Reflection Attenuator Calculator

Overview

This calculator helps you determine the required termination resistor values for a Reflection Attenuator. Ideally, a reflection attenuator uses a quadrature hybrid coupler terminated with two identical resistors (or variable loads).

The calculator provides two possible resistor solutions based on the system impedance ($Z_0$) and the desired attenuation:

1. High Resistance State: Where the resistor value ($R_1$) is greater than the system impedance ($R_1 > Z_0$).
2. Low Resistance State: Where the resistor value ($R_1$) is smaller than the system impedance ($R_1 < Z_0$).

Formulas

To calculate the resistor values, we first determine the Reflection Coefficient ($\Gamma$) based on the desired Attenuation ($A_{dB}$).

$\Gamma = 10^{-\frac{A_{dB}}{20}}$

Once we have the reflection coefficient, there are two formulas to find the resistance ($R_1$), depending on whether the resistance is higher or lower than the characteristic impedance ($Z_0$):

Case 1: $R_1 > Z_0$ (High State) $R_1 = Z_0 \times \frac{1 + \Gamma}{1 - \Gamma}$

Case 2: $R_1 < Z_0$ (Low State) $R_1 = Z_0 \times \frac{1 - \Gamma}{1 + \Gamma}$

Where:

• $R_1$: The calculated termination resistance ($\Omega$).
• $Z_0$: The system characteristic impedance (typically $50\Omega$).
• $\Gamma$: The voltage reflection coefficient derived from the desired attenuation.

Applications

General Function Attenuators are passive circuits used to reduce the amplitude of a signal without significantly distorting its waveform. They act as a bridge between a high-power source (transmitter) and a sensitive load (receiver/antenna), ensuring the signal level is within a safe operating range.

Why Use Reflection Attenuators? Unlike standard Pi or T-pad attenuators, Reflection Attenuators offer unique advantages in RF design:

• Variable Control: They are frequently used as variable RF attenuators by using PIN diodes or FETs as the variable resistors.
• Bandwidth: Depending on the type of coupler used (e.g., Lange coupler or Hybrid coupler), these attenuators can operate over broad bandwidths (often octave bandwidths).
• Digital Applications: They often feature discrete states, making them suitable for digital step attenuators. With careful design, they can provide a response that is invariant to phase changes.