Series Resistor Attenuator

Overview

The simplest attenuator configurations using a single resistor. Used as a lossy matching network or when impedance matching is not required.

Topology

Input ──[R]── Output

Single series resistor between source and load.

Design Equation

Given:

  • Source impedance: ZS

  • Load impedance: ZL

  • Desired power attenuation: α (linear power ratio, α < 1)

The series resistor value is:

R = (-1) × ((ZL + ZS) × α - 2√(ZL × ZS × α)) / α

Simplified for ZS = ZL = Z₀:

R = 2 × Z₀ × (1/√α - 1)

Impedances Seen

Input impedance (looking into attenuator from source):

Zin = R + ZL

Output impedance (looking back from load):

Zout = R + ZS

Power Dissipation

Pdiss = Pin × (1 - α)

All dissipated power goes into the single resistor.

Example: 10 dB, ZS = ZL = 50 Ω, Pin = 1 W

α = 10^(-10/10) = 0.1
√α ≈ 0.316

R = 2 × 50 × (1/0.316 - 1)
  = 2 × 50 × (3.162 - 1)
  = 216.2 Ω

Zin = 216.2 + 50 = 266.2 Ω
Zout = 216.2 + 50 = 266.2 Ω

Pdiss = 1 × (1 - 0.1) = 0.9 W

VSWR at Input

When ZS ≠ Zin:

VSWR_in = (Zin/ZS)    if Zin > ZS
        = (ZS/Zin)    if ZS > Zin

For the example above:

VSWR_in = 266.2 / 50 = 5.32:1  (poor match)

See Also