Series Resistor Attenuator | Qucs-S S-parameter Viewer Documentation

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# 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

- RF Circuit Synthesis Tools