects. A half-wave dipole in free space has a radiation resistance of about 73 ohms, a quarter-wave vertical over a perfect ground about 36 ohms, and a folded dipole about 292 ohms. A real dipole at a normal height above real ground shows values between roughly 50 and 90 ohms, because the ground changes the picture, and the value swings up and down as the height changes.

The loss part is where antennas can be poor. A short loaded antenna may show a feedpoint resistance of 20 ohms, but only a small part of it is radiation resistance, and most is loss. It looks well matched after a tuner, but the efficiency is low. This is why a good match is not the same as a good antenna, and why the resistance alone does not tell you how well the system radiates.

How R and X Produce the SWR

The SWR depends on how far the load impedance is from the impedance of the feedline, which is 50 ohms for most amateur systems. The reflection coefficient is the difference between the load and the line, divided by their sum, calculated with complex numbers, and the SWR is (1 + magnitude) divided by (1 – magnitude). You do not need to do the arithmetic by hand, but the table shows how typical combinations behave in a 50 ohm system.

Two lessons follow. First, a resistance error and a reactance error are not the same size of problem: 25 ohms of reactance gives almost the same SWR as an error of 25 ohms in the resistance, so a small amount of reactance is just as damaging as a large mismatch in resistance. Second, the SWR cannot tell the positive from the negative, so it hides the very information that tells you what to do. Our article on what an SWR meter tells you and what it hides makes the same point from the other side.

Reading R and X on an Analyzer

An antenna analyzer or a vector network analyzer measures R and X directly, at the end of the cable it is connected to. A sweep across the band gives you a curve: X falls from positive to negative as the frequency goes down through resonance, and R reaches its smallest or most stable value near the resonance. The point where X crosses zero is the resonant frequency. Our guide to the NanoVNA shows how to calibrate and sweep, and the article on the Smith chart shows the same data on a single picture, where the resonance is the point where the curve crosses the horizontal axis.

The reading depends on the cable. Unless the measurement is made at the feedpoint, the cable transforms the impedance, and the R and X that you see at the radio end are different from the values at the antenna. A cable that is an exact half wavelength long repeats the load; any other length changes it. That is why a coil of coax in the shack can change the numbers on the analyzer without any change in the antenna. If you want to know the truth about the antenna, calibrate at the end of the cable, or use a cable of known length and correct the result.

Using Reactance to Your Advantage

The same cancelling action that defines resonance is used to match an antenna that is not resonant. A short antenna has negative reactance, so a series coil with the same positive reactance cancels it; this is how a loading coil works, and it is the same idea as in an antenna tuner. A long antenna can be cancelled with a series capacitor. After cancelling, the remaining resistance may still not be 50 ohms, so a second step, such as a transformer or an L network, is needed. The guide to the L network covers the arithmetic of that second step.

It is useful to know the limits. A coil placed at the feedpoint cancels the reactance for the antenna, but the losses in the coil add to the loss resistance, and the bandwidth becomes narrower because the antenna with the coil has a higher Q. A tuner at the radio does the same job at a distance, but the feedline between the tuner and the antenna still carries the mismatch, with the added loss that this means. Cancelling the reactance as close to the antenna as practical is almost always the better solution when the SWR is high.

A Worked Example

Suppose a short antenna shows R = 30 and X = -40 at your operating frequency. The reactance is negative, so the antenna is capacitive. Add a series coil that has +40 ohms of reactance at that frequency, and the load becomes 30 + j0, which is a pure resistance. The SWR in a 50 ohm line is then 50 divided by 30, or about 1.7 to 1, which is acceptable for many purposes. Without the coil, the same antenna would have shown an SWR of 3 to 1, so a small coil makes a large difference. If you want a perfect match, an L network or a transformer that raises 30 ohms to 50 ohms is the next step.

Now take a different case: R = 60 and X = +20. The antenna is slightly long and slightly high in resistance, yet the SWR is only about 1.5 to 1. Many operators would leave it alone. Trimming a few centimeters from each end would bring X to zero, but the gain in SWR is small, and the work, with the antenna high in the air, may not be worth it. A little knowledge of R and X allows you to decide when a measurement needs action and when it does not.

Bandwidth and the Rate of Change

The reactance of an antenna changes with frequency, and how fast it changes is a measure of its bandwidth. A thick dipole, such as one made of tubing or a cage of wires, changes slowly and stays well matched over a wide range. A thin wire dipole changes faster, and a short loaded antenna changes fastest of all. When you see the SWR rise sharply on both sides of the resonance, you are looking at a high Q antenna, which is a sign of high reactance slope, and not a failure.

The practical consequence is for the choice of the center frequency. On 80 meters, the band is about 13 percent wide, which is too wide for a simple dipole, so the cutting frequency is chosen for the part of the band you use the most: the CW end, the phone end or the digital window. A dipole cut for the middle of the band is a compromise, and the SWR at both ends is usually higher than at the center.

Practical Tips

• Use the sign. Negative X means the antenna is too short; positive X means it is too long. Trim or extend accordingly.
• Measure at the feedpoint when you can. The cable changes R and X, so readings at the radio end are not the antenna’s own.
• Do not trust a low SWR alone. A lossy antenna or a dummy load also has a low SWR; check the efficiency by comparing signal reports.
• Cancel reactance first. Bring X to zero, then deal with the resistance with a transformer or an L network.
• Allow for the height. The resistance of a dipole changes with the height above ground, so trim only after the antenna is in its final position.

The Bottom Line

Antenna impedance is a combination of resistance R and reactance X. The resistance is partly useful radiation and partly loss; the reactance is stored energy that the antenna returns, positive when the antenna is electrically long and negative when it is short. Resonance is the point where X is zero. R and X together decide the SWR, and an analyzer that shows both gives you much more information than an SWR meter alone. Use the sign of X to trim the antenna, measure at the feedpoint when you can, cancel reactance before you transform resistance and remember that a low SWR is not the same as an efficient antenna.

Frequently Asked Questions

What is the difference between impedance and resistance?

Resistance is the part of impedance that dissipates power. Impedance also includes reactance, which stores energy and returns it, so it combines both parts in one complex number.

What does a negative reactance mean on my analyzer?

It means the load is capacitive, which for a simple dipole means the antenna is electrically too short for that frequency. A positive reactance means it is too long.

Is an antenna resonant when the SWR is lowest?

Not always. The minimum of the SWR can be at a slightly different frequency from the point where X is zero, especially when the resistance changes with frequency or when the feedline is long.

Why does my SWR change when I change the coax length?

The cable transforms the impedance at the antenna into a different one at the radio. In a lossy cable the SWR also falls with the length because the reflected power is attenuated on the way back.

Can I use a tuner instead of fixing the reactance?

Yes, a tuner can cancel reactance and transform resistance at the radio. The cable between the tuner and the antenna still carries the mismatch, so the loss on that cable is higher.

What impedance does a half-wave dipole have?

In free space about 73 ohms. Near the ground it changes with the height and usually falls between about 50 and 90 ohms.