Attenuators are circuits designed to introduce a known loss between input and output ports (1). The power ratio, expressed in decibels, between the input and output represents the loss in these circuits. The main use of attenuators is in measuring standing wave ratio (SWR) in antennas and the transmission coefficient. In SWR measurement (2), one adjusts the attenuation value to maintain equal outputs in the stationary wave detector at the maximum and minimum points. Then the SWR in dB is equal to the difference between the readings of the attenuator.

The external circuits connected to the input and output ports of the attenuator should present purely resistive impedances. These are always matched to the input and output impedances of the component. Therefore, the resistors always constitute the attenuator circuit. In general, these resistive circuits use the ‘‘T’’ and “П” circuit topologies. Figure 1 shows the ‘‘T’’ topology, where R1, R2, and R3 form the circuit. The external circuitry presents purely resistive impedances (Zi, Zo) at the input and output of the attenuator. Figure 2 shows the configuration of the ‘‘П’’ section. If the input and output impedances are the same Z = Zo), the circuits “T” and ‘‘П’’ become symmetrical, that is, R1 = R2.

R3 = 2(NZiZo )1/2/(N — 1)

R1 = Zi[(N +1)/(N — 1)] — R3 R2 = Zo[(N + 1)/(N — 1)] — R3

J. Webster (ed.), Wiley Encyclopedia of Electrical and Electronics Engineering. Copyright © 1999 John Wiley & Sons, Inc.

Figure 4. Balanced attenuator of the ‘‘O’’ type. The R3 resistor from the ‘‘П’’ circuit is distributed in the lower arm. |

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Figure 3. Balanced attenuator of the “H” type. The R1 and R2 resistors from the ‘‘T’’ circuit are distributed in the lower arms. |

Equations (5), (6), and (7) give the resistances for a type “П” circuit:

R3 = 1/2(N — 1)(ZiZo/N)1/2 (5)

1/Ri = (І/Z;)[(N + 1)/(N — 1)] — (I/R3) (6)

1/R2 = (1/Zo)[(N + 1)/(N — 1)] — (I/R3) (7)

Equations (2), (3), (4) and Eqs. (5), (6), (7) are also valid for symmetrical circuits (it is sufficient that Zi = Zo).

Attenuators “T” and ‘‘П’’ are applied to unbalanced systems, such as coaxial cables. Bifilar lines feed many antennas that are intrinsically balanced, such as dipoles. In this case, the circuits ‘‘T’’ and ‘‘П’’ change into their balanced versions and they are called ‘‘H’’ and ‘‘O’’ sections, respectively. Figure 3 shows the ‘‘H’’ circuit resistor configuration, and Fig. 4 illustrates the ‘‘O’’ circuit configuration. With respect to the circuits ‘‘T’’ and ‘‘П,’’ there is a distribution of the resistors R3 and R1, R2 in the lower branch. All equations shown previously are valid for this case. However, it is necessary to take the half of the values of the respective resistors and distribute them in the upper and lower branches of their circuits.