Fixed Attenuator S-Matrix Explained

This page describes the Fixed Attenuator S-Matrix (scattering matrix). It also covers the basics of Fixed Attenuators, along with their S-matrix representation. The common applications of attenuators are also mentioned.

What is a Fixed Attenuator?

Attenuators come in two main types based on the attenuation they provide: fixed and variable. They are also categorized by their control function, namely analog and digital.

• Analog Attenuators: Require an analog voltage for control.
• Digital Attenuators: Require digital values as control pins for operation.

A Fixed Attenuator provides a fixed, or constant, attenuation, unlike a variable attenuator, which can provide any attenuation within a specified range as determined by its control lines.

Figure 1: Fixed Attenuator

As shown in Figure 1, fixed attenuators are used to reduce signal power, functioning in the opposite way to an amplifier.

Fixed Attenuator S-Matrix and Applications

The Fixed Attenuator S-matrix is represented below. This S-matrix is for an ideal attenuator.

Figure 2: Fixed Attenuator S-Matrix

As evident from the S-matrix, the attenuator is a matched and reciprocal device but not lossless.

The attenuation of an attenuator is expressed as:

Attenuation = -10 * Log₁₀ |α|²

Typical values for fixed attenuators are 3 dB, 6 dB, 10 dB, 20 dB, and 30 dB. They are often referred to as “pads.”

• A 6dB attenuator pad attenuates the signal by 6dB. This means the output power is (1/4)th of the input power. Therefore, one key application of an attenuator is power reduction.

• Another significant application is improving return loss. This is illustrated in Figure 3.

Figure 3: Attenuator Application

In Figure 3, a 6 dB attenuator pad is inserted between a source and a load, where the matched load has a return loss value of 13 dB. This arrangement increases the return loss to 25 dB.

The return loss increases by approximately 12 dB (twice the attenuator value of 6 dB): once as the signal travels toward the load and again after it is reflected back.