RF Theory › Antennas & Arrays
Wave Polarisation Visualizer
Polarisation is usually summarised as three static pictures — a line, a circle, an ellipse. This page animates the actual electric field vector so you can see linear, circular and elliptical polarisation as what they really are: one rotating vector, with axial ratio and phase as the only two dials.
01 — The Physics
What Polarisation Means
An electromagnetic wave's electric field is always perpendicular to its direction of travel — but within that transverse plane, the field can point anywhere, and that direction can change with time. Polarisation is simply a description of how the tip of the E-field vector moves in that plane as the wave passes a fixed point.
The Electric Field, Transverse Plane, Fixed Point in Space
Ex(t) = Ax·cos(ωt) Ey(t) = Ay·cos(ωt + δ)Two orthogonal components, amplitudes Ax and Ay, with a relative phase δ between them. Every polarisation state — linear, circular, elliptical — is just a different choice of Ax, Ay and δ.
The one idea that unifies all of it: if δ = 0° or 180°, the two components rise and fall in lockstep (or opposition) and the vector tip only ever moves back and forth along one straight line — linear. If Ax = Ay and δ = ±90°, the tip traces a perfect circle — circular. Everything else traces an ellipse — elliptical, the general case that linear and circular are just special cases of.
02 — See It Live
Interactive Visualizer
The wave is travelling toward you, out of the screen. The bright dot is the instantaneous E-field vector; the faint trail is the path it traces over one full cycle. Watch the trail collapse to a line, close into a circle, or open into an ellipse as you change Ax, Ay and δ.
03 — Design Numbers
Axial Ratio & Handedness
The shape of the ellipse is fully captured by its axial ratio (AR) — the length of its major axis divided by its minor axis. AR = 1 (0 dB) is a perfect circle; AR = ∞ is a perfect line. Real "circularly polarised" antennas are specified with a maximum AR (commonly 3 dB or less near boresight) rather than an exact 0 dB, because perfect circularity only happens exactly on-axis.
Axial Ratio (Closed Form)
OA² = ½·[Ax²+Ay² + √((Ax²−Ay²)² + 4Ax²Ay²cos²δ)] (semi-major axis)OB² = ½·[Ax²+Ay² − √((Ax²−Ay²)² + 4Ax²Ay²cos²δ)] (semi-minor axis)
AR = OA / OB (1 ≤ AR ≤ ∞) · ARdB = 20·log₁₀(AR)
| Case | Condition | AR | Handedness |
|---|---|---|---|
| Linear | δ = 0°/180°, or Ax=0, or Ay=0 | ∞ (no rotation) | — |
| Circular | Ax=Ay, δ=−90° | 1 (0 dB) | RHCP |
| Circular | Ax=Ay, δ=+90° | 1 (0 dB) | LHCP |
| Elliptical | everything else, δ<0 | 1 < AR < ∞ | right-handed sense |
| Elliptical | everything else, δ>0 | 1 < AR < ∞ | left-handed sense |
Reading the sign of δ: in this animation (wave travelling toward you, out of the screen), δ < 0 means Ey lags Ex — the tip traces counter-clockwise, which is the standard engineering (IEEE) definition of right-hand circular/elliptical polarisation. δ > 0 (Ey leads) traces clockwise — left-hand. GPS, GNSS and most satellite downlinks use RHCP specifically to survive this handedness convention consistently through a chain of reflections and ionospheric rotation.
04 — Practical Consequence
Polarisation Mismatch Loss
A receiving antenna is itself polarised — it only picks up the component of the incoming E-field that matches its own polarisation. Any mismatch between the wave's polarisation and the antenna's polarisation is pure, unrecoverable loss, on top of whatever free-space path loss and gain the link budget already accounts for.
| TX Polarisation | RX Polarisation | Loss | Note |
|---|---|---|---|
| Linear | Same linear axis | 0 dB | perfectly aligned |
| Linear | Linear, offset by ψ | −10·log₁₀(cos²ψ) dB | e.g. 45° offset = 3 dB, 90° (cross-pol) = ∞ dB |
| Linear | Circular (either sense) | 3 dB, always | circular has no preferred axis to misalign |
| RHCP | RHCP | 0 dB | same sense — full transfer |
| RHCP | LHCP | very large (ideally ∞ dB) | opposite sense — this is how CP rejects same-frequency reuse on the opposite hand |
Why this bites people: a perfectly good link can fail entirely if someone points a horizontally-polarised Yagi at a vertically-polarised base station, or uses an LHCP feed to receive an RHCP satellite. Always confirm polarisation match before blaming the link budget for a "missing" 3 dB — cross-polarisation is a much larger and much more common error.
05 — Why It Matters
Polarisation Choices in Real Systems
| System | Typical Choice | Why |
|---|---|---|
| GPS / GNSS | RHCP | survives ionospheric Faraday rotation and multipath reflections without the receiver needing to track a rotating linear axis |
| Satellite TV / VSAT | Dual linear (H/V) or dual circular (L/R) | polarisation reuse — two independent channels share the same frequency by using orthogonal polarisations |
| WiFi / cellular handset | Linear (often vertical) | simple, cheap antennas; orientation-dependent loss is tolerated for short indoor/urban links |
| Cellular base stations (MIMO) | Dual-slant ±45° linear | polarisation diversity — two decorrelated multipath channels from one physical location, without needing two separated antennas |
| Weather / polarimetric radar | Dual linear (H/V), alternating or simultaneous | differential reflectivity between H and V returns reveals raindrop shape and distinguishes rain from hail or snow |