Mutual inductance / coupling factor in twisted wire transformer

[Swamp Thing]

I am trying to design UHF quadrature couplers from the following references:


[1] 'Broad-Band Twisted-Wire Quadrature Hybrids' , http://ieeexplore.ieee.org/xpl/freeabs_all.jsp?arnumber=1127996


[2] 'Twisted wire Quadrature Hybrid Directional Couplers' QST Vol 63 January 1978 pages 21-23


[3] https://awrcorp.com/download/kb.aspx?file=VHF_Lump_Coupler.pdf



Schematic diagram here :
http://www.seboldt.net/k0jd/TwPQH.gif
and here:
http://c15_manali.tripod.com/hybrid.htm

This circuit needs a 1:1 transformer that should ideally have a coupling factor of 1. In practice, coupling factors above 0.7 seem to work reasonably well.

My question is about estimating the coupling factor from information on the wire diameters, separation, and twist. Now, the characteristic impedance of the twisted pair can be estimated from equations, e.g.:

http://qucs.sourceforge.net/tech/node93.html


Is there a way to relate the characteristic impecance to the coupling factor, e.g. by using the basic equations on series / parallel coupled inductors with aiding / opposing connections ?

 

[anorlunda]

Is there a way to relate the characteristic impecance to the coupling factor, e.g. by using the basic equations on series / parallel coupled inductors with aiding / opposing connections ?

I don't think so. You can't use equivalent circuits. You need a 3D solution to Maxwell's Equations. Look into the Maxwell3D software tool.

 

[Swamp Thing]

Wow, thanks for taking the time to reply to that eight-year old question!

Although I have retired from that design job, it's still good to know the answer.