Impedance matching

It’s common practice to match the impedances of the antenna, transmission line, and either the receiver or the transmitter. The reason can be seen in FIG. 1. Although the example selected is for a transmitting antenna, because of reciprocity the same notions also apply to the receive antenna, although power flows are reversed (and considerably smaller).

The case shown in FIG. 1A is for the matched case, i.e. the transmitter output impedance, the transmission line impedance, and the antenna feedpoint impedance (which is the 'load') are all the same (e.g. 50 ohms).

The thickness of the arrow is intended to represent the relative power level.

In this situation, forward power from the transmitter is sent toward the load end of the transmission line. When the radio frequency (RF) signal reaches the load it’s completely absorbed. Some of it will go towards heating the load, and part of it will be radiated. The loss to heating in a well designed, properly installed antenna is negligible, so it’s not unreasonable to show the arrow representing the radiated portion as the same size as the forward power. The implication of the system being matched is that all of the power from the transmitter is radiated and can become a useful signal.

When the load and source are mismatched, as in FIG. 1B, not all of the forward power is absorbed by the load. Some of it’s reflected back down the transmission line toward the transmitter. When this reflected wave interferes with the forward waves still propagating up the line, the result is standing waves (see Section 2). The measure of the standing waves is the standing wave ratio (SWR, or VSWR if voltage is measured).

The existence of the reflected power wave has some implications in practical systems. First, it represents a loss. The reflected power is not available to contribute to the radiated signal. If no other losses occur, then this loss might prove tolerably low, but that is rarely the case. At some frequencies and in some situations, the goal is to squeeze out as much signal as possible.

Second, some transmitters, mostly modern designs with solid-state final RF power amplifiers, are intolerant of high VSWR loads. In the early days of solid-state transmitters, the first of which were CB rigs, the expensive output transistors would often blow out when even a transient high VSWR situation occurred. Older vacuum tube ('valve' to UK readers) designs were more tolerant of a high VSWR. Although those systems experienced the VSWR loss problem, the transmitter was not harmed. Modern transmitters, on the other hand, now include automatic load control (ALC) or other circuitry to begin reducing RF output power as the VSWR climbs. The shut down 'knee' usually starts somewhere around a VSWR of 1.5:1, and the rig will be completely shut down at some VSWR between 2.5:1 and 3:1.

One rig produced 100W of power at a VSWR of 1:1, but only 100mW at a VSWR of 2.5:1.

A third reason is that losses in coaxial cable can be quite severe, especially at higher frequencies. Those losses increase markedly with increasing VSWR, especially in the lower grades of coaxial cable normally used for radio antennas.

If the antenna feedpoint impedance does not match the feedline impedance, then a VSWR proportional to their ratio is created. Unfortunately, it’s not always possible to create an antenna with a feedpoint impedance equal to the characteristic impedance of the feedline. Unless some means is found to effect the match, then all of the gremlins associated with a high VSWR occur.

The solution to the problem is to provide an intermediate impedance matching device ( FIG. 1C) between the transmitter (or receiver) and the antenna. The matching device might be an inductor-capacitor (LC) network, a transformer (e.g. a BALUN), or a transmission line matching section. The impedance matching device can be considered as a 'black box' between two resistances (R1 and R2, as in FIG. 2). The property of the box is to provide the transformation that makes each resistor think it’s looking at another resistor of the same value as itself. Although these devices are bilateral, i.e. the transformation occurs in both directions, it’s common practice to use R1 to represent the transmitter output impedance or the receiver antenna input impedance, and R2 to represent the load impedance (e.g. antenna feedpoint impedance). In most cases, the value of R1 in transmitters is 50 ohms, and in receivers it will be either 50 ohms or 300 ohms.

LC MATCHING NETWORKS

LC matching networks are combinations of inductance and capacitance that will allow an input impedance (R1) to be transformed to an output impedance (R2). The common name for these circuits is antenna tuner or antenna tuning unit (ATU). Several common forms of ATU circuit are shown in FIGs 5.

FIG. 2

The circuits in FIG. 3 are for the case where R1>R2. This situation might occur in vertical antennas, For example, where the feedpoint impedance varies from a few ohms to about 37 ohms, both of which are less than the standard 50 ohms used by the rest of the system. The circuit in FIG. 3A is one variant of the L-section coupler (two other variants are shown in FIG. 4). In this version, the capacitor shunts the line at the input of the network, and the inductor is in series with the line.

Many homebrewed and commercial L-section couplers are designed so that changing jumpers or switch settings allows you to con figure the inductor and capacitor in any of the three variants ( FIGs 3A, 4A, and 4B).

FIG. 4

FIG. 5

The circuit in FIG. 4B is the _-network. This type of circuit is often used for impedance transformation when R1 is very much larger than R2 (R1 _ R2). It was once very common as a transmitter output network because vacuum tube RF power amplifiers needed to match 3000-6000 ohm anode impedances to 50 ohms for the antenna output. The network consists of two shunt capacitors on either side of a series inductor.

A series of four trans-match-style antenna tuning unit circuits is shown in FIG. 5. These circuits are used in a wide variety of commercially avail able high-frequency (HF) ATUs. Some of them use dual capacitors, i.e. two section capacitors in which two separate capacitors share the same shaft. All of the capacitors in these should be wide-spaced 'transmitting' capacitors if the ATU is used as part of a transmitting antenna. For receive-only cases, however, ordinary receiver-style variable capacitors can be used. Although the individual component values can be calculated, it’s common to use 140 or 250 pF for the capacitors, and either 18 mHor28 mH for the inductor.

The inductor is either a variable or switchable type. Variable inductors are built with a roller mechanism that selects the turns required for any specified value of inductance. However, these inductors can be quite pricey, so many builders opt instead for an air core inductor with several taps at various points along the coil. By selecting the tap one can change the inductance.

The calculation of values for the various style of LC impedance matching network is not terribly difficult if you are trained in mathematics. But if you either prefer the convenience of computer calculations, or are a person who found a first course in algebra and trigonometry a daunting and fearsome experience, then you might wish to take advantage of the software supplement to this guide.

QUARTER-WAVELENGTH MATCHING Sections

The quarter-wavelength matching section, also called the Q-section, is made of transmission line (segment 'A' in FIG. 6). The characteristic impedance of the Q-section line (ZA) is selected to provide impedance transformation of the load impedance (ZL)to the characteristic impedance of the line ('B')to the transmitter (ZB). In some cases, the Q-section is connected directly to the transmitter output (or receiver input), in which case ZL is transformed to ZS.

There are two things that you must calculate when making a quarter wave matching section: the physical length of the transmission line and the characteristic impedance required to match the load impedance to the source impedance. The physical length to make an electrical quarter wavelength is foreshortened from the physical quarter wavelength due to the velocity factor of the cable. The calculation is

L_meters = 75V F_MHz meters

…where L is the length in meters, F_MHz is the center operating frequency in megahertz, and V is the velocity factor of the transmission line (either 0.66 or 0.80 for coaxial cable - see Section 3).

Calculating the required characteristic impedance requires knowledge of the value of the load impedance and the characteristic impedance of the transmission line to the receiver or transmitter. The calculation is:

ZA =

ZLZB

For example, suppose we wish to make a Q-section for matching a 100 ohm impedance (such as found at the feedpoint of a quad loop)to 52 ohm coaxial cable. If the match is not made, then the VSWR will be about 2:1, which for many uses is clearly too high. The calculation is ZA = (100 ohms)_(52 ohms) p ZA = 5200 = 72 ohms

FIG. 6

The required characteristic impedance is 72 ohms, which is a very good match to 75 ohm coaxial cable. Lest you think this is an example contrived to make the arithmetic work out to a standard impedance found in coaxial cable catalogs (which it is), it’s also a very real example that is used for a number of practical antennas. Clearly, though, if the result of this equation is not near enough to some standard coaxial cable to reduce the VSWR to an acceptable level, then some other means of matching the impedance must be found.

FIG. 7

The method of FIG. 6 suffers from the limitations discussed above, namely the possible lack of a readily available characteristic impedance value. However, a much more general case is shown in FIG. 7. This is the series matching section method. Sections L1 and L3 are made of the same type of cable, with the same characteristic impedance. The center section, L2, is made of a cable with a different characteristic impedance, e.g. 75 ohm coaxial cable or 300 ohm twin-lead. The calculation of the different lengths is a bit daunting, so you are referred to the software supplement to this guide in order to make the calculations.

In both the series matching section and the Q-section (which is actually a limited special case of the series section), coaxial cable, twin-lead, or parallel line can be used for the transmission lines, even though only coaxial cable is shown here.

MATCHING STUBS

Another means for effecting the impedance match is to use either a quarter wavelength or half-wavelength matching stub ( FIG. 8). The stub is sometimes mounted at the feedpoint of the antenna, and the transmission line is tapped on the stub at a point (L1) that matches the impedance. In the case shown in FIG. 8A, a shorting bar is provided at the bottom of the stub. In some cases, the stub is open and the shorting bar is not used.

Another case is shown in FIG. 8B. In this circuit, the transmission line is connected directly to the antenna, and the stub is used to remove complex impedances by being positioned somewhere between the antenna feedpoint and a point (L1) that is a quarter wavelength down the transmission line from the feedpoint.

The final case is shown in FIG. 8C. In this scheme, the transmission line is coaxial cable, otherwise this scheme is like FIG. 8B. The three sections of coaxial cable are connected together using a coaxial 'tee' connector. Typically of the PL-259/SO-239 family, these connectors have three ports that are internally all connected together.

The lengths L1 and L2 depend on the VSWR experienced on the particular antenna, as well as the relationship of ZL and Z0. Two cases are seen:

FIG. 8

Note that the results of these equations are in degrees. In a transmission line, one wavelength equals 3608, a half wavelength is 1808, and a quarter wavelength is 90-degree. You can scale the actual length against these values, keeping in mind the velocity factor of the transmission line. Consider an example. Suppose we need to match an antenna that has a 3:1 VSWR on its resonant frequency of 9.75Mhz using 300 ohm twin-lead (V = 0:82).

Further, the impedance of the load is 900 ohms (note:

VSWR = 900=300 = 3:1). Because ZL > Z0, we use the first pair of equations:

[...]

The matching stub is used on a large number of antennas. Once you get away from the simple half-wavelength dipole fed with 75 ohm coaxial cable, the number of antennas that require some form of impedance matching increases considerably, and the matching stub is used for a lot of different designs.

FIG. 9

BALUN AND OTHER BROAD-BAND TRANSFORMERS

There are a number of different transformers used in impedance matching in antenna systems. The term 'BALUN' is used extensively, and it comes from BALanced-UNbalanced. Correctly used, then, the term 'BALUN' refers to a transformer that matches a balanced load (e.g. a dipole antenna feedpoint) to an unbalanced load (e.g. coaxial cable). However, it has become common (if erroneous) practice to use 'BALUN' in a generic sense to refer to any of the broad-band transmission line transformers. More correctly, some of those are balanced-balanced, so should be called BAL-BAL, and others are of an unbalanced-unbalanced configuration so are called UN-UN. I suppose BALUN sounds more like a word than BAL-BAL or UN-UN (note: some antenna and accessories catalogs do use these terms correctly, but the erroneous usage is also seen).

One of the earliest forms of BALUN transformer is the coaxial cable BALUN shown in FIG. 9. Both pieces of coaxial cable used in this BALUN transformer are of the same type (e.g. 75 ohm coaxial cable). When connected in this configuration, the BALUN transformer produces a 4:1 impedance transformation, which means that a 300 ohm balanced antenna (e.g. folded dipole) will look like a 75 ohm unbalanced load. The coaxial cable to the ham rig or receiver can be of any convenient length. The BALUN section, however, must be a half wavelength long (keeping in mind the velocity factor). The length of the BALUN section is found from:

L_meters = 150V F_MHz meters

… where F_MHz is the frequency in megahertz and V is the velocity factor (0.66 for polythene coaxial cable, and 0.80 for poly-foam coaxial cable).

A connection box for making the coaxial BALUN is shown in FIG. 9B. This box is intended for mounting on the antenna center insulator, and should not be used for supporting the antenna unless eye bolts or other more rugged fixtures are provided at the left and right ends. The balanced antenna feedpoint is connected to a pair of five-way binding posts, while the coaxial cable for the run to the rig or receiver and the BALUN sections (B1 and B2) are connected to SO-239 coaxial connectors.

The coaxial BALUN is designed for a specific frequency, but will work over a small margin either side of the design frequency (e.g. typically one HF ham band can be accommodated). But for wide-band operation, you might want to build a broad-band transformer such as those shown in FIG. 10. Note that some of these transformers only show one core symbol (e.g. FIG. 10A). Those transformers have all the windings on the same core. The dots show the phase sense of the windings and indicate the same end of the winding).

The two most common forms of BALUN transformer are those in FIGs 10A and 10B. The version in FIG. 10A has no impedance transformation, and is usually referred to as a 1:1 BALUN. The transformer in FIG. 10B, on the other hand, offers a 4:1 impedance transformation, so is equivalent to the coaxial BALUN shown in FIG. 9A. The transformers in FIGs 10C and 10D are both UN-UNs. The configuration in FIG. 10 produces a 9:1 impedance transformation, while that in FIG. 10D produces a 16:1 transformation.

FIG. 10

FIG. 11

The construction of coil BALUNs and broad-band transformers is shown in FIG. 11. The transformer shown in FIG. 11A is wound on a toroid core made of either powdered iron or ferrite material.

The toroid is doughnut shaped. It has the interesting attribute of containing the magnetic field to its own geometry, so has little interaction with its environment. This fact means that it will work like the guide says more often than certain other transformer core configurations.

Note how the wires are wound on the toroid core. They are kept paired and lay next to each other. In this manner they are wound together as if they were only one piece. When two wires are used, this form of winding is called bifilar winding. When three wires are wound together in this manner, a trifilar winding is produced. The bifilar method is used to wind the transformer in FIG. 10B, while trifilar winding is used for that in FIG. 10A.

The solenoid winding method is shown in FIG. 11B. The core can be either air (in which case a coil form is needed), or a ferrite rod (as shown).

Again we see the use of either bifilar or trifilar winding, depending on the nature of the transformer being made.

The so-called bazooka BALUN core is shown in FIGs 11C and 11D, using two different winding styles. In the style of FIG. 11C, the wire is passed through both holes to form a loop ('internal winding').

Counting the number of turns is a little different than one might suppose.

The case shown in FIG. 11C is one turn, even though many people erroneously assume that it’s half a turn. If one end of the wire is passed through both holes one more time, then there are two turns present. Both the primary and secondary windings can be wound in this same manner, laying one over the top of the other (the primary is usually laid down first).

The case shown in FIG. 11D shows an end view of the bazooka BALUN core. In this case, several turns are wound in both the internal and external winding styles. These two styles can be intermixed on the same form, but wherever possible you are advised to use the internal winding mode preferentially.

FIG. 12A shows how a toroid core inductor or transformer is mounted on either a printed circuit board (PCB) or metal chassis. Fiber or nylon washers are used to secure and protect the toroidal core, and nylon or other non-metallic fasteners (machine screw and hex nut) are used to keep it in place. It’s important to use non-metallic fasteners to keep from interfering with the operation of the transformer. Only in the case of the largest toroids (>5 or 6 cm in diameter) are metal fasteners usable, and even then there is some bad effect.

The scheme in FIG. 12B is used for transmitter Altus and similar applications where the power is higher. Two or more 5 cm or larger toroids are stacked one on top of the other. Each toroid core is first wound with fiberglass tape to insulate it from the other core. After the cores are wrapped with tape and stacked on top of each other, a final layer of tape can be added to keep the whole assembly stable. The bifilar or trifilar windings are then laid down on the stacked cores.

A number of manufacturers offer BALUNs, BAL-BALs, and UN-UNs, in both voltage and current configurations. Some are designed to replace the center insulator of an antenna such as the dipole. Others are intended for mounting elsewhere. The transformer in FIG. 13 is intended for use on vertical antennas. The feedpoint impedance of the quarter-wavelength vertical will vary from something less than 5 ohms to about 37 ohms, depending on the installation. The transformer of FIG. 13 is an UN-UN that has a single attachment point for 52 ohm coaxial cable to the rig or receiver.

FIG. 12 FIG. 13

The other four coaxial connectors are various load impedances that will be transformed to 52 ohms if that port is used.

COMMERCIAL ANTENNA TUNERS

An 'antenna tuner' located at the transmitter end of the transmission line won’t effect a good impedance match to the antenna, but it can mitigate the effects of a high VSWR on the transmitter. Even a single-band resonant antenna will exhibit a high enough VSWR at the ends of the band to upset the operation of the transmitter that is equipped with automatic load control (that is, all modern solid-state rigs). Although antenna tuner construction is well within the abilities of most do-it-yourself 'homebrewers,' it’s also likely that most will opt instead for a ready-built ATU. A number of reasonably priced models are available on the market.

FIG. 14 shows the MFJ-956 receiver S/M/L wave pre-selector/tuner.

This device places a series resonant circuit in series with the antenna down lead before it goes to the receiver. A single variable capacitor (365 pF maxi mum) is in series with an inductance. Four different switch-selected inductance values are provided (2.5 mH, 330 mH, 22 mH, and 1 mH) to cover the range 150 kHz to 30MHz. When the inductor switch is in the BYP ('bypass') position, the preselector/tuner is effectively out of the circuit, and the antenna-receiver combination works as normal. In the GND ('ground') position, the antenna input of the receiver (but not the antenna) is grounded.

FIG. 14

FIG. 15

FIG. 16

Tuners for transmitting use are shown in FIGs 15 and 16. The tuner in FIG. 15 is the MFJ-949E Deluxe Versa Tuner II, while that in FIG. 16 is the MFJ-986 Differential Tee tuner. These tuners are a bit larger than the standard receiver-only tuner, but are nonetheless just as useful to the receiver owner as well. The only thing that won’t work for receiver owners is the VSWR metering system. These are based on the same technology as RF wattmeters, so require the output of a radio transmitter for excitation. Both models allow more than one antenna (although only one at a time!) to be switch selected.

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