Is a ham transmitter conjugate matched to its load?

Following on from KL7AJ on the Conjugate Match Theorem, KL7AJ on the Conjugate Match Theorem – analytical solution asked the question Is a ham transmitter conjugate matched to its load?

The answer speaks to the relevance of Walt Maxwell’s Conjugate Mirror proposition to ham stations. Continue reading Is a ham transmitter conjugate matched to its load?

KL7AJ on the Conjugate Match Theorem – analytical solution – Winsmith

KL7AJ on the Conjugate Match Theorem asked the question Should we have expected this outcome?

Let us solve a very similar problem analytically where measurement errors do not contribute to the outcome.

Taking the load impedance to be the same 10.1+j0.2Ω, and calculating for a T match similar to the MFJ-949E (assuming L=26µH, QL=200, and ideal capacitors) we can find a near perfect match.

The capacitors are 177.2 and 92.93pF for the match.

Now turning the network around by swapping the capacitors and changing the load to 50+j0Ω. Continue reading KL7AJ on the Conjugate Match Theorem – analytical solution – Winsmith

KL7AJ on the Conjugate Match Theorem

KL7AJ proposed a little test for his readers on QRZ:

One of the most useful (and sometimes astonishing) principles in radio is the Conjugate Match theorem. In the simplest terms, what this says is that the maximum power will be transferred between a source (like a transmitter) and a load (like an antenna), when the source impedance is the COMPLEX CONJUGATE of the load impedance (or vice versa).
Here’s a neat little experiment to prove the conjugate match theorem. You need four basic ingredients: an antenna analyzer like the MFJ259 (or an actual impedance bridge, if you know how to use one). A good low loss antenna tuner. A good 50 ohm resistor. And a good 200 ohm resistor. And some appropriate connecting hardware, namely some short bits of coax.

Step 1) connect the 50 ohm resistor to the OUTPUT of the antenna tuner. Connect the antenna analyzer to the INPUT of the antenna tuner.

Step 2) Adjust the antenna tuner to get precisely 50 ohms, zero reactance on the antenna analyzer. This step simply confirms everything is working.

Step 3) Replace the 50 ohm resistor with the 200 ohm resistor. Readjust the antenna tuner to get 50 ohms, zero reactance on the antenna analyzer. Do not disturb the antenna tuner adjustments after this point.

Step 4) Remove the 200 ohm resistor and insert the antenna analyzer in its place (at the OUTPUT of the antenna tuner).

Step 5) Insert the 50 ohm resistor at the INPUT of the antenna tuner.

Step 6) Take a careful reading of the antenna analyzer. (What do you think it will say?)

10 points for anyone who will correctly explain why this works.

Some clarifications

Jacobi maximum power transfer theorem

Jacobi published his maximum power transfer theorem in 1840. It states that maximum power is transferred from a (Thevenin) source to a load when the load resistance is equal to the (Thevenin equivalent) source resistance.

It was later adapted to apply to AC circuits with sinusoidal excitation, maximum power is transferred from a (Thevenin) source to a load when the load impedance is the complex conjugate of the (Thevenin equivalent) source impedance.

Walt Maxwell’s Conjugate Mirror

(Maxwell 2001 24.5) states

To expand on this definition, conjugate match means that if in one direction from a junction the impedance has the dimensions R + jX, then in the opposite direction the impedance will have the dimensions R − jX. Further paraphrasing of the theorem, when a conjugate match is accomplished at any of the junctions in the system, any reactance appearing at any junction is canceled by an equal and opposite reactance, which also includes any reactance appearing in the load, such as a non-resonant antenna. This reactance cancellation results in a net system reactance of zero, establishing resonance in the entire system. In this resonant condition the source delivers its maximum available power to the load. …(1)

Note that it states that if a conjugate match is established an any junction, then a conjugate match occurs in any (all) other junctions, simultaneously a conjugate match exists everywhere. Continue reading KL7AJ on the Conjugate Match Theorem

True balanced tuner

A recent long running thread on QRZ entitled “True balanced auto-tuner” was sure to tease out some pretty woolly thinking… the word “true” was enough to signal the outcome.

There are only three words in the title, we can dismiss “true” as a harbinger of woolly thinking, and though people will argue the toss on the appropriateness of the term “auto-tuner’, most people share an understanding of the meaning. “Balanced” is another problem altogether.

After thirty odd posts, there has been no definition or discussion of the term balanced, or its advantages or disadvantages.

One of the recommendations by several posters is the old is new again solution, the once popular link coupled tuner and the work of W5ZQ featured in one of those recommendations.

W5ZQ and WW8J


W5ZQ describes a tuner inspired by WW8J. W5ZQ extended the design and provides a writeup on optimising balance.

Above is W5ZQ’s partial circuit. In the article he describes and shows:

  • adjustment of the grounding point of the output tank; and
  • current meters which presumably attach to J2 and J3.

Key to analysis of the topology is that the centre of the output inductor is grounded. This results in the circuit tending towards equal but opposite phase voltages on the output terminals. Continue reading True balanced tuner

Matching a 5/8λ ground plane

The 5/8λ ground plane is regarded by hams widely as a superb antenna for DX, and since the main reason for modern ham radio is DX, it is an antenna of interest.

The idea behind the 5/8λ ground plane popularity is that claim that it has higher gain at low angles than a simple 1/4λ ground plane.

The 5/8λ ground plane is not resonant, and the feed point impedance is hardly suited to direct coax feed.

The chart above is for a 5/8λ ground plane elevated to 5m height above average ground (σ=0.005, εr=13). The feed point impedance in this case at 5/8λ radiator height (14.2MHz) is about 110-j485Ω. Continue reading Matching a 5/8λ ground plane

Icom IC-7410 – PTT tuner start doesn’t work

I have an IC-7410 with R1 of the firmware installed.

I have attempted to use its PTT tuner start feature (triggers ATU tune on PTT if frequency changed a significant amount)  with an MFJ-993B ATU, but it fails.

The symptoms are that the IC-7410 does not transmit its tune carrier, it remains in the mode active when PTT was pressed.

Tuner operations initiated from the IC-7410 TUNE switch appear to all work as expected.

Above is a logic trace of the ATU control wires on PTT tune. everything looks good, when the /START signal is recognised as valid, the ATU asserts KEY and the IC-7410 should put tune carrier out… but it doesn’t and the ATU aborts after about 0.5s without tuning. Continue reading Icom IC-7410 – PTT tuner start doesn’t work

Walter Maxwell’s teachings on system wide conjugate matching

Walt Maxwell (W2DU) made much of conjugate matching in antenna systems, he wrote of his volume in the preface to (Maxwell 2001 24.5):

It explains in great detail how the antenna tuner at the input terminals of the feed line provides a conjugate match at the antenna terminals, and tunes a non-resonant antenna to resonance while also providing an impedance match for the output of the transceiver.

Walt Maxwell made much of conjugate matching, and wrote often of it as though at some optimal adjustment of an ATU there was a system wide state of conjugate match conferred, that at each and every point in an antenna system the impedance looking towards the source was the conjugate of the impedance looking towards the load.

This is popularly held to be some nirvana, a heavenly state where transmitters are “happy” and all is good. Happiness of transmitters is often given in online discussion by hams as the raison d’être for ATUs . Continue reading Walter Maxwell’s teachings on system wide conjugate matching

MFJ-993B internal balun review

The MFJ-993B auto antenna tuner includes an internal balun, this article is a review of that balun.

screenshot-29_09_16-10_02_24The schematic shows the balun as a Guanella 4:1 balun with the usual external link to one of the coaxial antenna sockets. (The label “Z balanced” is misleading, clearly one of the terminals is grounded and this is the unbalanced connection to the coax connector via a link. The antenna connects to the left hand terminals.)

Unlike almost all ATUs with an internal balun, this is a current balun (to their credit), but a 4:1 balun.

There are two aspects of balun behaviour that are of particular interest:

  • choking or common mode impedance; and
  • impedance transformation.

Continue reading MFJ-993B internal balun review

Shack entry / ATU configuration for my G5RV with tuned feeder

At MFJ-993B on my G5RV with tuned feeder I discussed first impressions of the replacement ATU.

This article documents the physical layout.

The antenna is a G5RV with tuned feeders (Varney 1958). The tuned feeder is home made two wire line using 2mm diameter copper spaced 50mm.


Above at the right, the open wire line terminates on a home made balun on the feed line entrance panel, see
Design / build project: Guanella 1:1 ‘tuner balun for HF’ – #4 for details of the balun. This is all under the building eaves, but it is waterproof… the area is regularly jetted with high pressure water to clean insects away. Continue reading Shack entry / ATU configuration for my G5RV with tuned feeder

Command adapter for JRC NFG-170 NFG-230 ATU

EA2BQH described an adapter to use a JRC NFG-170 / NFG-230 ATU.

The description is in Spanish, and a Google translation doesn’t help me much, his published HEX file for a PIC12C508A helps more.

Building the device and observing the output, it seems to have two input pins and when one is high OR the other is low, it sends a ASYNC command string at 1200Bd on its output pin. The command string is repeated every 2.5s if the input condition remains. This string appears to command the ATU to review / retune.

The 12C508A is a very old chip, still available, but in low cost form, an OTP.

I have written some code for a PIC12F510 from the ground up to do a similar thing as far as I can see, and built an adapter for testing by VK1EA.


My redesign uses different pins to the original to better cater for ISCP and to utilise weak pullup as much as feasible. IN1 is pin3 (GP4), IN2 is pin4 (GP3), TX is pin5 (GP2). IN1 OR /IN2 causes the adapter to send the configuration command. The output (TX) is open collector.



Above, a view of the adapter from chip side encapsulated in heatshrink and a patch of double sided adhesive foam to fix it in the ATU. Pin3 is wired to ground, Pin4 (IN2) is green, TX is yellow, ground is black and VDD (5V) is red. The TX pin is wired to pin 6 of the opto isolatorC next to the input terminal block TB1 on the ATU. (It may be possible to cut a track and insert the module after the opto isolator. Continue reading Command adapter for JRC NFG-170 NFG-230 ATU