Standing Waves – The Great Bay Radio Association Newsletter
August, 2015
INSIDE THIS ISSUE
1
The Prez says
2
July Meeting Minutes
3
Understanding SWR
7
Coming next month:
7
Club officers and contact information
Upcoming events
August meeting August 9. Dinner at
6, Business meeting from 6:40 to
abut 6:55, presentation on club test
equipment following business
meeting.
ARRL sponsored contests
September
5-6 EME - 2.3 GHz & Up
12-14 September VHF
19-20 10 GHz & Up– Round 2
The Prez Says ..
Greetings.
I apologize for the lateness of this issue of Standing Waves. We're all still adjusting to new roles, and rest
assured that September's issue will be on-time.
For the moment, your club officers are still working on establishing key committees, on developing a test
and class schedule for licenses and upgrades, and looking at ways to more formally document policies and
procedures that will help insure smooth running of our club in the future.
We hope that you are finding the new meeting schedule and the monthly programs helpful to your
enjoyment of the hobby, and we are open to suggestions from members who would like to see specific
topics addressed in future presentations.
If there is a way that we can help you enjoy Amateur Radio more, that's what we're here for – please don't
hesitate to let one of your club officers know what's on your mind.
73,
Dee – AB1ST
GBRA meeting minutes
July 13, 2015
Meeting called to order: 6:50
Roll call
Reading and approval of minutes
Read by Dee, approved
Treasurer Report
Read by George
Visitors
Correspondence
Letter to Janetos
Email from Steve Colello
Announcements
Old Business
George will be comparing coverage of ARRL with our current policy and see which is more
economical.
He will look again this month.
New Business
George will look into transaction fees for credit union account.
Development Committee
Technical Committee
Motion made to form committees – seconded and approved.
List of VEs
Find out about Fox Hunt – need to reach out to Larry.
Rick recommended sending out an extra reminder the day before any events.
Motion to adjourn made at 7:10 , accepted and approved.
Technical Corner
Understanding SWR
Every ham is concerned about Standing Wave Ratio – we know it's bad, but what exactly does it mean,
and exactly how much does it affect our signal? For the purpose of this article, we'll mostly consider
resistive loads, because they are quite easy to understand. At the end, we'll briefly look at reactive
loads, just to give an idea of how reactance can add a bit more drama to the picture.
To properly understand standing wave ratios, we need to know what is meant by the term. We can tell
from the term itself, that it's a ratio – but a ratio of what?
The definition of Standing Wave Ratio is “the ratio of the partial standing wave's amplitude at an
antinode (maximum) to the amplitude at a node (minimum) along the line. So, what does this mean?
As a signal travels along a transmission line, if the antenna, transmitter and transmission line all have
the same impedance, the maximum voltage at any point along that line will be the same as the
maximum voltage at any other point on that line. The voltage at any two points is equal – that is a 1:1
ratio.
In the image above, R1 and the AC source represent our transmitter with its characteristic output
impedance of 50 Ohms. R2 represents our antenna, and the wires are our feedline.
So let's pretend that our transmitter has an output signal of 100 volts – what will happen when we apply
a signal to this circuit? We remember that P = I^2 R, and E = IR. So our source of 100 volts sees a total
resistance of 100 Ohms – the 50 ohms of our transmitter's characteristic impedance, and the 50 Ohm
load of our transmission line and antenna. So the total current is 1 Ampere. At our antenna, we have 1
Ampere through 50 Ohms – I^2 R = power = 50 Watts. All is good.
So let's see what happens if we have a 25 Ohm load instead. Instead of 100 ohms, our total resistance is
now 75 Ohms. The current is now 100 V / 75 Ohms, or 1.333 Amperes, and the power dissipated at our
antenna = 1.333^2 x 25, or 44.44 Watts. That's interesting.
Let's see what happens now if we increase our antenna's impedance to 75 Ohms … now we have a total
of 125 Ohms. The current is 100V / 125 Ohms, or 800 milli-amperes. And the power at our antenna is
0.8 A ^2 x 75 Ohms, or 48 Watts.
Trying this with any different resistance for our antenna will yield the same result – the maximum
power transfer occurs when the load impedance is equal to the source impedance. Because of this, we
recognize one important fact: When the impedance of our antenna, the impedance of our feedline, and
the impedance of the output of our transmitter are matched, the Standing Wave ratio will be 1:1, and
the maximum power from our transmitter will be delivered to our antenna.
But something else also happens other than just an inefficiency when we have an impedance mismatch.
When a mismatch exists, part of the signal that is traveling down our feedline is reflected back. Our
transmitter is still producing 50 watts of power, so the power difference doesn't just disappear – it needs
to go somewhere – and so it is reflected back from the antenna, back through our feedline, and toward
the transmitter. Some of that power will be expended as heat in the feedline, and some of it will be reabsorbed by the transmitter.
When this happens, the instantaneous voltages from the reflected power are added to the instantaneous
voltage of our transmitted signal. Where these voltages are out of phase, that voltage is at a minimum –
and where they are in phase, they are added. This is where our term “standing wave ratio” comes into
play. If there is a mismatch, there will be places along our feedline where the voltage is low, and others
where it is high. VSWR is the ratio of the low voltage to the high voltage.
Calculating the exact VSWR requires a bit of math, and some understanding of complex numbers. We
need to know the absolute load impedance. If we pretend that our antenna is a pure resistive load, then
we could assume that the impedance is simple – but with antennas and RF, this is never the case – we
are always dealing with inductance and capacitance. When we are dealing with alternating current,
inductance and capacitance, we are always dealing with complex numbers.
But let's pretend just for now that our antenna is purely resistive – what will the SWR look like with a
50 Ohm transmitter impedance, and a 25 Ohm antenna? (We'll look at a more realistic situation a little
later.)
2
2
We'll need a few formulas – The Absolute Load impedance is √ (R + j )
In this case, R is the resistive part of our load impedance, and j is the complex part. As in this
simplified case, j will be 0, and R is 25. So the absolute load impedance is simply R, or 25 – the square
root of 25^2.
The next formula is the Reflection Coefficient, usually represented by the Greek letter Γ – Gamma.
Γ =√((R−Z 0)2 + j 2)/ √((R+Z 0)2 + j 2)
In this case, R is our load impedance (25 Ohms), and Z is the source impedance (50 Ohms), so this
formula simplifies down to:
Γ =√ ( 25−50)2 / √ (25+50) 2 or 25 / 75, or 0.333
Our formula for VSWR = VSWR=(1+Γ )/(1−Γ ) or 1+0.33 / 1-0.33 or 2:1 (Because the 3 is
repeating, your calculator might show 1.9999.... to 1, or something very close.)
You'll notice that this is the same ratio as our resistive impedances – 50:25 can be factored to 2:1 – and
if impedance was always resistive, this would always be the case. But even in this case, this means that
there will be standing waves on our transmission line, and the maximum voltage will be twice the
minimum, so if the AC voltage has a minimum of 25V, there will be maximums of 50V at some points
along our transmission line.
But knowing what the SWR is really doesn't tell us a great deal about how much power is being
radiated from our antenna – to calculate that, we need to know the mismatch loss.
Mismatch loss is expressed as: −10 log(1−Γ2) - in this case, 0.512 dB. 0.5 dB represents about a
10% change in power, which means that just about 10% of our signal will be lost and unavailable to the
antenna. This also means that a 2:1 VSWR results in only about 90% of our signal leaving our antenna.
Many transmitters will not tolerate more than a 1.5:1 VSWR, and will reduce power in that event.
When we see that VSWR means that voltage is being reflected and added to the original signal, this
makes a great deal of sense, especially for transistor amplifiers. If we are operating a transistor
amplifier, we need to recognize that transistors break down when the applied voltage is too high – we
might be looking at the Collector – Emitter voltage.
Let's take a look at one power transistor for HF / VHF use – the Philips BLW96. This transistor is rated
at 25 – 200 Watts P.E.P. At 200 Watts, the collector might be running at around 50V. But the Maximum
rating is 55V. This is common for transistor electronics – the operational voltages can be quite close to
the maximum voltage the device can withstand. This is why high SWR can be dangerous to transistor
amplifiers. Tube amplifiers may require tuning, and may be inconvenient, but tubes don't usually
operate as close to voltages that might actually damage the tubes. Certainly operating tube-transmitters
into high VSWR conditions will reduce the lifespan – just not as quickly or dramatically as might
happen with transistor amplifiers.
So, now that we've taken a look at purely resistive SWR, without complex impedance – without
reactance, how does reactance enter the picture? How does it change things? Let's look at the formula
2
2
for Absolute Load Impedance once again: √ (R + j )
The factor R is the real impedance – or the resistive component, while j is the imaginary part. (In many
areas of mathematics, the imaginary component is labeled “i” rather than “j” - in electronics, we use j
to avoid confusion with current.)
The term “imaginary” doesn't mean “pretend”, and it doesn't mean that there aren't real effects from
these terms. Rather, it implies the use of the number √ −1 . In actuality, there is absolutely nothing
imaginary about reactance. What we're really trying to do with imaginary numbers is to keep separate
reactance and resistance.
In basic electronics we learned about reactance, and we learned that capacitive reactance is represented
by the formula X C =1/( 2 π f C ) . For inductors, this is X L =ω L . The Greek letter ω is often
used in electronics to represent 2 * Pi * f, so you'll often see this formula shortened to 1/(ω C ) . In
these formulas, we see that reactance is dependent upon frequency. It's because of this that we have a
bit of a problem we have when trying to determine impedance is that the impedance of an inductor
increases with frequency. Z L = j ω L , while the impedance of a capacitor decreases with frequency
Z C =1/( j ωC ) . You'll note that when speaking of pure reactance, we have omitted the j, but that it's
added when speaking of impedance. This is something that you're likely to run across in the literature.
That's because when we're speaking only of reactance, we're not involving ourselves with phase
relationships; we're talking more about the opposition to flow of current at a particular frequency, of a
single component. When we speak of impedance, we are considering resistance, as well as inductive
and capacitive reactance, and the phase relationships between capacitive and inductive reactance – and
this is where the term j √−1 becomes necessary.
One important tool for understanding capacitive and
inductive reactance is a phasor diagram – shown at
right. In a phasor diagram, reactance is in the vertical
axis and resistance is horizontal.
In the diagram to the right, Inductive reactance (UL) is
larger than the capacitive reactance (UC). Had the
capacitive reactance been larger, the large body of this
diagram would have been below the horizontal axis.
What a phasor diagram shows is a graphical
representation of all of the reactance in a circuit. The
lengths of the individual lines represent the value of
impedance, while the angle of (URLC) represents the
phase angle created by that complex impedance.
As that angle increases – either above or below the
horizontal, in other words, as the impedance is more
reactive than resistive – that is where, in our antenna
system, the Standing Wave Ratio increases.
When we are matching the impedance of an antenna system to a transmitter, we're actually dealing with
two quantities represented by one number – resistance and reactance as represented by impedance. The
reason antenna tuners function is that they can add inductive or capacitive reactance to the antenna
system. If we look at a phasor diagram and see that we have more inductive reactance than capacitive
reactance, we can modify the inductance and capacitance to cancel out the reactive component and
make our antenna system appear to be a resistive load to our transmitter.
It's rather difficult to explain all of this in four pages or less, but if you'd like a really great primer on
reactance, I found a rather great video that you might be interested in. It's on a Youtube channel by a
DrPhysicsA, and you can find it here: https://www.youtube.com/watch?v=FEERuJlwBxE
It's probably more accessible if you have a basic understanding of trigonometry and a passing
acquaintance with some of the basic elements of Calculus – but even without these, I can guarantee
that you'll have a better understanding of impedance and reactance.
So, that's it for now 73
Dee - AB1ST
Coming next month:
A look at where new forms of communications may still interest the radio amateur:
Lasers, X-rays and more.
Do you have questions related to Amateur Radio?
Do you need help servicing your own gear?
Do you want to know how to properly construct, install, match or ground your antenna?
Send in your questions, and we'll try to answer them here, or we'll post them to see if anyone
else has an answer.
Or would you like to submit an article for publication yourself?
Email your questions, comments or submissions to deirdre@deesigned.net
GBRA OFFICIALS
President Deirdre Hebert, AB1ST
Vice President Jason Jasper,
K1FDP
Secretary Diane Leveille
KK6ECN
Treasurer George Whitehead
W1BOF
PIO Jason Jasper, K1FDP
Webmaster Jason Jasper K1FDP
ARRL Appointees:
Technical Coordinator, Deirdre
Hebert, AB1ST
SEC, Jason Jasper, K1FDP
Great Bay Radio Association Information
The Great Bay Radio Association is a nonprofit public service organization, with the
purpose of education, service and the advancement of Amateur Radio.
General Business Meetings are held the SECOND Monday of each month, at 7:00 pm, in
the Rochester Community Center located in Rochester, NH. Visitors are always welcome
and membership is open to anyone having an interest in Amateur Radio, whether a licensed
amateur or not.
Dues are $ 20.00 per year [individual],
$ 25.00 [family] and $ 10.00 [student].