# Resistive Attenuators Derived from Impedance Matching Voltage Dividers

Key Takeaways

• Resistive two-port networks designed for providing attenuation to the source voltage, along with impedance matching in the input and output ports, can be called resistive attenuators.

• Resistive attenuators are designed with two considerations:

Case 1: The source resistance Rs is equal to the load resistance RL.

Case 2: The source resistance Rs is not equal to the load resistance RL.

• Types of symmetrical resistive attenuators are a) symmetrical T-section attenuators, b)  symmetrical 𝜋-section attenuators, c) symmetrical lattice-section attenuators, and d) symmetrical bridged-T-section attenuators. Resistive voltage divider networks can be used as attenuators

Attenuators are two-port networks used to weaken the power supplied from the source to a level suitable for the connected load. Depending on its type, an attenuator reduces power to the load in a fixed or variable amount.

Resistive voltage divider networks are employed as attenuators in electronic equipment, radio, and communication systems to weaken the original signal. They can be considered impedance matching voltage divider circuits, which are purely resistive and employed for alleviating the effects of improper input and output terminations. These networks also provide isolation between each stage in circuits, especially in cascade connections.

## Using an Impedance Matching  Voltage Divider as an Attenuator

The resistive two-port networks designed to provide attenuation to the source voltage, along with impedance matching in the input and output ports, are called resistive attenuators. They are linear, time-invariant, two-port networks that do not cause any distortion to the input waveshape.

Resistive attenuators are designed with two considerations:

Case 1: Source resistance Rs is equal to the load resistance RL.

Case 2: Source resistance Rs is not equal to the load resistance RL.

In case 1, the two-port resistive voltage divider network is symmetrical. In case 2, the two-port resistive voltage divider is unsymmetrical.

## Symmetrical Resistive Attenuator

In the case of an attenuator design where the source resistance is Rs =RL=Ro, the propagation constant of the symmetrical resistive attenuator is a real number.

The real number value of the propagation constant implies the following:

a) The network is memoryless.

b) There will be no delay in the time-domain frequency components.

If the propagation constant of the symmetrical resistive attenuator is equal to 𝛼, then the absolute value of attenuation is given by ea, where attenuation is expressed in decibels. The performance of the attenuator expressed in decibels indicates how much input signal has decreased per frequency decade.

The equation of attenuation is as follows: In the design of a symmetrical resistive attenuator:

1) The ratio of source voltage to load voltage is kept greater than 1: The equation above indicates the action of the voltage divider network, which decreases the voltage across the load by dropping voltage across the resistors in the network.

2) N is the absolute value of attenuation and Rim1 and Rim2 are the image impedances at port 1 and port 2, respectively.

In a symmetrical resistive attenuator, Rs=RL, and Rim1=Rim2.

## Types of Resistive Attenuators

There are four types of resistive attenuators:

1. Symmetrical T-section attenuator- resistances are placed to form a T-section.

2. Symmetrical 𝜋-section attenuator- resistances are arranged so they form the shape of the mathematical symbol Pi (𝜋).

3. Symmetrical lattice-section attenuator- consists of two pairs of resistors in two legs, as shown in figure c (above).

4. Symmetrical bridged-T-section attenuator- independent control of attenuation and characteristic resistance are the advantages of this type of attenuator.

## Asymmetrical Attenuators

In the case of the circuits where Rs≠RL, asymmetrical attenuators are incorporated between the source and the load to provide attenuation as well as impedance matching. The three design specifications of asymmetrical attenuators are:

1. Rim1 , which is equal to Rs

2. Rim2, which is equal to RL

3. Attenuation, N

## Switched Attenuators

Switched attenuators are a form of variable attenuators that allow engineers to adjust the attenuation to the required value by connecting or cascading several numbers of attenuators. In this type of attenuator, attenuation can be increased step by step until the prescribed value is reached. Engineers can include or exclude each attenuator in the connection by using switches or connectors.

When used between the source and load, impedance matching voltage dividers can perform attenuation of signals. The so-called resistive attenuator is often applied in communication systems where it is necessary to match the transmitter and receiver. Impedance matching voltage dividers can also prevent interference issues in radio and TV signals. When designing wireless communication systems, consider incorporating attenuators.

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