• Skip to primary navigation
  • Skip to main content
  • Skip to primary sidebar
  • Skip to footer
  • Advertise
  • Subscribe

Test & Measurement Tips

Oscilloscopes, electronics engineering industry news, how-to EE articles and electronics resources

  • Oscilloscopes
    • Analog Oscilloscope
    • Digital Oscilloscope
    • Handheld Oscilloscope
    • Mixed-signal Oscilloscope
    • PC-based Oscilloscopes – PCO
  • Design
  • Calibration
  • Meters & Testers
  • Test Equipment
  • Learn
    • eBooks/Tech Tips
    • FAQs
    • EE Training Days
    • Learning Center
    • Tech Toolboxes
    • Webinars & Digital Events
  • Video
    • EE Videos
    • Teardown Videos
  • Resources
    • Design Guide Library
    • Digital Issues
    • Engineering Diversity & Inclusion
    • Leap Awards
    • White Papers
  • Subscribe
You are here: Home / Featured / The difference between VSWR and the S11 reflection coefficient

The difference between VSWR and the S11 reflection coefficient

March 11, 2022 By David Herres Leave a Comment

A traveling signal along an electrical transmission line reflects back toward the source when one or more events occurs:
One or both of the conductors is open at the far end (receiving end).
The conductors are shorted at the far end (very common).
There is a discontinuity in the characteristic impedance or an electrical fault at some point along the transmission line.
The transmission line is not terminated in its characteristic impedance at either end.

That said, there are numerous ways to characterize signal reflections in transmission lines. Two of the most fundamental ways which are sometimes confused are the voltage standing-wave ratio, or VSWR, and the reflection coefficient, normally represented on vector network analyzers as the S11 S parameter.

The VSWR is equal to the maximum voltage on the transmission line divided by the minimum voltage. The voltage fluctuations come about as a result of the constructive and destructive interference between voltage components from the forward power and the reflected power summing together. VSWR is actually a measure of how well or how badly the impedance of a load matches the characteristic impedance of a transmission line or waveguide. Impedance mismatches are what cause the standing waves along the transmission line.

The ratio part of VSWR arises because maximum and minimum voltages are expressed as a ratio. For example, the VSWR value 1.2:1 means standing waves along the transmission line gives the ac voltage a peak value 1.2 times that of the minimum ac voltage along that line, assuming the line is at least one-half wavelength long. When we are talking about the ratio of the maximum amplitude to minimum amplitude of the transmission line’s currents, electric field strength, or the magnetic field strength, rather than the ratio of the voltages, the more general term is the standing wave ratio. The SWR for all these entities is identical, neglecting transmission line loss.

VSWR serves as a measure of the degree to which the impedance of a load matches the characteristic impedance of a transmission line carrying radio frequency signals. Impedances match when the source impedance is the complex conjugate of the load impedance. The optimum scenario is for the imaginary part of the complex impedance of both the source and load to be zero, that is, pure resistances, equal to the characteristic impedance of the transmission line. A mismatch between the load impedance and the transmission line reflects part of the forward wave sent toward the load back towards the source. The source then sees a different impedance than it expects.

The mismatch causes the standing waves along the transmission line which magnify transmission-line losses. A matched load would mean a VSWR of 1:1 implying no reflected wave. An infinite VSWR represents complete reflection with all the incident power reflected back toward the source.

That brings us to the reflection coefficient. As we’ve noted, a wave in a transmission line is partly reflected when the line is terminated with an impedance unequal to its characteristic impedance. The reflection coefficient is often written as S11 in S parameters or as Greek capital gamma, Γ.

S11=Γ =Vr /Vf = (ZL-Z0)/(ZL+Z0)
where Vr is the complex magnitude of the reflected wave, Vf is the complex magnitude of the forward wave, ZL is the complex load impedance, and Z0 is the complex source impedance.  Thus Γ is a complex number that describes both the magnitude and the phase shift of the reflection. The simplest cases with Γ measured at the load are Γ=-1, meaning there is a complete negative reflection (when the line is short-circuited); Γ=0, meaning there is no reflection and the line is perfectly matched; and Γ=1 meaning  complete positive reflection and the line is open-circuited.

Further, the VSWR directly corresponds to the magnitude of Γ. This becomes evident by considering that at some points along the transmission line, the forward and reflected wave interfere constructively with the resulting amplitude Vmax given by the sum of the wave amplitudes:

|Vmax| = |Vr |+|Vf| = |ΓVf|+|Vf| = (|Γ|+1) |Vf|

At other points, forward and reflected waves are completely out of phase and the amplitudes cancel:

|Vmin| = |Vf |-|Vr| = |Vf|-|ΓVf| = (1-|Γ|) |Vf|

Then VSWR = |Vmax|/|Vmin|  = (|Γ|+1)/(1-|Γ|)

slotted line
We found this slotted line kit on eBay for $200. Prices there seem to range up to about $1,000 depending on the frequency range.

The old way of measuring VSWR and reflection coefficients is with a slotted line. It consists of a precision transmission line with a movable insulated probe inserted into a longitudinal slot cut into the line. In a co-axial slotted line, the slot is cut into the outer conductor of the line. A probe is inserted past the outer conductor, but not far enough to touch the inner conductor. In a rectangular waveguide, the slot is usually cut along the center of the broad wall of the waveguide.

The probe samples the electric field inside the transmission line. For accuracy, the probe must disturb the field as little as possible, so the probe diameter and slot width are kept small (usually around 1 mm). In waveguide slotted lines the slot must be positioned where the current in the waveguide walls is parallel to the slot. Then the slot won’t disturb the current as long as it is not too wide. For the dominant mode this is on the center-line of the broad face of the waveguide, but for some other modes it may need to be off-center. This is not an issue for coax lines because they operate in the TEM (transverse electromagnetic) mode and the current is everywhere parallel to the slot.

There are two parts to the disturbance to the field inside the line caused by the insertion of the probe. The first comes from the power the probe has extracted from the line and manifests as a lumped equivalent circuit of a resistor. Minimizing the distance the probe is inserted into the line also minimizes the amount of power extracted. The second part of the disturbance is from energy stored in the field around the probe and appears as a lumped equivalent of a capacitor. This capacitance can be cancelled out with an inductance of equal and opposite impedance. Lumped inductors are impractical at microwave frequencies. so instead, an adjustable stub with an inductive equivalent circuit is used to tune out the probe capacitance. The result is an equivalent circuit of a high impedance shunting across the line which has little effect on the transmitted power in the line.

Of course, slotted lines can only carry out a measurement at one frequency at a time so a fair amount of manual labor must go into producing a plot of a parameter versus frequency. Consequently, VNAs have replaced slotted lines for work at lower RF frequencies. VNAs used at millimeter wave frequencies still tend to be pricey, so slotted lines can still be found in labs that do work at those frequencies.

You may also like:

  • music on scopes
    Making pictures from sound on an oscilloscope
  • Havana syndrome
    Microwaves and the Havana Syndrome
  • 5G
    Will 5G be lethal?
  • rental instruments
    The modern economics of renting test instruments
  • no you can't detect ghosts with a gauss meter
    No, you can’t detect ghosts with a gauss meter

Filed Under: FAQ, Featured, New Articles, Test Equipment, vector network analyzers Tagged With: FAQ

Reader Interactions

Leave a Reply Cancel reply

You must be logged in to post a comment.

Primary Sidebar

Featured Contributions

Why engineers need IC ESD and TLP data

Verify, test, and troubleshoot 5G Wi-Fi FWA gateways

How to build and manage a top-notch test team

How to use remote sensing for DC programmable power supplies

The factors of accurate measurements

More Featured Contributions

EE TECH TOOLBOX

“ee
Tech Toolbox: Internet of Things
Explore practical strategies for minimizing attack surfaces, managing memory efficiently, and securing firmware. Download now to ensure your IoT implementations remain secure, efficient, and future-ready.

EE TRAINING CENTER

EE Learning Center

EE ENGINEERING TRAINING DAYS

engineering
“test
EXPAND YOUR KNOWLEDGE AND STAY CONNECTED
Get the latest info on technologies, tools and strategies for EE professionals.
“bills

RSS Current EDABoard.com discussions

  • Wireless microphone reviews
  • audio transformers impedance
  • ISL8117 buck converter blowing up
  • Help Creating .lib File for SCR in LTspice
  • Editing posts

RSS Current Electro-Tech-Online.com Discussions

  • RS485 bus: common ground wire needed or not?
  • Kawai KDP 80 Electronic Piano Dead
  • Good Eats
  • What part is this marked .AC ?
  • Photo interrupter Connections
Search Millions of Parts from Thousands of Suppliers.

Search Now!
design fast globle

Footer

EE World Online Network

  • 5G Technology World
  • EE World Online
  • Engineers Garage
  • Analog IC Tips
  • Battery Power Tips
  • Connector Tips
  • DesignFast
  • EDA Board Forums
  • Electro Tech Online Forums
  • EV Engineering
  • Microcontroller Tips
  • Power Electronic Tips
  • Sensor Tips

Test & Measurement Tips

  • Subscribe to our newsletter
  • Advertise with us
  • Contact us
  • About us

Copyright © 2025 · WTWH Media LLC and its licensors. All rights reserved.
The material on this site may not be reproduced, distributed, transmitted, cached or otherwise used, except with the prior written permission of WTWH Media.

Privacy Policy