Shunt 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 ──┬── Output
        │
       [R]
        │
       GND

Single shunt resistor to ground.

Design Equation

Given:

  • Source impedance: ZS

  • Load impedance: ZL

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

The shunt resistor value is:

R = (2√(ZL × ZS × α) × ZL × ZS + (ZL² × ZS + ZL × ZS²) × α) / 
    (4 × ZL × ZS - (ZL² + 2×ZL×ZS + ZS²) × α)

Simplified for ZS = ZL = Z₀:

R = Z₀ × (1 + √α) / (1 - √α)

Impedances Seen

Input impedance:

Zin = R ∥ ZL = (R × ZL) / (R + ZL)

Output impedance:

Zout = R ∥ ZS = (R × ZS) / (R + ZS)

Power Dissipation

Pdiss = Pin × (1 - α)

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

α = 0.1
√α ≈ 0.316

R = 50 × (1 + 0.316) / (1 - 0.316)
  = 50 × 1.316 / 0.684
  ≈ 96.2 Ω

Zin = (96.2 × 50) / (96.2 + 50) ≈ 32.9 Ω
Zout = (96.2 × 50) / (96.2 + 50) ≈ 32.9 Ω

Pdiss = 1 × (1 - 0.1) = 0.9 W

VSWR at Input

VSWR_in = 50 / 32.9 ≈ 1.52:1  (better than series, but still mismatched)

Comparison: R-Series vs. R-Shunt

10 dB Example (ZS = ZL = 50 Ω)

Parameter

R-Series

R-Shunt

R value

216.2 Ω

96.2 Ω

Zin

266.2 Ω

32.9 Ω

Zout

266.2 Ω

32.9 Ω

VSWR (50Ω system)

5.32:1

1.52:1

Power dissipation

0.9 W

0.9 W

Key observations:

  • R-series: Increases impedance (poor match)

  • R-shunt: Decreases impedance (better match, but still poor)

  • Both: Same power dissipation

  • Shunt has better VSWR for same attenuation

Attenuation Range

Attenuation (dB)

R-Series (Ω)

R-Shunt (Ω)

VSWR_in (Series)

VSWR_in (Shunt)

3

70.7

183.3

2.41:1

1.37:1

6

100.0

125.0

3.00:1

1.60:1

10

216.2

96.2

5.32:1

1.52:1

20

495.0

55.3

10.9:1

1.11:1

Trend:

  • R-series: VSWR worsens dramatically with attenuation

  • R-shunt: VSWR improves slightly with attenuation (but output impedance drops)

Advantages

  1. Extremely simple

  2. Low cost:

  3. Broadband: Resistive, works DC to GHz (limited by parasitics)

  4. Small size: Smallest footprint

  5. Predictable: No resonances or complex behavior

Limitations

  1. Poor impedance match: High VSWR at both ports

  2. Attenuation depends on source/load impedances: Not constant like matched designs

  3. Reflections: Standing waves in transmission line systems

  4. Bidirectional mismatch: Both input and output are affected

  5. Not suitable for RF: Mismatch causes measurement errors, signal integrity issues

See Also