A doublet into a remote tuner

A popular all-band HF station: a flat centre-fed doublet, window line down to a balun, and an L-network tuner at the bottom of the line, with coax from there to the rig. Mike, WA7ARK, posted the numbers for his on QRZ and asked how one would do it in antennaknobs. The catalog design wire.doublet_remote_tuner is that station:

rig (50 Ω) → L-network tuner → balun 1:1 or 1:4 → window line → doublet centre

Open it in the workbench. The knobs are in feet, the units you would measure the real thing in:

knob	stock	what it is
`length_ft`	130	the doublet, tip to tip
`height_ft`	30	its height
`line_ft`	30	window line from the feed to the balun
`balun_ratio`	1:1	1:1 or 1:4
`tuner_l_uH`	1.87	the tuner’s series coil
`tuner_c_pF`	413	the tuner’s shunt capacitor
`tuner_c_side`	rig	which side the capacitor sits on: across the balun, or across the rig

The line is Mike’s: Wireman #552 with his 0.97 velocity factor and the nominal ~400 Ω he gives it. (Its loss comes from the catalog’s window-450 entry: no citable loss figures for #552 turned up.) The coil and capacitor range over an MFJ-926B remote tuner’s published ranges, 0–24.86 µH and 0–3961 pF, so every setting is one that box can reach. The coil has a Q of 200 and the capacitors are ideal.

The stock tuner setting matches the stock station at 7.15 MHz. Because the knobs are lengths in feet, the design has no band row: set the frequency directly. Every band solves on the same mesh, one fine enough for 10 m.

The planes

The readout’s plane selector picks the point along the chain where the impedance, SWR and Smith chart are read (how planes work). This design names three, source to antenna:

rig (tuner input): what the rig sees, and the plane where SWR 1 means “tuned”;
inside tuner (L–C): the node between the coil and the capacitor;
tuner output / balun input: the load the tuner has to match, i.e. the doublet’s feed impedance carried down the line and through the balun.

Tuning it by hand on the Smith chart

An L network is two parts. You turn the one nearer the antenna until the point lands on the circle that the other part moves it along. Then you turn the other part to slide along that circle to the centre. The design draws the circle for you.

When the load at the tuner has more than 50 Ω of resistance, put the capacitor across the balun. The coil is then the last part, and a series coil moves the point along a circle of constant resistance, R = 50 Ω. When the load’s resistance is below 50 Ω, put the capacitor across the rig. The coil comes first, the capacitor last, and the circle is one of constant conductance, G = 20 mS. The chart’s Y button adds the admittance grid that circle belongs to. With the 1:1 balun, only 40 m wants the capacitor on the rig side.

20 m, at 14.3 MHz

Set the frequency to 14.3 MHz, and tuner_c_side to balun.
Pick the plane tuner output / balun input. The load is about 308 + j921 Ω, an SWR of 61 on 50 Ω coax.
Pick inside tuner (L–C). The chart highlights the R = 50 Ω circle. Turn tuner_c_pF until the point sits on it: 39 pF puts it at about 50 − j389 Ω. (Sweep this knob… in the knob’s menu traces its path, so you can see where it crosses. On this design it sweeps the capacitor from 1 pF to its maximum in 81 log-spaced points, about 11 % apart, and the coil from 0.05 µH the same way, so one sweep shows the whole path on any band. To look closer, narrow the range in the sweep’s header, say 10–100 pF on 20 m.)
Pick rig (tuner input) and turn tuner_l_uH until the point reaches the centre: 4.32 µH gives SWR 1.05. The coil’s Q is why it isn’t exactly 1: the resistance at the rig is 52 Ω.

80 m, at 3.75 MHz

The same three moves. The load at the tuner is about 128 + j456 Ω, so the capacitor goes across the balun again. 228 pF puts the inside-tuner point on the circle (about 50 − j291 Ω), and 12.38 µH then gives SWR 1.03 at the rig.

How far can you QSY?

Run a frequency sweep at the rig plane after tuning. The parts are fixed, so the curve shows how far the match holds:

The 20 m tune at 14.3 MHz is still SWR 1.2 at 14.35 MHz, but 3.2 at 14.0 MHz.
The 80 m tune at 3.75 MHz reaches 6.5 at 3.6 MHz and 6.7 at 3.9 MHz.

A remote auto-tuner retunes for exactly this reason.

All of these numbers are on bs2 (momwire’s B-spline solver) over the workbench’s default Sommerfeld ground (13 / 0.005 S/m).

You can also let the optimizer do it: mark tuner_l_uH and tuner_c_pF, set the objective to SWR, and run it at the frequency you’re on. The optimizer can’t flip tuner_c_side, so if a run ends far from SWR 1, switch the capacitor’s side and run it again. From the command line:

antennaknobs optimize --builder wire.doublet_remote_tuner --bands 14.2 \
    --params tuner_l_uH tuner_c_pF --set tuner_c_side=balun

Band by band: what would an auto-tuner pick?

The design’s analysis tuner per band puts the tuner in its automatic mode (it picks its own parts at every frequency, capacitor side included) and tabulates Mike’s frequencies from 3.6 to 28.5 MHz, for both baluns. Each row gives:

the load at the tuner and the parts the tuner picks;
the SWR at the rig;
where the power goes: the line, the balun, the coil, and the share that reaches the antenna.

A band the MFJ’s part ranges can’t match is flagged.

antennaknobs analyze --builder wire.doublet_remote_tuner --analysis "tuner per band"

A few rows, with the 1:1 balun (bs2, Sommerfeld 13 / 0.005):

MHz	load at the tuner	capacitor	coil	capacitor value	reaches the antenna
3.6	73.9 + j293.9 Ω	across balun	10.7 µH	317.5 pF	95.3 %
7.0	27.2 − j79.8 Ω	across rig	2.38 µH	408.3 pF	92.1 %
14.0	211.8 + j712.7 Ω	across balun	4.00 µH	46.4 pF	92.6 %
28.0	98.1 + j186.8 Ω	across balun	0.803 µH	59.7 pF	94.9 %

With a 1:4 balun every load is a quarter of these. The balun is modelled as a current balun: only its winding resistance, and no magnetizing inductance.

Choosing the line length and the balun. With an auto-tuner every band matches, so the question becomes how much power is lost on the worst band. band-loss answers it by retuning on every band at each line length:

antennaknobs band-loss --builder wire.doublet_remote_tuner \
    --each balun_ratio=1:1,1:4 --search line_ft=30:100:1

On this antenna:

With the 1:1 balun, the 30 ft line is already the best. The worst band is 25 MHz, where 91.9 % reaches the antenna.
With the 1:4 balun, 30 ft gives 91.4 % (worst at 7 MHz), and the best length, 35.2 ft, gives 92.2 %.

The spread is under a percentage point, a tenth of a dB. A tuner at the bottom of 30 ft of window line is within a whisker of the best these parts can do. (The line here is dry. Wet window line loses several times as much.)

Against Mike’s own table

Mike’s EZNEC/AutoEZ model and this design agree at 3.6 MHz: 75.6 + j289.8 Ω there against 73.9 + j293.9 Ω here, and parts within a few percent. On the upper bands the loads differ.

The tuner and the line are not where the difference comes from:

The tuner: fed his loads, the tuner arithmetic here picks his parts to within 2 %.
The line: varying the line’s impedance and length doesn’t close the gap.

So the difference is in the antenna model itself: the ground, the wire and any insulation, which his table doesn’t state. Settling it needs his model.

If you have your own EZNEC model of a station like this, you don’t need this design at all. Since v0.101.0 you can Open… the .ez itself, and its wires, transmission line and transformer come across as they are (EZNEC .ez models). The source at the end of the line is what your tuner sees, so a frequency sweep gives the tuner’s load on every band. One limit for now: a line with loss is held at the model’s own frequency, and the app flags the others.

Engines

bs2 and PyNEC solve this design and agree to within 1.2 % on the tuner’s load. The NEC-5 engine solves it too from v0.101.1 (v0.101.0 refused it). The refusal was ours, not NEC-5’s: the centre gap’s two sides go to different parts of the station, and antennaknobs, not the engine, connects them (AK#1977). On the 20 m tune the three engines agree to about 2 Ω at the rig.