The Standing Wave Ratio (SWR) is a measure of how efficiently power is transmitted from a source to a load through a transmission line. It indicates the presence of standing waves due to impedance mismatch.
Table of Contents
Definition
The standing wave ratio (SWR) is defined as the ratio of the maximum amplitude of the voltage (or current) along a transmission line to the minimum amplitude of the voltage (or current).
Mathematical Expression
Voltage SWR (\(S\)) is given by:
\[
S = \frac{V_\text{max}}{V_\text{min}}
\]
Alternatively, using reflection coefficient (\(\Gamma\)):
\[
S = \frac{1 + |\Gamma|}{1 – |\Gamma|}
\]
- \(V_\text{max}\) = maximum voltage along the line
- \(V_\text{min}\) = minimum voltage along the line
- \(|\Gamma|\) = magnitude of reflection coefficient
Reflection Coefficient
The reflection coefficient is defined as:
\[
\Gamma = \frac{Z_L – Z_0}{Z_L + Z_0}
\]
- \(Z_L\) = load impedance
- \(Z_0\) = characteristic impedance of the transmission line
Properties
- \(S = 1\) → perfect matching, no reflections
- \(S > 1\) → presence of standing waves, some power is reflected
- Higher SWR → higher reflection and power loss
Applications
- Transmission line analysis
- Antenna matching
- RF and microwave engineering
- Power delivery optimization