Pi Attenuator Calculator Formula
The Pi Attenuator Calculator computes the resistor values for a Pi-type attenuator using the following formulas:
R1 = Z₀ × (K + 1) / (K – 1)
R2 = Z₀ × (K² – 1) / (2 × K)
where K = 10^(A / 20), A is the desired attenuation in dB, and Z₀ is the system impedance in ohms.
Formula Explanation
This formula calculates the two resistor values for a Pi-type attenuator. R1 is the shunt resistor connected to the input and output, while R2 is the series resistor between them. The factor K represents the voltage ratio corresponding to the attenuation in decibels. Using these equations ensures the attenuator provides the correct attenuation while maintaining impedance matching.
Uses of Pi Attenuator Calculator
- Designing RF attenuators for signal conditioning and testing.
- Matching impedance in RF and microwave circuits.
- Creating precision attenuation networks for laboratory setups.
- Learning and educational purposes in RF electronics courses.
Formula Example
Example: Suppose you want a 6 dB Pi attenuator for a 50 Ω system.
K = 10^(6 / 20) ≈ 1.995
R1 = 50 × (1.995 + 1) / (1.995 – 1) ≈ 149.9 Ω
R2 = 50 × (1.995² – 1) / (2 × 1.995) ≈ 49.9 Ω
The Pi Attenuator would use R1 ≈ 150 Ω (shunt) and R2 ≈ 50 Ω (series) to achieve 6 dB attenuation with 50 Ω system impedance.