T Attenuator

Calculator and formulas for calculating the resistances of a T attenuator

T 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
Series resistance R₁:
Parallel resistance R₂:

T Attenuator

T attenuator circuit

Circuit diagram of a T attenuator

Purpose and Application
  • Impedance matching at high frequencies
  • Input and output impedance equal to characteristic impedance
  • Controlled signal attenuation without distortion
  • T-shaped resistor arrangement
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 input and output impedance must equal the characteristic impedance of the transmission lines.

Formulas for T Attenuator

Basic Formulas

The resistances R₁ and R₂ of the T 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
\[R_1 = Z \frac{a-1}{a+1}\]

Resistances in the signal line

Parallel Resistance R₂
\[R_2 = Z \frac{2a}{a^2-1}\]

Resistance between the lines

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: \[R_1 = 50 \times \frac{1.995-1}{1.995+1} = 50 \times \frac{0.995}{2.995} = 16.6Ω\]
3. R₂: \[R_2 = 50 \times \frac{2 \times 1.995}{1.995^2-1} = 50 \times \frac{3.99}{2.98} = 66.9Ω\]

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: \[R_1 = 75 \times \frac{3.162-1}{3.162+1} = 75 \times \frac{2.162}{4.162} = 39.0Ω\]
3. R₂: \[R_2 = 75 \times \frac{2 \times 3.162}{3.162^2-1} = 75 \times \frac{6.324}{8.998} = 52.7Ω\]

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: \[R_1 = 600 \times \frac{5-1}{5+1} = 600 \times \frac{4}{6} = 400Ω\]
4. R₂: \[R_2 = 600 \times \frac{2 \times 5}{5^2-1} = 600 \times \frac{10}{24} = 250Ω\]

Classic audio technology with 600Ω impedance

Applications and Comparison with Pi Attenuator

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
Comparison: T vs. Pi Attenuator
Property T Attenuator Pi Attenuator
Structure 2×R₁ in series, R₂ parallel R₁ in series, 2×R₂ parallel
Impedance behavior Lower impedance at high attenuation Higher impedance at high attenuation
Application Preferred for low-impedance systems Preferred for high-impedance systems
Symmetry Symmetrically constructed Symmetrically constructed
Advantages of T Attenuator
  • Constant impedance matching
  • Good broadband characteristics
  • Symmetrical input and output impedance
  • Lower parallel resistance at high attenuation
  • Lower power dissipation in parallel resistance
Design Guidelines
  • Use precision resistors (1% or better)
  • Pay attention to power handling capability
  • Minimize parasitic capacitances at RF
  • Use short, symmetrical 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
  • Prefer T attenuator for low-impedance systems
Related Calculators

For alternative topology:

Pi Attenuator

Frequency Response and Application Limits

Frequency Dependence

The T attenuator shows good broadband behavior when correctly dimensioned. The cutoff frequency is mainly determined by parasitic reactances and component geometry.

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

Choice between T and Pi attenuator: T attenuators are particularly suitable for low-impedance systems, as the parallel resistance R₂ remains relatively low even at high attenuation.

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Circuits with resistors

Ohms Law  •  Total resistance of a resistor in parallel  •  Parallel- total resistance of 2 resistors  •  Series resistance for a voltmeter  •  Parallel resistance for an ampere meter  •  Voltage divider  •  Loaded voltage divider  •  Pi Attenuator  •  T Attenuator  •