# Antennas – disturbing the thing being measured – open wire lines #5

The articles Antennas – disturbing the thing being measured – open wire lines #3 Antennas – disturbing the thing being measured – open wire lines #4 demonstrated an inconsistency between a partial linear circuit model and a complete NEC model for predicting common mode current behaviour.

One of the oft proposed solutions to characterising a balun is to find the Common Mode Rejection Ratio (a term carried over from other applications, eg voltage driven operational amplifiers). (Anaren 2005) explains a method of finding balun CMRR.  (Skelton 2010) goes so far as to say

The Common Mode Rejection Ratio (CMRR) of a balun is defined in professional literature as the ratio of wanted to un-wanted transmitted power. As rejection of common-mode transmission is the primary purpose of a balun, it follows that CMRR should be the key figure of merit.

Let us take the model scenario used in Antennas – disturbing the thing being measured – open wire lines #4 and lower the height of the dipole 10 10m, and compare the model ratio of Ic/Id.

Again, we will use Python to do the complex maths for the without and with scenarios at 20m height, and without and with at 10m height.

```import os
os.system('cls')

import math
import cmath

#dipole at 20m height and ideal voltage balun drive

i1=-0.3-0.84j
i2=0.64+1.01j
id=(i1-i2)/2
ic=(i1+i2)/2
cmath.polar(id)
cmath.polar(ic)
20*math.log10(cmath.polar(ic)/cmath.polar(id))

#dipole at 20m height and current balun Zcm=1130+j1657Ω

i1=-0.4-1.11j
i2=0.38+1.13j
id=(i1-i2)/2
ic=(i1+i2)/2
cmath.polar(id)
cmath.polar(ic)
20*math.log10(cmath.polar(ic)/cmath.polar(id))

#dipole at 10m height and ideal voltage balun drive

i1=-0.2+0.38j
i2=0.14-0.15j
id=(i1-i2)/2
ic=(i1+i2)/2
cmath.polar(id)
cmath.polar(ic)
20*math.log10(cmath.polar(ic)/cmath.polar(id))

#dipole at 10m height and current balun Zcm=1130+j1657Ω

i1=-0.2+0.22j
i2=0.18-0.12j
id=(i1-i2)/2
ic=(i1+i2)/2
cmath.polar(id)
cmath.polar(ic)
20*math.log10(cmath.polar(ic)/cmath.polar(id))
```

… and with the results…

```>>> import math
>>> import cmath
>>>
>>> #dipole at 20m height and ideal voltage balun drive
...
>>> i1=-0.3-0.84j
>>> i2=0.64+1.01j
>>> id=(i1-i2)/2
>>> ic=(i1+i2)/2
>>> cmath.polar(id)
(1.0375572273373648, -2.040909362946856)
>>> cmath.polar(ic)
(0.19006577808748215, 0.4636476090008062)
>>> 20*math.log10(cmath.polar(ic)/cmath.polar(id))
-14.742162640762551
>>>
>>> #dipole at 20m height and current balun Zcm=1130+j1657Ω
...
>>> i1=-0.4-1.11j
>>> i2=0.38+1.13j
>>> id=(i1-i2)/2
>>> ic=(i1+i2)/2
>>> cmath.polar(id)
(1.185959527134042, -1.9058794244856845)
>>> cmath.polar(ic)
(0.014142135623730885, 2.3561944901923506)
>>> 20*math.log10(cmath.polar(ic)/cmath.polar(id))
-38.47109740837243
>>>
>>> #dipole at 10m height and ideal voltage balun drive
...
>>> i1=-0.2+0.38j
>>> i2=0.14-0.15j
>>> id=(i1-i2)/2
>>> ic=(i1+i2)/2
>>> cmath.polar(id)
(0.31484122982862334, 2.1411796084448382)
>>> cmath.polar(ic)
(0.11884864324004712, 1.825978717415715)
>>> 20*math.log10(cmath.polar(ic)/cmath.polar(id))
-8.461947438341843
>>>
>>> #dipole at 10m height and current balun Zcm=1130+j1657Ω
...
>>> i1=-0.2+0.22j
>>> i2=0.18-0.12j
>>> id=(i1-i2)/2
>>> ic=(i1+i2)/2
>>> cmath.polar(id)
(0.25495097567963926, 2.4116929954380617)
>>> cmath.polar(ic)
(0.050990195135927854, 1.7681918866447774)
>>> 20*math.log10(cmath.polar(ic)/cmath.polar(id))
-13.979400086720375```

So, we see the magnitude of Ic (the first element of the tuple (cmath.polar(ic)) is quite different in all cases, and the ratio Ic/Id in dB is -38dB vs -13.9dB for the same balun but with the changed dipole height.

If you were to calculate or measure the CMRR of that balun using Anaren’s or Skelton’s method, you would need to make a choice of the load impedance to use and the results would depend on that choice. So implicit in a specified CMRR is the load impedance at which it was taken. Since the scenario balun as a Guanella 1:1 balun in a 50Ω system, we might expect the differential load impedance is 50+j0Ω.

Now how do you use that information to solve for Ic in an antenna scenario?

CMRR means more to lab techies than to real world antenna applications.

So, I leave you with the question whether CMRR is a generally useful  ‘property’ of a balun, and whether is Skelton right when he says:

As rejection of common-mode transmission is the primary purpose of a balun, it follows that CMRR should be the key figure of merit.

## References

• Anaren. May 2005. Measurement Techniques for Baluns.
• Skelton, R. Nov 2010. Measuring HF balun performance in QEX Nov 2010.