3.2 Standing Wave Ratio (SWR) and Reflection Loss

3.2 Standing Wave Ratio (SWR) and Reflection Loss

ACMA Exam Focus: Standing Wave Ratio (SWR) is one of the most frequently tested topics in the ACMA Standard Theory syllabus. Candidates must master VSWR calculations, understand forward vs. reflected power, calculate reflection coefficients, identify operational thresholds (1:1, 2:1, infinite SWR), and explain the physical consequences of severe impedance mismatches.

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1. Fundamentals of Standing Waves

When a transmitter sends radio frequency energy down a transmission line of characteristic impedance $Z_0$, an RF voltage wave travels toward the antenna. This is the forward wave ($V_{\text{fwd}}$).

If the antenna load impedance ($Z_{\text{load}}$) perfectly matches the feedline characteristic impedance ($Z_{\text{load}} = Z_0$):

• All RF power arriving at the load is completely absorbed and converted into electromagnetic radiation and heat.
• Zero energy is reflected back down the feedline.
• The line is termed flat or matched.

However, if $Z_{\text{load}} \neq Z_0$, the load cannot absorb all arriving RF energy. The unabsorbed portion reflects back toward the transmitter as a reflected wave ($V_{\text{ref}}$).

As the forward wave ($V_{\text{fwd}}$) and reflected wave ($V_{\text{ref}}$) travel in opposite directions along the feedline, they continuously interfere constructively and destructively. This interference establishes stationary peaks ($V_{\text{max}}$) and troughs ($V_{\text{min}}$) along the line, known as standing waves.

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2. Reflection Coefficient ($\Gamma$) and Forward / Reflected Power

The Voltage Reflection Coefficient ($\Gamma$) is the complex ratio of reflected voltage to forward voltage at the load:

$\Gamma = \frac{V_{\text{ref}}}{V_{\text{fwd}}} = \frac{Z_{\text{load}} - Z_0}{Z_{\text{load}} + Z_0}$

Because power is proportional to the square of voltage ($P \propto V^2$), the ratio of reflected power ($P_{\text{ref}}$) to forward power ($P_{\text{fwd}}$) equals the magnitude of the reflection coefficient squared:

$\frac{P_{\text{ref}}}{P_{\text{fwd}}} = |\Gamma|^2 \implies |\Gamma| = \sqrt{\frac{P_{\text{ref}}}{P_{\text{fwd}}}}$

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3. Voltage Standing Wave Ratio (VSWR) Formulas

Voltage Standing Wave Ratio (VSWR)—commonly abbreviated simply as SWR—is defined as the ratio of the maximum RF voltage node ($V_{\text{max}}$) to the minimum RF voltage node ($V_{\text{min}}$) along the transmission line:

$\text{VSWR} = \frac{V_{\text{max}}}{V_{\text{min}}} = \frac{V_{\text{fwd}} + V_{\text{ref}}}{V_{\text{fwd}} - V_{\text{ref}}}$

Expressing VSWR in terms of the reflection coefficient magnitude ($|\Gamma|$):

$\text{VSWR} = \frac{1 + |\Gamma|}{1 - |\Gamma|}$

Conversely, if VSWR is known, $|\Gamma|$ can be calculated:

$|\Gamma| = \frac{\text{VSWR} - 1}{\text{VSWR} + 1}$

Purely Resistive Load Formula

When the load impedance is purely resistive ($Z_{\text{load}} = R_L + j0$), VSWR can be calculated directly without complex numbers:

$\text{VSWR} = \frac{R_L}{Z_0} \quad (\text{when } R_L > Z_0) \qquad \text{or} \qquad \text{VSWR} = \frac{Z_0}{R_L} \quad (\text{when } R_L < Z_0)$

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4. Key SWR Benchmarks and Power Reflection Table

The table below summarises critical SWR benchmarks tested on the ACMA exam:

| SWR Ratio | Reflection Coeff. ($|\Gamma|$) | Power Reflected (%) | Operating Condition & Practical Significance | | :--- | :--- | :--- | :--- | | 1:1 | $0.00$ | 0% | Perfect Match ($R_L = 50,\Omega$). 100% power absorbed by load. | | 1.5:1 | $0.20$ | 4.0% | Excellent match. Ideal operating range for all transceivers. | | 2:1 | $0.333$ | 11.1% | Acceptable match limit. Modern solid-state PAs begin power foldback. | | 3:1 | $0.500$ | 25.0% | High mismatch. 1/4 of power reflected. ATU required to protect PA. | | infinity:1 | $1.000$ | 100% | Open Circuit ($R_L = \infty$) or Short Circuit ($R_L = 0$). Total reflection. |

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5. Physical Consequences of High SWR

Operating a station into a high-SWR feedline ($> 2:1$ or $3:1$) causes three major problems:

1. Solid-State Power Amplifier Foldback

Modern transceivers utilise solid-state bipolar or MOSFET power amplifier (PA) transistors designed for a strict $50,\Omega$ load. Reflected power returning to the PA creates high RF voltage spikes across the collector/drain terminals. To protect output transistors from catastrophic over-voltage breakdown, automatic protection circuits (ALC power foldback) throttle back transmitter output power.

2. Dielectric Breakdown and Arcing

At voltage standing wave maxima ($V_{\text{max}} = V_{\text{fwd}} + V_{\text{ref}}$), peak RF voltage can exceed the dielectric breakdown rating of the coaxial insulator or connectors, causing destructive electric arcing. Conversely, at current maxima ($I_{\text{max}}$), extreme current causes heavy $I^2 R$ resistive heating.

3. Additional Line Loss (SWR Loss)

When power is reflected from a mismatched antenna, it travels back down the feedline toward the transmitter. On this return journey, it suffers normal line attenuation. When it reaches the transmitter, it is re-reflected forward, suffering line attenuation a second time. This repeated attenuation of reflected power is called SWR loss (or additional line loss).

ACMA EXAM TRAP: An SWR meter placed at the transmitter end of a long, lossy coaxial cable will read a lower (better) SWR than actually exists at the antenna! This occurs because the reflected wave travels the length of the cable twice and is therefore attenuated twice, while the forward wave is attenuated once - so the reflected-to-forward ratio seen at the transmitter end is smaller than the true ratio at the antenna.

6. SWR Meter Operation and Calibration

An SWR meter (directional wattmeter) uses a directional coupler circuit or sampling bridge transformer to measure forward and reflected voltage samples separately.

Procedure to Measure SWR Correctly

1. Insert the SWR meter in series with the coaxial line.
2. Set the meter selector switch to FWD (Forward).
3. Key the transmitter in a continuous-carrier mode (CW, AM, or RTTY) at reduced power.
4. Adjust the meter sensitivity calibration knob until the needle aligns exactly with the CAL (Full Scale) mark.
5. Flip the selector switch to REF (Reflected).
6. Read the VSWR ratio directly on the calibrated meter scale.

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7. Worked ACMA Exam Calculations

Calculation 1: VSWR from Forward and Reflected Power

Question: A transmitter delivers $100\text{ W}$ of forward power ($P_{\text{fwd}}$) into a feedline, and the SWR meter indicates $11.1\text{ W}$ of reflected power ($P_{\text{ref}}$). Calculate the reflection coefficient ($\Gamma$) and VSWR.

Step 1: Calculate reflection coefficient magnitude: $|\Gamma| = \sqrt{\frac{P_{\text{ref}}}{P_{\text{fwd}}}} = \sqrt{\frac{11.1}{100}} = \sqrt{0.111} = \mathbf{0.333}$

Step 2: Calculate VSWR: $\text{VSWR} = \frac{1 + |\Gamma|}{1 - |\Gamma|} = \frac{1 + 0.333}{1 - 0.333} = \frac{1.333}{0.667} = \mathbf{2.0:1}$

Calculation 2: VSWR from Known Load Resistance

Question: A $50,\Omega$ coaxial cable is terminated by a non-inductive $150,\Omega$ dummy load resistor. What is the VSWR on the line?

Solution: Since $R_L > Z_0$ ($150,\Omega > 50,\Omega$): $\text{VSWR} = \frac{R_L}{Z_0} = \frac{150}{50} = \mathbf{3.0:1}$