#1: "An Antenna Tuner Does Absolutely Nothing Except Make The Transmitter Happy."

by Cecil Moore, www.W5DXP.com, Rev. 1.5, Jan 9, 2014

Wikipedia's Take on Old Wives' Tales

Introduction

Judging from the number of Old Wives' Tales that abound in amateur radio, there must be more old wives in amateur radio than can be found in The Call Book. The author hears this one at least twice a week on some ham radio newsgroup. This article is an attempt to debunk that myth using the most simple of examples hopefully that everyone can understand. This will be the first in a series of "Old Wives' Tales" articles that will be compiled into chapters on the author's web page.

Let's not quibble over whether a transmitter is capable of human-like feelings or not. What is meant by "making the transmitter happy" is the concept that an antenna tuner presents a resistive load of 50 ohms to a transmitter designed to drive a 50 ohm load, usually of the solid-state variety. The author conceeds the idea that an antenna tuner "makes the transmitter happy". The question remains: Is "making the transmitter happy" all that an antenna tuner does or does the antenna tuner also have an effect at the antenna, i.e. does that 50 ohm Z0-match that "makes the transmitter happy" also have a system-wide effect that makes the entire system, including the antenna, happy? (If a transmitter can be happy, why can't an antenna be happy?)

We are going to look at some simple examples. The source will be a voltage source, (VS), with an associated source impedance of the complex form (RS ± jXS). Any transmission line will be one wavelength long and lossless (1WL T-Line). The load will represent an antenna feedpoint impedance of the complex form (RL ± jXL). We will represent such systems using one-line diagrams of the form:

(VS)--(RS ± jXS)----------(RL ± jXL)

The Maximum Power Transfer Theorem

The maximum power transfer theorem was first used with DC circuits. Given a source and a load, the theorem says that: Maximum power transfer will occur if the source resistance is equal to the load resistance. This is probably the origin of the myth that, for maximum power transfer to occur, an antenna must present a purely resistive, e.g. 50 ohm impedance, i.e. must be resonant.

When AC circuit theory was developed, it was apparent that the resulting reactive impedances would require the DC maximum power transfer theorem to be updated. That's when the conjugate matching theorem came into existence. Given an AC circuit: Maximum power transfer will occur if the source impedance is equal to the conjugate of the load impedance. Note that the conjugate of 100+j100 ohms is 100-j100 ohms and the conjugate of 50-j200 ohms is 50+j200 ohms. Both the above theorems apply to lumped-circuits.

When networks that are an appreciable percentage of a wavelength were introduced, it again became apparent that the maximum power transfer theorem needed to be updated since a transmission line with reflections is capable of transforming the complex load impedance to an infinite number of other complex impedances and also to some purely resistive impedances. Let's take a look at how the maximum power transfer theorem can be updated to handle distributed networks. We can do that by looking at one characteristic of the maximum power transfer theorem for an AC circuit represented by the one-line diagram introduced above with point 'x' added.

(VS)--(RS ± jXS)-----x-----(RL ± jXL)

The voltage source, (VS), just by itself is defined as having a zero impedance. So if we measure the impedance looking back from point 'x' toward the source, we will measure the source impedance, (RS ± jXS). If we measure the load impedance looking toward the load from point 'x', we will measure the load impedance, (RL ± jXL). So another way of stating the maximum power transfer theorem for an AC circuit is: From a point between the source and the load, if the impedance looking back toward the source is equal to the conjugate of the impedance looking toward the load, then maximum transfer of power will occur. That is also the definition of a "conjugate match".

When the maximum power transfer theorem is applied to a lumped-circuit, it is assumed that the only losses in the circuit are losses in the source resistance and the load resistance. If we adopt that same assumption for distributed networks, we can now take the liberty to state the maximum power transfer theorem for a typical amateur radio antenna system (assuming lossless transmission lines.)

(VS)--(RS � jXS)-----Transmission-Line-----(RL � jXL)

A maximum transfer of power will occur in an antenna system when, at any point on the lossless transmission line, the impedance looking back toward the source is equal to the conjugate of the impedance looking toward the load.

Once again, the above statement can be considered as a necessary and sufficient condition to define a conjugate match.

Numbered Step-By-Step Examples

For the remainder of this article, we will assume that VS=100v, RS=50 ohms, and XS=0 ohms, i.e. a standard voltage source and RL=50 ohms. Also remember that all transmission lines are lossless.

So here we have a matched system with 50 watts delivered to the load which is the maximum transfer of power. What happens to the power delivered to the load if we mismatch the system by adding -j500 ohms of capacitive reactance to the load?

Only 1.92 watts are delivered to the load for example (2). The current through the load resistor is 0.196a and the voltage across the load resistor is 9.8 volts. What can we do to change those conditions at the load? How about adding a loading coil with a reactance of +j500 ohms?

So the loading coil reactance of +j500 ohms neutralizes the load reactance of -j500 ohms and, once again, as in (1) above the maximum power of 50 watts is delivered to the load.

Question: In a lossless system, does the loading coil installed at the source cause the same effects at the load (antenna) as it did when it was located at the load (antenna), i.e. do the same conditions exist at the load in example (4) as in example (3)?

What if we put the "loading coil" in a box at the source and call it an "antenna tuner"?

Question: In a lossless system, does an antenna tuner have considerable effect at the antenna or does it "do absolutely nothing except make the transmitter happy"?

Note that, no matter where the loading coil is located above, in a lossless system, it has the same effect of establishing a system-wide conjugate match thus ensuring maximum power transfer. If we calculate the impedance looking back down the transmission line from the load, the result will be the conjugate of the feedpoint impedance in both examples (3) and (4) above. The effect on the antenna (load) is the same whether the loading coil is located at the antenna or at the source (shack).

Now we are ready for the next logical step from lossless systems to systems with losses where we know that lossless transmission lines and system-wide conjugate matches are impossible.

Given: In a lossless system, an antenna tuner has the same effect whether it is located at the load or source.

Question: In a system with losses, does an antenna tuner located at the source have SOME effect at the load - not the same effect as in a lossless system, but ANY effect at all at the load? Does adding real-world losses to a lossless system cause the antenna tuner in the shack to have ZERO effect at the antenna feedpoint?

Hopefully by now, everyone recognizes those questions as rhetorical

It seems to this author that since a tuner has the SAME effect no matter where it is located in a lossless system, and since a tuner must therefore necessarily have at least SOME effect no matter where it is located in a low-loss system, that an old wives' tale has bit the dust. In a low-loss antenna system, an antenna tuner in the shack indeed does have an effect on the power radiated by the antenna at the antenna.

One can see for oneself the effect that an antenna tuner has at the antenna. After adjusting the antenna tuner for a match, disconnect the transmitter and install a dummy load on the tuner input. (That step can be eliminated if the receiver in the transceiver has a 50 ohm input impedance.) At the antenna feedpoint, disconnect the feedline and connect it to an antenna analyzer. In a low-loss system, the impedance will be somewhat close to the conjugate of the antenna feedpoint impedance. Let's call it a "near-conjugate match" if the impedances are within 10% of an ideal conjugate match. Have someone twist the knobs on the tuner and observe the impedance change at the antenna. Then who can truthfully say that an antenna tuner has "absolutely no effect at the antenna"?

A grid dip meter can be used to verify that when the tuner is adjusted to "make the transmitter happy", i.e. adjusted for a 50 ohm Z0-match at the tuner input, the result for a low-loss system is that the entire antenna system is resonant, according to The IEEE Dictionary definition of "resonant". When the tuner has been properly adjusted, disconnect the transmitter and attach a 50 ohm dummy load to the tuner input. Then take the grid dip meter and couple it to the antenna, e.g. with a loop of wire in one of the elements. The grid dip meter will dip at a resonant frequency that is somewhat close to the frequency to which the transmitter was tuned when the antenna tuner was adjusted. It doesn't matter where the grid dip meter is coupled to the antenna system - it will indicate resonance close to that single frequency from one end of the antenna system to the other.

For the sake of simplicity in the calculations, transmission line losses, which make the calculations much more complex, have not been taken into account. Failure to include losses in the calculations does not negate the concepts presented in this article. Note that the conjugate matching theorem applies only to lossless networks and can only come close (assume within 10%) for low-loss networks. Assume that if the impedance is not within 10% of a conjugate match, that the system doesn't qualify as a "low-loss" system.

Here is an example of a near-conjugately matched system using the transmission line loss calculator located at:

Assume an antenna with a feedpoint impedance of 102-j480 ohms used on 14.2 MHz. Feed the antenna with 63.75 feet of "Generic 600 ohm Open" feedline from the menu of transmission lines. The impedance looking into the transmission line at the shack end will be 105.9-j471.6 ohms according to the calculator. If we want to resonate the system at the antenna feedpoint, we install a +j480 ohm loading coil. If we want to resonate the system at the shack end, we install a +j471.6 ohm loading coil. That's a ~2% difference in impedances. In fact, the same loading coil will work pretty well at both ends. It's certainly not a perfect result but this author doesn't require or expect perfection from the real world.

The following conclusion seems obvious: