Pads and Attenuators

Figure 21. Chart for determining reflection losses when two circuits having different impedances are connected.

Notes:

Values of the reflection loss for any two impedances Z_x and Z_y are here given as a function of the ratio

where A is the ratio of the magnitudes and θ is the difference between the angles of the two impedances. The ratio is always to be taken by dividing the larger impedance by the smaller, i.e., so that A will not be less than unity. It is immaterial whether θ is positive or negative.

Negative values of reflection losses are reflection gains.

Examples:

(1) Find reflection loss for the impedances 200/60° and 700/30°

Reflection loss = 1.4 db. (2) Find reflection loss for the impedances 400/35° and 680/45°

Reflection loss = -1.8 db,

(a gain)

of a wave without introducing appreciable distortion," may be necessary at the receiving end of the line to reduce the signal volume to the desired amount. An attenuator, defined¹ as an "adjustable transducer for reducing the amplitude of a wave without introducing appreciable distortion," is used in radio speech-input equipment to vary the volume of the program signal.

Pads are made of fixed resistors and will function over a wide frequency range, determined by the high-frequency characteristics of the resistors. Pads are commonly made in the form shown in Fig. 22, particularly if they are to be used with balanced circuits. In the design of pads, the facts known are usually the impedances of the devices with which the pad is to be associated and the loss in decibels that the pad is to have.

In accordance with the theory on page 156, the iterative impedance of the pad of Fig. 22 is

Figure 22. Circuit for studying the design of a balanced pad. For a pad, the iterative impedance ZK is resistance, often RK.

the letter R_K being used because the iterative impedance wall be resistance.

The power loss in decibels introduced by the pad can be found from power, voltage, or current ratios. If a voltage E₁₂ is impressed at the sending end, the input current will be I₁₂ = E₁₂/R_K, because the pad is symmetrical and is terminated in R_K. The voltage across the junctions x-y will be

The current through R_K will be E_xy/(0.5R₁ + R_K), and this current multiplied by R_K will give the output voltage E₃₄ across R_K. Thus,

and

As an illustration of the use of this equation, suppose that a pad such as Fig. 22 is to introduce a loss of 10 decibels and must have an iterative impedance of 600 ohms. The voltage ratio E₁₂/E₃₄ = 10^0.05x10 = 3.162, and, from equation 56a, the value of R₁ will be 622.5 ohms. With R_K and R₁ both known, from equation 55 R₂ = 422 ohms. Thus the pad of Fig. 22 should be composed of four 156-ohm resistors, and one 422-ohm resistor. Sometimes unsymmetrical taper pads⁶ having different image impedances are used between circuits of different iterative impedances.

Attenuators are made of variable resistors, usually arranged so that they are varied by a common knob. An attenuator of the configuration shown in Fig. 22 is a symmetrical, balanced device. The various resistances that an attenuator must have can be calculated as just explained for each different attenuator setting in decibels. Or calculations can be made at several settings, and curves can be plotted from which the values at other settings can be obtained. An unbalanced pad commonly used is shown in Fig. 23a. This pad also can be designed as just explained. The L-section attenuator of Fig. 23(b) is widely used in unbalanced circuits where the input and the output impedances offered by the attenuator need not remain fixed. This is an unsymmetrical device, but it is satisfactory for many purposes. Equations for the design of this attenuator can be derived in the same way as for the symmetrical pad.