NEC-LIST: Maximum Coupling

Re: Maximum coupling (CP)

Determining the maximum coupling of a source to a load is simple.
Just use the conjugate-matched impedance. It is not so easy for the
coupling from one port to another. NEC can give the input impedance
looking into each port. However, when you put a load on one port it
changes the input impedance at the other port when they are coupled.
It looks like it would take an iterative approach to find the
impedances that simultaneously match the two ports.

However there is an easy way called the Linville method. It is
described on page 78 of the NEC-2 manual or page 93 of the NEC-4
manual. That is where the CP numbers come from. NEC prints the
maximum coupling, the load that would match the 2nd port and the
resulting input admittance at the first port. It has been suggested
that it might be better to give the matching load admittances at both
ports to be consistent. The matched load (or generator) impedance for
port 1 is just the conjugate of the input impedance given.

The maximum coupling is useful in situations where transmitting and
receiving systems are interacting outside of their operating bands, so
that the impedance of at least one is not known. If you know the
source and load impedances, you probably do not need to use the CP
command. Just put the known impedances on the ports, put one volt on
port 1 and get the current at port 2. NEC only gives the currents, so
you have to calculate the power yourself.

For anyone who does not have a NEC manual, equations for maximum
coupling are:

Gmax = (1-Sqrt[1-L^2])/L
where
L = Abs[Y12*Y21]/(2*Re[Y11]*Re[Y22] - Re[Y12*Y21])

where Y11, Y12, Y21 and Y22 are the short-circuit admittance
parameters at the two ports determined by exciting a port with the
other port shorted and getting the currents.

The matched load admittance on antenna 2 for maximum coupling is

        ( 1-rho )
YLoad = ( ----- +1 ) * Re[Y22] -Y22
        ( 1+rho) )
where
rho = Gmax*Conjugate[Y12*Y21]/Abs[Y12*Y21]

and the corresponding input admittance at antenna 1 (which must be
conjugate-matched by the transmitter admittance for maximum coupling)
is

Yin = Y11- Y21*Y12/(YLoad +Y22)
 
Hopefully those are typed correctly and NEC is programmed correctly.

Jerry Burke
LLNL
Received on Fri Jan 07 2000 - 06:02:19 EST