Adams Unequal Resistive Splitter | Qucs-S S-parameter Viewer Documentation

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# Adams Unequal Resistive Splitter

## Overview

2-way unequal-split resistive power divider based on the Adams topology. Unlike the symmetric Wye and Delta splitters, this network distributes power unevenly between two output ports while simultaneously matching all ports to Z₀. The split ratio is a free design parameter. Four resistors are used: two series arms on the high-power path, one shunt isolation resistor between the two output nodes, and one shunt resistor to ground on the low-power output.

## Topology

    Port_in ──[Rs]──── N1 ────[Rs]──── Port 1  (higher power)
                        │
                       [Rt]
                        │
                       N2 ──────────── Port 2  (lower power)
                        │
                       [Ru]
                        │
                       GND

Key features:

- Two equal series resistors (Rs) on the high-power branch

- One inter-node shunt resistor (Rt) providing isolation between outputs

- One grounded shunt resistor (Ru) on the low-power output node

- All ports matched to Z₀ for any split ratio

- Very broadband. Extremely compact.

## Design Equations (Unequal Split)

Let α be the voltage split ratio, defined from the desired power ratio P₁/P₂:

    α = 1 / OutputRatio    (where OutputRatio = 10^(dB_split/20))

The four resistor values are then (normalised to Z₀, before scaling):

    Rs  = Z₀ × (1 − α) / (1 + α)

    Rp  = Z₀ × (1 − Rs²) / (2 × Rs)        [intermediate]

    Ru  = Z₀ × sqrt(1 / (1 − 4 / (2×Rp + Rs + 1)))

    Rt  = Z₀ × (Rp − Ru / (Ru + 1))

## References

[1] Greg Adams, “Designing Resistive Unequal Power Dividers”, High Frequency Electronics, 2007.

[2] “Resistive power splitters”, Microwaves101.
https://www.microwaves101.com/encyclopedias/resistive-power-splitters

## See Also

- RF Circuit Synthesis Tools