An example and explanation of unexpected common mode choke flashover

An online discussion is developing the design of an ultimate common mode choke, at it reached a stage considered final when a transmit test revealed it could not withstand the unstated transmitter power.

The designer did report measurement at the choke looking into the feed line giving Z=493-j740Ω @ 3.8MHz. There are questions about the validity / uncertainty of the measurement, but let’s take is as correct for the purpose of this discussion.

We can calculate the expected differential peak voltage at a given power level at the point where Z=493-j740Ω.

Let’s use Python as a complex number calculator to calculate based on Z=493-j740Ω.

>>> import math
>>> import cmath
>>> p=1500
>>> z=493-740j
>>> g=(1/z).real
>>> '%0.2e'%g
'6.24e-04'
>>> vpk=(2*p/g)**0.5
>>> '%0.2e'%vpk
'2.19e+03'

Above, the solution of $$V_{pk}=\sqrt{\frac{2 p}{real(\frac1{z})}}$$ gives the peak voltage as 2190V.

If your analyser / VNA gives the impedance as an equivalent parallel Rp || Xp, then the following might be more convenient using Rp.

>>> import math
>>> import cmath
>>> p=1500
>>> rp=1603.75
>>> vpk=(2*p*rp)**0.5
>>> '%0.2e'%vpk
'2.19e+03'

Above, the solution of $$V_{pk}=\sqrt{2 p r_p}$$ gives the peak voltage as 2190V.

Another simpler alternative is Calculate Vmax, Vmin, Imax, Imin for lossless line from Z (or Y or VSWR) and Zo.