Tuning a 4 Square

Steve Fraasch Steve_Fraasch at GATEWAY1.ATK.COM
Thu Jul 2 12:26:48 EDT 1992

                       Subject:                               Time:11:21 AM
  OFFICE MEMO          Tuning a 4 Square                      Date:7/2/92
My wife's allowing me two free days in Wisconsin to tune W0AIH's 160m 4
square.  In summary, the design stuff was done similarly to the method
presented by Forrest, K2BT in Ham Radio back in '83:  The desired current
distribution is found using array theory, and serves as a known ( current
vector [I] ) when solving the linear system [V] = [Z] [I].  MININEC is used
to find self and mutual impedances, for a single element, Zii, and for the
mutual terms, Zij.  A math software package (you can do it by hand if you
want) such as Mathematica, or MATHCAD is used to solve for [V], from [V] =
[Z] [I].  The drive impedances to each tower are found by Zi = Vi/Ii.  I
used RF CAD Software SUPER COMPACT to design the network.  To confirm that
the solution is right, I re-applied the volage excitation solution from
Mathematica to a 4 square on MININEC (Method of moments software like NEC
solves for the current distribution by feeding the system known terminal
excitations).  The desired current distribution appears, which squares the
RF-CAD network solution.  Great theory, now for the hardware...and here's
the problem:

The towers are an odd length (185' -> ~1/3 wave length @ 160m), and closed
spaced (~.13 wave - the thing was originally designed for 80m).  The towers
are on a hill - not on level ground - and they are as much as 15 feet in
height from each other.  Lots of radials, but they're too short, and the
ground is low conductivity rocks and loamy soil.  Theoretical gain - even
measured - is OK, but to really tweak it in and get all of that gain & F/B,
we need to tune it.  One method would be to actually measure the self and
mutual impedances.  But we cannot simply measure them, given the coupling
among the array and scatterers nearby (Check your EM Green's functions,
that's rubbish about 1/4 waves being decoupled.  Anything out there is
coupled.)  The broadcaster's method is to sample the current of each tower
at the maxima, and compare the relative phases and amplitudes.  In our case,
the current maxima occurs at 55', making this the best spot to sample it. 
Anyways, last November, I installed current sampling coils on each tower at
55'.  I thought we'd have a great system to measure the relative tower
currents.  No, the system was corrupted by RF: a finger touch of the scope
and sampling coax connector would change everything.  I could not find any
chokes large enough to decouple the shield current, so I gave up.  We
operated the ARRL 160m contest, saw gain and some F/B, but not enough (But
it did work far better than Paul's elevated quarter wave, especially into
EU).  JAs heard (but not on the elevated), but not worked, hmmm (almost
embarassing to admit for a 4 square).  So, it seems it close, but not quite.
 Most of the contest was spent being jammed (25 hz off freq) by K3LID, and
saying "what if this damn thing worked right?"

Since December, I've pondered this problem, and I've decided that a current
probe at the tower bottom is better than none.  I've read a lot of applied
EM books and IEEE articles, and the best hand wave I've seen is that the
field is transitional at the base, forcing the current distribution on the
tower to be misleading.  The broadcasters say stick the probe at least 10 -
20 feet off the ground.  Despite that, they still recommend double shielded
coax, bonding to tower, and decoupling with that big choke again.  Stepping
over the fence at some local Minneapolis AM radio stations revealed that
they indeed go to all of that trouble.  My God, it's only ham radio, right?

We go with current probes at the base, along with Paul listening at his home
QTH (5 miles away), WA0PEV in his car talking back on 2 meters, K0KX in the
shack, and me in the dog house twiddling as I'm stung by wasps.  There's got
to be a better way.  Help!

It's only a hobby,
Steve, K0SF

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