Coax Traps are LC traps using the inherent capacitive properties of coaxial cable, wrapped around a form to create an inductive coil. The resonant frequency of an LC trap is defined by the following formula:
where






Inductance

Where



Capacitance,

Where









Ok… That’s nice. So what do we do with that information? Well, let’s start with what we know and what we want to find out. Our inputs should be the frequency of the trap , the diameter of the form we’re wrapping around
, the diameter of the coax we’ve chosen
and the capacitance of the coax
. The rest must be found. Unfortunately, none of our formulae are directly solvable with just these pieces of data, so we’re going to need to do some manipulation. Let’s start with the simple ones.
simplified as
In other words, the diameter of the coil is equal to the diameter of the form plus the diameter of the coax. We measure our diameter from the center of the coax on one side of the form to the center of the coax on the other side. On to the length of the coil.
The length of the coil is equal to the number of revolutions time the diameter of the coax, since each revolution of the coil is one coax next to another.
The length of the coax is equal to

Now lets clear the unknown variables from the formula for Inductance:
Things are starting to shape up here. What we really need to know now is the number of turns in our coil. I’m not going to lie… this part sucks. We might need to use all of our cunning. Our objective is to generate a formula that expresses





Let’s go!
Substitute and
in our resonance equation.
This looks ok. We have only one unknown variable here:

And that, my friends, is a cubic equation. We can solve this, but we’re going to need some help. Let’s start with the basic form of a cubic equation.
Just like quadratic equations, there is a formula to solve it. Only this one is exponentially more complicated (pun intended.)
Pressing on… let’s assign values for








Now, we could just plug those numbers in to our cubic formula and find value, but as it turns out, there’s a better way. It’s described here. I’ll plug our values for a,b,c,d in where appropriate.
According to our algorithm, there are three ways this can go, depending upon the value of










Let’s start with

Now let’s look at



And finally, the special case where



And that’s it! Given values for resonant frequency, coax capacitance, coax diameter, and coil form diameter, we can calculate the number of turns necessary… not that you’d ever want to solve it by hand.