Voltage
standing wave ratio (VSWR)
Updated August
28, 2011
Click here
to go to our VSWR calculator
Click
here to learn about VSWR problems in medical applications (new
for September 2011!)
Click
here to learn abour designing for high peak power (also new
for September 2011!)
Click
here to learn about Microwave101's reflection coefficient "Sniffer"
circuit
Click
here to learn about that pesky minus sign in return loss measurements
Click
here to go to a page on visualizing VSWR
Click
here for a discussion of maximum power transfer
Click
here to learn about slotted line measurements
Click
here to go to our discussion on mismatch loss (and other cool
stuff!)
What is all this talk about "viswar"
(or "viswah" if you are in Taxachusetts? The voltage standing
wave ratio is a measure of how well a load is impedancematched
to a source. The value of VSWR is always expressed as a ratio with
1 in the denominator (2:1, 3:1, 10: 1, etc.) It is a scalar measurement
only (no angle), so although they reflect waves oppositely, a short
circuit and an open circuit have the same VSWR value (infinity:1).
A perfect impedance match corresponds to a VSWR 1:1, but in practice
you will never achieve it. Impedance matching means you will get
maximum power transfer from source to
load.
In some old microwave text books
the Greek lowercase letter sigma ()
is used to denote VSWR. We don't use this at Microwaves101.
Here's an index to our material
on VSWR:
Slotted
line measurements (separate page)
Mismatch
loss (separate page)
Standing
waves in nature
Voltage standing
waves
Other ways
to express VSWR
Calculating
VSWR from an impedance mismatch
Standing
waves in nature
What's a standing wave? Luckily
there are tons of examples in nature. Any stringed instrument such
as a guitar or piano makes makes music using standing waves. But
what about a traveling wave that reflects off of an object and creates
a standing wave due to constructive interference? Let's go to the
beach. Breakers roll in off the ocean, come up on the sand, and
disappear; no standing wave occurs. What's happening? The beach
is absorbing all (or at least most) of the energy, in effect it
is "matched" to the wave front. Now let's go next door
to marina where all of those expensive yachts are moored... chances
are there are vertical concrete seawalls inside the marina to allow
owners to bring their boats close enough so that only a small walkway
is needed to get to them. Now notice the breakwater that extends
around the marina, with only a narrow opening for boats to go in
and out. That's there because the vertical walls in the marina offer
near perfect reflection to moving waves (an "open circuit").
Without the breakwater wall (which absorbs energy) huge standing
waves are possible due to constructive interference, and all those
boats would bob up and down like crazy corks and eventually everything
would get smashed to tiny bits.
If you live in Arizona, lakes
that were created by flooding canyons can offer excellent standing
waves to for you to jump in your annoying personal watercraft...
BY FAR the roughest water can be found on Lake Powell. Lake Powell
was made by flooding Glen Canyon, and a large amount of its shoreline
consists of literally vertical cliffs. This lake gets way rougher
than Lake Mead, for example, with similar wind speeds. Lake Mead
has longer and wider channels than Lake Powell (which should allow
larger waves to build up), but most of its shoreline is gently sloped.
The vertical walls of Lake Powell act as "open circuits"
to the water waves, whereas the sloped beaches at Lake Mead act
like "loads".
Enough talk about beaches, water
and boats, it's summer, and we've got to get back to work!
Breakwater doing
its job
Voltage standing
waves
Here's a great applet for visualizing
the concept of the voltage standing wave ratio from our friends
at Bessernet.Update October 2006: Rafael points out that
the applet has been improved so that it knows the difference between
an open circuit and a short circuit... we;d guess that the author
reads Microwaves101! Here's the difference we are talking about:
loads that are greater than Z_{0} (such as reflection coefficient=1,
which is an open circuit) have a peak VSWR at the interface, loads
that are less than Z_{0} (such a reflection coefficient=1
which is a short circuit) have a null at the interface. Check it
out!
http://www.bessernet.com/Ereflecto/tutorialFrameset.htm
Visualizing VSWR
Consider the stuff below obsolete.
Visit our new page on visualizing
VSWR for a better explanation!
Warning: this applet might not
work if your browser is finicky! We were so intrigued by this applet
that we created a version of it in Excel! OK, ours doesn't "move"
like theirs, but you will find it more useful for generating graphics
for presentations. Just remember where you got it, it's in our download
area.
In the next three plots, we illustrate
how a standing wave arises at a change in transmission line impedance
(a mismatch). In the first plot, pretend that there is a reflection
coefficient of magnitude 0.3 at the Xvalue of 25. It this point,
70% of the wave continues on (blue trace) and 30% of the wave is
reflected backwards (purple trace). The composite wave is the simple
addition of the forward and backward waves at distance<25. The
wave forms here are instantaneous, meaning that you are looking
at a single moment frozen in time. In real life the waves are continuously
moving.
Now let's look at 20 snapshots
in time, equally spaced in one wavelength. At this point we will
ignore the forward wave after the interface, and just look at the
composite wave at distance<25. What's this, a pattern is emerging?
Now using the "MAX"
function of Excel, we can trap the maximum of all of the composites
(just like a microwave detector would),
and draw the standing wave:
From the Excel sheet, we get
a peak of 1.299987 and a null of 0.697579. That's a standing wave
ratio of 1.863569:1.
Let's check our math and recalculate
the reflection coefficient from the Excelgenerated VSWR:
= reflection coefficient=(VSWR1)/(VSWR+1)
=(1.8635691)/(1.863569+1)=0.301571
That's an error of less than
0.3 percent (the exact value of rho should be 0.3, remember?) Not
bad considering we only "looked" at 10 snapshots in time.
For the record, let's look at
the difference in wave patterns for a short circuit and an open
circuit below (short circuit plot is first). Again, the mismatch
is placed at X=25. Note that the minimum voltage of the standing
wave in each case is zero, which means the standing wave ratio is
infinite.
Now you can see
the difference, the waves all go to zero at a short circuit, and
go to a maximum at an open circuit.
Other ways
to express VSWR
The reflection coefficient
is what you'd read from a Smith chart. A reflection coefficient
magnitude of zero is a perfect match, a value of one is perfect
reflection. The symbol for reflection coefficient is uppercase Greek
letter gamma ().
Note that the reflection coefficient is a vector, so it includes
an angle. Unlike VSWR, the reflection coefficient can distinguish
between short and open circuits. A short circuit has a value of
1 (1 at an angle of 180 degrees), while an open circuit is one
at an angle of 0 degrees. Quite often we refer to only the magnitude
of the reflection coefficient. The symbol for this is the lower
case Greek letter .
The return loss of a load
is merely the magnitude of the reflection coefficient expressed
in decibels. The correct equation for return loss is:
Return loss =
20 x log [mag()]
Thus in its correct form, return
loss will usually be a positive number. If it's not, you can usually
blame measurement error. The exception to the rule is something
with negative resistance, which implies that it is an active
device (external DC power is converted to RF) and it is potentially
unstable (it could oscillate). Not something you have to worry about
if you are just looking at coax cables! However, many engineers
often omit the minus sign and talk about "9.5 dB return loss"
for example. People that find it necessary to correct engineers
who do this have underwear that is too tight.
We have more to say on this topic
on this page.
Here are the equations that convert
between VSWR, reflection coefficient and return loss (as well as
mismatch loss which we will cover later):
Let's end our discussion with
a table of reflection VSWR, refection coefficient and return loss
values (and remember that our VSWR calculator
can provide any values you need). If you want to impress your friends,
memorize as much of this table as you can. Yes, rounding off is
permitted, Thanks for the correction, Dan!
VSWR 
Reflection coefficient 
Return loss 
Notes 
1:1 
0.00 
infinity 
a perfect match 
1.1:1 
0.05 
26.44 

1.2:1 
0.09 
20.83 

1.3:1 
0.13 
17.69 

1.4:1 
0.17 
15.56 

1.5:1 
0.20 
13.98 
A good rule
of thumb: 1.5:1 = 14 dB 
1.6:1 
0.23 
12.74 

1.7:1 
0.26 
11.73 

1.8:1 
0.29 
10.88 

1.9:1 
0.31 
10.16 
A good rule
of thumb: 1.9:1 = 10 dB 
2.0:1 
0.33 
9.54 

3.0:1 
0.50 
6.02 
A good rule
of thumb: 3:1 = 6 dB 
4.0:1 
0.60 
4.44 

5.0:1 
0.67 
3.52 

6.0:1 
0.71 
2.92 

10:1 
0.82 
1.71 

infinity:1 
1.000 
0.00 
short or open
circuit 
Calculating
VSWR from impedance mismatches
The mismatch of a load Z_{L}
to a source Z_{0} results in a reflection coefficient of:
=(Z_{L}Z_{0})/(Z_{L}+Z_{0})
Note that the load can be a complex
(real and imaginary) impedance. If you can't remember in which order
the numerator is subtracted (did we just say "Z_{L}Z_{0}"
or Z_{0}Z_{L}"?), you can always figure it
out by remembering that a short circuit (Z_{L}=0) is on
the left side of the Smith chart (angle
= 180 degrees) which means =1
in this case, which means that the minus sign belongs in front of
Z_{0}.
The magnitude of the reflection
coefficient is given by:
=mag()
For cases where Z_{L}
is a real number,
=abs((Z_{L}Z_{0})/(Z_{L}+Z_{0}))
Note that "abs" means
"absolute value" here. VSWR can be calculated from the
magnitude of the reflection coefficient:
VSWR=(1+)/(1)
For cases where
Z_{L} is real, with a little algebra you'll see there are
two cases for VSWR, calculated from load impedance:
For Z_{L}<Z_{0}:
VSWR=Z_{0}/Z_{L}
For Z_{L}>Z_{0}:
VSWR=Z_{L}/Z_{0}
Just remember to
divide the larger impedance by the smaller impedance, because VSWR
is always greater than 1. Hey, this calculation is so easy you can
do it in your head!!!
Let's look at the
special case where you mix up 50 ohm parts into a 75 ohm system
(or viceversa). In either case, the resulting VSWR is 1.5:1. Yes,
we did that without a calculator. While we're at it, the reflection
coefficient is:
=(7550)/(75+50)=0.2
VSWR problems in medical applications
This topic is discussed on a
separate page.
