The Polaplexer Revisited
By Ed Munn, W6OYJ

Introduction

The Polaplexer is a microwave antenna, or antenna feed, which supports two
simultaneous inputs or outputs that are independent and isolated from each other by use
of orthogonal (at right angles) linear polarization. The isolation can be as much as 30 -
35 dB. Its main use is to permit full duplex operation with a single antenna, in which one
port is used to transmit and the other to simultaneously receive. As long as the transmit
power input to the Polaplexer is limited to 100 milliwatts or so, the receiver input stages
are unlikely to be damaged by the transmitter's continuous output.

Polaplexer is a coined word describing a polarization-based diplexer first
developed in the late 1940s by the late Donavan Thompson, W6IFE. In the 1950s through
70s it was used it on the 2300, 3300, 5600, and 10,000 MHz amateur bands with reflex
klystron and lighthouse triode oscillators as the transmitter signal sources and with crystal
diode mixers as the receiver input stages. The Polaplexer, having only a few dB gain as
an antenna itself, was primarily used as a feed for a parabolic dish or conical horn
antenna with much higher gain. In more recent times, the development of ferrite
circulators provided a way to separate receiver and transmitter signals from a single
antenna using a single linear polarization.

Today, Polaplexers still offer a good approach for microwavers who want to
construct simple low-power full-duplex transceivers. They are easy to build and low-loss
Polaplexer materials can be almost free, such as beer cans, coffee cans, etc. More on that
later.

In the simplest type of full duplex system the transmitter's carrier signal is also
used to provide the receiver's local oscillator (LO) signal. By doing so, only one
microwave oscillator is required for each transceiver. The distant station transmits with a
frequency offset equal to the i.f. frequency used by both stations. When either carrier
frequency is modulated, both receivers will detect the modulation and the audio will be
heard at both ends, provided the stations are within range of each other and properly
tuned. The Polaplexers also have to be properly aligned so that each station's outgoing
transmit polarization matches the receiver polarization at the distant station. This is
automatically accomplished when each station uses an outgoing transmit polarization
rotated 45 degrees clockwise from vertical, as viewed looking toward the distant station.

Polaplexer Theory

The Polaplexer is made from a short section of circular waveguide, closed
(shorted) at one end, and with input/output ports installed at distances of 1/4 guide
wavelength, and 3/4 guide wavelengths from the shorted end. The optimum overall
length should be about 5/4 guide wavelengths. See the attached drawing. At these
distances from the shorted end, a high impedance exists. Each port consists of a
connector, typically type N or SMA, with a quarter-wave linear probe attached. The two
probes must be installed so that they are aligned 90 degrees (orthogonal) from each other
as viewed from the open end. This permits two independent linear polarized waves to
coexist within the waveguide.

This article describes a Polaplexer design for a joint project with N6IZW and
WB6IGP to build a simple 2.3/2.4 GHz transceiver. The first decision made was the
operating frequency (FO) for the design. Band edges, frequency stability of the
oscillators, and choice of i.f. frequency drove this decision. For this project the bottom
and top band edges are 2300 and 2450 MHz, we will be using precision frequency
control, and we selected an i.f. frequency of 146.00 MHz. We can just fit two
frequencies 146 MHz apart inside the band edges at 2302 and 2448 MHz. For the design
of the Polaplexer we can split the difference and use the mid-frequency. A more precise
method is to take the square root of the product of the two frequencies. In this case the
mid-frequency is 2375 MHz, and the square root method gives 2373.9 MHz. I will use
2375 MHz as the design frequency (FO) in the following example.

Waveguide Propagation Modes and Guide Wavelength

Unlike coaxial cable, waveguides operate over limited frequency ranges
determined by their dimensions. They have much lower losses than coax at microwave
frequencies. For propagation to take place in waveguides, the configuration of electric
and magnetic fields of the wave must satisfy certain boundary conditions. There are
several possible configurations, called modes. Propagation can occur with very low loss
provided that the operating wavelength is shorter than a critical value for the mode being
used. This is called the cutoff wavelength, and if the wavelength is longer, or the
corresponding operating frequency is lower than the cutoff, extremely high losses will
occur.

For each mode, there is a different cutoff wavelength or frequency, determined, in
circular waveguide, only by the inside diameter of the guide. The lowest frequency mode
that will propagate in the waveguide is the Transverse Electric 1,1 (TE11) mode, and is
called the dominant mode. That is the mode we will use.

Here are the circular waveguide relationships for cutoff wavelength (Wx) and
cutoff frequency (Fx). Different cutoff coefficients apply if rectangular guides are used.

( W in cm,       F in MHz,     Diameter D in cm.  )
 Mode             Cutoff wavelength    Cutoff Frequency
 ---------------  ------------------  -----------------
 TE11 (Dominant)  W1 = 1.71*D         F1=30000/(1.71*D)
 TM01             W2 = 1.31*D         F2=30000/(1.31*D)
 TE21             W3 = 1.03*D         F3=30000/(1.03*D)

It is best to choose a waveguide diameter so that the desired operating frequency
falls between the TE11 and TM01 mode cutoff frequencies. This will absolutely prevent
the possibility of multiple moding within the guide, which could produce SWR problems.
For the polaplexer port design described in this article, the chance of initiating the TM01
mode is small, and I decided to push the design above the TM01 cutoff frequency in
order to use an easily available waveguide size. However, the operating frequencies must
be always kept below the cutoff frequency of the TE21 mode because the type of
monopole probes used will certainly excite the higher E-field modes.

For a particular frequency and propagation mode in waveguides, the wavelength
will differ from that in free space, often by a considerable amount. In measuring where
to install the ports or terminations along the length of a waveguide, you must first
calculate and use this "Guide Wavelength". Here is the formula for Guide Wavelength:

WO=30000/FO    (FO in MHz)
              WO             WO=design wavelength in cm
WG= ----------------------   WG=guide wavelength in cm
      SQR(1-((WO/W1)^2))     W1=TE11 cutoff w.l. in cm

At this point I suggest you do some calculations to determine the approximate
range of diameters you can use for your chosen operating frequency. It will be bounded
at the outside limits by the TE11 and TE21 cutoff frequency limits. One way to get
started is to calculate the diameter of guide that produces a TE11 cutoff wavelength about
fifteen percent longer than that of the lowest operating frequency you will use. This
leeway is my empirical way to avoid unreasonably long guide wavelengths. With this
approach you calculate the smallest diameter you might use.

Example: FL =0.85*2302      = 1957 MHz
DL=30000/(1.71*FL)   =30000/3346   =8.96 cm or 3.53 in.
 

Now calculate the diameter that will give a TE21 cutoff wavelength about five
percent higher than your highest operating frequency. This will give you the largest
diameter you should use.

Example: FH =1.05*2448     = 2570 MHz
DH=30000/(1.03*2570)  =30000/2647  =11.33 cm or 4.46 in.

Probe Length vs. Diameter

You probably know that the driven element of simple monopole (ground plane
vertical) antennas is usually a little shorter than a calculated free-space quarter
wavelength. In fact, the thickness or circumference of the element has a bearing on both
the resonant frequency and the bandwidth of such an antenna. The fatter the probe, the
shorter its length and the broader its bandwidth. The two probes inside a Polaplexer
essentially perform the same function as a monopole antenna and their length must be
shortened accordingly. George Tillitson, K6MBL, described an empirically based
formula for probe length versus thickness in a March 1977 Polaplexer article in "Ham
Radio Magazine". Here it is:

For FO=operating frequency in MHz, WO=Operating wavelength in cm 
               and PM=Probe diameter in mm
P=0.31416*PM/WO (ratio of probe circum. to wavelength)
L=2950.7*(1+P-SQR(P))/FO        Probe length in inches.
 Or L=74948*(1+P-SQR(P))/FO       Probe length in mm.

The LO insertion adjustment screw

In the simple full duplex transceiver, we need to be able to upset the isolation
between the transmit and receive polarization modes, so that some of the transmitter
signal will be coupled to the receiver port to provide adequate local oscillator injection
for the mixer. This can be accomplished by inserting an adjustable length conductive
post (a screw) on a line midway between the two polarization planes. A good location for
this is to position it one-third guide wavelength from the shorted end of the Polaplexer.

Polaplexer Design Software

With this article I have included a pair of software design programs for
Polaplexers written in BASIC. One is for inch dimensions, and the other is for metric.
From the web page you can save these programs as "plain text" files with your browser.
They should run when loaded with a ".bas" extension in QBasic or in the earlier DOS-
based GWBasic or IBM Basica. With this software, try some waveguide diameters
between the limits you calculated above, using your chosen design frequency and see
what the Polaplexer length dimensions and cutoff frequencies will be. This will prepare
you for your search for circular waveguide material.

Going to the Supermarket ??

Tin cans are the favorite material to use for Polaplexers (actually they are steel)
because it is easy to directly solder the probe connectors to the can, or solder on an extra
bottomless can when you need to reach an optimum length. Unfortunately they are
harder to find these days, aluminum being much more common. When exploring the
aisles with your tape measure you should also check the rims to see if they are shiny
(steel) or dull (aluminum). I prefer unpainted cans with paper labels that can be removed
to allow easier soldering. Another thing to observe is the relative number and depth of
the strengthening ridges used crosswise to the length of the can. If they are too deep it's
harder to flatten them out in the place where you want to install a connector. If the can
has a paper label, you can run your fingernail along the paper to judge these ridges. This
search process may require several trips to the grocery store, and your spouse or friends
will probably not want to be seen with you during these events.

If tin cans are not classy enough for your application, you can of course use other
cylindrical materials. These can range from sections of copper or brass pipe or tubing, to
rolled sheet metal for the larger diameters. The plumbing or hardware store may have
what you want.

Constructing the Polaplexer

I decided to use a "one pound" coffee can as the basis for the 2.3/2.4 GHz
transceiver project, based on knowledge that others had used this type of can for this
same band. They measure 3.875 inches inside diameter. I ran the software program
"POLPLXIN.bas" for that diameter, and a design frequency of 2375 MHz. Here are the
results:

TE11 Mode cutoff frequency =  1782  MHz
  TM01 Mode cutoff frequency =  2327  MHz
  TE21 Mode cutoff frequency =  2959  MHz
  Guide Wavelength (TE11)    =  7.53 inches
  1st probe spacing          =  1.88 inches
  2nd probe spacing          =  5.64 inches
  LO adjust screw spacing    =  2.51 inches
  Overall Length             =  9.4 inches
  Probe length (for # 18 wire) = 1.07 inches

At the grocery story I found a standard coffee can and a shorter gourmet coffee
can, both "tin" with shiny steel rims. The combined length was about 9 inches. Both had
paper labels. I saved the coffee in plastic containers, soaked the labels off, and cut out
the bottom of the short can. With a heavy duty Weller soldering gun, I carefully aligned
the cans and tacked them together in four places, rim-to-rim, before soldering all around
the rims. To check the joint, I doused the room lights and moved a flashlight beam
around the seam from the outside as I peered into the open end; missed spots were
obvious, marked, and corrected.

I then scribed two perpendicular lines across the bottom center of the assembly,
and extended these orthogonal lines along the sides of the cans to indicate where the
probes would be placed. Because the closed (shorted) end of the can is inset slightly from
the rim itself, I used a steel rule to measure the inside depth of the can from the open end.
I re-calculated the depth for the probe locations to correct for this inset and marked them
on the orthogonal lines.

I prepared two SMA connectors by cutting and soldering probes to them, made of
# 18 wire. Then I drilled the mounting holes in the can and flowed some solder around
the edges before soldering the connector/probe assemblies to the Polaplexer. Last, I
drilled a hole slightly smaller than the size of the LO adjustment screw, and flowed some
solder around the edges of that hole. I ran a brass nut part way up a 2-inch brass screw
and force-started the screw into the hole. Then I tightened the nut down to press against
the can and flowed solder around its edges to permanently affix it to the can. This
concluded the construction of the Polaplexer. It can be easily mounted to a supporting
bracket or strut by using a large metal hose clamp.

See photos of the completed polaplexer.

Test Results

With a 25 milliwatt source and a power meter, I measured the isolation between
ports at just over 30 dB at both 2302 and 2448 MHz. When two of these Polaplexers
were used as antennas with 25 milliwatt nbfm transceivers, I measured over 30 dB signal
margin on an 18 mile clear path before full quieting began to fall off.

Acknowledgments

In 1955 I built my first beer can Polaplexer for 3335 MHz, under the watchful eye
of Donavan Thompson, W6IFE. He and Bill Baird, W6VIX are both silent keys now, but
the San Bernardino Microwave Society which they founded that year has encouraged
many of us in a lifelong enchantment with amateur microwave communications and
experimentation. In San Diego, Kerry Banke, N6IZW and Chuck Houghton, WB6IGP
have played a similar role in recent years. With their concept of a simple 2.3/2.4 GHz
transceiver, they stirred me into once again into the world of Polaplexers. It's been fun!

References

1. "A Radio Club for Microwave Enthusiasts", W. H. Baird, W6VIX, QST, Dec 1957.
2. "Let's Go Microwave", A. D. Bredon, W6BGK, QST, Jun 1958.
3. "Standards for Amateur Microwave Communications", Richard Kolbly, K6HIJ,
HAM RADIO, Sep 1969.
4. "A Low Cost Amateur Microwave Antenna", Richard Kolbly, K6HIJ, HAM RADIO,
Nov 1969.
5. "Microwave DX California Style", Richard Kolbly, K6HIJ and Ed Munn,
W6OYJ, QST, Sep 1970.
6. "The Polarization Diplexer a Polaplexer", George F. Tillitson, K6MBL, HAM
RADIO, Mar 1977.


Submitted by Ed Munn, W6OYJ, 6255 Radcliffe Drive, San Diego CA 92122. Phone (858) 453-4563
or email to : edmunn@compuserve.com

Last updated Oct 11, 1999