Coupling Networks of Lumped Reactances

Author: Edmund A. Laport

This method of coupling is customary in the range of low and medium frequencies where the use of self-matching line techniques is impractical because of cost. Such networks may be designed for almost any desired impedance match and phase difference. The synthesis of electrical networks 52-53 can be quickly solved graphically by the methods described in Chap, 5.

FIG. 4.30. Self-matching of antenna to line, using a single reactive element for power-factor correction.

The elimination of advanced mathematics places this method within reach of any radio technician.

Electrically short antennas are characterized by very low radiation resistance and very high capacitive reactance and by having one input terminal at ground potential. The coupling network must usually have a large impedance transformation ratio, and it therefore introduces considerable selectivity in addition to that associated with the antenna proper. Multiple tuning may be used to present a more favorable value of input resistance at the feed point, as described in Chap. 1. If equal currents can be maintained in each down lead by symmetry of antenna layout, the input resistance will increase approximately as the square of the number of down leads used and the reactance is increased roughly in direct proportion with the increase in the number of down leads. Therefore multiple tuning is a useful device for reducing the impedance transformation ratio of the coupling network, which in turn increases the bandwidth of the antenna proper and of the coupling network.

Figure 4.31 shows an arrangement for coupling a low-frequency antenna to a feeder, where the feeder is electrically short and merely acts as additional shunt capacitance across the antenna terminals. Tuning is performed at the input end of the feeder where it is coupled to the transmitter. With this connection the input impedance will vary as the same antenna is used for different operating frequencies.

FIG. 4.31. Short feeder used as an extension leadin.

Figure 4.32 shows a feeder-terminating and antenna-coupling network where the antenna series inductor does not completely neutralize the antenna reactance but leaves a value of capacitive reactance which, when tuned to parallel resonance with a parallel inductor, gives a resistive impedance of a value that will match the impedance of an unbalanced feeder of any prechosen value.

FIG. 4.32. Antenna-coupling circuit.

The advantage of this circuit is its easy adjustability to a desired resistance value over a range of operating frequencies with the same antenna. This permits the transmitter to work into a fixed resistive load at all frequencies. Furthermore, the selectivity of the terminal network is nearly the same as that of the antenna itself, assuming the use of high-Q inductors in the circuit. The vector diagram of Fig. 4.32B exhibits these conditions. From this vector diagram one can see immediately how the transformation is made.

The antenna current I₀ flowing through the antenna impedance R_a-jX_a (Fig. 4.32A) produces the potential drop V_0R = I₀R_a, in phase with I₀ , and V_0X = I₀X_a lagging 90 degrees. Their vector sum is V₀ in a direction that lags I₀.

Voltage V₂ is across the inductor L_p and sustains the current I₁ through it. The direction of I₁ must lag that of V₂ by 90 degrees, and the reactance of L_p is varied until the vector sum of I₀ and I₁ is in phase with V₂. This makes V₂/I₂ a resistance. By adjusting L_s and L_p the input impedance to the antenna coupling network can always be made to be a resistance that will match a transmission line of characteristic impedance Z₀ provided that Z₀ > R_a

It is interesting to indicate at this point that if V₁ > V₀x, V₂ then leads I₀. To attain a resistive input impedance to the network, it is then necessary that L_p be changed to a capacitance. The vector conditions for this case are shown in Fig. 4.32B by the dotted lines in the upper part of the diagram.

The use of an inductor as shown in Fig. 4.32A is preferable to using a capacitor in place of L_p for the following reasons:

The energy storage in the coupling network is less and therefore has less selectivity (desirable in cases where bandwidth is important).

It is sometimes more convenient and economical to use a variable inductor than a variable capacitor (at high power and at low frequencies).

The use of a parallel inductor provides a conductive path to ground which serves as a static drain.

To make this adjustment in practice, one can preset an impedance bridge for balance at a resistance of Z₀ ohms, the feeder characteristic impedance. Then the bridge is connected to the input terminals of the coupling network, and L_p and L_s are manipulated until the bridge is again balanced. The settings of taps and variometers may then be logged and the operation repeated for another frequency. For fixed-frequency operation, permanent connections are made and checked again with the preset impedance bridge. Exact balance is obtained by adjusting the position of the leads themselves by flexing slightly. At exact balance, the movement of the antenna in the wind and the effect of fog and moisture on the system are easily detectable with the bridge. For still more perfect adjustment, the bridge can be connected to the input to the feeder and adjustments made for a specific resistance value at that point. The coupling adjustments between feeder and power-amplifier anodes can also be made precisely by presetting the bridge to the correct operating value of anode resistance at the sockets and adjusting the power-amplifier circuits until balance is obtained at the anodes.

The use of this coupling circuit permits the power-amplifier output circuits to be designed for working into a fixed value of resistance at all working frequencies. This enables the transmitter designer to use the coupling circuit of Fig. 4.33 between feeder and tank circuit with excellent harmonic-suppression properties, a minimum number of components, and satisfactory tuning flexibility.

Referring now to the more general ranges of antenna impedances such as those encountered with medium-frequency-broadcast nondirective and directive antennas, one may be required to match almost any antenna impedance whose resistance may be larger or smaller than Z₀ and whose reactance is positive or negative in any degree.

Fig. 4.33 : Transmitter output-coupling circuit

If the phase difference between antenna current and feeder current is immaterial, as is usual with nondirective antennas, the impedance match can always be made with two reactive elements in an L network. The low-pass form of L network should always be chosen for its harmonic-reducing property. The L network can transform resistance upward or downward, depending upon whether the shunt element is on the feeder side or the antenna side of the series element. The T and π forms of network provide means for making specified impedance transformations with specified phase differences between load (antenna) current and feeder current, as required in the feeding of directive arrays for medium-frequency broadcasting.