Bridged-Tee Attenuator | Qucs-S S-parameter Viewer Documentation

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# Bridged-Tee Attenuator

## Overview

The Bridged-Tee attenuator is a bilateral matched attenuator topology that offers improved VSWR characteristics and unique resistor value distributions compared to standard Pi and Tee configurations.

## Topology

    Input ──┬──[R1]──┬── Output
            │        │
          [R2]      [R3]  (both equal to Z₀)
            │        │
            └──[R4]──┘
                 │
                GND

Key characteristic: R2 and R3 are always equal to Z₀, regardless of attenuation level.

## Design Equations

    L = 10^(0.05 × Attenuation)

    R₁ = Z₀ × (L - 1)

    R₄ = Z₀ / (L - 1)

    R₂ = R₃ = Z₀

Constraint: Requires Zin = Zout (bilateral matched design).

## Power Dissipation

Let:

    K = (R₁ × R₄ + Z₀ × (2×R₄ + Z₀))²

Then:

R1 (series resistor):

    Pdiss_R1 / Pin = (4 × R₁ × R₄² × Z₀) / K

R2 (first shunt to bridge):

    Pdiss_R2 / Pin = (R₁ × R₄ + Z₀²)² / K

R3 (second shunt to bridge):

    Pdiss_R3 / Pin = 0   (carries no current at DC/low frequencies)

R4 (bridge to ground):

    Pdiss_R4 / Pin = (4 × R₄ × Z₀²) / K

## Example: 10 dB, Z₀ = 50 Ω, Pin = 1 W

    L = 10^(0.05 × 10) = 10^0.5 ≈ 3.162

    R₁ = 50 × (3.162 - 1) = 108.1 Ω
    R₄ = 50 / (3.162 - 1) = 23.1 Ω
    R₂ = R₃ = 50 Ω

Power dissipation:

    K = (108.1 × 23.1 + 50 × (2×23.1 + 50))²
      = (2497.1 + 4810)²
      ≈ 5.34×10⁷

    Pdiss_R1 ≈ (4 × 108.1 × 23.1² × 50) / K ≈ 0.022 W
    Pdiss_R2 ≈ (2497.1 + 2500)² / K ≈ 0.468 W
    Pdiss_R3 = 0 W
    Pdiss_R4 ≈ (4 × 23.1 × 2500) / K ≈ 0.004 W

    Pout = 1 - 0.022 - 0.468 - 0.004 ≈ 0.506 W  (≈ 0.1 W for 10 dB attenuation)

Note: Most power is dissipated in R2, which is always equal to Z₀.

## Power Distribution Analysis

Attenuation (dB) | R₁ (Ω) | R₂ (Ω) | R₃ (Ω) | R₄ (Ω) | Power in R2 (%)
--- | --- | --- | --- | --- | ---
3 | 20.5 | 50 | 50 | 121.9 | ~35%
6 | 49.9 | 50 | 50 | 50.1 | ~45%
10 | 108.1 | 50 | 50 | 23.1 | ~50%
20 | 495 | 50 | 50 | 5.05 | ~90%

Note: Most power is dissipated in R2, whose value is constant and equal to Z₀.

## Advantages

1. Constant R2, R3 values

2. Low power in R1, R4: Good for PIN diode-based variable attenuators

   - R1 and R4 can be PIN diodes (controlled by bias current)

   - R2, R3 are fixed SMD resistors

## Limitations

1. Zin = Zout: It cannot be used for impedance transformation

2. R2 power dissipation: At high attenuation, R2 handles most of the power

## References

[1] Vizmuller, P. (1995). RF Design Guide: Systems, Circuits, and Equations, Chapter 3. Artech House.

[2] Doherty, W. E., & Joos, R. D. (1998). The PIN Diode Circuit Designer’s Handbook, Chapter 4. Microsemi Corp.

## See Also

- RF Circuit Synthesis Tools