
Electronic Warfare and Radar Systems Engineering Handbook  Voltage Standing Wave
Ratio (VSWR)/  Reflection Coefficient / Mismatch Loss


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VOLTAGE STANDING WAVE RATIO (VSWR) / REFLECTION COEFFICIENT RETURN LOSS
/ MISMATCH LOSS
When a transmission line is terminated with an impedance, Z_{L}, that is not equal to the
characteristic impedance of the transmission line, Z_{O}, not all of the incident power is absorbed by the
termination. Part of the power is reflected back so that phase addition and subtraction of the incident and
reflected waves creates a voltage standing wave pattern on the transmission line. The ratio of the maximum to
minimum voltage is known as the Voltage Standing Wave Ratio (VSWR) and successive maxima and minima are spaced by
180° (λ/2).
The
reflection coefficient, ρ, is defined as E_{r}/E_{i} and in general, the termination is complex in
value, so that ρ will be a complex number.
Additionally we define:
The
refection coefficient, ρ, is the absolute value of the magnitude of Γ.
If the equation for VSWR is solved for the reflection coefficient, it is found that:
The return loss is related through the following equations:
Return loss is a measure in dB of the ratio of power in the incident wave to that in the reflected wave,
and as defined above always has a positive value. For example if a load has a Return Loss of 10 dB, then 1/10 of
the incident power is reflected. The higher the return loss, the less power is actually lost. Also of considerable
interest is the Mismatch Loss. This is a measure of how much the transmitted power is attenuated due to
reflection. It is given by the following equation:
Mismatch Loss = 10 log (1  ρ^{2})
For
example, an antenna with a VSWR of 2:1 would have a reflection coefficient of 0.333, a mismatch loss of 0.51 dB,
and a return loss of 9.54 dB (11% of your transmitter power is reflected back). In some systems this is not a
trivial amount and points to the need for components with low VSWR.
If 1000 watts (60 dBm/30 dBW) is
applied to this antenna, the return loss would be 9.54 dB. Therefore, 111.1 watts would be reflected and 888.9
watts (59.488 dBm/29.488 dBW) would be transmitted, so the mismatch loss would be 0.512 dB.
Transmission line attenuation improves the VSWR of a load or antenna. For example, a transmitting antenna with
a VSWR of 10:1 (poor) and a line loss of 6 dB would measure 1.5:1 (okay) if measured at the transmitter. Figure
1 shows this effect.
Therefore, if you are interested in determining the performance of antennas, the VSWR
should always be measured at the antenna connector itself rather than at the output of the transmitter. Transmit
cabling will load the line and create an illusion of having a better antenna VSWR. Transmission lines should have
their insertion loss (attenuation) measured in lieu of VSWR, but VSWR measurements of transmission lines are still
important because connection problems usually show up as VSWR spikes.
Historically VSWR was measured by
probing the transmission line. From the ratio of the maximum to minimum voltage, the reflection coefficient and
terminating impedance could be calculated. This was a time consuming process since the measurement was at a single
frequency and mechanical adjustments had to be made to minimize coupling into circuits. Problems with detector
characteristics also made the process less accurate. The modern network analyzer system sweeps very large
frequency bandwidths and measures the incident power, P_{i}, and the reflected power, P_{r} .
Because of the considerable computing power in the network analyzer, the return loss is calculated from the
equation given previously, and displayed in real time. Optionally, the VSWR can also be calculated from the return
loss and displayed real time.
If a filter is needed on the output of a jammer, it is desirable to place it
approximately half way between the jammer and antenna. This may allow the use of a less expensive filter, or a
reflective filter vs an absorptive filter.
Special cases exist when comparing open and shorted circuits.
These two conditions result in the same ∞ VSWR and zero dB return loss even though
there is a 180° phase difference between the reflection coefficients. These two conditions are used to calibrate a
network analyzer.
Table of Contents
for Electronics Warfare and Radar Engineering Handbook
Introduction 
Abbreviations  Decibel  Duty
Cycle  Doppler Shift  Radar Horizon / Line
of Sight  Propagation Time / Resolution  Modulation
 Transforms / Wavelets  Antenna Introduction
/ Basics  Polarization  Radiation Patterns 
Frequency / Phase Effects of Antennas 
Antenna Near Field  Radiation Hazards 
Power Density  OneWay Radar Equation / RF Propagation
 TwoWay Radar Equation (Monostatic) 
Alternate TwoWay Radar Equation 
TwoWay Radar Equation (Bistatic) 
Jamming to Signal (J/S) Ratio  Constant Power [Saturated] Jamming
 Support Jamming  Radar Cross Section (RCS) 
Emission Control (EMCON)  RF Atmospheric
Absorption / Ducting  Receiver Sensitivity / Noise 
Receiver Types and Characteristics 
General Radar Display Types 
IFF  Identification  Friend or Foe  Receiver
Tests  Signal Sorting Methods and Direction Finding 
Voltage Standing Wave Ratio (VSWR) / Reflection Coefficient / Return
Loss / Mismatch Loss  Microwave Coaxial Connectors 
Power Dividers/Combiner and Directional Couplers 
Attenuators / Filters / DC Blocks 
Terminations / Dummy Loads  Circulators
and Diplexers  Mixers and Frequency Discriminators 
Detectors  Microwave Measurements 
Microwave Waveguides and Coaxial Cable 
ElectroOptics  Laser Safety 
Mach Number and Airspeed vs. Altitude Mach Number 
EMP/ Aircraft Dimensions  Data Busses  RS232 Interface
 RS422 Balanced Voltage Interface  RS485 Interface 
IEEE488 Interface Bus (HPIB/GPIB)  MILSTD1553 &
1773 Data Bus  This HTML version may be printed but not reproduced on websites.



