25.pdf

Coupling the

Transmitter to

the Line

Chapter

How many times have you heard someone on the air

saying how he just spent hours and hours pruning his antenna

to achieve a 1:1 SWR? Indeed, have you ever wondered

whether all that effort was worthwhile? Now don’t get the

wrong impression: a 1:1 SWR is not a bad thing! Feed-line

loss is minimized when the SWR is kept within reasonable

bounds. The power for which a particular transmission line

is rated is for a matched load.

Modern amateur transceivers use broadband, untuned

solid-state final amplifiers, designed to operate into 50

matching network was often called a Transmatch . This is a

coined word, referring to a “Transmitter Matching” network.

Nowadays, radio amateurs commonly call such a device an

antenna tuner .

The function of an antenna tuner is to transform the

impedance at the input end of the transmission line—

whatever it may be—to the 50

needed to keep the

transmitter loaded properly. An antenna tuner does not alter

the SWR on the transmission line going to the antenna. It

only ensures that the transmitter sees the 50-

Ω

Such a transmitter is able to deliver its rated output power—

at the rated level of distortion—only when it is operated

into the load for which it was designed. An SSB transmitter

that is splattering is often being driven hard into the wrong

load impedance.

Further, modern radios often employ protection

circuitry to reduce output power automatically if the SWR

rises to more than about 2:1. Protective circuits are needed

because solid-state devices can almost instantly destroy

themselves trying to deliver power into the wrong load

impedance. Modern solid-state transceivers often include

built-in antenna tuners (often at extra cost) to match

impedances when the SWR isn’t 1:1.

Older vacuum-tube amplifiers were a lot more forgiving

than solid-state devices—they could survive momentary

overloads without being instantly destroyed. The pi-networks

used to tune and load old-fashioned vacuum-tube amplifiers

were able to match a fairly wide range of impedances.

Ω

load for which

it was designed.

Column one of Tables 1 and 2 list the computed

impedance at the center of two dipoles mounted over average

ground (with a conductivity of 5 mS/m and a dielectric

constant of 13). The dipole in Table 1 is 100 feet long, and

is mounted as a flattop, 50 feet high. The dipole in Table 2

is 66 feet long overall, mounted as an inverted-V, whose

apex is 50 feet high and whose legs have an included angle

of 120

. The second column in Tables 1 and 2 show the

computed impedance at the transmitter end of a 100-foot

long transmission line using 450-

window open-wire line.

Please recognize that there is nothing special or “magic”

about these antennas—they are merely representative of

typical antennas used by real-world amateurs.

The impedance at the input of the transmission line

Ω

Table 1

Impedance of Center-Fed 100' Flattop Dipole,

50' High Over Average Ground

Frequency Antenna Feed-Point

MATCHING THE LINE TO THE TRANSMITTER

As shown in Chapter 24 , the impedance at the input of

a transmission line is uniquely determined by a number of

factors: the frequency, the characteristic impedance Z 0 of

the line, the physical length, velocity factor and the matched-

line loss of the line, plus the impedance of the load (the

antenna) at the output end of the line. If the impedance at

the input of the transmission line connected to the transmitter

differs appreciably from the load resistance into which the

transmitter output circuit is designed to operate, an

impedance-matching network must be inserted between the

transmitter and the line input terminals.

In older ARRL publications, such an impedance-

Impedance at Input of

MHz

Impedance, Ω

100' 450- Ω Line, Ω

1.83

4.5 – j 1673

2.0 – j 20

3.8

39 – j 362

888 – j 2265

7.1

481 + j 964

64 – j 24

10.1

2584 – j 3292

62 – j 447

14.1

85 – j 123

84 – j 65

18.1

2097 + j 1552

2666 – j 884

21.1

345 – j 1073

156 + j 614

24.9

202 + j 367

149 – j 231

28.4

2493 – j 1375

68 – j 174

Coupling the Transmitter to the Line

25-1

chassis. The line to the antenna, however, may be unbalanced

(coaxial cable) or balanced (parallel-conductor line),

depending on whether the antenna itself is unbalanced or

balanced.

Table 2

Impedance of Center-Fed 66' Inv-V Dipole, 50' at

Apex, 120 ° Included Angle Over Average Ground

Frequency

Antenna Feed-Point

Impedance at Input of

MHz

Impedance, Ω

100' 450- Ω Line, Ω

Harmonic Attenuation in an Antenna Tuner

This is a good place to bring up the topic of harmonic

attenuation, as it is related to antenna tuners. One potentially

desirable characteristic of an antenna tuner is the degree of

extra harmonic attenuation it can provide. While this is

desirable in theory, it is not always achieved in practice. For

example, if an antenna tuner is used with a single, fixed-

length antenna on multiple bands, the impedances presented

to the tuner at the fundamental frequency and at the harmonics

will often be radically different. The amount of harmonic

attenuation for a particular network will thus be dramatically

variable also. See Table 2. For example, at 7.1 MHz, the

impedance seen by the antenna tuner for the 66-foot inverted-

V dipole is 1223 – j 1183

1.83

1.6 – j 2257

1.6 – j 44

3.8

10 – j 879

2275 + j 8980

7.1

65 – j 41

1223 – j 1183

10.1

22 + j 648

157 – j 1579

14.1

5287 – j 1310

148 – j 734

18.1

198 – j 820

138 – j 595

21.1

103 – j 181

896 – j 857

24.9

269 + j 570

99 – j 140

28.4

3089 + j 774

74 – j 223

varies over an extremely wide range when antennas like these

are used over the entire range of amateur bands from 160 to

10 meters. The impedance at the input of the line (that is, at

the antenna tuner’s output terminals) will be different if the

length of the line is changed. It should be obvious that an

antenna tuner used with such a system must be very flexible

to match the wide range of impedances it will encounter—

and it must do so without arcing or blowing up.

. At 14.1 MHz, roughly the second

harmonic, the impedance is 148

Ω

−

j 734

Ω

Trapped Antennas

There are some situations in amateur radio where the

impedance at the second harmonic is essentially the same

as that for the fundamental. This often involves trapped

antenna systems or wideband log-periodic designs. For

example, a system used by many amateurs is a triband Yagi

that works on 20, 15 and 10 meters. The second harmonic

of a 20-meter transmitter feeding such a tribander can be

objectionably strong for nearby amateurs operating on

10 meters. This is despite the approximately 60 dB of

attenuation of the second harmonic provided by the low-

pass filters built into modern solid-state transceivers. A linear

amplifier can exacerbate the problem, since its second

harmonic may be suppressed only about 46 dB by the typical

pi-network output circuit used in most amplifiers.

Even in a trapped antenna system, most amateur

antenna tuners will not attenuate the 10-meter harmonic

much at all, especially if the tuner uses a high-pass

T-network. This is the most common network used

commercially because of the wide range of impedances it

will match. Some T-network designs have attempted to

improve the harmonic attenuation using parallel inductors

and capacitors instead of a single inductor for the center

part of the tee. Unfortunately, this often leads to more loss

and more critical tuning at the fundamental, while providing

little, if any, additional harmonic suppression in actual

installations.

The Matching System

Over the years, radio amateurs have derived a number

of circuits for use as antenna tuners. At one time, when open-

wire transmission line was more widely used, link-coupled

tuned circuits were in vogue. With the increasing popularity

of coaxial cable used as feed lines, other circuits have become

more prevalent. The most common form of antenna tuner in

recent years is some variation of a T-network configuration.

The basic system of a transmitter, matching circuit,

transmission line and antenna is shown in Fig 1 . As usual,

we assume that the transmitter is designed to deliver its rated

power into a load of 50

. The problem is one of designing

a matching circuit that will transform the actual line

impedance at the input of the transmission line into a

resistance of 50

Ω

. This resistance will be unbalanced; that

is, one side will be grounded, since modern transmitters

universally ground one side of the output connector to the

Ω

Harmonics and Pi-Network Tuners

In a trapped antenna system, if a different network is

used for an antenna tuner (such as a low-pass Pi network),

there will be additional attenuation of harmonics, perhaps

as much as 30 dB for a loaded Q of 3. The exact degree of

harmonic attenuation, however, is often limited due to the

stray inductance and capacity present in most tuners at

harmonic frequencies. Further, the matching range for a Pi-

Fig 1—Essentials of a coupling system between

transmitter and transmission line.

25-2

Chapter 25

network tuner is fairly limited because of the range of input

and output capacitance needed for widely varying loads.

the desired value of R2 is obtained when

(Eq 2)

Harmonics and Stubs

Far more reliable suppression of harmonics can be

achieved using shorted quarter-wave transmission-line stubs

at the transmitter output. A typical 20-meter

This means that the desired value of R2 may be obtained

by adjusting either the coupling, k, between the two coils,

or by changing the Q of the circuit L1-C1-R1, or by doing

both. If the coupling is fixed, as is often the case, Q must be

adjusted to attain a match. Note that increasing the value of

Q is equivalent to tightening the coupling, and vice versa.

If L2 does not have the optimum value, the match may

still be obtained by adjusting k and Q, but one or the other—

or both—must have a larger value than is needed when X L2

is equal to R2. In general, it is desirable to use as low a value

of loaded Q as is practical. Low Q values mean that the circuit

requires little or no readjustment when shifting frequency

within a band (provided the antenna R1 does not vary

appreciably with frequency). A low value of loaded Q also

means that less loss occurs in the matching network itself.

/4 shorted stub

(which is an open circuit at 20 meters, but a short circuit at

10 meters) will provide about 25 dB of attenuation to the

second harmonic. It will handle full legal amateur power

too. See Chapter 26 for more details on stubs. In short, an

antenna tuner that is capable of matching a wide range of

impedances should not be relied on to give additional

harmonic suppression.

MATCHING WITH INDUCTIVE COUPLING

Inductively coupled matching circuits are shown in

basic form in Fig 2 . R1 is the actual load resistance to which

the power is to be delivered, and R2 is the resistance seen

by the power source. The objective is to make it R2 = 50

L1 and C1 form a resonant circuit capable of being tuned to

the operating frequency. The coupling between L1 and L2

is adjustable.

The circuit formed by C1, L1 and L2 is equivalent to a

transformer having a primary-to-secondary impedance ratio

adjustable over wide limits. The resistance coupled into L2

from L1 depends on the effective Q of the circuit L1-C1-

R1, the reactance of L2 at the operating frequency, and the

coefficient of coupling, k, between the two coils. The

approximate relationship is (assuming C1 is properly tuned)

R2 = k 2 X L2 Q (Eq 1)

where X L2 is the reactance of L2 at the operating frequency.

The value of L2 is optimum when X L2 = R2, in which case

Ω

Circuit Q

In Fig 2A, where a parallel-tuned network is used, Q P

is equal to

(Eq 3)

This assumes L1-C1 is tuned to the operating frequency.

This circuit is suitable for comparatively high values of R1—

from several hundred to several thousand ohms.

In Fig 2C, which is a series-tuned network, Q is equal

(Eq 4)

Again, we assume that L1-C1 is tuned to the operating

frequency. This circuit is suitable for low values of R1—

from a few ohms up to a hundred or so ohms. In Fig 2B the

Q depends on the placement of the taps on L1 as well as on

the reactance of C1. This circuit is suitable for matching all

values of R1 likely to be encountered in practice.

Note that to change Q in either Fig 2A or Fig 2C, it is

necessary to change the reactance of C1. Since the circuit is

tuned essentially to resonance at the operating frequency,

this means that the L/C ratio must be varied in order to change

Q. In Fig 2B a fixed L/C ratio may be used, since Q can be

varied by changing the tap positions. The Q will increase as

the taps are moved closer together, and will decrease as they

are moved farther apart on L1.

Reactive Loads—Series and Parallel Coupling

More often than not, the load represented by the input

impedance of the transmission line is reactive as well

as resistive. In such a case the load cannot be represented

by a simple resistance, such as R1 in Fig 2. As stated in

Chapter 24 , for any one frequency we have the option of

considering the load to be a resistance in parallel with a

Fig 2—Circuit arrangements for inductively coupled

impedance-matching circuit. A and B use a parallel-

tuned coupling tank; B is equivalent to A when the taps

are at the ends of L1. The series-tuned circuit at C is

useful for very low values of load resistance, R1.

Coupling the Transmitter to the Line

25-3

reactance, or as a resistance in series with a reactance. In

Fig 2 , at A and B, it is convenient to use the parallel equivalent

of the line input impedance. The series equivalent is more

suitable for Fig 2C.

Thus, in Fig 3A and 3B the load might be represented

by R1 in parallel with the capacitive reactance C, and in

Fig 3C by R1 in series with a capacitive reactance C. In

Fig 3A, the capacitance C is in parallel with C1 and so the

total capacitance is the sum of the two. This is the effective

capacitance that, with L1, tunes to the operating frequency.

Obviously the setting of C1 will be at a lower value of

capacitance with such a load than it would with a purely

resistive load such as in Fig 2A .

In Fig 3B the capacitance of C also increases the total

capacitance effective in tuning the circuit. However, in this

case the increase in effective tuning capacitance depends on

the positions of the taps. If the taps are close together the

effect of C on the tuning is relatively small, but it increases

as the taps are moved farther apart.

In Fig 3C, the capacitance C is in series with C1 and so

the total capacitance is less than either. Hence the capacitance

of C1 must be increased in order to resonate the circuit, as

compared with the purely resistive load shown in Fig 2C .

If the reactive component of the load impedance is

inductive, similar considerations apply. In such case an

inductance would be substituted for the capacitance C shown

in Fig 3. The effect in Fig 3A and 3B would be to decrease

the effective inductance in the circuit, so C1 would require a

larger value of capacitance in order to resonate the circuit at

the operating frequency. In Fig 3C the effective inductance

would be increased, thus making it necessary to set C1 at a

lower value of capacitance for resonating the circuit.

Effect of Line Reactance on Circuit Q

The presence of reactance in the line input impedance

presented to the matching network can affect the Q of the

matching circuit. If the reactance is capacitive, the Q will

not change if resonance can be maintained by adjustment of

C1 without changing either the value of L1 or the position

of the taps in Fig 3B (as compared with the Q when the load

is purely resistive and has the same value of resistance, R1).

If the load reactance is inductive, the L/C ratio changes

because the effective inductance in the circuit is changed

and, in the ordinary case, L1 is not adjustable. This increases

the Q in all three circuits of Fig 3.

When the load has appreciable reactance, it is not

always possible to adjust the circuit to resonance by

readjusting C1, as compared with the setting it would have

with a purely resistive load. Such a situation may occur when

the load reactance is low compared with the resistance in

the parallel-equivalent circuit, or when the reactance is high

compared with the resistance in the series-equivalent circuit.

The very considerable detuning of the circuit that results is

often accompanied by an increase in Q, sometimes to values

that lead to excessively high circulating currents in the

circuit. This causes the efficiency to suffer. (Ordinarily the

power loss in matching circuits of this type is

inconsequential, if the loaded Q is below 10 and a good coil

is used.) An unfavorable ratio of reactance to resistance in

the input impedance of the line can exist if the SWR is high

and the line length is near an odd multiple of

/8 (45

Q of Line Input Impedance

The ratio between reactance and resistance in the

equivalent input circuit—that is, the Q of the impedance at

the line’s input—is a function of line length and SWR. There

is no specific value of this Q of which it can be said that

lower values are satisfactory while higher values are not. In

part, the maximum tolerable value depends on the tuning

range available in the matching circuit. If the tuning range

is restricted (as it will be if the variable capacitor has

relatively low maximum capacitance), compensating for the

line input reactance by absorbing it in the matching circuit—

that is, by retuning C1 in Fig 3—may not be possible. Also,

if the Q of the matching circuit is low, the effect of the line

input reactance will be greater than it will when the matching-

circuit Q is high.

As stated earlier, the optimum matching-circuit design

is one in which the Q is low, that is, a low reactance-to-

resistance ratio.

Compensating for Input Reactance

When the reactance/resistance ratio in the line input

impedance is unfavorable, it is advisable to take special steps

to compensate for it. This can be done as shown in Fig 4 .

Fig 3—Line input impedances containing both

resistance and reactance can be represented as

shown enclosed in dashed lines, for capacitive

reactance. If the reactance is inductive, a coil is

substituted for the capacitance C.

25-4

Chapter 25

Compensation consists of supplying external reactance of

the same numerical value as the line reactance, but of the

opposite kind. Thus in Fig 4A, where the line input

impedance is represented by resistance and capacitance in

parallel, an inductance L having the same numerical value

of reactance as C can be connected across the line terminals

to cancel out the line reactance. (This is actually the same

thing as tuning the line to resonance at the operating

frequency.) Since the parallel combination of L and C is

equivalent to an extremely high resistance at resonance, the

input impedance of the line becomes a pure resistance having

essentially the same resistance as R1 alone.

The case of an inductive line impedance is shown in

Fig 4B. In this case the external reactance required is

capacitive, of the same numerical value as the reactance of

L. Where the series equivalent of the line input impedance

is used, the external reactance is connected in series, as

shown at C and D in Fig 4.

In general, these methods are not needed unless the

matching circuit has insufficient range of adjustment to

provide compensation for the line reactance as described

earlier, or when such a large readjustment is required that

the matching-circuit Q becomes undesirably high. The latter

condition usually is accompanied by heating of the coil used

in the matching network.

Methods for Variable Coupling

The coupling between L1 and L2, Figs 2 and 3 ,

preferably should be adjustable. If the coupling is fixed, such

as with a fixed-position link, the placement of the taps on

L1 for proper matching becomes rather critical. The

additional matching adjustment afforded by adjustable

coupling between the coils facilitates the matching procedure

considerably. L2 should be coupled to the center of L1 for

the sake of maintaining balance, since the circuit is used

with balanced lines.

If adjustable inductive coupling such as a swinging link

is not feasible for mechanical reasons, an alternative is to

use a variable capacitor in series with L2. This is shown in

Fig 5 . Varying C2 changes the total reactance of the circuit

formed by L2-C2, with much the same effect as varying

the actual mutual inductance between L1 and L2.

The capacitance of C2 should resonate with L2 at the

lowest frequency in the band of operation. This calls for a

fairly large value of capacitance at low frequencies (about

1000 pF at 3.5 MHz for 50-

line) if the reactance of L2 is

equal to the line Z 0 . To utilize a capacitor of more convenient

size—maximum capacitance of perhaps 250 to 300 pF—

a value of inductance may be used for L2 that will resonate

at the lowest frequency with the maximum capacitance

available.

On the higher frequency bands the problem of variable

capacitors does not arise since a reactance of 50 to 75

Ω

within the range of conventional components.

Circuit Balance

Fig 5 shows C1 as a balanced or split-stator capacitor.

This type of capacitor is desirable in a practical matching

circuit to be used with a balanced line, since the two sections

are symmetrical. The rotor assembly of the balanced

capacitor may be grounded, if desired, or it may be left

floating and the center of L1 may be grounded; or both may

float. Which method to use depends on considerations

discussed later in connection with antenna currents on

transmission lines. As an alternative to using a split-stator

type of capacitor, a single-section capacitor may be used.

Fig 4—Compensating for reactance present in the line

input impedance.

Fig 5—Using a variable capacitance, C2, as an alternative

to variable mutual inductance between L1 and L2.

Coupling the Transmitter to the Line

25-5

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