A receiver can tell you a signal is there, and - with the right demodulator - what it says. What one receiver cannot tell you is where it came from. Finding that out is direction finding, and it is one of the oldest and most useful techniques in signals work, because it turns an anonymous transmission into a place on a map.

The core idea is almost disappointingly simple: a single receiver can measure a bearing - the direction a signal arrives from - but not a distance. A bearing is a line, not a point. You need several lines, from several places, and the transmitter is where they cross.

[INFO]
Fundamentals only - the geometry of bearings and fixes, as taught in amateur radio foxhunting and basic signals theory. The demo computes every bearing and intersection live. Builds on the modulation and spectrum foundation.
◈ interactive artifact
Triangulate the Emitter
Three receivers, each measuring only a bearing. Drag the emitter and watch the lines of position cross. Toggle realistic bearing error to see why the fix is a region, not a point.

//A Bearing Is a Line

How does a receiver get a direction at all? The simplest way is a directional antenna - one that hears better in some directions than others. Rotate it, find the peak (or, more precisely, the sharp null where the signal disappears), and you have the line the signal is arriving along. A Yagi, the arrow-shaped TV-style antenna, does this; so does a simple loop, which has deep nulls off its edges. More sophisticated systems use an array of fixed antennas and compare the tiny differences in arrival time or phase between them to compute the angle electronically, with nothing moving. That is how a system gets a bearing in milliseconds instead of by hand.

Either way, the output is the same: an angle, and therefore a line extending from the receiver across the map. The transmitter is somewhere on that line. That is all one receiver knows.

//The Crossing Is the Fix

Put a second receiver somewhere else and you get a second line. Two lines cross at a point, and in a perfect world that point is the transmitter. This is triangulation, and it is why direction finding is fundamentally a network activity: one antenna gives you a direction, a spread of them gives you a location.

The real world is not perfect, which is the most important thing the demo shows. Flip on bearing error and the three lines stop meeting at a single point - they bound a small triangle instead. Surveyors and signals operators call it the "cocked hat." The true transmitter is somewhere inside it, and the size of that triangle is your uncertainty. Everything about doing direction finding well is about shrinking that triangle.

What shrinks the triangle

More receivers. Three lines bound a triangle; five or six overdetermine the fix and average out individual errors.

A wider baseline. Receivers far apart see the emitter from genuinely different angles, so a small bearing error moves the crossing point less. Receivers bunched together give lines that are nearly parallel, and nearly parallel lines cross badly - a tiny angular error smears the intersection far down-range.

Lower bearing error. Better antennas, cleaner signal, and known corrections for the terrain around each receiver (nearby metal and hills bend the apparent direction). This is the hardest to improve and usually dominates.

//Time Is the Transmitter's Only Defence

Here is the part that connects back to operational reality without needing anything operational. Getting a good fix takes measurements from several receivers on the same transmission. A signal that keys up for a fraction of a second, at low power, on a frequency nobody was already watching, may simply not last long enough for the network to collect enough bearings before it stops. A signal that transmits for minutes, repeatedly, at power, is easy - every extra second is more data for the fix.

That is the real lesson, and it is the same one the intercept chain and frequency hopping pieces arrive at from other directions: brevity and unpredictability are what protect a transmitter, because the location leaks from the act of transmitting, not from the content. You can encrypt the message perfectly and still be found by the fact that you spoke.

//Where You Have Seen This

Direction finding is not exotic. Amateur radio operators do it for sport - "foxhunting," chasing a hidden transmitter with a handheld Yagi. Aviation and marine rescue runs on it: an emergency beacon is useful precisely because searchers can home on its bearing. Your phone does a cousin of it every time it estimates position from the relative timing of cell towers. The physics in the demo is the physics behind all of them.

[TECHNICAL NOTE]
A practical rule of thumb: the down-range position error from a single bearing grows with distance. A 2-degree bearing error at 10 km puts the line off by roughly 350 metres at the target; at 100 km, 3.5 km. That linear growth with range is why a distant emitter needs either a very accurate bearing or a wide baseline to pin down, and why the cocked hat in the demo balloons as you drag the emitter toward a corner, far from the receivers.

//Sourcing and Framing

The bearing-and-fix geometry, the cocked-hat concept, and the factors that improve a fix are standard direction-finding fundamentals from amateur radio and basic signals theory. The demo computes bearings with atan2 and draws the true lines of position, with fixed, deterministic per-receiver offsets standing in for real-world bearing error so the cocked hat behaves correctly.

As with the rest of the cluster, this stays at the published, textbook layer - the geometry of locating a transmitter - and deliberately avoids any specific operational system or capability. The geometry alone is enough to understand why a transmission is a location, and why time is the thing that protects one.