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All about Transmission lines

Kenwood Antenna Tuner AT-230.

Coupling the transceiver to the line (IV)

Before going in emission there are still two circuits to tune, the coupling between the transmitter and the line, and the coupling between the line and the antenna.

In the field, in using a feed line the transmitter does not "sees" directly the antenna constituting the load, but rather the input impedance of the line. In other words, at stricto senso an antenna tuner does not tune the antenna but transforms its impedance to match the one of the transceiver or receiver.

We have seen previoulsy that the antenna impedance is determined by the characteristic impedance of the line (Zo), its length and the antenna impedance.

In practice, even if the antenna impedance can be unkown from the user, with the characteristic impedance on the line it will determine the standing-wave ratio. The SWR is thus with Zo the main parameters that will infuence the ouput power of the transmitter.

As most transceivers deliver their full power into 50-75 Ω, and that the SWR on the line is dictated by the antenna system used, a matching circuit is required in-between to match the 50-75 Ω to the actual input impedance of the line. Such a circuit is called a matching network like the famous L network or the Universal Transmatch.

This coupling circuit is mainly used when the feed line displays a high impedance like an open-wire and is usually not necessary when a coaxial line is used since the SWR is low enough to be adjusted by the tansmitter antenna tuner.

Basically matching circuits use either fixed-value components (like a L network) but that requires to know with accuracy the actual line-input impedance or less restricting, the circuit is arranged such a way that the matching is done with inductive coupling. This last solution takes advantage of a load resistance, another one that is seen by the power source offering a impedance similar to the first with, in-between, L and C components forming a resonant circuit capable of being tuned to the working frequency.

The coupling between both coils is adjustable in order to transform if necessary impedance over wide limits. For information, the coefficient of coupling, k, is equals to 1/√>Q.

An example of parallel-tuned coupling tank used to adapt the input impedance between the transmitter and the line. In this example the line is purely resistive.

Knowing that in most matching circuits the coupling between the two coils is fixed, Q is adjusted to attain the match. In the previous schematic, Q is adjusted in the circuit L1-C1-R1, and is equal to R1 divided by the reactance of C1 (assuming that L1-C1 is tuned on the working frequency). This circuit is suitable to support relatively high values of the load resistance R1 up to several kΩ. Conversely, a series-tuned circuit is suitable for very low value of load resistance (1-100 Ω).

Our explanation consider that the input impedance of our transmission line is resistive. In the field this is rarely the case and the line is as reactive as resistive or almost. We have thus to modify the line model for a more conform circuit made of a resistance placed in parallel with a capacitive reactance (a capacitor). In most cases, if the reactance of the line imput impedance is capacitive, the resonance can be maintained in adjusting C1 and the Q-factor will not change. But if the reactance is inductive, the L/C ratio changes, but ordinary L1 is not adjustable and from then on the Q increases. From this detuning high currents might flow in the coupling circuit and drastically reduce the efficiency of the system. It can even result in power losses for Q over 10 if you use low quality coils.

If the ratio of reactance to resistance is unfavorable, we can say that the Q of the line input impedance is unfavorable too and this ratio need to be compensated. As Q is a function of the line length and SWR, we need to supply external reactance opposed to value of the line reactance. Usually the coupling circuit is able to make this adjustment. In the worst case, if the Q becomes too high to be adjusted the coil used in the matching network can heat and thus lost its characteristics.

In practice, the adjustment consists is finding the proper settings for the taps on L1 or even using the proper settings of capacitance in Transmatch circuits. The best solution stays however to find the correct adjustment in using a SWR-meter called a "SWR bridge" between the transmitter and the matching circuit.

Balun coils

Matching impedances can also be done using balun coils. There are of two types : air-core balun and toroidal transformer balun. 

Air-core baluns are made of a bifilar winding with a air core. When considered as a pair of parallel conductors, such a balun is equivalent to a transmission line. When a voltage is applied between the two terminals at one end of the winding, the parallel conductors have a characteristic impedance that depends on their diameter and spacing. For short, this arrangement working in parallel, the total resistance toward the antenna is one-fourth of the one of the line. This 4:1 ratio means that such a balancing circuit is mainly used to match a ladder line of 300 Ω to a 75 Ω coaxial.

Different types of toroid-core transformers

In practice this design is no more used because it is complicated due to coupling between turns, and it is bulky, its enclosure measuring about 25 cm a side to handle 250W. So amateurs prefer using toroidal cores that are easily four times smaller and easy to made.

Typically ferrite toroidal-core baluns have bandwidths of 10 to 1 in order to cover frequencies from 3 to 30 MHz and constructed such a way that they are able to handle over 1 kW. To build a broad-band balun transformer able to sustain high power, bifilar windings are recommended for balun. Use for example a Ferramic Q1 toroidal core of 63 mm (2.5") outer diameter, with 17 mm (.5") cross section wound with No.14 Formex copper wire, seven turns per windings for a permeability of 125. Place it in a small enclosure 70 mm wide (3") on a piece of phenolic insulating board epoxy cemented to prevent short-circuiting and connect it to two terminals and an SO-239 plug. Your toroidal transformer is ready.

Coupling the line to the antenna

At last ! Since the first page of this discussion we have considered the antenna as an abstract "load" displaying some resistance or reactance. First, we have to insist on the fact that any kind of transmission line can be used with any kind of antenna, at the condition to properly couple the two together. Then the transmission line is not the antenna : the antenna is considered as a load for the feed line.

To understand how operates a feed line in relation with an antenna, it is essential to know on what frequency range works the antenna and thus to calculate the standing-wave ratio on the line, its SWR.

There are in practice two methods of coupling a line to an antenna : the unmatched and the matched one.

The unmatched method consists in searching to operate in the most amateur bands as possible, with few considerations for the SWR. In this case the standing-wave ratio is secundary and often large (up to 12:1 using a 300 Ω line), and the input impedance of the line depends on several factors like the line length and the working frequency. Of course, in working this way the transmission line will not be "flat" and will lost quite a lot of power by radiation, up to exceed 90% on high frequencies. When this solution is well suited to the working frequency it is used by many unmatched wire antennas like FD4, Windom, Zeppelin, etc.

According what we told previously, these systems operating at a high SWR, the best solution is to use 300 Ω open-wire lines like a Twin-Lead or a ladder line. Usually in standard sizings, using a matched 300 Ω line such antennas can carry a current of 2A what corresponds to a power of 1.2 kW. When there are standing waves the safe power must be divided by the SWR. Therefore in a center-fed half-wave system, a ladder line is often restricted to power ouputs up to 250W or so.

In practically all designs of multi-band antennas, the point at which the transmission line is attached is fixed. The antenna length is resonant at some frequency in the lowest frequency band to be used, and the feed line is connected either to the center or to the end. 

Current and voltage distribution at the fundamental frequency. The feed line can be attached either at the end or at the center.

The current (I) and voltage (V) distribution along an antenna fed at both points respect the drawing displayed at right. With end feed, there is always a voltage loop at the feed point. From the current distribution it appears that in all cases this antenna operates as a true harmonic radiator.

With center feed, the feed point is always at a current loop on the fundamental frequency and all odd multiples of the fundamental. In this case the current and voltage distribution are identical with the distribution on a end-fed antenna. Therefore on odd multiples of the fundamental frequency, this antenna operates as a true harmonic antenna too.

On even multiples of the fundamental frequency the feed point with center feed is always at a voltage loop. The currents in both half-waves sections of the antenna are in the same phase, but with end feed the current in one half-wave segment is in reverse phase to the current flowing in the other part. This behaviour has not disadvantage but both design have different directional characteristics. The end-fed for example is required only when the antenna is operated on an even harmonic to obtain some directivity and when the operator want to work on more than one band.

 The center-fed arrangement is known as "two half-waves in phase" while the end-fed system is called a "one-wavelength antenna" or an antenna of the "second harmonic".

With end feed, the currents in the two line wires do not balance exactly and there is always some radiation escaping from the line. Therefore it is always best to feed the antenna at its center of symmetry.

With center-fed antenna, at the fundamental frequency and usual antenna heights, the antenna resistance is between 50-100 Ω, what using a open-wire line, gives an SWR of 300/100 or 5:1 at best. Knowing that the higher the multiple of the fundamental frequency the lower the resistance at a voltage loop, the SWR is expected to decrease on higher frequencies.

At last it is always assumed that the two conductors of a transmission line carry equal but opposite currents thoughout their length. This ideal condition is not always realized in practice due to variation in coupling between the antenna and the position of conductors and other sources (wires) of electromagnetic fields. In fact the the degree of coupling depends on the position of the conductor in respect to the antenna, with a minimum coupling (zero) when both wire systems are perpendicular (90°) at center. In this position the voltage induced by currents flowing in both segments of a symmetric antenna are balanced and cancel exactly because of they flow in opposite direction, displaying the same amplitude but with an opposite polarity.

The matched method for coupling a line to an antenna consists is matching perfectly the antenna impedance to the characteristic impedance of the line. This method will gives a very low SWR, below 1.5:1, less than 1/20th of the input power is reflected, and the input impedance will be purely resistive, regardless the line length. In other terms the line will be "flat" or at least its lost by radiation are considered as negligible. 

Working with a transmission line at a low SWR requires that the line be terminated output side, in a resistive load matching the characteristic impedance of the line as close as possible. To solve this problem there are two solutions : selecting a transmission line which characteristic impedance matches the antenna resistance or transforming the antenna impedance to a value matching the characteristic impedance of the line.

The first method is the easier to install and does not require complex constructions. It is used by most half-wave antennas center fed including the G5RV dipole in its multi-band version. Instead of developping in depth how operate such matched systems, using machted lines (e.g. ladder line) or direct matching (e.g. coaxial) I suggest you to read the pages dealing with the G5RV multi-band dipole on this site, adapted from an article published by his creator himself, Louis Varney.

The second method consisting in transforming the antenna impedance is required with all directive arrays. When placed about 1/2λ above ground, the driven element of a Yagi, a resonant dipole, shows an impedance of about 70 Ω. But once elements are added (a reflector and several directors or parasitic elements) the impedance at center of the dipole changes drastically and is usually as low as 20 Ω with some reactance. If we try to connect it directly to the feedline of 50 Ω, we will get a SWR on the transmission line of 2.5:1. Hence the necessity to transform this low impedance of the Yagi's driven element to match de 50 Ω characteristic impedance of the coaxial. Several techniques are available.

Quarter-wave transformer

It is well known that the impedance transforming properties of a quater-wave transmission line can be used for matching the antenna impedance (Zs) to the characteristic impedance of the line (Zo). The next formula has to be used :

Zo = √(ZrZs)

where Zr is the load resistance, the resistive impedance of the antenna placed at the end of the line.

That means that the factor limiting the matching impedances is the range of value for Zo physically realizable. This latter ranges approximately between 50-600 Ω. Using this method you can easily insert a matching section of λ/4 between your dipole and the transmission line if both offer a high impedance. This arrangement is known as a "Q" matching system.

Delta, T, Gamma and Omega match

We can also match a line to an antenna using a resonant circuit constituted of a coil and a capacitor. This arrangement is called a Delta matching system. When the center impedance of a half-wave dipole is too low to be matched with an open-wire, it is always possible to find, between two points of the antenna, a value of impedance that can be matched when a "fanned" section or delta is used toi couple the line and antenna. Working with usual dipoles sizings coupled to a 600 Ω line, the total distance between the ends of the delta are 0.120λ for frequencies below 30 MHz while the length of the delta is 0.150λ.

There is also the "T" matching system. To create the matching section we use a so-called folded dipole which secundary or folded segment is shorter than the antenna (40-60%). The T matching system is center fed and offers more flexibility in impedance ratio and is easier to build than a folded dipole when a parasitic element is used.

Each arm of the T conductor being much shorter than λ/4, it has inductive reactance. If the antenna is well resonant at the working frequency, the reactance can be tuned out either by shortening the antenna or by inserting a capacitance in series at the input terminals as display in the below graph.

Three methods to match the line to the antenna. From left to right, the delta matching system, the T matching system and the Omega match.

The Gamma arrangement is an unbalanced version of the T matching system. Except for the fact that the matching section is connected between the center and one side of the antenna, the same remarks as for the T system apply here also. The gamma match is well-known because it is used for decades to match coaxial cable to all-metal beams. Although many parameters determine the matching (as the driven element length, gamma rod length, rod diameter, spacing between rod and driven element, etc.) a few rules of thumb can be successfully applied. So for matching an array made of aluminium tubing to 52 Ω line, the length of the gamma rod should be 0.04-0.05λ with a diameter between 1/2-1/3 to that of the driven element, and a spacing of about 0.007λ or about 140 pF for work on the 20 m band.

At last the Omega match is a modified form of the gamma match. In addition to the series capacitor, a shunt capactor is used to cancel as much as the inductive reactance introduced by the gamma section. An additional variable capacitor is used to shorten the gamma rod or to get the matching when the driven element is resonant

Bandwidth, Q and SWR limits

By way of conclusion, tell a short word about the bandwidth in terms of SWR limits. Indeed if an antenna is well tuned at center of a band, a few hundreds kilohertz up or down, we usually observe an increasing of the SWR. If the antenna was purely resistive the SWR should not change but in the field no antenna displays an SWR as flat. Out of the antenna resonance region, the reactive component of the antenna impedance change, increasing quite rapidely the SWR. Being given that we can compare an antenna resonating at a frequency to a series-resonant circuit, we can define a Q-factor to measure the antenna's selectivity, just as the Q of an ordinary circuit measures its selectivity. The Q of an antenna is given by the next formula :

where X and R are the measured reactance and resistance at some frequency close to the resonant frequency, and n is the percentage difference expressed as a decimal, between the exact resonant frequency and the frequency at which X and R were measured (5%=0.05). For an ordinary half-wave dipole Q is ranging from 8 to 14 but can exceed 50 in parasitic arrays (Yagi) depending on the spacing and tuning.

For more information

Books

Many books have been published about radio systems and their circuits, the properties of antennas and other subjects related to RF designs. I suggest you to read the advertisings of your favorite ham magazine in which you will the list of their publications. Here is however a short list of books related to the subjects developped in these pages :

- ARRL Antenna Book

- ARRL Handbook for Radio Communciations, ARRL

- Smith Chart Calculation (PDF), ARRL

- The Smith Chart: An ‘Ancient’ Graphical Tool Still Vital in RF Design, Digi-Key

- XLZIZL, AC6LA

- Electronic Applications of the Smith Chart, ARRL

- winSmith 2.0 (incl. software for Windows, released in 1995), ARRL

- Reflections II - Transmissions Lines and Antennas, ARRL

- Radio-Electronic Transmission Fundamentals, ARRL

- The Antenna File, RSGB

- The Antenna Experimenter's Guide, RSGB

- Radio Communication Handbook, RSGB

Without to forget ham magazines like QST, CQ, QEX, and their european couterparts too numerous to be listed here.

About Smith chart, electrical tables and conversion units

- Smith Chart Calculator (Java software)

- Standard Solid Copper

- Metric conversion

- TranslatorsCafé.

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