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

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# 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

- RF Circuit Synthesis Tools