T-Junction Power Divider | Qucs-S S-parameter Viewer Documentation

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# T-Junction Power Divider

## Overview

The simplest RF power divider using only transmission line impedance transformations. Provides matched input port but no isolation between outputs. Ideal for applications where isolation is not required and high power handling is needed.

## Topology

                        ┌──[Z₂, λ/4]── Port 2
                        │
    Input ──[Z₀, λ/4]───┤
         (Port 1)       │
                        └──[Z₃, λ/4]── Port 3

Basic structure:

- Input λ/4 line at Z₀

- Two output λ/4 branches at Z₂, Z₃

- Physical T-junction connection point

For unequal split, additional matching:

                        ┌──[Z₂, λ/4]──[Z₂ₘ, λ/4]── Port 2
                        │
    Input ──[Z₀, λ/4]───┤
                        │
                        └──[Z₃, λ/4]──[Z₃ₘ, λ/4]── Port 3

## Design Equations

### Power Split Ratio

K = P₂/P₃ = (Port 2 power / Port 3 power)

### Branch Impedances (First Stage)

Branch impedance to the higher-power output (Port 2):

\[Z_2 = Z_0 \times (K + 1)\]

Branch impedance to the lower-power output (Port 3):

\[Z_3 = Z_0 \times \frac{K + 1}{K}\]

### Matching Sections (Unequal Split Only)

For K ≠ 1, add λ/4 matching transformers:

\[Z_{2m} = \sqrt{2 \, Z_0^2 \,(K + 1)}\]
\[Z_{3m} = \sqrt{2 \, Z_0^2 \,\frac{K + 1}{K}}\]

### Equal Split (K = 1)

    Z₂ = Z₃ = 2 × Z₀

    No additional matching needed

For Z₀ = 50 Ω:

    Z₂ = Z₃ = 100 Ω

Critical: Ports 2 and 3 are directly connected through the junction, so there’s no isolation between them.

## Advantages

1. Simplest design: Only transmission lines, no resistors

2. Low insertion loss: Only conductor/dielectric losses

3. Small size: Compact layout (equal split)

4. Low cost: No isolation resistors to specify/purchase

## Limitations

1. No isolation: S₂₃ ≈ 0 dB

   - Signals at Port 2 leak directly to Port 3

   - Impedance at one output affects the other

2. Impedance mismatch

## Comparison with Wilkinson

Feature | T-Junction | Wilkinson
--- | --- | ---
Isolation | None (~0 dB) | Excellent (>20 dB)
Components | TL only | TL + Resistor
Power handling | Very high | Limited by R
Insertion loss | Very low | Low
Complexity | Simplest | Simple
Bandwidth | Narrow (10-15%) | Medium (20-40%)
Combining | Cannot combine | Can combine
Cost | Lowest | Low

## References

[1] Pozar, D. M. (2012). Microwave Engineering (4th ed.), Section 7.3. Wiley.

## See Also

- RF Circuit Synthesis Tools