# (T7C04) SWR

T7C04 from the Technician License Course section 7.2, SWR:

What reading on an SWR meter indicates a perfect impedance match between the antenna and the feed line?

A. 2 to 1
B. 1 to 3
C. 1 to 1
D. 10 to 1

The standing wave ratio (SWR) is a measure of how well a load, such as an antenna, is matched to a transmission line, such as your antenna system coaxial feedline. By “match” we mean impedance match, the electrical measure of opposition to the flow of alternating current in a circuit.

To have a good impedance match the impedance of the antenna and the impedance of the feedline must be near the same value. The impedance of the most commonly used coaxial cables in typical amateur radio installations is 50 ohms. Thus, a typical goal is to have an antenna feedpoint at which the impedance is also near 50 ohms.

If the antenna feedpoint impedance and the feedline impedance are mismatched, some of the power of a transmitted signal will reflect back down the feedline toward the transmitter rather than contribute to the radiation of RF waves from the antenna. This power reflection will occur at the point of the impedance mismatch, usually at the antenna feedpoint, but reflections may also occur at the position of a faulty connector or damaged feedline cable. Power reflections are generally undesirable since they reduce the efficiency of your transmission system, reducing the effective radiated power at your antenna. Most amateur stations will have at least some reflections due to a minor impedance mismatch at the antenna feedpoint. A perfect impedance match is rarely achieved.

The transmitter’s forward power and the reflected power travel in the feedline in opposite directions. The oppositely traveling signals are of equivalent frequency, and they interact in the feedline. The two traveling signals will superimpose, alternating between a constructive superposition in which the signal amplitudes build upon one another to produce a greater combined amplitude, and a destructive superposition that diminishes the combined signal amplitude. For signals of equivalent frequency the resultant effect is a standing wave in the feedline that oscillates between the constructive and destructive amplitudes.

In the graphic below the forward power is represented as the blue waveform and the reflected power is the brown waveform. The forward power travels toward the antenna and the reflected power travels toward the transmitter. The red waveform depicts the superimposed forward and reflected signals in two relative positions of the traveling waves: 1) the position of maximum reinforcement or constructive superposition, and 2) the position of minimum reinforcement or destructive superposition. The constructive position has the two traveling waveforms perfectly in-phase, while the destructive position has them perfectly out-of-phase. As the waveforms travel they will pass through all possible relative phase positions with one another, affecting interim amplitude values of the standing wave, but the perfectly in- and out-of-phase positions are significant for SWR determination.

The SWR is the comparison of the in-phase constructive amplitude with the out-of-phase destructive amplitude of the standing wave (red waveform). It is, as the name indicates, the ratio of the standing wave’s values. If the power of each directional signal is measured, perhaps with a directional wattmeter, the SWR may be computed as follows:

$latex SWR=\frac{\sqrt{Fwd Pwr}+\sqrt{Refl Pwr}}{\sqrt{Fwd Pwr}-\sqrt{Refl Pwr}} &s=2&bg=e5e6db$

Example:
$latex SWR=\frac{\sqrt{81}+\sqrt{9}}{\sqrt{81}-\sqrt{9}} &s=2&bg=e5e6db$
$latex SWR=\frac{9+3}{9-3} &s=2&bg=e5e6db$
$latex SWR=\frac{12}{6} &s=2&bg=e5e6db$
$latex SWR=\frac{2}{1} &s=2&bg=e5e6db$ or a ratio, 2:1

Consider the ratio resulting from a reflected power value of zero. With zero reflected power the ratio is always the forward power value compared to itself, or 1:1. A perfect impedance match produces no reflected power and the resulting SWR will be 1:1. As reflected power increases with impedance mismatch, the SWR climbs to ratios greater than 1:1. This is why SWR is used as a measure of antenna system efficiency, with higher SWR indicating reduced efficiency of transmissions due to reflected power in the feedline not contributing to the antenna’s radiated RF power.

The answer to Technician Class question T7C04, “What reading on an SWR meter indicates a perfect impedance match between the antenna and the feed line?” is “C. 1 to 1.

Related Questions: T4A05, T7C03, T7C05, T7C06, T7C07, T7B09, T5C12, T5C13, T9B02