or Where to Place Your Impedance Matching Efforts

The array of combinations of antennas and feedlines can be bewildering. There are so many combinations and options for matching that tracking them all seems an impossible task. A few combinations-- like the standard dipole of Vee plus a 50-ohm coaxial feedline--seem to be inherently well matched to the transceiverþs 50-ohm input/output.

Most combinations, however, require some form of impedance matching network somewhere in the system. And so, once more, we must go back to basics and begin again. Where can we effect a good match for SWR and an efficient match for maximum power transfer and minimum power loss?

**The system that needs the match**: Ultimately, the system consists of three parts: the transceiver, the transmission line, and the antenna. The transceiver is normally a fixed part of the system, with a given input/output impedance that has been designed into the unit by the manufacturer.

At the other end of the line is the antenna. First, unless feedlines are unbalanced and act as part of the antenna, the antenna itself will radiate in just the same way, whatever feed and matching system is in use. Moreover, an antenna (and here we are talking mostly of center-fed horizontal wires) will convert to radiation all the rf electrical energy at its feedpoint after a few cycles (out of the millions per second). Third, resonance in an antenna is simply the condition of having no reactance, either inductive or capacitive. Resonance is a very narrow frequency phenomena, but one which occurs repetitively as one scans up the frequency spectrum. Note that resonance does not specify any particular resistive impedance, only zero reactance. Hence, feedpoint resistance can be higher or lower than the characteristic impedance of a proposed transmission line.

Between the antenna and the transceiver is the transmission line or lines. The characteristic impedance of a transmission line is always considered resistive. However, no feedline is perfect, and there is always a small amount of reactance. Moreover, although the characteristic impedance does not itself dissipate power as heat or some other form of energy, transmission lines do have small loss factors which do dissipate a bit of the energy.

Parallel transmission lines have the lowest losses, almost insignificant in the HF bands. Even with a fairly high SWR along the line, total losses may still be insignificant. Well-made coaxial cables have more significant losses. Transmission line losses increase with frequency. At 160 through 40 meters, cable losses may be low enough that the increase in loss due to SWR along the line may result in total losses that are still insignificant. However, on the upper HF bands, the same level of SWR may yield unacceptably high losses. For any installation, when losses reach the point of being unacceptably high is a judgment call.

**Where to effect a match**: Against the background of these system elements we can pose our basic question. If the impedance at the antenna feedpoint does not match the characteristic impedance of a transmission line, where can we effect a match? The answer is simple: anywhere between the antenna terminals and the transceiver terminals (output/input connector).

**At the antenna terminals**: If the resistive part of the antenna's impedance is close to that of our feedline, we can introduce for a given frequency reactances of equal magnitude but opposite type and present the feedline with a resistive impedance. We can also place a network at these terminals, not different in priciple from ATU networks, to achieve both a compensation for reactance and a transformation of resistance to the desired level. In fact, with some ingenuity, we might place the final amp of a rig at the antenna terminals, with remote signal and power feed, and eliminate all feedline losses.

Much more common are a variety of matching networks used to transform the antenna feedpoint impedance, whatever its value, to the characteristic impedance of the transmission line. Essentially, these networks consist of two varieties: transformers and L-C networks.

Transformers come in three general types. First is the broad-band inductively coupled transformer. Although not widely used today, such transformers are capable of 98-99% efficiency if the load is resistive and the turns ratio is correct. Second are the transmission-line transformers (which may also function as UNUNs or BALUNs). Transmission line transformers can be better than 99% efficient, if the load is resistive and the required transformation ratio matches the transformer design. No one has done as much work on these devices as Jerry Sevick, W2FMI. Any one of his books is a good starting point for understanding these devices. Both of these methods of impedance transformation are generally used with coaxial cable feedlines and with antenna impedances that are not too distant (say, 4:1) from the feedline characteristic impedance, although some larger transformation ratios (say, up to 9:1) are possible.

Transformers may also be in the form of transmission line lengths that vary their characteristic impedance continuously to change from one impedance to another. The delta and Tee matches (when used without capacitors) are versions of this type of transformation.

LC networks consist of Pis, Tees, and Ls, the same array of networks that we often use in ATUs. When used at the antenna terminals, they most commonly transform low antenna impedances up to the characteristic impedance of a coaxial cable. The well-known beta match is actually a form of L-circuit used to transform a lower antenna impedance to a higher value of transmission line impedance. L-circuits require both a series reactance and a shunt or parallel reactance. In most cases, the shunt reactance is inductive, either in the form of a coil or in the form of a shorted transmission line stub (or hairpin). The invisible series capacitive reactance is a part of the antenna feedpoint impedance and thus does away with the need for a second physical component.

The gamma and similar matches use another principle: intercepting the antenna element at a point where a match may be made and the reactance tuned out by a series capacitor. A Tee with a series capacitor becomes a matching network of this form.

Although none of the matching systems is perfectly efficient, system losses are often least when the match is effected at the antenna. However, LC matching networks placed at the antenna terminals often apply only to monoband antennas. On the other hand, transformers are wide-band devices; however, they are not without limits.

**At the station (transmitter/receiver location)**: This location is generally chosen for convenience, not for best efficiency. And this is where ATU networks and inductively coupled circuits come into play. They have losses, but when well designed with high-Q components and adjusted for maximum efficiency settings, losses can be quite low--a few percent for most loads presented by incoming feedlines. When ATUs use low Q (lossy) components, are set to inefficient settings (sometimes by poor designs that only permit inefficient settings), use poor physical layouts that create stray inductances and capacitances, etc., losses can be considerable.

Between the ATU and the antenna terminals, standard practice is to use feedline with the lowest loss, which usually means 300- 450- or 600-ohm parallel feedline. Losses multiply with SWR on the line; hence a low starting loss figure provides the most efficient power transfer. With any load.

The ATU-parallel feedline system of matching the load to the transceiver is most used with multiband antennas, such as the 135 doublet. It is also used where the width of the band is a high percentage of the operating frequency, such as 160 meters. On such bands, different ATU settings may be required across the band.

Network ATUs, such as C-L-C Tees, L-C-L Tees, and Pis, are ordinarily designed as single-ended or unbalanced networks. Most are designed for use with coaxial cables, with balanced transmission line use an afterthought. The afterthought is a 4:1 balun, often of dubious design. The efficiency of such a balun in the presence of highly reactive loads presented by the feedline is often questionable. Moreover, the use of a 4:! Impedance transformation presumes that the load will be much higher than 50 ohms. With a random length of parallel transmission line to the antenna, it is very likely that the load will be less than 100 ohms, which the balun than transforms downward to something far less than 50 ohms. Although network ATUs may sometimes effect an efficient match with parallel transmission lines, just as often they are far from maximally efficient.

More suited to parallel transmission lines are inductively-coupled antenna tuners, such as the Johnson Match Box series. Perhaps in the not-to-distant future, both finished and kit models will once more become available. In the interim, home brewing will have to do. A basic tutorial on these designs is available in a 5-part series published in QRP Quarterly.

**Anywhere along the line**: Technically, although the ATU is installed near the transceiver--or even inside the same case--it is never quite at the exact input-output point of the transceiver. Thus, it ordinarily qualifies as a matching unit that is installed somewhere along the transmission line. Actually, every ATU is an impedance conversion device to permit changing from one value of transmission line characteristic impedance to another value of transmission line characteristic impedance. Of course, we can effect that conversion anywhere along the transmission line we choose, so long as the impedance at that point is suited to both the amount of conversion and the technique of conversion we try to use.

When we choose to place the impedance transformation somewhere along the transmission line, we have to pay attention to losses from the point of match back to the antenna. Most of the techniques apply to coaxial cable installations, where basic cable losses, multiplied by significant SWR levels, may create unacceptably large total losses, especially on upper HF bands. Hence, a technique useful for 160-40 meters may not be acceptable on 20-10 meters. Of the many techniques and rationales, we can cite only a few examples to illustrate this idea.

*Stub matching*: For any frequency and antenna feedpoint antenna impedance and feedline characteristic impedance, there will usually be points where one may introduce series or parallel reactances to achieve a resistive impedance of some desired level. This technique is widely useful, especially for high-impedance antennas, such as the extended double Zepp. However, the technique is not absolutely universal, since certain lines and antenna impedances will not together reach a resistive value matching a desired line. When the reactance component is a parallel-connected device, it is usually called stub matching, since common practice in pre-WW II days was to use a shorted or open length of feedline as the reactance rather than using a lumped component (capacitor or inductor). HAMCALC has a program for calculating stubs for any feedpoint impedance and proposed feedline.

*Series matching*: The math of series matching, that is, using feedline lengths as series sections, was worked out by Regier and appears in the IEEE proceeding for 1970 and Electronic Engineering for 1973, as well as QST for July 1978 (and subsequent editions of the Antenna Book). As with stubs, there are antenna impedance-feedline characteristic impedance combinations that do not permit a match, but most cases will work. These techniques are--from the perspective of convenience--best suited to monoband antennas, although one might develop switching or clipping techniques for multiband use of an antenna.

*Delayed series matching*: When the antenna feedpoint impedance is higher than the characteristic impedance of the proposed feedline, we often insert a quarter wavelength section of an intermediate impedance to effect a match. Thus, for impedances in the 100-ohm range, a 75- ohm quarter wavelength section will often transform the impedance to a very good match for 50-ohm coaxial cable.

However, we may insert between the antenna and the quarter wavelength section a length of 50-ohm coax that is either « wavelength or a multiple of « wavelength long. At the design frequency, the impedance is the same at each end of the 50-ohm line. Below the design frequency, the 50-ohm length is a bit short, resulting in a higher impedance at the matching section end than at the antenna terminals for the low end of the band. Above the design frequency, the 50-ohm line length is long, again resulting in an impedance higher than that at the antenna terminals for that end of the band.

The result is a set of impedances across the band which the 75-ohm quarter wavelength section can transform into values closer to 50 ohms. The effect is to provide a wider operating bandwidth. Remember, however, that the antenna feedpoint impedance has not changed; hence, the SWR relative to the antenna-to-matching section run of 50-ohm coax has not changed. Hence, this technique is usually confined to the lower HF bands where the SWR loss multiplier for the antenna-to-matching section 50-ohm cable does not yield unacceptable total losses along the line.

*50-75-50-Ohm system*s: It is not necessary to restrict our systems to a single impedance transformation. The strongest and lowest-loss coaxial cables available at reasonable cost are often 75-ohm hardlines. When towers and antennas are distant from the station, these cables can cut losses. However, commercially-made antennas and transceivers are 50-ohm devices. Many operators insert high- efficiency transmission-line transformers at each end of the line to go from 50 to 75 and back to 50 ohms again.

**So, what have we accomplished?** In many high power applications, especially where radiated power from the antenna is the user's critical question, efficiency of the matching network may not be considered significant, since lost power (so long as it does not harm the components) can be made up by adding power to the system. For QRPers, there is no such luxury. Hence, it is very useful to learn all we can of ways to improve the efficiency of our matches--wherever along the line we place them.

This survey of possibilities is not to provide any absolute rules (or even rules of thumb). Instead, it is intended to put some of the chief methods and placements of impedance-matching techniques into some perspective.

But this survey is just a start. Some future episodes in this series may be devoted to individual matching techniques mentioned along the way in this brief account. However, excellent information is available from many sources--especially from antenna handbooks. Although it is very useful to work hard at understanding the math involved in impedance transformation techniques, most of the drudgery of making complex calculations can be side-stepped with simple BASIC utility programs, such as those in HAMCALC. We can never learn too much.

*Updated 03-17-2001. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.*