Simple Half-Wave Trapped Antennas Part 2 - Calculating Trap Values

Antenna "traps" are nothing more than parallel LC (inductor/capacitor) circuits -- also called "tank" circuits. The derivation of "tank" and "trap" is intuitive once one understands how a parallel resonant circuit works or, more specifically, the nature of LC circuits.

There is a great discussion of these on Wikipedia and other renditions abound all over the internet.

But, basically, the take away on these is that -- at a circuit's resonant frequency -- the impedance of the series LC circuit is zero and the parallel LC circuit is [almost] infinite. Leaving the series LC circuit, the parallel resonant circuit's high impedance is due to the interaction between the capacitor[s] and inductor[s] in the circuit. I stole this image from the Wikipedia article but it shows this graphically:

Again, borrowing from the article, this animated diagram showing the operation of a tuned circuit (LC circuit). The capacitor C stores energy in its electric field E and the inductor L stores energy in its magnetic field B (green). The animation shows the circuit at progressive points in the oscillation. The oscillations are slowed down; in an actual tuned circuit the charge may oscillate back and forth thousands to billions of times per second.

Gradually without replenishment, this activity will dissipate. However, with an oscillating power source like energy from your transmitter or received at your antenna, the activity will continue uninterrupted by accepting the energy into the "tank" and or "trapping" it and not letting it pass further - hence the high impedance. (I am beginning to skate on thin ice here and suggest you seek hard tech info elsewhere before this erupts into a fount of formulas.)

The steps to build a trap are as follows:

 (1) Determine the resonant frequency of your trap.
 (2) Calculate the capacitance and inductance values.
 (3) Calculate the number of turns for your inductor.
 (4) Construct the trap.
 (5) Measure the resulting resonant frequency.

We'll cover steps #1 through #3 here and take up #4 and #5 in the subsequent post on building and measuring the traps.

For the moment, let's assume we're building a 40m/20m trap dipole. (For the sake of this whole series, we are talking about a two-band antenna. I will comment on constructing three or more band trap antennas in the building segment.)

Determine Resonant Frequency of the Trap
The resonant frequency of the trap should be a shade under the starting frequency of the higher frequency band you are designing, in this case 20m. So we are looking for a trap that is resonant in the range of slightly less than 14 MHz (around 13.5 MHz will be fine) so that it will cut off all frequencies above that frequency and acting like the automatic switch described in the first segment.

Calculate Capacitance and Inductance Values
This is almost arbitrary; you can obtain the same resonant frequency by selecting one LC combination and achieve the same resonant frequency with another difference set of values. Avoiding formulas, there's a nice parallel LC calculator to be found here -- and below, I have used it to demonstrate different values achieving almost the same resonant frequencies.

Note that with the selection of two pairs of components -- 27 pF cap and 5 uH inductor or 14 pF cap and 10 uH inductor -- we have achieved traps with approximately the same resonant frequencies and either one would be suitable. Of course, there are other design niceties to be observed in selecting values of components but that is left for your further study.

Further restrictions are, of course, the availability of the values selected. We can wind inductors (which will be covered below),  but capacitors come in discreet values. You can kluge a desired capacitance value by either connecting two or more in series where, like resistors, you are adding the reciprocal of the values) or parallel where you are just adding the values.

The voltage handling capacity of inductors and capacitors need to be considered as well. Since traps are at "the end" of the 20m antenna, they will be at a voltage node and that has to be accounted for. If you are working QRP any decent working voltage or gauge of wire should be fine; you can even construct the inductance (coils) from toroids. However, the kilowatt level is another matter so be very careful. (I will probably do a fourth segment on these considerations.)

Also, I need to pause here and enunciate a prejudice. Research into this subject will show you that hunks of coax can be used to build traps. As you can imagine, coaxial cable has, in effect, capacitance between the shield and center conductor and, as such, can serve both as an inductor or capacitor when wound around a form. The advantage to this that you only need to cut off the appropriate length and build the trap. I chose to keep the components separate so you got a better notion of the LC principles.

Calculate Number of Inductor Turns
Inductors take many forms: single-winding layer, multiple-winding layers, toroidal, etc. For our traps, we are constructing a single layer inductor; I pilfered these formulas from the 1981 ARRL Handbook:

Of course, you can enter this into your calculator laboriously, build a spreadsheet, or just use one of the internet sites to do this :

This covers the first three of our five above steps and, since this is somewhat long, we'll leave the rest for the third segment on actually building the traps, measuring the resonant frequency, and building the antenna.