How to read this notebook
Log 1 sets out the problem. Logs 2 and 3 describe the hardware. Logs 4 and 5 are the physics, worked from first principles. Logs 6 and 7 are the first measurements and what a model makes of them. Logs 8 and 9 are where this might go. Every log carries a tag that says how far along it is.
- Overview:
- background, not a result.
- Built:
- the hardware exists and is photographed here.
- Theory:
- standard electromagnetics, worked through for this geometry.
- Not yet calibrated:
- real readings off the instrument, but with known errors not yet removed.
- Idea:
- where this could lead if it holds up. Not a claim.
- Planned:
- the next steps, in order.
Box colours
The impedance extraction and the thin-wire model in Logs 6 and 7 were worked out with Claude AI from photographs of the analyzer screen. They have not been checked against an independent solver or against calibrated data. Where that matters, it is said in the log. If any of it is wrong, the correction will be published here.
The need: why matching is not free
An antenna has a natural length. A straight wire fed at its centre wants to be half a wavelength from tip to tip. Make it shorter than that and it looks capacitive at the feed; make it longer and it looks inductive. Only at the right length does the reactance vanish and the antenna accept power cleanly.
Radios have to work across many frequencies, and the wavelength changes with every one of them. A radio covering 100 MHz to 866 MHz spans wavelengths from three metres down to 35 centimetres, a range of almost nine to one. No fixed piece of wire is the right length across that span.
The near-universal answer is to keep the wire fixed and add a matching network: a bank of inductors and capacitors, switched to cancel whatever reactance the antenna presents. Every modern phone does this, and it works.
Note 1.1 (what the cancellation costs). A real inductor or capacitor is not pure reactance. It has a loss resistance, summarised by its quality factor \(Q_c = |X|/R_{\text{loss}}\). Cancelling a reactance \(X\) therefore inserts a resistance of roughly \(|X|/Q_c\) into the signal path. The larger the mismatch being corrected, the more resistance comes with the correction.
That resistance competes directly with the antenna's radiation resistance, \(R_r\), which is the part of the feed resistance that corresponds to power actually leaving as a wave. The efficiency is
$$\eta=\frac{R_r}{R_r+R_{\text{loss}}}. \tag{1.1}$$and the trouble is that \(R_r\) collapses when an antenna is electrically short. For a short dipole of effective length \(\ell_{\text{eff}}\),
$$R_r = 20\pi^2\left(\frac{\ell_{\text{eff}}}{\lambda}\right)^{2}. \tag{1.2}$$Example 1.2 (how small the numbers get). A 25 mm element at 100 MHz is \(\ell/\lambda = 0.0083\), so by (1.2) its radiation resistance is about 0.014 Ω. Two ohms of loss anywhere in the path, which is an unremarkable amount for a switched network, leaves an efficiency of under one percent. The same element at 700 MHz, now 200 mm of wire, has \(R_r \approx 43\ \Omega\) and the same two ohms barely matter.
This is the asymmetry that makes wideband small antennas disappointing at their low end and fine at their high end. It is not a manufacturing problem. It is the geometry.
Result 1.3 (the size limit). Chu and Wheeler showed that an antenna fitting inside a sphere of radius \(a\) has a minimum quality factor[1][2]
$$Q_{\min}=\frac{1}{(ka)^{3}}+\frac{1}{ka},\qquad k=\frac{2\pi}{\lambda}, \tag{1.3}$$and since fractional bandwidth is roughly \(1/Q\), a small antenna cannot be both efficient and broadband. This is a conservation argument, not an engineering difficulty, so no cleverness in the matching network escapes it.
| Frequency | Radius \(a\) | \(ka\) | \(Q_{\min}\) | Best possible bandwidth |
|---|---|---|---|---|
| 100 MHz | 12.5 mm | 0.026 | 55 653 | 1.8 kHz |
| 433 MHz | 12.5 mm | 0.113 | 694 | 624 kHz |
| 100 MHz | 100 mm | 0.210 | 113 | 882 kHz |
| 700 MHz | 100 mm | 1.467 | 1.0 | no constraint |
The question this build asks. If the penalty comes from forcing a fixed wire to behave as though it were a different length, what happens if the wire is simply made that length instead? Equation (1.3) still applies at every instant, so the antenna is still narrowband at any one setting. But (1.1) and (1.2) are no longer working against you, because \(R_r\) stays near its resonant value and there is no large reactance for a lossy network to cancel.
The build
The frame is 3D printed in one piece: a hollow horizontal crossbar on top of a vertical spine with a rack cut along it. Two lengths of stranded steel wire run from a sliding carriage up the spine and into the crossbar from both ends. A pinion drives the carriage. The feed is a U.FL pigtail at the carriage.
Note 2.1 (what is deliberately absent). There are no inductors, capacitors, diodes, varactors or switches anywhere in this device, and no power is supplied to it. Everything between the connector and free space is wire and printed plastic. That is the point of the experiment: whatever the sweeps show, no part of it can be attributed to a tuning circuit, because there isn't one.
Parts
| Part | What it does |
|---|---|
| Printed T frame with rack | Holds the geometry fixed and guides the wire. The crossbar is hollow so wire can be driven into it. |
| Two stranded steel wires | The conductor. One per arm, continuous from the carriage to the arm tip. |
| Sliding carriage and pinion | Converts rotation into the push or pull that sets the arm length. |
| U.FL pigtail | Feed. Connects the carriage to the analyzer. |
How the mechanism works
The frame never moves. What moves is the wire inside it, and only in one way: further into the horizontal crossbar, or further out of it. The vertical run between the carriage and the crossbar stays the same length in every state. This is the whole mechanism, and it took a few rounds of looking at the hardware to state it correctly.
Definition 3.1 (the tuned variable). Let \(h\) be the length of wire extending from the centre of the crossbar to one arm tip, so the antenna's tip-to-tip length is \(2h\). Driving the pinion changes \(h\) and nothing else. Every quantity in Logs 4 to 7 is a function of \(h\).
Why the vertical run does not radiate
The two wires running down the spine sit side by side and carry currents that are equal in size and opposite in direction, because one goes to each arm of a centre-fed antenna. At any distance large compared with their separation \(s\), the fields from the two cancel.
Result 3.2 (the vertical pair is a feedline, not a radiator). A parallel pair carrying \(+I\) and \(-I\) separated by \(s \ll \lambda\) radiates a power smaller than a single wire of the same length by a factor of order \((s/\lambda)^2\).
This is what makes the device a dipole with a feedline rather than a monopole or a loop. The radiating structure is the horizontal pair of arms; the vertical section only carries power to them. It also means the arms, not the overall device height, set the resonance.
Note 3.3 (but the line still transforms). Not radiating is not the same as having no effect. A two-wire line of length \(d\) and characteristic impedance \(Z_c\) transforms whatever is at its far end:
$$Z_{\text{in}}=Z_c\,\frac{Z_L+jZ_c\tan\beta d}{Z_c+jZ_L\tan\beta d}. \tag{3.1}$$With \(d\) of 150 to 200 mm and a wavelength near 380 mm, \(\beta d\) is a substantial fraction of a radian, so the impedance seen at the connector is rotated well away from the impedance at the arms. This is the single largest known error in Log 6, and removing it is the first item in Log 9.
The electromagnetics
This log works through why changing \(h\) changes the resonance, using nothing beyond standard thin-wire antenna theory. The results are textbook[3][4]; what is specific to this build is that \(h\) is a variable rather than a constant.
The current on the wire
Charge cannot flow past an open end, so the current must vanish at both tips. For a thin wire the standing-wave solution that satisfies this is sinusoidal:
$$I(z)=I_0\,\sin\!\big[k\,(h-|z|)\big],\qquad k=\frac{2\pi}{\lambda},\qquad |z|\le h. \tag{4.1}$$Everything else follows from (4.1). The feed sits at \(z=0\), where the current is \(I_0\sin(kh)\).
Definition 4.1 (electrical length). The quantity \(kh = 2\pi h/\lambda\) is the arm's length measured in radians of wave. It, and not \(h\) in millimetres, is what the antenna responds to. Changing \(h\) at fixed \(\lambda\) and changing \(\lambda\) at fixed \(h\) are the same operation.
Where resonance comes from
Integrating the fields that (4.1) produces back onto the wire itself gives the input impedance by the induced-EMF method. Written compactly,
$$Z_{\text{in}}(kh)=\frac{R(kh)+jX(kh)}{\sin^{2}(kh)}, \tag{4.2}$$where \(R\) and \(X\) are combinations of the sine and cosine integrals \(\mathrm{Si}\) and \(\mathrm{Ci}\),
$$R=\frac{\eta}{2\pi}\Big[\gamma+\ln(2kh)-\mathrm{Ci}(2kh)+\tfrac12\sin(2kh)\big(\mathrm{Si}(4kh)-2\,\mathrm{Si}(2kh)\big)+\tfrac12\cos(2kh)\big(\gamma+\ln(kh)+\mathrm{Ci}(4kh)-2\,\mathrm{Ci}(2kh)\big)\Big], \tag{4.3}$$with \(\eta=376.73\ \Omega\) the impedance of free space and \(\gamma=0.5772\) the Euler constant. The exact form of \(X\) is longer and is in the reference; the behaviour that matters is simple.
Result 4.2 (the sign of the reactance). \(X_{\text{in}}<0\) for \(kh<\pi/2\), \(X_{\text{in}}=0\) at \(kh\approx\pi/2\), and \(X_{\text{in}}>0\) for \(kh>\pi/2\). In words: short arms look capacitive, long arms look inductive, and the crossing is the resonance. Setting \(kh=\pi/2\) gives
$$h=\frac{\lambda}{4},\qquad 2h=\frac{\lambda}{2},\qquad f_{\text{res}}=\frac{c}{4h}. \tag{4.4}$$(4.4) is the design equation for this device. It says the resonant frequency is inversely proportional to the arm length, so the mechanism's travel maps directly onto a tuning range. It also provides the test: every measured reactance implies an arm length, and those lengths can be checked against a ruler.
Example 4.3 (what the frame can cover). Taking (4.4) literally, arms of 97 mm resonate at \(c/(4\times0.097)=773\) MHz and arms of 107 mm at 701 MHz. The exact thin-wire result in (4.2) puts the same two lengths at 734 MHz and 667 MHz, roughly five percent lower, because end effects make a real wire electrically longer than its physical length. Both numbers are useful: the first is the pocket estimate, the second is what to expect on the instrument.
What actually leaves the antenna
Substituting (4.1) into the radiation integral gives the far field,
$$E_\theta(r,\theta)=j\,\frac{\eta I_0 e^{-jkr}}{2\pi r}\cdot\frac{\cos(kh\cos\theta)-\cos(kh)}{\sin\theta}, \tag{4.5}$$with \(\theta\) measured from the wire axis. The bracketed factor is the pattern. For \(kh=\pi/2\) it is the familiar figure of eight: nothing off the tips, maximum broadside.
Result 4.4 (the upper limit on useful travel). The pattern in (4.5) keeps a single broadside maximum only while \(2h \lesssim 1.25\lambda\). Beyond that the main lobe splits. This, and not the mechanism, sets how far the arms can usefully be extended at a given frequency.
Why resizing preserves efficiency
Combining the pieces. The radiation resistance at resonance is a property of the shape, not the size: a thin half-wave dipole sits near 73 Ω in free space, and the model used in Log 7, with this wire radius, gives 63 Ω. The loss resistance of a short length of steel wire is of order tenths of an ohm and changes little with \(h\). So by (1.1),
$$\eta_{\text{resized}}=\frac{R_r}{R_r+R_{\text{wire}}}\approx\frac{63}{63+R_{\text{wire}}}, \tag{4.6}$$which stays close to unity at every setting. Compare this with the fixed-antenna case, where \(R_r\) falls as \((\ell/\lambda)^2\) by (1.2) while the network's loss resistance grows as the reactance it must cancel grows. The two effects multiply in the wrong direction.
Note 4.5 (what this does not escape). Equation (1.3) still holds at every setting. A resized antenna is not broadband; it is narrowband in a place you chose. The claim is about efficiency across a tuning range, not about instantaneous bandwidth, and the two are often confused. Nothing here is a way around the Chu limit.
What the E field does
The electric field is the part of this that is easiest to picture and hardest to state loosely, so it is worth being precise about which field is meant. Close to the wire there is a reactive near field that stores energy and gives it back each cycle. Far away there is a radiation field that leaves and does not return. Changing \(h\) changes both, in different ways.
The near field: where the stored energy is
When the arms are short the current cannot complete its half sine before it runs out of wire. It is cut off partway, so a large charge accumulates at the tips each half cycle. That charge is what makes the structure look capacitive, and the field lines it produces arc from one tip straight back to the other without ever getting far from the antenna. That energy is stored and returned, not radiated, which is exactly what a large negative \(X_{\text{in}}\) means.
As the arms extend, the current distribution fills out. Less charge piles at the tips, the field lines reach further before closing, and the stored energy falls relative to the radiated energy. The reactance climbs toward zero.
Definition 5.1 (effective height). The single number that captures how much field the current actually produces is the effective height,
$$h_{\text{eff}}=\frac{1}{I_0}\int_{-h}^{h} I(z)\,\mathrm{d}z = \frac{2}{k}\tan\!\left(\frac{kh}{2}\right), \tag{5.1}$$the right-hand form following from (4.1). It is the length a uniform current of \(I_0\) would need to produce the same field.
Example 5.2 (the gain from extending). At 782.6 MHz, \(\lambda = 383\) mm. Arms of 96.9 mm give \(kh = 1.589\) and \(h_{\text{eff}} = 124\) mm by (5.1). Arms of 106.8 mm give \(kh=1.752\) and \(h_{\text{eff}}=146\) mm. A 10 percent change in physical length produces an 18 percent change in effective height, and since radiated power goes as \(h_{\text{eff}}^2\), about a 39 percent change in radiated power for the same feed current.
This is the useful statement about the E field: extending the arms does not merely retune, it increases how strongly the same current couples to free space. That is the mechanism behind the rising feed resistance seen in Log 6, and it is why a rising \(R\) in that data is not automatically a sign of loss.
The far field: what changes in the pattern
In the radiation zone the field is (4.5), and the pattern factor depends on \(kh\) alone. Over the range this device covers, roughly \(kh = 1.59\) to \(1.78\), the pattern stays a single broadside lobe and narrows slightly: more of the radiated power goes broadside and less at angles near the wire. Directivity rises gently from about 1.64 (the short-dipole value) toward the 2.15 dBi of a half-wave dipole and a little beyond.
Note 5.3 (polarisation and orientation). The radiated E field is parallel to the arms, so this antenna is linearly polarised along the crossbar. Rotating it 90° about the feed axis will cost most of the signal against a fixed correspondent. A loop or a crossed pair would avoid that; this geometry does not, and any application has to live with it or add a second element.
The first sweeps
Sixteen captures were taken on a NanoVNA, seven with the marker at 782.6 MHz and nine at 855 MHz. The analyzer was sweeping 1.5 kHz to 1.7 GHz across 101 points. The readings below were transcribed from photographs of the instrument screen.
Note 6.1 (errors that have not been removed). These are raw readings, and four known problems remain in them.
- No short-open-load calibration was performed at the antenna connector, so the cable is inside the measurement.
- 101 points across six decades is about 17 MHz per step, far too coarse to resolve a resonance.
- The two-wire vertical run has not been de-embedded, so (3.1) is still acting on every number below.
- Values were read off photographs of a small screen; the phase digits in particular carry perhaps a degree of transcription uncertainty.
Nothing here should be read as a calibrated measurement of this antenna. What the data can support is the subject of Log 7.
From the screen to an impedance
The analyzer reports \(|\Gamma|\) as SWR and the angle of \(\Gamma\) as phase. Recovering the complex impedance is the standard inversion:
$$|\Gamma|=\frac{\mathrm{SWR}-1}{\mathrm{SWR}+1},\qquad \Gamma=|\Gamma|e^{j\phi},\qquad Z=Z_0\,\frac{1+\Gamma}{1-\Gamma}. \tag{6.1}$$| Capture | f (MHz) | SWR | ∠Γ (°) | R (Ω) | X (Ω) | Leq (nH) | Cmatch (pF) |
|---|---|---|---|---|---|---|---|
| A1 | 782.6 | 2.973 | 68.16 | 42.9 | 52.5 | 10.7 | 3.87 |
| A4 | 782.6 | 2.673 | 57.55 | 55.1 | 53.5 | 10.9 | 3.80 |
| A3 | 782.6 | 2.891 | 59.56 | 51.4 | 56.3 | 11.5 | 3.61 |
| A2 | 782.6 | 3.145 | 49.30 | 61.8 | 66.2 | 13.5 | 3.07 |
| A5 | 782.6 | 3.791 | 43.55 | 66.7 | 81.1 | 16.5 | 2.51 |
| A6 | 782.6 | 4.890 | 41.02 | 64.1 | 98.6 | 20.1 | 2.06 |
| A7 | 782.6 | 7.458 | 30.30 | 78.8 | 145.6 | 29.6 | 1.40 |
| B7 | 855.0 | 8.243 | 29.59 | 76.8 | 154.0 | 28.7 | 1.21 |
| B3 | 855.0 | 9.003 | 30.18 | 70.1 | 156.6 | 29.1 | 1.19 |
| B4 | 855.0 | 10.230 | 31.32 | 59.8 | 157.5 | 29.3 | 1.18 |
| B2 | 855.0 | 8.893 | 29.13 | 74.9 | 160.0 | 29.8 | 1.16 |
| B1 | 855.0 | 7.826 | 26.60 | 93.4 | 161.0 | 30.0 | 1.16 |
| B8 | 855.0 | 9.176 | 29.28 | 72.7 | 161.1 | 30.0 | 1.15 |
| B5 | 855.0 | 10.020 | 30.20 | 64.7 | 161.4 | 30.0 | 1.15 |
| B6 | 855.0 | 8.828 | 27.75 | 81.4 | 165.1 | 30.7 | 1.13 |
| B9 | 855.0 | 8.554 | 26.36 | 90.0 | 168.6 | 31.4 | 1.10 |
The inversion above and the three observations below were produced with Claude AI from the screen photographs. They have not been reproduced with an independent tool or against calibrated data.
Observation 6.2 (every state is inductive). All sixteen reactances are positive, spanning +52.5 Ω to +168.6 Ω. By Result 4.2 this places the device above its own resonance in both measurement sets. No capture is anywhere near the zero crossing.
Observation 6.3 (the 855 MHz set is one state, not nine). The nine B captures have \(X = 160.6 \pm 4.1\ \Omega\), a spread of 2.7 percent, against a 93 Ω swing across the A set. Nine repeats of one setting therefore give a working noise floor for this setup of about ±4 Ω, which confirms that the A-set spread is a real change and not measurement drift.
Observation 6.4 (the mismatch is almost entirely reactive). The resistances cluster between 43 Ω and 93 Ω, within a factor of two of 50 Ω throughout, while the reactances run to more than three times that. A single series capacitance between 1.10 pF and 3.87 pF cancels \(X\) in every state, which would take the worst capture from SWR 10.23 to 1.87 and the best from 2.67 to 1.03.
Measured series reactance, every capture, sorted. Orange: the 782.6 MHz set. Blue: the 855 MHz set.
Fitting a thin-wire model
Log 4 gives \(Z_{\text{in}}\) as a function of \(kh\). The measurements give \(Z\) at two known frequencies. Inverting (4.2) numerically turns each capture into the arm length that would produce it. Because the model is independent of the hardware, this is a real test: the lengths it returns can be compared with the frame.
Method 7.1. For each capture, solve \(\operatorname{Im}Z_{\text{in}}(f_{\text{meas}},h)=X_{\text{meas}}\) for \(h\) by bisection over 70 to 135 mm, using (4.2) with a wire radius of 0.5 mm. Then evaluate \(f_{\text{res}}\) for that \(h\) as the lowest upward zero crossing of the reactance.
| Set | Captures | X measured (Ω) | Implied arm h (mm) | Implied tip-to-tip (mm) | Implied fres (MHz) |
|---|---|---|---|---|---|
| A — 782.6 MHz | 7 | 52.5 to 145.6 | 96.9 to 106.8 | 194 to 214 | 667 to 734 |
| B — 855 MHz | 9 | 154.0 to 168.6 | 98.7 to 100.0 | 197 to 200 | 712 to 721 |
The model, the inversion and the agreement claimed below are Claude AI's work from the transcribed readings. The prediction in Finding 7.3 has not yet been checked against the hardware.
Finding 7.2 (the two sets agree). The seven A captures and the nine B captures were taken at different frequencies and inverted separately. They land on overlapping arm lengths: 96.9 to 106.8 mm from set A, 98.7 to 100.0 mm from set B. The nine B captures agree among themselves to 99.3 ± 0.4 mm. Two independent frequencies returning the same physical length is the kind of consistency a wrong model does not usually produce by accident.
Finding 7.3 (a falsifiable prediction). The radiating arms are between 97 and 107 mm each, the device's tip-to-tip length is between 194 and 214 mm, and its resonance lies between 667 and 734 MHz. All three are checkable: the first two with a ruler, the third with a narrow sweep. If the crossbar measures 200 mm across, the model is doing its job. If it measures 120 mm, the model is wrong and so is the interpretation in Log 6.
Finding 7.4 (why nothing was matched). If \(f_{\text{res}}\) really is near 700 MHz, then both measurement sessions were run above resonance, where (4.2) is inductive for any setting. The device was never swept through the frequency where its own geometry resonates. That is a measurement-planning error, not a fault in the hardware, and it is the first thing Log 9 fixes.
Model curve from (4.2). The shaded band is where all sixteen captures land once inverted. Orange points: the 782.6 MHz set. Blue points: the 855 MHz set.
Note 7.5 (what the model leaves out). The thin-wire result assumes a straight, isolated, centre-fed wire in free space. The real device has a printed frame with its own permittivity near the conductor, a two-wire feed section that (3.1) says is transforming everything, a hand nearby during the measurement, and stranded rather than solid wire. Any of these could move the inferred length by several millimetres. The agreement in Finding 7.2 is better than the model deserves, which is itself a reason for caution rather than confidence.
Where this could be useful
Nothing in Logs 6 and 7 establishes that this antenna is efficient. The case below is what would follow if the efficiency measurement in Log 9 comes out well, and it is written to be read that way.
What it would replace
Current practice for covering a wide band from a small antenna is a tuner integrated circuit: a switched capacitor array with a control bus, firmware, and a per-band calibration table. The part is inexpensive in volume. The engineering around it is not, and the insertion loss, typically one to one and a half decibels, is paid on every transmission and reception.
A mechanism that retunes the radiator removes the network from the signal path entirely. There is no insertion loss to pay because there is nothing in line to lose it in, and no calibration table because the geometry is the state.
Note 8.1 (what it costs instead). It buys that with moving parts, actuation time measured in milliseconds rather than microseconds, wear, and a motor or actuator with its own power draw and failure modes. For a phone switching bands mid-packet this is disqualifying. For anything that changes frequency on a human timescale, or rarely, it is not.
Where the trade would land well
- Wideband monitoring and receive. A receiver that sweeps slowly across a large span, or parks on one frequency for a long time, pays the actuation cost once and keeps the efficiency. This is the most natural fit and the easiest to test.
- Fixed installations that must cover several bands. Base stations, repeaters and remote sensors retune on a schedule, not per packet, and often have power available for an actuator.
- Low-power long-range links. Where every decibel is range, trading one or two decibels of network loss for a mechanism may be worth the complexity.
- Teaching. A device where the resonance is visibly a length is a good way to make (4.4) concrete.
Where it would not
- Phones and anything doing fast carrier aggregation. Milliseconds are far too slow.
- Anything that must survive vibration, shock or a drop test with a sliding mechanism inside.
- Very low frequencies. At 100 MHz the resonant length is 1.5 m tip to tip, which the mechanism does not make smaller. Resizing beats matching, but it does not beat the wavelength.
Note 8.2 (prior art). Mechanically retuned antennas are an old idea. Motorised screwdriver antennas for amateur HF work move a contact along a coil; telescopic whips have always been variable-length; and there is a patent literature on motor-driven tunable elements. What is being tested here is a specific compact geometry, not the general principle, and any claim of novelty would have to survive a proper search. Nothing on this page has had one.
What's next
- Measure the frame with a ruler. Tip-to-tip at both mechanism extremes, the vertical run length, and the wire spacing. Finding 7.3 is a numerical prediction about these three lengths, and a tape measure either confirms it or kills it in two minutes.
- Calibrate at the antenna connector. Short, open and load at the U.FL end, with the real cable in place. Removes the cable from every number in Log 6, which is the largest removable error.
- Sweep 500 to 900 MHz with 101 points. Four megahertz per step instead of seventeen. If the resonance is really near 700 MHz, this is the sweep that shows it as a dip rather than leaving it to be inferred.
- One continuous sweep per mechanism position. Step the carriage through its travel and record a full sweep at each stop. A family of curves walking across the band is the whole claim in one picture, and it is what a single marker reading cannot show.
- De-embed the two-wire section. Measure its length and spacing, compute \(Z_c\), and invert (3.1). Until this is done, the impedance at the arms is not known, and Log 7's agreement could be partly coincidence.
- Measure efficiency against a reference. Two antennas at a fixed distance, comparing \(|S_{21}|\) with this device against a cut quarter-wave at the same frequency. This is the number the whole argument in Log 8 rests on, and nothing measured so far bears on it at all.
- Add a counterpoise, then choke the feedline. In that order. A choke added before there is something for the antenna to work against would strand it; the order matters more than either step.
- Publish the raw Touchstone files. Using the logger from the VNA and GPS toolkit, so the sweeps are data rather than photographs of a screen.
Join the conversation
We would rather be corrected early than be wrong in public later. This page publishes a model that fits better than it probably should, built on readings that are not calibrated. If you see the mistake, please say so.
Questions we would like help with
- Is the thin-wire inversion in Log 7 doing something it should not, given that the feedline has not been de-embedded?
- What is the cleanest way to measure antenna efficiency without an anechoic chamber? Wheeler cap, three-antenna method, something else?
- Has anyone built a compact mechanically retuned antenna and measured its efficiency against a fixed resonant reference?
- For a two-wire line of unknown spacing inside printed plastic, what is the most reliable way to get \(Z_c\)?
- What actuator would survive this duty cycle in something handheld?
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