Standing Waves

When you send an RF signal down a transmission line and the load at the far end perfectly absorbs all of the power, the signal simply travels from source to load with no reflections. But this perfect match is the exception, not the rule. When any mismatch exists between the line's characteristic impedance and the load — and in real-world antenna installations some mismatch almost always exists — a portion of the power is reflected back toward the source. That reflected wave combines with the incident (forward) wave to create a pattern of voltage and current that does not travel: it stands in place. These are standing waves, and they are the physical reality that the Standing Wave Ratio (SWR) number describes.

Voltage and current standing wave patterns on a mismatched transmission line. Note that current maxima coincide with voltage minima and vice versa — they are exactly 90° out of phase along the line.

View Larger

What Standing Waves Are

The word "standing" is key — unlike a traveling wave, which moves along the line in one direction, a standing wave appears stationary. If you could take an instantaneous snapshot of the voltage at every point on a mismatched transmission line and plot it, you would see a sinusoidal pattern with fixed maxima and minima at specific positions along the line. Those positions do not move as time passes — they stand in place.

A standing wave is actually the superposition (sum) of two traveling waves: the incident wave moving toward the load and the reflected wave moving back toward the source. At any given point along the line, these two waves add together. Sometimes they add constructively (at voltage antinodes), producing voltage levels higher than either wave alone. Sometimes they add destructively (at voltage nodes), producing voltage levels lower than either wave.

The analogy of a guitar string is instructive. When you pluck a guitar string, the wave energy bounces off the fixed ends (analogous to mismatched loads) and the forward and backward waves combine to form standing modes — the vibrating patterns you see on a guitar string. The fixed points that do not move are nodes; the points of maximum vibration are antinodes. A transmission line with reflections behaves exactly the same way, just at radio frequencies.

How Standing Waves Form

Consider a transmission line of characteristic impedance Z₀ = 50 ohms terminated in a load Z_L = 100 ohms (a 2:1 impedance mismatch). The incident wave travels toward the load with a voltage amplitude V_i and current amplitude I_i = V_i/50.

When this wave reaches the load, it cannot simply be absorbed because the load's impedance ratio V/I is 100 ohms, not 50 ohms. Kirchhoff's voltage and current laws must be satisfied at the load terminals — the voltage and current must be continuous. The only way to satisfy these boundary conditions is for a reflected wave to be generated. The reflected wave travels back toward the source with an amplitude determined by how severe the mismatch is.

The fraction of the incident voltage that is reflected is given by the voltage reflection coefficient Γ (gamma):

Once the reflected wave is created at the load, it travels back toward the source. The source (transmitter) has its own output impedance, and if the source is not perfectly matched to the line, a portion of the reflected wave will be re-reflected from the source toward the load again. In a well-designed transmitter or amplifier, the output impedance is close to 50 ohms, so most of the returning reflected wave is absorbed and not re-reflected. Modern solid-state transceivers typically fold back power rather than absorb large reflected waves, which is why they reduce output power in response to high SWR.

Voltage and Current Patterns

At any point along the mismatched line, the total voltage is the sum of the incident and reflected voltage waves, and the total current is the sum of incident and reflected current waves. Because the two waves are traveling in opposite directions, the phase relationship between them changes continuously along the line.

The result is that the RMS (time-averaged) voltage and current magnitudes follow a sinusoidal pattern along the line:

• Voltage maximum (antinode): where incident and reflected voltage waves add constructively. Here |V| = |V_i| + |V_r|.
• Voltage minimum (node): where they add destructively. Here |V| = |V_i| − |V_r|.
• Current maximum (antinode): where current waves add constructively. This is always at the same location as the voltage minimum.
• Current minimum (node): always at the same location as the voltage maximum.

This 90° offset between voltage and current standing wave patterns is a fundamental feature of lossless transmission lines. Where the voltage is highest, the current is lowest, and vice versa — exactly the relationship you would expect from an impedance perspective (high V/I = high impedance; low V/I = low impedance).

The positions of the voltage maxima and minima are fixed in space (that is what makes them "standing"), but they depend on the position of the load and the frequency. Change the frequency or change the load, and the positions shift.

Special Cases: Short, Open, and Matched Loads

Three special termination conditions produce the most extreme and instructive standing wave patterns:

Short-circuit termination (Z_L = 0)

Γ = (0 − Z₀)/(0 + Z₀) = −1. The reflection coefficient is −1: total reflection with polarity inversion. The voltage at the short is zero (because a short circuit forces V = 0). The current at the short is maximum (because all the incident wave current adds to the reflected wave current). Moving quarter-wavelength back from the short, the situation reverses: voltage is maximum, current is minimum. The standing wave pattern has voltage null at the load and maxima every half-wavelength back.

This explains why a short-circuit stub, exactly quarter-wave long, presents an open circuit (maximum impedance, zero current) at its input — the current minimum corresponding to the voltage maximum at a quarter-wave from the short.

Open-circuit termination (Z_L = ∞)

Γ = (∞ − Z₀)/(∞ + Z₀) = +1. Total reflection without polarity inversion. The voltage at the open is maximum (the reflected voltage adds to the incident voltage with the same polarity). The current at the open is zero (no current can flow through an open circuit). A quarter-wavelength back from the open, the situation reverses: voltage minimum, current maximum. An open-circuit stub, quarter-wave long, presents a short circuit at its input.

Matched termination (Z_L = Z₀)

Γ = 0. No reflection at all. The voltage and current are constant (no variation) along the entire line — the pattern is flat. This is the ideal condition for a transmission line: all the incident power is absorbed by the load, nothing returns. The SWR is 1:1.

Standing waves form from the superposition of an incident wave (traveling right) and a reflected wave (traveling left). The sum creates a stationary pattern of maxima and minima whose positions depend on the load impedance and frequency.

View Larger

What SWR Measures

The Standing Wave Ratio is the ratio of the maximum voltage amplitude to the minimum voltage amplitude along the line:

The SWR gives you a single number that characterizes the severity of the mismatch: 1:1 is perfect, 1.5:1 is excellent, 2:1 is acceptable for most amateur radio purposes, and anything above 3:1 starts causing significant additional feedline loss (particularly on lossy coaxial cable runs). Numbers like 10:1 or ∞ indicate serious mismatch problems.

SWR is also related to reflected power through the reflection coefficient:

Reflected power = |Γ|² × incident power = ((SWR − 1)/(SWR + 1))² × incident power

At SWR 2:1: |Γ| = 1/3, reflected power = 1/9 = 11.1% of incident power

At SWR 3:1: |Γ| = 1/2, reflected power = 1/4 = 25% of incident power

These calculations will be developed in full detail in the next lesson (M13H).

Nodes, Antinodes, and Half-Wave Periodicity

The standing wave pattern along a transmission line repeats every half-wavelength. If you have a voltage maximum at some point on the line, the next voltage maximum is exactly half a wavelength farther toward the source. Voltage minima are also spaced a half-wavelength apart. Voltage maxima and minima are spaced a quarter-wavelength apart from each other.

This half-wavelength periodicity is why SWR measurements do not depend on how far the meter is placed from the load (at least on a lossless line) — the ratio V_max/V_min is the same everywhere along the line. An SWR meter placed at the transmitter reads the same SWR as one placed right at the antenna feedpoint (for a lossless line; real lossy lines produce slightly different readings because the reflected wave is attenuated as it travels back).

On a real feedline with loss, the SWR reading decreases as you move from the antenna toward the transmitter. This is because the lossy line attenuates the reflected wave more than the incident wave (the reflected wave has already traveled through the cable to the antenna and is traveling back through it again). An SWR meter at the transmitter therefore underreads the true SWR at the antenna. This effect is most significant on high-loss feedlines and at high SWR. A meter in a low-loss feedline like LMR-400 will read very close to the true antenna SWR.

Practical Consequences of Standing Waves

Understanding standing waves reveals several important practical points:

High voltage at voltage antinodes

At a voltage antinode, the voltage on the line is V_max = V_i(1 + |Γ|). At SWR 5:1, this is 1.67 × V_i — the peak voltage is two-thirds higher than the incident wave amplitude. This elevated voltage can stress connectors, damage cable jackets that are nicked or damaged, and cause voltage breakdown in poor-quality connectors. It is one reason why operating at very high SWR requires careful attention to connector quality.

High current at current antinodes

At a current antinode, the current in the conductor is I_max = I_i(1 + |Γ|). Higher current means more I²R resistive heating at that point. If the current antinode falls at a connector or at a section of damaged cable, the concentrated heating can damage or destroy that component.

The feedline is not the only thing that matters

Standing waves are a symptom of a mismatch — and the mismatch itself does not directly destroy power. The reflected power does not simply disappear; it bounces between the load and the source. In a system where the source absorbs the reflected power (as a well-designed transmitter does), that power is turned into heat in the transmitter's output stage. Modern solid-state transceivers typically reduce their output power in response to SWR above about 2:1, to protect their output transistors from excessive voltages. This protection fold-back does reduce the effective transmitted power, but it is preferable to burning out the transistors.

Standing waves do not indicate antenna efficiency

A low SWR reading does not tell you that your antenna is radiating efficiently. A dummy load (50-ohm resistor) gives a perfect 1:1 SWR while radiating zero power. What SWR measures is impedance match — whether the load impedance matches the feedline impedance. Whether that load is efficiently radiating, or just dissipating power as heat, is a separate question entirely.