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