## Antenna Couplers

Antenna Couplers/Aerial couplers/ATUs/Transmatches, call them what you will. Peter Chadwick G3RZP explains all.

**Antenna Couplers/Aerial couplers/ATUs/Transmatches, call them what you will. Peter Chadwick G3RZP explains all.**

Opinions vary about antenna couplers (or whatever you choose to call them), varying from my ‘antennas are resonant so I don’t need one’, which illustrates a degree of ignorance − because an antenna can be resonant and still lead to a very high SWR on the feeder – to ‘I always use one’. Another complication is the transceiver with a built-in automatic tuner, which may or may not be able to convert the impedance presented to it by the feeder into that which the transmitter wishes to see. A further (but not primary) reason for their use is with older transmitters (and some newer ones, especially from the US where the requirements are less stringent) in meeting the regulatory requirements regarding harmonics.

**Introduction**

The primary purpose of the coupler is make the impedance at the end of the feedline one that the transmitter wishes to see – usually 50Ω these days but 75Ω was fairly common in the 1950s and early 60s. This is often called ‘matching the transmitter’, with the implication that it is a Thévenin match, meaning that the load impedance is equal to and the complex conjugate of the source (transmitter) impedance. By complex conjugate, it is meant that the inductive and capacitive reactances of source and load cancel. Interestingly, **Hermann von Helmholtz** used the principle some 30 years before **Leon Thévenin** set forth the theorem in a clear manner. The question arises as to whether or not the transmitter is a sufficiently linear system for the principle to apply. It seems that most transmitters with a linear amplifier are, but transmitters with a Class C final stage generally are not.

A generalised equivalent series circuit of an antenna is shown in **Fig. 1**. It could be represented as the same basic components but with different values in parallel.

A resonant antenna is one where the L and C reactances are equal, while the resistor represents a number of resistances in series – these are the ‘radiation resistance’*,* which is the real part of the impedance measured at a current maximum and is the part that radiates the energy, the resistive loss in the antenna and end insulators, the induced loss caused by nearby RF absorbing objects such as close trees to a vertical and ground loss in the case of antennas fed against earth, such as verticals, inverted L and T antennas and random length wires fed against earth rather than those fed against a counterpoise, such as the W3EDP.

**Series and Parallel Equivalences**

At any one frequency, a resistance and reactance in series have a ‘dual’, that is a parallel resistance and reactance that, as far as measurements at that frequency are concerned, give exactly the same impedance. It is this duality that makes the analysis of coupler designs possible. The equations for this transformation are:

R_{s} = R_{p}/(1 + [R_{p}/X_{p}]^{2}) X_{s} = (R_{s}R_{p})/X_{p} (Equation 1)

R_{p} = R_{s}(1 + [X_{s}/R_{s}]^{2}) X_{p} = (R_{s}R_{p})/X_{s (}Equation 2)

where R_{s} and R_{p} are, respectively, the series and parallel resistances and X_{s} and X_{p }the corresponding reactances.

**The ‘L’ Network**

The simplest impedance transforming network is the L network, **Fig. 2**, requiring one capacitor and one inductor. To transform ‘any’ impedance to, for example, 50Ω, they need to be arranged in one or more ways.

The network in Fig. 2 transforms the resistance at the load into a higher resistance at the input. This is because the inductance in series with the resistance is equivalent to a different inductance with larger resistance in parallel, see **Fig. 3** and Equation 2.

The values of the inductance and resistance are such that the *Q* in both cases is the same – otherwise there would not be equivalence.

Having transformed the resistance to the required parallel resistance, the addition of a parallel capacitor causes resonance and the result is a purely resistive load presented to the RF source, **Fig. 4**.

In order to transform any impedance without needing an excessive range of values of inductance and capacitance, four different circuit arrangements are required − see Figs. 2 and **5a**, **b** and **c**.

The captions are somewhat simplified since each configuration has a fairly wide range of impedance transformation ability, capable of handling various amounts of inductive and capacitive loads. The actual boundaries of the impedances that can be transformed for each circuit configuration are best demonstrated by the use of Smith Charts, which is a topic beyond the scope of this article. For those interested, in this writer’s opinion, by far the best book on the subject is *Electronic Applications of the Smith Chart* by **Phillip H. Smith**, published by various US publishers over the years. Now (2018) it is apparently out of print and copies are selling for hundreds of pounds on the second-hand market but the local library may be able to obtain a copy on loan.

Notice that some networks have a series inductance and shunt capacitance. This means increased discrimination against frequencies above the working frequency (a Low Pass characteristic), which can help with obtaining the necessary harmonic suppression. The other − or ‘dual’ circuits – have a High Pass characteristic, which can be useful in those locations where there are strong broadcast stations present in the Long or Medium wavebands.

The general equations for determining the value of components in the L network are:

X_{1} = ±R_{1}√r-1 (Equation 3)

X_{2} = -/+rR_{1}/rR_{1}/Ö(r-1 (Equation 4)

Where r = R_{2}/R_{1} and r >1 (always)

It should be noted that the working *Q* of the L network, **Fig. 6**, is dependent on the impedance transformation ratio and that high values of working *Q* can prove to have higher losses – doubling the working *Q* doubles the current in an inductor or capacitor and so increases losses by a factor of four.

The photograph, **Fig. 7**, shows a remotely-controlled L-match tuner relay-switched between the 160 and 80m bands for a folded unipole vertical antenna having a high feedpoint impedance, over 1200Ω, with appreciable reactance and thus being required to handle high voltages and currents. Note that there is provision for local control for fault finding and testing. Mounted outdoors in a weatherproof GRP (Glass Reinforced Polyester) cabinet, it also contains a 47Ω metal-clad resistor screwed to the metal base plate and permanently dissipating some 12W to maintain a substantially condensation-free interior. The components were chosen to handle the high voltages and currents that can be present when feeding high-impedance, highly-reactive loads.

**Balanced Loads and L Networks**

When feeding a balanced load, one approach is to use a balun (**Bal**ance to **un**balance transformer) at the output of the L network. This can be unsatisfactory in that the balun is unlikely to be the correct impedance so may well be subject to excessive voltages or currents. The best approach is to use a current balun at the input of the network and a balanced network, as in **Fig. 8**.

**Pi and T networks**

By adding a third variable to transform the L network to a pi or T form, **Figs. 9a** and **b**, the matching range is considerably extended, and many commercial antenna couplers do this. However, with some load impedances, it is possible to adjust the variables such that large currents flow in the coupler circuit itself and very little in the desired load. This is especially so in the T. In general, it is best to have the capacitors at the largest capacity value that enables a low input VSWR to be obtained.

Again, it should be noted that the pi network has a lowpass transfer function, while the T network has a high-pass function. One use of pi networks is in the input circuit of a grounded grid valved linear amplifier. In a Class AB amplifier, the anode and cathode currents have an appreciable second harmonic component, approximately 6dB below the fundamental current. Especially with solid-state exciters, which may object to a load with a high SWR, the pi network has the advantage that the output capacitor of the pi can be connected between cathode and earth right at the valve holder. Where the network is band-switched, at least the capacitor for the highest frequency band can be placed there. Such networks are usually designed for a working *Q* of about two to three.

Whereas the working *Q* in an L network is determined by the impedance transformation ratio, in the case of the pi or T networks, the value of *Q* is another variable that can be chosen in the design stage. There are thus four variables – working *Q* and the physical values for the inductors and capacitors − these are, of course, interdependent.

**The Z Match**

The Z match first appeared in the US in the early 1950s. At the time, the use of the ‘multiband tank circuit’, **Fig. 10**, was popular. This was a circuit where one control covered all the HF bands.

The principle of the multiband tank circuit is simple. L1 with C1a and C1b in series tunes the HF bands, with L2 having little effect, while on the LF bands, L1 looks like a long lead connecting C1a and C1b in parallel. By correctly proportioning the components, there is a single control circuit that can tune 3.5 to 30MHz. One drawback is that when used as the tank circuit in a power amplifier stage, careful design is needed so that the resonant frequencies of the HF circuit do not coincide with the harmonics of the LF circuit. Multiband tank circuits of this sort were more popular in the US than the UK and were commercially available from National. This is the basis of the Z match tuner, **Fig. 11**.

L1 and L1a form an RF transformer with approximately a 1:1 ratio. Typical values for operation from 80 to 10m are for L1, five turns of 14SWG or 2mm wire, with L1 being 2.5in in diameter and L1a being 3in in diameter, mounted coaxially, with a turns spacing of about one wire diameter. L2 is also 2.5in diameter and consists of eight turns, again 14SWG or 2.0mm, with a turns spacing of one wire diameter. L2a is six turns of 3in diameter, again mounted coaxially with L2. C1 is about 250pF per section and C2 is 500pF.

Consider operation on higher frequency bands. The antenna impedance is transformed by the RF transformer to appear in series with L1, while C1a and C1b in series tune the circuit to somewhere near resonance. L2 effectively reduces to some extent the effective capacity of C1b and the inductive reactance across C1b is then converted into a low input resistance to the tuner by C2. On the lower frequency bands, L1 reduces the effective capacity of C1a and that, in parallel with C1b and the transformed impedance of the antenna with the inductance of L2, again produces an inductive impedance, which C2 again transforms to a low input resistance.

The working *Q* of the tuned circuits is dependent on the coupling factor of the RF transformers and the actual antenna impedance and is therefore not under the control of the operator. Certain antenna impedances can lead to very high values of working *Q*, leading to difficulties with coils on plastic formers melting and the capacitors flashing over.

One advantage of the Z match is the ability to provide a balanced output without the use of a balun and the difficulties that can entail. However, in the circuit as shown in Fig. 11, there is no DC connection to the antenna, which can lead to problems with static build up. This can be obviated by providing a centre tap on L1a and L2a, connected to earth preferably by an RF choke so that should the tap not be completely at the electrical centre of the coil, the balance is not disturbed.

**‘Aperiodic’ Coupling Units**

It seems that especially in the US but to a growing extent in Europe, there is reluctance, especially amongst newer operators, to make their own wire antennas, instead preferring to buy. Although trap dipoles have been sold for many years, there are now various end-fed antennas, often called ‘End Fed Half Wave’ or similar. One minor difficulty when applied to a multiband antenna is that the lengths for resonance on harmonics are slightly different. Many of these antennas are fed with UnUns (a shortened term for Unbalanced-to-Unbalanced transformer, in the same way that ‘balun’ is a contraction of Balanced-to-Unbalanced’ transformer). UnUns are generally wound on a ferrite or possibly iron dust core in order to obtain wideband performance. For a true end-fed half-wave antenna, the feedpoint impedance is very high – in the region of between 2,000 and 5,000Ω, depending on height above ground, wire size and so on. The efficiency of the UnUn at such transformation ratios can become questionable, especially because at such impedances, the effects of stray capacity cannot be ignored. However, if the feed impedance to the UnUn is low enough (typically a VSWR of less than 3:1), most built-in transceiver auto-tuners can provide a match. It would be very interesting to compare the current fed into the ‘End Fed Half Wave’ from the UnUn coupler as compared with a tuned coupler.

**Tuner Circuits with Controlled Working Q**

A tuner circuit with Controlled Working *Q, ***Fig. 12**, is a very effective coupler, in that the working *Q* is controlled by the position of the taps. The value of tuning capacitor is chosen to be approximately 1.5pF/metre of wavelength, giving a reactance of about 380Ω. If the taps are adjusted to obtain a working *Q* of about 10, this means that an antenna with a resistance of 3800Ω can be matched when connected to the top of the tuned circuit. Even higher resistance values can be matched if the working *Q* is allowed to rise.

A practical example of such a coupler is shown in the photo, **Fig. 13**. By dint of diving in scrap bins and attending a radio club junk sale, the total cost of the coupler in 1969 was under 5p. It covered the bands 80 to 10m and even 160m with an extra capacitor attached by crocodile clips. It worked well for powers up to about 150W but, at higher power, some impedances led to capacitor arcing.

The operation can be envisaged as a tuned autotransformer, with the antenna tapped down the coil until a reasonable working *Q* – say between 5 and 20 − is obtained. This can be judged by the ‘sharpness’ of the tuning for minimum SWR. The nearer to the ‘earthy’ end of the coil, the higher the working *Q* will be.

The tuned circuit at resonance looks like a pure resistance – the ‘dynamic resistance’, with a value of *Q*_{w}ωL where *Q*_{w} is the working *Q* and ωL is the reactance of the inductor. Tapping the antenna onto the circuit will reduce the working *Q*, while any reactance will be compensated by adjustment of the capacitor. Rather than adjusting the input tap, it is possible to link couple with a ‘swinging’ link, where the link is moved into and out of alignment with the axis of the coil or, alternatively, is rotated inside the coil, providing minimum coupling when its axis is at 90° to the axis of the coil.

A very effective alternative is to use a fixed link and a series capacitor, as in **Fig. 14**. For use in a nominal 50Ω system the link winding inductance should have a reactance of about 100Ω and the series variable capacitor have a maximum value of about 9pF/metre of operating wavelength. Tight coupling between the link and the main inductor is required. For example, with a 2.5in diameter main inductor, a 1.75in diameter link inductor is mounted inside it.

Adjustment of the couplers of Figs. 12 and 14 is done by starting with low power and the antenna disconnected. The input tap in Fig. 12 starts very low on the coil and similarly the series capacitor in Fig. 12 is set to about 3pF/metre. The tuning capacitor is then adjusted for a dip in input SWR, the antenna is tapped about one-third of the way up the coil from the ‘earthy’ end and the input tap or series capacitor adjusted in conjunction with the tuning capacitor for minimum VSWR. If the tuning capacitor tunes very sharply, then move the antenna tap further up the coil and readjust the tuning. If the tap is too low, then full power may cause arcing in the tuning capacitor and it is probably better to err on the side of tapping too far up the coil rather than too far down.

The balanced variety of the controlled *Q* coupler is shown in **Fig. 15**. It is possible to earth the centre of the two variable ganged capacitors rather than the centre tap of the coil but it is then desirable connect the centre tap of the coil to earth via an RF choke to provide a drain for static build up on the antenna.

Low load impedances may give problems with obtaining sufficient coupling because of leakage inductance. Under these circumstances, series tuning is desirable as in **Fig. 16**, although the problem of bleeding static charge to earth still exists.

A variant of this is shown in **Fig. 17**. It requires tight coupling between the link winding and the tuned inductors and the voltage across the single gang capacitor can be quite high at modest powers. It can be considered as a hybrid between the pi network and the series tuned circuit and, again, the antenna has no direct earth connection for bleeding off static charge.

**Components for Antenna Couplers**

The photograph, **Fig. 18**, shows typical components for high power antenna couplers and even these may not be able to handle power of, say, 100W at some frequencies. For example, a 16ft long fibreglass whip antenna on a frequency of 2182kHz (the maritime MF distress frequency) would typically look like about 50pF in series with 10Ω or an impedance of 1459Ω. Fed with 100W of RF, this would result in some 4.6kV at the antenna terminal. Admittedly, this can be considered an extreme case but two or three thousand volts for an input of 400W is not an excessive amount. This means that sharp bends in conductors and sharp points of joints should be avoided. Another situation in multiband couplers using ‘roller coaster’ variable inductors is whether or not the unused portion of the coil should be left open- or short-circuited. If it is shorted out, then on bands where most of the coil is in use, the shorted portion can have a large current induced in it, reducing the output and heating the coil. If it is left open-circuit, then on higher frequency bands, the unused portion of the coil can resonate with stray capacity at the frequency of operation and develop a high voltage, acting very much as Tesla coil. One way to partially get around the problem is to use a construction where the variable inductor consists of a tape wound on an insulating former while the unused portion is wound on a metal former that shorts it out. This technique was used by Marconi in the D11 and D13/NT201 transmitters as well as by Collins and Plessey but has the problem of stray capacity to earth, which in itself can lead to problems, especially where parasitic resonances fall on harmonics of the operating frequency.

The majority of automatic couplers us an L network, relay-switched, with a binary bank of capacitors such as 1, 2, 4, 8, 16, 32, 64 and 128pF, which gives a range of 255pF in 1pF steps. In practice, because of stray capacity in the relays, the step size is somewhat larger. For high powers, vacuum relays are required.

It is now getting much easier to measure the feed impedance of an antenna in terms of R ± jX and, from that measurement, design a coupling unit to provide optimum efficiency. But small antennas are always a problem and such techniques as using two whips in parallel on a vehicle or two inverted-L antennas on a small fishing vessel can significantly reduce the problems of high voltage and current and inefficiencies in coupling units.

*This article was featured in the October 2018 issue of Practical Wireless*