Some claim that larger diameter “choke baluns” are less effective than their smaller diameter counterparts, even when the turns count is reduced to maintain equal inductances in both designs.  It has been claimed this is due to “stray capacitance” in the larger diameter coils.

 

This analysis casts doubt on that claim by asking “ Where is the stray capacitance formed?”

 

Note: A large part of this page is used to prove a standard result that is crucial to the question. 

 

Starting with the standard inductance formula:

 

 

 

L = inductance (in Henry)

u₀  &   u_r   are the permeability of free space and the relative  permeability of the coil core respectively

 

N is the number of turns

 

A the cross sectional area of the coil (in sq. metres)

 

d the coil length (in metres)

 

Now, if we assume we use a wire of diameter w for the coil

 

d =  w N

 

Also, A =  pr²  where r is the radius of the coil.

 

Our formula now becomes:

 

 

 

Several these terms are constant:   u₀  ,  u_{r ,}   w , p   so can be combined into the composite term K :

 

 

 

 

 

 

We can also “cancel the N” in the numerator and denominator so we have:

 

 

 

 

Next we assign variables for the two coils:

 

N and R are number of  turns and radius for the large coil.

 

 n and r are number of  turns and radius for the large coil.

 

Use L_s and L_L   for the inductances of the coils.

 

 

So:

 

 

 

 

BUT the coils are intended have equal inductance, ie the turns are reduced as the radius  (and thus diameter)  increases, so:

 

 

 

K is non-zero so we can divide both sides by it and cancel it:

 

(Big K often seems to go this way ;-)  )

 

 

 

Now, looking what happens as we vary  the radius and have to adjust the number of turns to maintain the equality (and thus L), we see that if we double the diameter we must divide the turns by 4.

 

(Thus  is not a surprise, indeed it is a standard result, although some seem to dispute it.)

 

Now, having shown how we must reduce the turns count as we increase the diameter, we look at the cable length required.

 

The length of wire needed to wind a coil of n turns and r radius is:

 

Length =  2 n p r

 

So, if we double r we double the length of cable.

 

BUT , if we are to maintain the inductance, n  must be divided by 4.

 

The net effect is thus that the length of cable is halved.

 

 

So, there is less cable to provide surface area to form “stray capacitance” and, with fewer turns,  fewer regions where the  “stray capacitors” can be.

 

So, if we wind a choke balun on a larger diameter form, with reduced turns to maintain the design inductance, where is the extra “stray capacitance” some claim this introduces coming from?