I'm here to eat some words.

For a long time, I've promoted the idea of putting a 1:1 current balun at
the input of a tuner to improve current balance. This doesn't work. In
fact, neither the current balance in the output conductors nor the voltage
across the balun are any different when the balun is put at the input or
output of the tuner. I want to thank Tom Rausch, W8JI, for making this
statement in a posting some time ago. It prodded me into doing a more
detailed analysis, plus doing a careful experiment to confirm the results.

I'll briefly post the results here. If you'd like a more detailed analysis,
you can get it by anonymous ftp from ftp.teleport.com/vendors/w7el. If
you'd like the detailed analysis and are unable to ftp, I'll email it to
you.

Model for a 1:1 current balun using either symmetrical line (e.g., twisted
pair) or coax:

                   1:1
                  ideal
                  xfmr 
       a ---------UUUUUU---------- c
       b --.------UUUUUU-------.-- d
           |     ________      |
           |    |        |     |
            ----|  Zw    |-----
                |________|                         

(For this entire discussion, the assumption is made that the length of the
transmission line used to construct the balun is short in terms of
wavelength, so it can be accurately represented by lumped elements. The
analysis isn't valid if this assumption isn't true.)

Zw is the winding impedance. It's the impedance that the winding would have
if the winding were made of a single conductor.

A simplified model of the balun's environment is:

                Is    ___________         Z1    I1
               -->   |           |        ___  -->
           +  -----a-|           |-c-----|___|------.
          Vs         |  BALUN    |        ___       |
           -  --.--b-|           |-d-----|___|------.
                |    |___________|             <--  |
                |                         Z2    I2  |
               GND                                 GND

A very important point is that the two places labeled "GND" are THE SAME
POINT. If Z1 and Z2 represent an antenna or antenna/feedline, the path back
to the balun input must be included in values Z1 and Z2. Or, to put it
another way, Z1 is the impedance measured between terminals c and b, and Z2
the impedance between d and b, with the balun disconnected.

Using this simple circuit and the two balun rules, we can calculate the
following:

        Ratio of currents in Z1 and Z2: I1/I2 = (Z2 + Zw) / Zw

        Balun input impedance: Vs/Is = Z1 + (Z2 || Zw)

        Voltage across balun winding:
          Vb - Vd = Vs * (Z2 || Zw) / (Z1 + (Z2 || Zw))

        Ratio of coax outer shield current or twinlead "antenna current" to
        the total conductor current):
          (I1 - I2) / (I1 + I2) = (R2 || Zw) / (Zw + (R2 || Zw))
        

                 where Z2 || Zw = the value of Z2 in parallel with Zw.

As Zw gets very large, I1 and I2 become equal and the "antenna current"
drops to zero. This represents the perfect current balun, and shows why we
strive to maximize the balun impedance.

What happens when a tuner is used? To analyze this, I modeled a simple
"tuner" as a 1:n turns ratio transformer: 

               __________   _________
                --> Iin  | |  --> Iout
                         | C
                         C C
             in       1  C C  n      out
                         | C
                         | |
               __________|_|_________


Here's a representation of a typical hookup with a tuner. 

                Is   _________       ___________         Z1    I1
               -->  |         |     |           |        ___  -->
           +  ------|         |---a-|           |-c-----|___|------.
          Vs        | TUNER   |     |  BALUN    |        ___       |
           -  --.---|         |---b-|           |-d-----|___|------.
                |   |_________|     |___________|             <--  |
                |                                        Z2    I2  |
               GND                                                GND

Notice that no additional connection to "GND" is shown, since the tuner's
connection to the common point called "GND" is via its lower terminal(s).

Results:


        Ratio of currents in Z1 and Z2: I1/I2 = (Z2 + Zw) / Zw

        System input impedance: Vs/Is = (Z1 + (Z2 || Zw)) / n^2

        Voltage across balun winding:
          Vb - Vd = n * Vs * (Z2 || Zw) / (Z1 + (Z2 || Zw))

        Ratio of coax outer shield current or twinlead "antenna current" to
        the total conductor current):
          (I1 - I2) / (I1 + I2) = (R2 || Zw) / (Zw + (R2 || Zw))
        
The only changes from the no-tuner case are the input Z, which is
transformed by n^2 as expected, and the voltage across the balun winding
which has increased by a factor of n. Again, to achieve good current
balance requires only that Zw be much greater than Z2. However, some
situations requiring a tuner present a high value of Z2, making good
current balance difficult to achieve.

When the balun is moved to the tuner input, all four results are identical.

If you have questions, please first get the more detailed analysis.

73,
Roy Lewallen, W7EL
w7el@teleport.com