L-Pad (1st Shunt) Attenuator

Overview

L-pad attenuators are essentially broadband L-section matching networks. They are used mainly for impedance transformation (e.g. in network analyzers 50 Ohm to 75 Ohm).

Topology

Input ──┬──[R2]── Output
        │         Zout ≠ Zin
       [R1]
        │
       GND

Shunt resistor R1 followed by series resistor R2.

Design Equations

α = 10^(-Attenuation/10)    (power ratio, α < 1)

R₁ = Zin / (1 - √α)         (shunt)

R₂ = Zin × (1 - √α) / √α    (series)

Zout = -Zin × (α - 2√α + 2) / (α - 2√α)

Power Dissipation

Pdiss_R1 = Pin × √α × (1 - 2√α + α) / (1 - √α)

Pdiss_R2 = Pin × (1 - √α)

Example: 10 dB, Zin = 50 Ω, Pin = 1 W

α = 0.1
√α ≈ 0.316

R₁ = 50 / (1 - 0.316)
   ≈ 73.1 Ω

R₂ = 50 × (1 - 0.316) / 0.316
   ≈ 108.2 Ω

Zout = -50 × (0.1 - 2×0.316 + 2) / (0.1 - 2×0.316)
     = -50 × 1.468 / (-0.532)
     ≈ 138.0 Ω

Power dissipation:

Pdiss_R1 = 1 × 0.316 × (1 - 0.632 + 0.1) / (1 - 0.316) ≈ 0.216 W
Pdiss_R2 = 1 × (1 - 0.316) ≈ 0.684 W

Pout = 1 - 0.216 - 0.684 = 0.1 W  ✓

Comparison: First Series vs. First Shunt

10 dB Example (Zin = 50 Ω)

Parameter

First Series

First Shunt

R₁ value

34.2 Ω

73.1 Ω

R₂ value

23.1 Ω

108.2 Ω

Zout

20.0 Ω

138.0 Ω

Power in R1

68.4%

21.6%

Power in R2

21.6%

68.4%

Key observations:

  • First series: Zout < Zin (impedance step-down)

  • First shunt: Zout > Zin (impedance step-up)

  • Power distribution is reversed between topologies

Output Impedance vs Topology

Attenuation (dB)

First Series Zout

First Shunt Zout

3

35.4 Ω

70.7 Ω

6

25.0 Ω

100.0 Ω

10

20.0 Ω

138.0 Ω

20

16.7 Ω

500.0 Ω

  • First series: Zout decreases with attenuation

  • First shunt: Zout increases with attenuation

See Also