A highly efficient multiband QRP L-match builder project

Here is a project that provides a much more efficient way of matching an End-Fed Half Wave antenna than the usual 49:1 impedance transformer. High ratio transformers are prone to inductance leakage, core saturation and overheating leading to low efficiency. Although a 49:1 (or similar high ratio) transformer can present a low SWR to a transceiver, that is not a good indicator of the transformer’s efficiency. It only tells us our radio will not be damaged; it provides no useful information about how much of our signal will actually be radiated. Also, even though a low SWR can be obtained on multiple bands, the radiation pattern breaks up into multiple lobes and nulls on the higher harmonics. End-Fed Half-Wave antennas should really only be used on their fundamental frequency band and its second harmonic.

This L-match can also be used with other high impedance long wire antennas, for example, random wires. With the flick of a switch it can also be used to match low impedance antennas such as verticals.

Here is an interior view of the L-match. Note the “expedient” use of T37 toroids since I didn’t have any larger ones. To compensate I used 2 T37-6 toroids for the 0.5uH inductor; 2 T-37-2 toroids for each of the 1.0 – 4.0uH inductors and 4 T37-2 toroids for the 8uH inductor. I have tested the device using 4.5 watts into a dummy load and noted stable SWR with no noticeable core heating. I recommend the use of T50 or T68 toroid cores for anybody wanting to build their own version. The variable capacitor is a 160pF polyvaricon.

There are 10 kinds of people ... those who understand binary notation and those who don’t.

It’s an old joke but it’s quite true. In the binary system there are only two digits to remember: “1” and “0”. We can count from decimal 0 to 31 using only 5 binary digits.

Therefore, with only 5 inductors: 0.5uH, 1.0uH, 2.0uH, 4.0uH and 8.0uH we can select up to 32 values of inductance by binary operation of the switches (NB: “u” in this post represents the Greek letter “mu”, uH referring to microhenries). Inductance values can be selected in increments of only 0.5uH for fairly precise tuning.

A few years ago I built a “Super Tee” QRP tuner that has 7 coils and 7 switches. Additional 0.25uH and 0.125uH inductances were available providing 128 different selectable inductances in increments of 1/8 of a microhenry. My experience has been that it is rarely necessary to use that level of precision in inductance values.

The table below shows how binary selection can vary the inductance between zero (all switches closed) and 31.5 uH in 32 increments of 0.5uH.

8uH coil	4uH coil	2uH coil	1uH coil	0.5uH coil	Total inductance
Switch closed	Switch closed	Switch closed	Switch closed	0.5uH	0.5uH
Switch closed	Switch closed	Switch closed	1uH	Switch closed	1uH
Switch closed	Switch closed	Switch closed	1uH	0.5uH	1.5uH
Switch closed	Switch closed	2uH	Switch closed	Switch closed	2uH
Switch closed	Switch closed	2uH	Switch closed	0.5uH	2.5uH
Switch closed	Switch closed	2uH	1uH	Switch closed	3uH
Switch closed	Switch closed	2uH	1uH	0.5uH	3.5uH
Switch closed	4uH	Switch closed	Switch closed	Switch closed	4uH
Switch closed	4uH	Switch closed	Switch closed	0.5uH	4.5uH
Switch closed	4uH	Switch closed	1uH	Switch closed	5uH
Switch closed	4uH	Switch closed	1uH	0.5uH	5.5uH
Switch closed	4uH	2uH	Switch closed	Switch closed	6uH
Switch closed	4uH	2uH	Switch closed	0.5uH	6.5uH
Switch closed	4uH	2uH	1uH	Switch closed	7uH
Switch closed	4uH	2uH	1uH	0.5uH	7.5uH
8uH	Switch closed	Switch closed	Switch closed	Switch closed	8uH
8uH	Switch closed	Switch closed	Switch closed	0.5uH	8.5uH
8uH	Switch closed	Switch closed	1uH	Switch closed	9uH
8uh	Switch closed	Switch closed	1uH	0.5uH	9.5uH
8uh	Switch closed	2uH	Switch closed	Switch closed	10uH
8uh	Switch closed	2uH	Switch closed	0.5uH	10.5uH
8uh	Switch closed	2uH	1uH	Switch closed	11uH
8uh	Switch closed	2uH	1uH	0.5uH	11.5uH
8uh	4uH	Switch closed	Switch closed	Switch closed	12uH
8uh	4uH	Switch closed	Switch closed	0.5uH	12.5uH
8uh	4uH	Switch closed	1uH	Switch closed	13uH
8uh	4uH	Switch closed	1uH	0.5uH	13.5uH
8uh	4uH	2uH	Switch closed	Switch closed	14uH
8uh	4uH	2uH	Switch closed	0.5uH	14.5uH
8uh	4uH	2uH	1uH	Switch closed	15uH
8uH	4uH	2uH	1uH	0.5uH	15.5uH

If we look at the table below we can see that it would be possible to use even fewer coils and switches if we wanted to operate on fewer bands. For example, if we wanted to operate only on the 20m, 30m and 40m bands we would need only three values of inductance. With five inductances and five switches we can operate on seven bands: 80m, 40m, 30m, 20m, 17m, 15m and 12m. It might be possible to also get a match on the 10m band. The maximum inductance in this project is 15.5uH, but there is additional stray inductance within the internal wiring.

Frequency (MHz)	Inductance (microhenries)	Capacitance (picofarads)
3.7	15.1	120
7.15	7.8	62
10.125	5.5	44
14.15	3.9	31
18.11	3.1	25
21.2	2.6	21
24.93	2.2	18
28.5	2.0	16

Why choose binary selection?

Many designs for L-match devices use a single toroid core inductance with selectable taps as shown in the diagram below. I have built one myself, but as Shakespeare would have said: “Here’s the rub”. It is not easy to build a single inductor with 32 taps at 0.5uH increments. Even if that could be achieved where would we source a 32-way switch? We could use a lead with an alligator clip to select the taps but that would be inconvenient and potentially unreliable out in the field for portable operations.

My own version of this kind of L-match had only 12 taps with a 12-way rotary switch and worked fairly well but was not as versatile as binary selection.

I would like to add my gratitude to Martin K1FQL who provided the math equations and a lot of guidance to me in understanding how L-matches work. I have not included the equations in this post, but if anybody is interested I recommend reading Martin’s post at this link: Highly Efficient L-Matching Networks for End-Fed Half-Wave Antennas.

Coming up on Ham Radio Outside the Box

— Improving the efficiency of an antenna – by burying half of it underground? —

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