ANTENNAS, FEEDERS, SWR AND MATCHING

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This article is slanted towards the newcomers rather than the old hands, so please forgive any teaching of granny to suck eggs.  Despite the huge amount that has been written on the subject, there still appear to be a large number of misconceptions and "old wives tales" surrounding antennas and feeders.

I have omitted some subjects completely, e.g. detailed discussion of Maxwell's Equations, and dealt with others in a superficial manner.  There is just not sufficient space in an article of this type to deal with any of the aspects in great detail.  I have kept the maths to a minimum as it is not necessary to calculate anything to appreciate the basic principles involved but it is essential if an actual design exercise is to be carried out.  Even then, the algebra involved is that which I learned in the fourth or fifth year at school, so it is not very taxing.  Note that all logarithms are common logs (logs to base 10).

We all have our own pet theories, some based on book learning, some on personal experience and some on intuition.  This article is biased towards HF antennas, but the basic theory applies equally well to VHF and UHF types, although some of the techniques used at HF do not lend themselves to VHF and vice versa.

Antennas

There are dozens of different types of antenna and it is beyond the scope of this article to describe any of them in detail but there are a few general points to note.

According to Maxwell, an electric field cannot change without creating a magnetic field, and a magnetic field cannot change without creating an electric field.  In other words, assuming one or other field could exist as a stationary entity, as soon as it moved, the other field would be created.  Electromagnetic waves have both electric (E) and magnetic (H) components, and propagate as "ripples in the fabric of our space-time continuum", the words of William E. Payne, N4YWK, not me.  The E and H components are 90 degrees apart in the space domain but in phase in the time domain as shown in the diagram below:-

Loops of wire are often used as antennas to interact with and detect only the magnetic component of the electromagnetic wave.  I wonder if anyone followed the ongoing saga in RADCOM and elsewhere, about the magnetic loop theories of Professor Mike Underhill, G3LHZ?  Much of the argument seems to be about semantics rather than antenna theory.  The two sides do not appear to be able to agree what is actually meant by antenna efficiency, radiation resistance and similar basic terminology, let alone be able to debate the theory rationally.  I have yet to be convinced that either party is entirely correct or completely wrong.  I suspect that the truth lies somewhere in the middle ground.

Antennas do not need to be self-resonant on the frequency in use but their efficiency and ease of matching is often improved if they are.  VHF and UHF antennas are nearly always self-resonant or include a resonant driver element as in the case of a resonant dipole at the focus of a parabolic dish.

When the transmitter is located in an upstairs room and an end fed wire is being used, there will always be RF on the case of the transmitter or ATU, regardless of how thick the earth lead is.  It is a popular misconception that the impedance of the earth connection must be as low as possible and this will prevent the dreaded "RF in the shack".  If the antenna is 90ft long and the earth connection is 10ft long, the actual antenna length is 100ft and it will be fed at a point 10% along its length.

The only effective answer is to have an ATU at ground level and feed the RF from the transmitter to the ATU via coaxial or open wire line.  Obviously, the ATU would need to be automatic or be remotely controlled.  Under these conditions, a good low impedance earth connection to the transmitter would be advantageous in reducing RF in the shack as this earth lead is not part of the antenna system.  This is the system that I use to feed my Carolina Windom.

The manufacturer of the Carolina Windom recommends the use of specific lengths of coaxial feeder to connect the ATU, which, they say, should be located in the shack, to the bottom end of the vertical section of the antenna.  This arrangement is not good practice.  If the length of the feeder affects the match, it is acting as an impedance transformer and its effect will vary with frequency.  Since an ATU is still necessary, it implies that the impedance "looking into" the feeder is not 50ohms.

It is the current flowing in an antenna that radiates the signal, not the voltage that may exist on it.  However, voltage nodes can be a problem if they are close to telephone wires, TV downleads or mains wiring, as there could be capacitive coupling.  It is important to arrange for current nodes to be as high above ground as possible and away from surrounding objects, whilst keeping voltage nodes as close to true ground as possible.

The open end remote from the driven point of any antenna that is fed and tuned against ground will always be a voltage node, whether the antenna is resonant or not.  This is because an antenna is an electrical circuit and current must have some medium to flow through.  The open end of an antenna is, by definition, insulated and therefore current cannot flow.  It is obvious that when power is being applied to the antenna, there will always be a voltage node at the open end of the antenna.  Before somebody mentions the "Grounded Marconi" antenna, where current flows in the remote end, I would point out that the end is not open but is connected to ground, allowing current to flow.

Any electrical circuit must have both an outward and return path.  With a DC circuit or a mains AC circuit, this is obvious and the current flows into the load along one connection and returns from the load via the other connection.  If 10A goes in, then 10A must come out (Kirchoff's Law).  Consider a voltage of 100V connected across a resistance of 10 ohms.  By Ohms Law a current of 10A will flow and 1000W will be dissipated by the resistance.  No current is "lost" in the circuit as the same current leaves the circuit as enters it.  However, the ingoing current is at a relative potential of 100V, whereas the outgoing current is at a relative potential of 0V.  Hence it is the voltage that has been "lost", not the current, when producing the power dissipated in the resistance.

The same argument applies to antennas but it is more difficult to visualise, especially with end fed antennas.  All antennas are two terminal devices where current flows from the generator (transmitter) into one terminal and returns to the generator via the other terminal.  The radiated power is the power "dissipated" by the radiation resistance of the antenna, which forms the load.  With dipoles or doublets, this is easy to imagine, as there are obviously two connections to the antenna system, with the radiation resistance located at the far end of the feeder.  It becomes more difficult to visualise what is happening in the case of end fed wires and when the antenna is not resonant and therefore there will be reactive components to the feed current which, in turn, give rise to reactive components of voltage.  However, the basic concept remains the same.

Let us consider an end fed quarter wavelength antenna tuned against ground.  In a perfect world, the antenna will present a low, purely resistive, load of about 50ohms relative to ground.  But, you might say, there is only one terminal, so how does the current flow back to the transmitter?  The answer is, of course, the ground connection, which forms the second terminal of the antenna system.  Whatever current flows into the antenna wire, will return to the transmitter via the ground connection, which should be a dedicated ground stake or mat but will probably also include the mains earthing system.  Note that the current entering the antenna wire is not mysteriously lost into the ether.  It is the power dissipated in the radiation resistance that is radiated.

The case of dipoles and doublets is more straightforward, as there are two antenna terminals, with current flowing into one and returning via the other.  If coaxial cable is used to feed such an inherently balanced antenna, the return current will flow on the outside of the coaxial cable's shield, whereas it should ideally flow on the inside of the shield.  When current flows on the outside of the shield, instead of the inside, cancellation of the magnetic fields resulting from the outgoing and return currents is impaired and a degree of feeder radiation will result.  In many cases, this is of no consequence, but it is not aesthetically pleasing and could give rise to TVI and similar problems.

This may be a suitable point to mention baluns, although I will refer to them again later.  The term "balun" is derived from the words "balanced" and "unbalanced" and describes a device that converts a balanced line to an unbalanced line or vice versa and may also change the impedance at the same time, depending on the type.  Baluns only perform correctly when presented with resistive loads.  When presented with reactive loads, the reactive component is also transformed, often with unpredictable results.

Baluns are used to ensure that the balanced currents at the actual antenna terminals are transformed into the unbalanced currents required for coaxial cables.  A radio antenna is the device that actually radiates or receives a radio signal.

Any conductor, including the proverbial "piece of wet string" or the "straightened paper clip", will radiate all the power absorbed by its radiation resistance but obviously some are a great deal more efficient than others.  By "efficient" I mean how big a signal does it radiate, rather than the power-in-against-power-out-plus-heat mathematical calculation.  The problem is actually getting the RF into the radiation resistance.

One concept is that an antenna can be regarded as a device to match the feeder impedance to the impedance of free space.  The characteristic impedance of free space, also called the Zo of free space, is an expression of the relationship between the electric-field and magnetic-field intensities in an electromagnetic field (EM field) propagating through a vacuum.  The Zo of free space, like characteristic impedance in general, is expressed in ohms, and is theoretically independent of wavelength.  It is considered to be a physical constant.   Mathematically, the Zo of free space is equal to the square root of the ratio of the permeability of free space in henrys per meter (H/m) to the permittivity of free space in farads per meter (F/m).

The exact value of the Zo of free space is 120pi ohms or approximately 377ohms, where pi is the ratio of the circumference of a circle to its diameter.  The implication of this is that a dipole with a nominal feed impedance of 75ohms is in fact acting as an impedance matching transformer with a ratio of 5:1.  This is an academically interesting, but not very useful concept as it does not differentiate between radiated power and losses.

Another, more useful, concept is that an antenna is a load that absorbs the energy fed to it and then dissipates it, not as heat but as radiation.  The load resistance that is presented to the feeder by an antenna is the radiation resistance of the antenna.  In the MKS system, the radiation resistance of a straight antenna of length l is:

Before we go any further, note that the transmitting and receiving characteristics of antennas are reciprocal.  In this article, I will describe points by considering either the transmitting condition or the receiving condition depending upon which illustrates the point best.  Also, I assume perfect lossless systems unless otherwise stated.

Calculations show that a quarter wavelength inverted "L" antenna tuned against ground will exhibit an impedance of:

Note that the feed impedance of a quarter wave vertical with radials is somewhat lower and only approaches this figure when the radials are sloped down at about 42° to the horizontal.

In the real world, the load presented by the antenna is a combination of radiation resistance, resistive losses in the antenna and any coupled objects in the near field, ground losses, and a component related to return loss.  The only useful power is that absorbed by the radiation resistance.  Power dissipated in the other components is merely heat.  Consider an antenna (actually 1/6 wavelength long) with a radiation resistance of 20ohms that is tuned against ground.  If the ground resistance is 30ohms, the apparent feed impedance will be 20+30 = 50ohms.  The VSWR on a 50ohm coaxial cable feeding this antenna will be very close to unity (1:1) but three fifths of the available power will be wasted heating up mother earth, with only two fifths being available for radiation.

There are three other important parameters relating to antennas, aperture, gain and radiation pattern.  Antenna aperture is a concept that may need some explanation.  It is a way to describe how effective an antenna is at absorbing RF energy from a passing signal.  In a directional antenna, it is the portion of a plane surface very near the antenna and normal to the direction of maximum radiant intensity, through which the major part of the radiation passes.  It is often expressed as "an aperture of n square metres".  This means that the antenna will absorb an amount of RF energy equivalent to all the energy coming through a "window" of n square metres area.  Note that it does not refer to the physical size of the antenna (as viewed by eye from the "front.").

A good example of this is the long Yagi beam antenna.  Viewing it from the front, it looks to the human eye to be no bigger than a single dipole, yet its aperture is very much bigger than a dipole.  The long Yagi is what is called a Slow Wave Structure.  The director elements interact with the moving wave front to slow down the speed of radio signals whose frequency is close to the design frequency for the antenna.  This slowing effect causes the wave front close to the directors to lag behind the energy farther off-axis with the antenna.  This causes the wave front to become curved, like the surface of a bowl, with the open face of the bowl facing towards the driven element.  This bending of the RF wave front acts to bring energy that initially was not directly in line with the antenna to a focus at the driven element.  It does so because energy flow is always perpendicular to the wave front.  The curvature of the wave front has been bent (by the directors) such that the perpendicular to the wave front points towards the driven element.  Thus energy flows to the driven element from positions considerably off-axis.  Hence, a large aperture.

The gain of an antenna is primarily related to its radiation pattern.  The ERP (Effective Radiated Power) is the power input into the antenna multiplied by the antenna gain.  There is this concept that, the moment they exhibit gain, antennas magically create power within themselves.  Sadly, this is not the case.  If one examines an antenna it will be noted it is constructed of basic materials, the best being silver and copper, with gold and aluminium not far behind.  These materials in themselves cannot create power.

Antenna Gain is the relative increase in radiation, in the direction of maximum radiation, expressed as a value in dB above a standard, in this case a perfect half-wave dipole in free space.  The reference is known as dBd (decibels with reference to a dipole).  An antenna from which the effective radiated power in the direction of maximum radiation is twice the input power to the antenna has a gain of 10 x log(2/1) = 3dBd.  However, there is a second method used to express antenna gain figures but it implies that an antenna has a higher gain figure than that actually achieved.  It is expressed in dBi and represents a gain of an antenna referenced to an imaginary isotropic radiator, which is one that radiates equally in all directions, i.e. it has a spherical radiation pattern.  This method gives an antenna gain 2.14dB higher than that referred to a standard dipole as the gain of a perfect dipole in free space is 2.14dBi.  In the above example, the gain of the specified antenna would be 5.14dBi.

In the real world, neither a perfect dipole in free space, nor an isotropic radiator can actually exist but for all practical amateur radio purposes, a standard dipole is a good enough yard-stick.

The radiation pattern of an antenna is a graphical representation of the antenna's gain in azimuth and elevation.  It is often referred to as the polar diagram.  All too often, only the azimuth pattern is considered, but the elevation pattern is also very important.  An antenna with a forward gain of 30dBd is not much use for DX working if the elevation of the maximum lobe is at an angle of 80° to the horizontal, as the radiation will be going almost straight up, to be reflected by the ionosphere back to where it came from, or to pass through into outer space.  Such an antenna is good for local working but for DX working a much lower radiation elevation angle is required.  Unfortunately, on the lower bands (160m, 80m, and 40m), most amateurs are not able to achieve wire antenna heights that would give a low radiation angle.  Vertical antennas are better and low radiation angles becomes less difficult to achieve with wire antennas as the frequency increases.  Antennas such as the "Carolina Windom" and the "G5RV" have a vertical "feeder" that radiates and these antennas are a reasonably good compromise for the normal back yard antenna farm.

I recommend a computer antenna analysis program, such as EZNEC, if you want to investigate the effects of height, length or direction of antennas.  The registered version of this program costs about Ł40.00, but a free demo version is available, which is capable of analysing simple antennas.

Feeders

What is a feeder?  They are often called transmission lines and, in the present context, they are devices for transferring power from a generator to a load.  In the case of transmitting, this usually means sending the transmitter's output to an antenna.  In the case of receiving, it means coupling the antenna to the receiver.  Feeder theory, like antenna theory, applies equally to both cases.  There are many types of feeder and we will discuss the most important later in this article.

Before we continue, we must discuss "characteristic impedance" and "velocity factor".  A lossless transmission line can be represented by a series of small inductors and capacitors connected in an infinitely long line.  Each inductor represents the inductance of a very short section of one wire and each capacitor represents the capacitance between two such short sections.

Each series inductor acts to limit the rate at which current can charge the following shunt capacitor and in so doing establishes the surge impedance of the line, more commonly referred to as the characteristic impedance Zo.

In a vacuum, radio waves travel at the speed of light.  In other media, the waves travel at a lower velocity, although the difference in velocity between a vacuum and air can usually be ignored.

However, in other media, such as polythene or PTFE, the velocity is noticeably decreased.  The same is true when a wave travels down a feeder cable.  If the dielectric is air, the velocity of propagation will be very close to the speed of light.  However, if it is a plastic material, the velocity will be reduced.  The ratio of the velocity in a vacuum to the velocity when using a different dielectric is called the velocity factor of the cable and is obviously always less than one.

Velocity factor is important when cutting cable to form a phasing or delay line, as the physical length could well be considerably shorter than the wavelength.  For example, the velocity factor of solid dielectric coaxial cable is approximately 0.66 and that of semi-air-spaced coaxial cable is around 0.85.  Open wire line has a velocity factor of approximately 0.97 and that of ribbon feeder is around 0.8.

There are basically two types of feeder, balanced (open wire line) and unbalanced (coaxial).  With balanced open wire line, the input power is applied between the two wires, neither being earthed.  In actual fact, a virtual earth exists half way between the two wires of the feeder when the system is perfectly balanced.  We will discuss the pros and cons of making use of this when we discuss matching later.

With unbalanced coaxial feeder the input power is still applied between the two elements of the feeder (inner and screened outer) but the outer is normally earthed.

Single Wire Feeder

Single wire feeders, as opposed to single wire transmission lines of the Goubau line type, are seldom used these days and, arguably, do not come into the category of feeders at all, as they always form part of the antenna's radiating system.  At first sight it is difficult to see the difference between a single wire feeder and an end fed wire.  The subtle difference is that a single wire feeder is connected at a point remote from either end of the horizontal top wire of the antenna.  If the single wire is connected at the centre of the top wire, the antenna becomes a "T" antenna.  The Goubau line, or G-line, is a type of single wire transmission line intended for use at UHF and microwave wavelengths.  The line itself consists of a single conductor coated with dielectric material.  Coupling to and from the G-line is done with conical metal "launchers" or "catchers," with their narrow ends connected for example to the shield of coaxial feed line, and with the transmission line passing through a hole in the points of the cones.

Probably the most common use of an actual single wire feeder is in the true Windom Antenna (not the Carolina Windom). This type of antenna is fed at a point approximately one third along the length of the top.  The feeder should be a smaller diameter wire than the top and the system is tuned against ground.  The lengths of both the feeder and the horizontal top affect the self-resonant frequency and the feed impedance.   It is debatable whether the true Windom is a separate type of antenna or an offset fed "T" antenna.  On 160m, I feed my Carolina Windom in this manner by connecting the inner and outer of the coaxial feeder together at the ATU "live" terminal and tuning the antenna against ground.

Two Wire Feeder

Two wire feeders are normally referred to as "open wire line" or "ladder line".  They usually consist of two parallel wires spaced apart by insulating spreaders.  The characteristic impedance is determined by the diameter of the wires and the spacing between them.  It is also affected by the dielectric constant of the material between the wires but since this is predominantly air, except for the spreaders, this can be ignored.

This form of feeder is probably the most versatile and lowest loss of the types normally available to amateurs.  However, it can be a little unsightly and care must be taken to keep it well clear of metallic objects such as masts, gutters and pipes.

One of the more common uses of open wire line is to feed a doublet antenna, which consists of a centre fed dipole, which may or may not be resonant.  The driven end of the feeder is connected to a balanced ATU, which can be in the shack.  The ATU is used to ensure a 50ohm load is presented to the transmitter.

At first sight, it might appear that this arrangement contradicts my statements regarding ATUs in the shack, but more of that later when we come to consider matching.  The apparent contradiction is not strictly true, as the feeder forms part of the antenna although, unlike the Carolina Windom or G5RV arrangements, it does not radiate.  This is because, being a symmetrical balanced system, the currents in the two wires of the feeder are equal but flowing in opposite directions and therefore the resulting radiation cancels out.

The doublet also provides a good example of how an antenna and feeder system is capable of being represented in more than one way.  It can be regarded as two "inverted L" end fed wires with the horizontal portions in line, end-to-end, but with the vertical portions run parallel and close together.  Alternatively, it can be regarded as a dipole, centre fed with open wire transmission line which forms an impedance transformer converting the actual feed impedance to some other impedance, the value of which being determined by the physical dimensions of both the feeder and the antenna top.  In either case the system forms a balanced antenna that is not tuned against ground.  A balanced ATU is essential, as the impedance "looking into" the feeder will vary considerably with frequency and will only be 50ohms at a few frequencies which may or may not be usable.

Many ATUs, both homebrew and commercial, employ ferrite baluns as a cheap and cheerful way of matching balanced loads with a single ended ATU.  It is not a practice to be recommended as it is usually inefficient and can even result in overheating the balun, sometimes to the point of spontaneous ignition!  You may remember that I mentioned earlier, the problems encountered with baluns and reactive loads.  Remember that the power required to heat up the ferrite is being provided by the transmitter and is contributing nothing to the radiated signal.

Ribbon feeder

Ribbon feeder is a type of two wire feeder where the wires are held apart by a plastic dielectric.  The impedance of commercially available ribbon feeder is 300ohms but other impedances, such as 600ohms, are available.

As the dielectric constant of the insulating material will be greater than unity, it follows that the spacing will be less than that for open wire line of the same characteristic impedance.  Although less unsightly than open wire line, it is still important to avoid close proximity to metal objects.

A variation on the theme of ribbon feeder is the slotted ribbon type where the centre web is partially cut away to form a cross between open wire line and normal ribbon feeder.  This type is less affected by rain than normal ribbon feeder.

Coaxial Cable

There are several different types of coaxial cable but they are all basically a centre conductor surrounded by a metallic shield.  Commercially available cables are normally produced with characteristic impedances of 50ohms, 75ohms or 96ohms but other types are produced for specialised purposes.  Within the basic framework of coaxial cables, there are a large number of variations such as standard general purpose, semi-air-spaced low-loss, helically sealed air spaced, semi-rigid, miniature, high power, high temperature, ultra flexible, microwave, cheap TV downlead, data, video and several other more esoteric types such as delay cable and leaky feeder.

Microphone, audio and general purpose screened cable are coaxial in the dictionary sense but are not suitable for use as RF transmission lines as they are very lossy at RF and their characteristic impedances are not controlled.  They are, however, very effective for screening wires from RF fields where their inherent loss is actually advantageous.

Waveguides

Waveguides are normally used only at microwave frequencies above 1GHz and normally consist of a mechanically accurate, rectangular metal tube, although circular waveguide is sometimes used.  Waveguides do exist for use at around 350MHz but they are rare and large, having internal dimensions of approximately 23" x 11.5" (WG00).  The mathematics of waveguide theory is way beyond the scope of this article.  The size of the waveguide determines the cut-off frequency, which is the lowest frequency that can be propagated.  Waveguides are usually manufactured from brass and they are occasionally silver plated, especially for the smaller sizes used at millimetric wavelengths.

Probably the most common size found in amateur radio equipment is intended for use round 10GHz and this type has internal dimensions of 0.9" x 0.4" (WG16).  The smallest size waveguide is 0.034" x 0.017" and is used at frequencies around 300GHz (WG32).

Waveguides are not very convenient to use as they are rigid metal tubes that cannot be bent or twisted easily.  Flexible waveguide does exist but it is more lossy than standard waveguide and is very expensive.  The advantages of waveguide are the very low propagation losses and the almost total absence of signal leakage.  The disadvantages include mechanical size and inflexibility, the need for accurate flanges, with or without choke slots, for joining lengths together and cost.

Other Types of Feeder

There are several variations on the themes of open-wire and coaxial feeders but they are seldom encountered in amateur radio.  They include shielded balanced twin, balanced four wire, unbalanced five wire, single wire above ground-plane, balanced twin above ground-plane and several sub-variations of these types.

Fibre optic cables are not RF transmission lines at all but may be thought of as circular waveguides for use at optical wavelengths.  Like standard RF waveguides, they exhibit very low propagation loss but, unlike metal waveguide, they are flexible and mechanically easy to use.  However, connectors require specialised optical techniques.  Obviously, fibre optics cannot be used to feed power to an antenna in the RF sense.

Standing Wave Ratio

Before we go any further, it is vital to understand the terms "standing wave ratio", "reflection coefficient" and "return loss".  If an alternating current signal is sent down a feeder but not all of it is absorbed by the load, ie there is a mismatch, some of the incident signal will be reflected back down the feeder towards the source.  Obviously, at any given point along the feeder, the instantaneous power will be the vector addition of the incident (forward) power and the reflected (backward) power.  It is easier to visualise what is happening if we consider the instantaneous voltage on the feeder.  The ratio of the maximum to minimum value is called the voltage standing wave ratio, (VSWR).  We could equally well consider the instantaneous current, which would give the same answer.  The reflection coefficient, is the ratio of the amplitude of the reflected voltage vector to the amplitude of the incident voltage vector.

Return loss, RL, is the reflection coefficient expressed in dB and is a measure of the amount of power reflected back by a mismatched load expressed as a ratio, relative to the incident power.  Note that the bigger the return loss, the better the match.

Some of the mathematicians amongst you may argue that infinity divided by infinity is either still infinity or it is indeterminate, not one as stated above.  Also, any number divided by zero is either infinity or it is indeterminate, not infinity as stated above.  However, if you think of infinity as being an unimaginably huge, but still finite, number, adding or subtracting one from such a number is going to change its value by an unimaginably small (infinitesimal) amount.  Dividing one of these numbers by the other is going to give a result so close to one as makes no practical difference.  Similarly, an infinitesimally small number can be divided into any normal number an infinite number of times.

In the real world, it is never possible to have a totally lossless feeder or a perfect total mismatch and therefore the academic niceties of the meanings of zero and infinity can be ignored.

SWR can also be expressed in terms of the characteristic impedance of a feeder and the terminating impedance.

Note that VSWR is always quoted as a ratio greater than unity.  If the load impedance is greater than the characteristic impedance of the cable, by convention, the reciprocal of the resulting VSWR is used.

It should be further noted that a five to one mismatch results in a VSWR of 5:1, regardless of whether the load is less than or greater than the characteristic impedance of the cable.

Contrary to widely held belief, particularly among the CB fraternity, it is not necessary to achieve a perfect match (VSWR = 1:1, return loss = 0dB) in order to achieve efficient communication.  A VSWR of 2:1 will result in a 10dB return loss (100W incident power, 10W reflected, giving 90W in the load).  A 3:1 VSWR would result in a 6dB return loss (25W being reflected ) and a 5.4:1 VSWR would still only result a return loss of 3dB (half the power being reflected), although the transmitter's PA stage might be a little unhappy.

Before we leave the subject of VSWR, it might be interesting to discuss another popular misconception.  Consider a transmitter driving a length of 50ohm cable terminated with a 50ohm resistor.  Under these conditions, the VSWR will be 1:1, regardless of the losses in the feeder.  If we short or open circuit the load, the VSWR should be infinity as all the incident power will be reflected back down the feeder.  Is this statement correct?  The answer is no, unless there were no losses in the feeder, a situation that does not exist in the real world.  Let us assume the cable has a loss of 10dB.  If the transmitter is producing 100W, only 10W would reach the far end of the cable, where it would be reflected back and would undergo another 10dB loss on the way back.  Therefore 1W would arrive back at the transmitter.  A VSWR measurement at the transmitter would indicate that the return loss was 20dB, giving a VSWR of 1.2:1.  Thus the VSWR measurement would indicate a very good match even though the cable was completely mismatched by a short or open circuit.

The moral of this story is that measurement of VSWR is a very unsatisfactory method of checking whether all is well with an antenna system, especially if the feeder length is long or poor quality feeder is used.  Even when using a good quality cable with a loss of 2dB from transmitter to antenna, a VSWR of about 4.5:1 will esult if the antenna was open or short circuit.  Cable loss can only be ignored if there is no reflected power, i.e. the VSWR really is 1:1.

A much better indication is given by ignoring VSWR altogether and only checking the reflected power level, which should obviously be as close to zero as possible.  Fortunately, most VSWR bridges can be switched to this mode, although the "crossed pointer" types are also calibrated to read forward power and VSWR.

One further myth concerning SWR and feeders is that high SWR causes unwanted radiation from a feeder.  This is not true as feeder radiation is caused by unbalance, i.e. unequal currents flowing in the two wires comprising the feeder, not high SWR.  Balance and SWR are not related.   Unbalanced currents do not, in themselves, cause high SWR, any more than high SWR necessarily results in unbalance.  However, a fault condition on a previously satisfactory system resulting in unbalanced feeder currents could also cause high SWR and vice versa.

Antenna Matching

This section is called "Antenna Matching" rather than "Antenna Tuning" because a so called antenna tuning unit (ATU) does not actually tune the antenna in the sense of changing its resonant frequency.  What it does is to take the impedance presented by the antenna, R ± jX, and convert it to 50ohm resistive by cancelling out the +jX (or -jX) component with an equal -jX (or +jX) component and transforming the R component to 50ohms.  This is often achieved by using a tuned circuit, hence the misnomer of the antenna tuning unit.  However, since it is widespread custom and practice to refer to antenna matching devices as ATUs, I will use that term during this article.

There is insufficient space to deal with specific types of ATU as there are so many different types such as the Series tuned, Parallel tuned, L-match, T-match, Z-match, Transmatch and a multitude of others.

However, in the context of antenna matching, they all perform the same task, which is to transform the complex impedance seen when looking into a feeder to a known (usually 50ohms) non-reactive value.  In general, balanced feeds should use balanced ATUs and unbalanced feeds should use unbalanced ATUs.

The use of baluns, particularly ferrite cored baluns, should be avoided if at all possible.  A good maxim when dealing with matching devices is "keep it simple" as the more components and switches used, the lower the efficiency.  Usually it is better to use a separate simple ATU for each band, rather than use a multi-band, match-anything-to-anything device, but this is not always an acceptable option.

In theory, it should be possible to earth either a centre tap of a coil directly feeding an open wire line or the balanced null point of any more complex circuit.  However, in the real world, balanced feeders or matching circuits are never truly balanced and introducing a "hard" earth connection will almost certainly result in unbalanced feeder currents, the exact reverse of what we are trying to achieve.  It is a total myth that a "hard" earth connection forces the system to be balanced.  In fact, exactly the opposite is true.

The preferred method is to allow the driven end of the feeders to "float" about earth, which will result in a virtual earth being established at the electrical balance point, rather than the theoretical (physical) balance point.  A good analogy is when using push-pull devices in an amplifier.  If the input and output use tuned circuits, there will be a theoretical balance point at the electrical centre of the input and output coils and capacitors, all of which could be theoretically earthed.  This is never done in practice and it is normal to earth only one of these points, usually the centre of a split-stator capacitor in either the input or output circuit.  This allows the circuit to be automatically balanced about its actual null point.

Having said that I do not recommend the use of ferrite cored baluns, I must admit to using a Carolina Windom antenna, which uses what the manufacturer calls a 4:1 balun but I prefer to think of it as a 4:1 impedance matching transformer.  This transformer is positioned at the feed point of the wire, which is 50ft along the 133ft top.  I can't see how it can act as a true balun, as it is not positioned at a balanced feed point on the antenna.  One of the "features" of this type of antenna is that the vertical feeder is expected to exhibit a high VSWR and to have RF flowing on the outer of the coaxial cable causing the feeder to radiate and contribute a vertical component to the radiation pattern, hardly the ideal environment in which to operate a balun!

Maximum power is transferred to the load when the characteristic impedance of the feeder equals the load impedance.  In this condition, the standing wave ratio on the feeder will be 1:1 and it is very important to note that the source impedance of the generator has no effect on the feeder's VSWR.  It follows from this statement, that an ATU installed at the transmitter end of the feeder cannot be used to improve the feeder VSWR, although it can be used to "fool" the transmitter into thinking that it is looking into a matched feeder.

It is extremely difficult to achieve a constant source impedance within a transmitter.  Without getting into a discussion on the necessity, or otherwise, of conjugate matching, it must be appreciated that, in itself, a less than perfect VSWR on a feeder is not of great importance with respect to radiated signal strength.  It can, however, have a detrimental effect on linearity, the generation of inter-modulation products and power dissipation in the PA stage of a transmitter when it is not presented with a 50ohm non-reactive load.

If using 50ohm coaxial cable to feed an antenna, any tuning or matching device must be at the far end of the feeder, directly at the antenna terminals.  This will ensure that a low VSWR can be achieved on the feeder.  The fact that the impedance "looking back" into the transmitter might, and probably will, be anything but 50ohms will not affect the feeder VSWR although it will affect the power transfer efficiency of the system.  In the receiving condition, the antenna is the source and the receiver is the load.  Fortunately, it is relatively easy to arrange for the receiver input impedance to be 50ohms, thus producing a good match to a 50ohm coaxial feeder.

Methods of Matching

Direct Matching

Very often, the antenna itself can be designed to present a resistive load equal to the characteristic impedance of the feeder being used, thus requiring no other matching device.  By definition, this implies an antenna that is intrinsically self-resonant at the frequency in use such as a half wave dipole or folded dipole.  A dipole will be a reasonable match to 75ohm twin feeder and a folded dipole will match to 300ohm ribbon reasonably well.  Note that the use of 75ohm coaxial cable is not recommended without the use of a 1:1 balun at the antenna terminals.

Gamma Matching

A resonant antenna, such as a half wave dipole will exhibit a very low, essentially resistive, impedance at the centre and a very high impedance at the open ends.  It therefore follows that somewhere along either leg of the dipole, close to the centre, will be a point corresponding to 50ohms.

If the screen of a coaxial feeder is connected to the centre point of a half wavelength antenna (one complete length of wire, no break in the centre) and the inner conductor of the cable is connected to one of the 50ohm points, a reasonable match will be obtained but the system will suffer from the balanced-antenna- unbalanced-feeder problem.  This is called a gamma match.

A more elegant solution is the double gamma match using 50ohm twin feeder.  Here, one side of the feed line is connected to a point on one side of the antenna's centre corresponding to 25ohms and the other side of the feeder is connected to a similar point on the other side of the antenna's centre.  A good match will be obtained and the system will be balanced without the use of a balun.

With both the single and double gamma match, a better SWR is obtained if a small series capacitor is used in series with the gamma matching element.  The value of this capacitor is adjusted to "tune out" the inherent inductance of the matching element and is especially important in VHF and UHF systems.  In HF systems, the end of the feeder is often some distance away from the antenna wire but the gamma matching elements are still connected from the feeder to the appropriate points on the antenna.

Obviously with this arrangement, the matching elements approach the antenna at an angle, rather than running parallel to it.  This has the effect of lowering unwanted inductive and capacitive coupling between the antenna and the gamma match.

Mike Underhill G3LHZ uses a type of gamma match with his magnetic loops, but in his design, the capacitive and inductive coupling between the loop and the matching element is deliberately made high by wrapping the matching element around the loop itself.  Mike insists that this arrangement improves the match over an extended frequency range, although his theories are disputed by many.  The mathematical analysis of this type of gamma match is extremely complex and way beyond the scope of this article.

Tuned Circuit Matching

One of the oldest ATUs for relatively high feed impedances, such as with half wave end fed antennas, is a simple parallel tuned circuit with the antenna tapped onto the coil at a point corresponding to the resistive element of the feed impedance.  The transmitter is connected either to a tapping point corresponding to 50ohms or to an appropriate link coil coupled to the main coil.  When the coil is brought to resonance, by definition, the reactive components are cancelled out leaving the tuned circuit appearing to be a resistor of several hundred ohms.  This resistance is called the dynamic resistance and its value depends on the LC ratio and the intrinsic series resistances of the components, in other words, the Q of the circuit.

The intrinsic series resistance of a capacitor is negligible compared to the intrinsic resistance of an inductor.  Hence the dynamic resistance of a parallel tuned circuit is determined by the LC ratio and the intrinsic resistance of the inductor.

Assuming we are operating on a frequency of 3.6MHz, typical values would be a tuned circuit loaded Q of 10 and a tuning capacitance of 300pf with an inductance of 6.5µH.

Obviously, if one side of this coil is connected to earth, there will be points on the coil where the apparent resistance is between zero ohms and the circuit's dynamic resistance value, which, in our example, is 1470ohms.  It should be noted that the Q is the loaded Q of the circuit with the antenna and the transmitter connected, not the Q of the tuned circuit in isolation, which could be 100 or more.  Also, the settings of the tapping points and the tuning capacitance are highly interdependent.

Many pre-war transmitters used a parallel tuned circuit in the anode of the final power amplifier and it was not uncommon for the antenna to be tapped onto this directly, hopefully via a DC blocking capacitor.  Apart from the obvious safety issues, this is not good practice as the inherent rejection of harmonics and other unwanted emissions is very low.

When feeding low impedance antennas, such as a quarter wave end fed, a series tuned circuit is used.  In this case the antenna is connected to one side of the coil via the tuning capacitor, the other end of the coil being earthed.  Again, at resonance, the reactive components are cancelled out and the transmitter is connected to a tapping point on the coil corresponding to 50ohms or via a link coil.

One practical difficulty with this circuit configuration is mechanical rather than electrical.  As both rotor and stator plates of the variable capacitor are "hot", the capacitor must be insulated from any metal chassis or cabinet and an insulated spindle must be used.

L Matching

The arrangements discussed so far are essentially single band, single antenna solutions.  Most of us do not have the luxury of a special antenna for each band and have to be content with one or two antennas, which are pressed into service for use on several bands.  Almost by definition, this is going to be a compromise but it can be a perfectly acceptable compromise.

I use a 160m Special Carolina Windom with a remote Picatune ATU directly underneath the antenna at the bottom of the vertical coaxial section.  The system is fed with 70 feet of 50ohm coaxial cable buried under the back lawn.  This antenna works very well on all bands from 80m through to 10m, including 60m but is not very good on 160m.  The manufacturer states that the integral line choke and transformer have been "specially beefed up" to cater for the high currents involved when using the antenna on top-band.  In my experience, they have not been beefed up enough and the transformer gets so hot that the ferrite core reaches its Curie point and loses most of its inductance after less than one minute of use.  In any case, the feed impedance in this configuration is about 10-j1000, which is very difficult to efficiently match to 50ohms.

I solved this problem by connecting the inner and outer of the coaxial downlead at the remote ATU when using it for 160m and feeding the antenna as a "T" antenna tuned against ground.  I think the manufacturer knows he has a potential problem because he has chosen to use very expensive glass-fibre covered wire for the transformer windings, presumably to stop them catching fire.

In all fairness, a computer simulation indicates that there is much less of a problem when the antenna top is at a height of 50ft or more, rather that the 30ft I use and the manufacturer's data sheet does state a minimum height of 35ft.  With my configuration, the line choke becomes a base loading coil and I have no idea what is going on in the transformer but at least it does not get hot and the antenna works very well.

Picatune uses switched L-match configurations to cater for either low or high impedance antennas.  An L-match consists of a series inductance (reactance = XL) connected between the two impedances to be matched (ZLO and ZHI) and a parallel capacitance (reactance = XC), which is connected across ZHI.  The "earthy" ends of both ZLO and ZHI are connected together.  Picatune is essentially an unbalanced tuner using this arrangement, although it can be configured to "float" when connected to balanced lines.  Whilst not perfect, this solution is to be preferred to using a balun for the reasons stated earlier.  It is possible to have balanced L-match networks where there are two coils, one in each line connecting ZLO and ZHI, with neither side of the input or output being earthed but this becomes physically difficult when using switched components to achieve multi-band working.

This is a photgraph of my Picatune taken with the enclosure door open.

 

The component values for the unbalanced arrangement are calculated from the following formulae, assuming that the impedances to be matched are purely resistive.  Any reactive components will need to be incorporated into the calculated values.  Again, it should be noted that the Q is the loaded Q of the circuit, not the Q of the tuned circuit in isolation and is normally between 5 and 15.

The same formulae are used to calculate the component values for the balanced configuration but the inductance of each coil will be half the value calculated above.  Similarly, if using a split stator capacitor, the capacitance of each half will be twice the value calculated above, but if using a single "floating" capacitor, its value will be the same as for the unbalanced network.

Pi Matching

There are several other matching circuits, one of the most common being the PI-network.  Nearly all post war valve transmitters and linears use this type of circuit to match the output impedance of the PA valves to the feeder.  Obviously, this circuit can be used to match a feeder to an antenna or a transmitter to a feeder.  The component values can be calculated using the following formulae, again assuming the impedances to be matched are purely resistive.  As before, the Q is the loaded Q of the circuit, which is usually between 5 and 15 and any reactive components in the impedances to be matched will need to be incorporated into the calculated values.

Summary

The subject we have been discussing is very broad and I have tried to cover the salient points only, which has resulted in the glossing over of some of the finer points and the total omission of others.  Don't be put off by the maths involved.  It need not be very complex and has been included to "put some meat on the bones".  If maths is your forté, then you can get more deeply involved, beginning with Maxwell's Equations:-

It should be possible to grasp the basic principles without recourse to maths at all.  When you have played about with ATUs and matching systems for a little while, the approximate values and physical sizes of components becomes "second nature" but the mathematical approach does provide a starting point.

Please study the available literature if you want to delve more deeply into the subject but be warned that the maths can become a little daunting, starting with Maxwell's equations.  The Internet is a very useful source of information.  Try entering "radiation resistance" or "circuit Q" or some other seemingly innocuous phrase into Google and you will be amazed at how many references will be found, some simplistic, some submerged in higher mathematics from the start and some just plain wrong or irrelevant.

I hope you have all found this article informative and perhaps some of the more common misconceptions have been banished to the realms of myth.

 

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