A
little history:
Ten or so years ago,
the 145.270 repeater was owned and operated by the STARS repeater group.
Then, the 27 was a single site repeater located at the TV13 transmitting
site on the West side of Grand Rapids. Just about that time, the
Lowell Amateur Radio Club acquired the allocation and equipment from STARS
and moved it to the Lowell area. There the repeater was converted
into a multisite system with three remote receivers. The local receiver
and an additional control station was placed between the remote sites and
the 145.270 transmitter. Being in the right place at the right time
with the right connections made it possible to make a home for the 145.27
transmitter at the WODJ tower site about four miles North of Lowell.
From there, the transmitting antenna at nearly 400 feet above ground has
been the shining star of the LARC repeater system.
501C3:
The 27 was constructed
of older commercial radios and lots of hard work. Several compromises
were made because funds just werent always available to buy the right
stuff. One example was the 75 ohm cable TV hard line that was used
to feed the main transmitting antenna. A couple of years ago the
big break came when the LARC applied for and received the taxexempt status
of 501C3. Soon thereafter the Lowell Community Fund awarded the
club a cash grant for the purchase of new equipment to really upgrade the
145.27 repeater.
Accomplished:
1. 
One at a time the
equipment from each remote receive site was brought in for a complete rebuild
19 rack style. Each site got a new plug and play transmitter and
receiver, new controller, and a bulletproof battery backup system.
Intermod and lightening protection was also upgraded. 
2. 
The control station
between the remote sites and the main transmitter was eliminated. 
3. 
A new transmitting
antenna and local link receiver antenna was installed on the WODJ tower.
The 75 ohm feed line was replaced with 11/4 50 ohm hard line.The local
 link antenna was fed with 7/8 50 ohm hard line. 
4. 
A new equipment rack
was installed at the WODJ site. The rack was outfitted as follows: 

Plug and play receivers
and transmitters 
An antenna combiner
and a UHF antenna multicoupler for the link receivers 
Three TXRX cavities 
New voter 
VHF test transmitter
complete with sine wave generator for voter calibration. 
Automatic audio level
controller 
Automatic cooling
fan control 

Coaxial Cable Lengths
and Stubs
If the cable is open, the first null will occur
at the ¼ wavelength. Successive nulls will occur at
every odd multiple of ¼ wavelength.
The span between any two nulls will be the second harmonic of ¼
wavelength.
An open stub cut to the third harmonic of
the operating frequency will pass the operating frequency and cancel odd
harmonics.
Nulls are reflections that arrive at the
feed point 180 degrees out of phase with the input signal and present very
low impedance at their wavelength.
If a cable is terminated into its characteristic
impedance, there will be no nulls (reflections).
If the cable is shorted, the first null will
occur at the second harmonic of the ¼ wavelength. Successive
nulls will occur at every even multiple of ¼ wavelength. The span
between any two nulls will be the second harmonic of ¼ wavelength.
In addition to providing lightening protection,
a shorted ¼ wavelength stub will pass the operating frequency and
cancel even harmonics. One stub can be cut to shortout the even
harmonic and can be cascaded with a second stub to eliminate odd harmonics.
The impedance of a device connected to one
end of a ¼ WL section of cable (or odd multiple of ¼ wavelength)
is transferred to the end of the section. Therefore, a ¼ wavelength
section of coaxial cable (or odd multiples) can be used to transfer the
output Z of one device to the input Z of another.
The Feet calculation:
To determine the distance to a fault (open
or short) sweep the feedline into a T and use the following formula:
(492 x F) / VF = Distance (In feet) to a
fault (open or short),
F = the frequency span between any two nulls
in MHz.
VF is the velocity factor of the cable
Free space WL :
In feet: ¼ wavelength = 245.9
/ F
Electrical length:
In feet: ¼ wavelength = 245.9
/ F x VF
In inches (more accurate) ¼
wavelength = ((11808 / F) x VF ) / 4
Making cables:
Determine or verify the VF:
1. Put a connector on one end of a cable
and leave the other end open. Connect the cable to a T and sweep
it with your spectrum analyzer tracking generator.
(Cable lengths from the generate and analyze
ports to the T are not critical.)
2. Find the lowest frequency null (the
¼ WL frequency) ( F ). Record it.
3. Determine the free space ¼ WL (in
inches) = (11808 / F) / 4 Record it.
4. Measure from the center of the T
to the open end of the cable to determine the actual length of the cable
in inches. Record it.
5. Determine the VF VF
= Free space WL / Actual length Record it.
No Spectrum Analyzer?
To calculate the ¼ wavelength of
a cable when the VF and length in inches are known:
F = (VF / (L x 4) ) x 11808
Example: Operating frequency: 45.65
MHz.
1. Find the free space ¼ length:
11808 / 45.65 = 258.66 / 4 = 64.66
2. Measure the stub from the center
of the T to the open end: 80.74
3. VF = 64.66 / 80.74 = .800
4. Determine the electrical ¼
wavelength: = free space ¼WL x VF 64.66 x .8 = 51.728
5. Determine the length of the required
cable:
Measure the approximate length of cable
that is required to connect device A to device B, then round off the length
to the next odd number of ¼ wavelengths. For example 3.
51.728 x 3 = 155.184 (Actual
length in inches, 3  ¼ WL)
Tricks to cutting cables:
Measurements must include the following:
1. The distance to the center of a T
2. Any couplers or adapters (Heaven forbid)
N Connectors
Figure the length of the cable from the
shoulder of one male pin to the shoulder of the next male pin. This
applies to any type of connector. The length should calculated as
if it were fully engaged with its mate.
Notes:
Use ¼ wavelength sections (or odd
multiples) to couple the following devices
Cavities in series or a duplexer
Transmitter and duplexer input, cavity and
amplifier
Receiver and duplexer input, cavity and
amplifier
The pass frequency of an open stub should
be an even harmonic of the ¼ wavelength.
The pass frequency of a shorted stub should
be an odd harmonic of the ¼ wavelength.
Cable length calculations for cavities and
duplexers should always be based on the PASS frequency.
Velocity factor is also defined as the square
root of e, where e = the dielectric constant.
Exercise:
Fabricate a stub of RG8U that would provide
lightening protection and pass 145.27 MHz.
1. The first null will occur at the second
harmonic of the ¼ wavelength.
145.270 x 2 = 290.54 MHz. First null
when shorted.
2. Calculate the electrical length (in inches)
of a ¼ wavelength at 145.270 MHz. (VF = .66)
(11808 / 145.270) = 81.283 x .66 = 53.64
/ 4 = 13.41 To the shorting point.
Allow the center conductor to extend a foot
or so for the ground connection.
Velocity factors for popular 50 ohm cables
Cable

VF

RG58 (Polly)

.66

RG8 (Polly)

.659

RG8X

.84

LMR400

.85

RG142 (Teflon)

.695

RG214

.66

3/8 Superflex (Blue)

.801

¼ Hard

.841

½ Hard

.81

7/8 Hard

.81

Matching a line to a load of different
impedance:
Problem: Match a 600ohm line to an
antenna with 72ohm feed point impedance.
The Z of the section is determined by: The
square root of (72 x 600) = 208 ohms
(The antenna should be tuned to resonance
before the matching section is connected.)
A few theoretical notes:
Characteristic impedance: Z0 is determined
by spacing between the conductors and the conductor size.
Calculate the free space wavelength when
the frequency is known:
300 / F (MHz.) = 1WL (in meters) Example:
300 / 146.52 = 2.047 meters
Calculate the frequency when the wavelength
is known
300 / WL = F (MHz.) Example:
300 / 2.047 = 146.52 MHz.
Conversions:
1 foot = .3047 meter
1 meter = 3.28 feet 