Pi Attenuator

Calculator and formulas for calculating the resistances of a Pi attenuator

Pi Attenuator Calculator

Input Modes

Enter either the attenuation in dB or the voltage ratio U₁/U₂. The impedance must be specified for both modes.

Choose Input Mode
Ω
dB
V
V
Results
Resistance R₁:
Resistance R₂:

Pi Attenuator

Pi attenuator circuit

Circuit diagram of a Pi attenuator

Purpose and Application
  • Impedance matching at high frequencies
  • Input and output impedance equal to characteristic impedance
  • Controlled signal attenuation
  • Simultaneous attenuation and impedance matching
Input Modes
Attenuation in dB: Direct entry of the attenuation value
Voltage ratio: Ratio U₁/U₂ of input and output voltage
Important Note
For attenuators at high frequencies, attention must be paid to impedance matching. The calculated resistances ensure equal input and output impedance.

Formulas for Pi Attenuator

Basic Formulas

The resistances R₁ and R₂ of the Pi attenuator are calculated from the impedance Z and the attenuation factor a. The attenuation factor a is calculated from the ratio of output voltage to input voltage (U₁ / U₂), or from the attenuation ΔL in dB.

Attenuation Factor
\[a = \frac{U_1}{U_2} = 10^{\frac{\Delta L}{20 \text{ dB}}}\]

Ratio of input to output voltage

Series Resistance R₁
\[R_1 = Z \frac{a^2-1}{2a}\]

Resistance in the signal line

Parallel Resistance R₂
\[R_2 = Z \frac{a+1}{a-1}\]

Resistance between signal and ground

Practical Calculation Examples

Example 1: 6dB attenuation at 50Ω

Given: Z = 50Ω, ΔL = 6dB

1. Attenuation factor: \[a = 10^{\frac{6}{20}} = 10^{0.3} = 1.995\]
2. R₁: \[R_1 = 50 \times \frac{1.995^2-1}{2 \times 1.995} = 16.6Ω\]
3. R₂: \[R_2 = 50 \times \frac{1.995+1}{1.995-1} = 150.3Ω\]

Standard 6dB attenuation for 50Ω systems

Example 2: 10dB attenuation at 75Ω

Given: Z = 75Ω, ΔL = 10dB

1. Attenuation factor: \[a = 10^{\frac{10}{20}} = 10^{0.5} = 3.162\]
2. R₁: \[R_1 = 75 \times \frac{3.162^2-1}{2 \times 3.162} = 96.2Ω\]
3. R₂: \[R_2 = 75 \times \frac{3.162+1}{3.162-1} = 144.3Ω\]

Typical attenuation for cable TV applications

Example 3: Voltage ratio at 600Ω

Given: Z = 600Ω, U₁ = 10V, U₂ = 2V

1. Attenuation factor: \[a = \frac{U_1}{U_2} = \frac{10V}{2V} = 5\]
2. Attenuation in dB: \[\Delta L = 20 \times \log_{10}(5) = 20 \times 0.699 = 13.98dB\]
3. R₁: \[R_1 = 600 \times \frac{5^2-1}{2 \times 5} = 600 \times \frac{24}{10} = 1440Ω\]
4. R₂: \[R_2 = 600 \times \frac{5+1}{5-1} = 600 \times \frac{6}{4} = 900Ω\]

Classic audio technology with 600Ω impedance

Applications and Design Guidelines

Typical Applications

  • RF measurement technology: Calibrated attenuation for measurements
  • Antenna technology: Matching between transmitters and antennas
  • Cable TV: Signal level attenuation in distribution systems
  • Laboratory measurement: Defined signal attenuation
  • EMC testing: Controlled signal reduction
  • Audio measurement: Precise level attenuation
Advantages of Pi Attenuator
  • Constant impedance matching
  • Good broadband characteristics
  • Symmetrical input and output impedance
  • Simple calculation and implementation
  • Low frequency dependence
Design Guidelines
  • Use precision resistors (1% or better)
  • Pay attention to power handling capability
  • Minimize parasitic capacitances at RF
  • Use short connections
  • Consider temperature coefficients
Practical Tips
  • Standard impedances: 50Ω (RF), 75Ω (Video), 600Ω (Audio)
  • Attenuation values: 3dB, 6dB, 10dB, 20dB are common
  • For high attenuation: Cascade multiple stages
  • At very high frequencies: Use stripline technique

Frequency Response and Limitations

Frequency Dependence

The Pi attenuator shows good broadband behavior when correctly dimensioned. The cutoff frequency is mainly determined by parasitic reactances.

DC to 100MHz:
Discrete resistors
Standard packages
100MHz to 1GHz:
SMD packages
Short connections
Above 1GHz:
Stripline technique
Microwave design

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