Calculate physical dimensions for a 180° hybrid microstrip coupler based on your substrate parameters and design frequency.
Design Parameters
Ring Impedance (Zᵣ)–
Feed Line Width (w₀)–
Ring Line Width (wᵣ)–
Guided Wavelength (λg)–
Mean Ring Radius (R)–
λ/4 Segment Length–
3λ/4 Segment Length–
What is a Rat-Race Coupler?
A Rat-Race Coupler, also known as a 180-degree hybrid coupler, is a passive four-port microwave device used for power division or power combining. It consists of a ring with a circumference of 1.5 times the guided wavelength (1.5λg), where the ports are strategically spaced to achieve specific phase relationships.
Port Functionality
Power Division: If power is input at Port 1, it splits equally between Ports 2 and 4, while Port 3 remains isolated. The outputs are in-phase.
180° Hybrid: If power is input at Port 3, it splits between Ports 2 and 4, but the outputs are 180° out of phase.
Sum and Difference: This device is commonly used in mixers and antenna feed networks to generate sum (Σ) and difference (Δ) signals.
Calculation Logic
The characteristic impedance of the ring line must be:
Z_ring = Z₀ × √2
The ports are spaced at specific intervals around the ring:
Distance between Port 1 & 2: λg/4 (90°)
Distance between Port 2 & 3: λg/4 (90°)
Distance between Port 3 & 4: λg/4 (90°)
Distance between Port 4 & 1: 3λg/4 (270°)
Design Example
For a standard FR4 substrate (εᵣ = 4.4, h = 1.6mm) at 2.4 GHz:
A 50Ω feed line is approximately 3.05mm wide.
The ring requires an impedance of 70.7Ω, resulting in a narrower width of approx 1.63mm.
The total circumference is 1.5 times the guided wavelength, defining the mean radius for the layout.
function calculateRatRace() {
var f = parseFloat(document.getElementById('frequency').value);
var z0 = parseFloat(document.getElementById('z0').value);
var er = parseFloat(document.getElementById('epsilon').value);
var h = parseFloat(document.getElementById('height').value);
if (isNaN(f) || isNaN(z0) || isNaN(er) || isNaN(h) || f <= 0 || z0 <= 0 || er < 1 || h 1.52) {
w_h = 8 * Math.exp(a) / (Math.exp(2 * a) – 2);
} else {
w_h = (2 / Math.PI) * (b – 1 – Math.log(2 * b – 1) + ((er – 1) / (2 * er)) * (Math.log(b – 1) + 0.39 – 0.61 / er));
}
return w_h * h;
}
function calculateEeff(w, er, h) {
var u = w / h;
var e_eff = (er + 1) / 2 + ((er – 1) / 2) * Math.pow(1 + 12 / u, -0.5);
return e_eff;
}