Interactive · receiving side

How a radio pulls one 400 MHz wave out of the air

The air around you is full of radio waves at thousands of frequencies, all at once. A receiver has three jobs: catch them (antenna), pick one (a resonant LC circuit, i.e. tuning), and unpack the message hidden in it (demodulation). Everything below is interactive. Drag the sliders and watch what changes.

Dashed = transmitter side (covered briefly, so you know what the receiver is unpacking). Solid = receiver side, which is the focus here.

Part 1 · How a signal really leaves an antenna

It's a donut: the real 3D shape of a radio signal

A vertical antenna doesn't shoot a beam, and it doesn't radiate equally in every direction either. Electrons rushing up and down the rod throw off rings of electric field that grow outward at the speed of light. The strength forms a donut (torus) around the rod: strongest all around its "waist", and zero straight above and below. Everything in this view is computed from the real dipole-antenna equations. Only the speed is slowed down.

Slow-mo · grid rings = 1 λ = 75 cm · drag to orbit
donut = power pattern
/E-field lines (+ / −)
B-field rings
your receiver
This view needs WebGL and an internet connection (it loads three.js from a CDN).

The donut is cut in half so you can see inside it. The glowing slice is the electric field at one instant: bright = pointing up, violet = pointing down. The lines are the exact field lines of a dipole. Watch them pinch off the antenna as closed loops and drift away. That is the radio wave.

Place a receiver

Pattern gain at this angle—
Extra loss vs. 1 λ away—
—

Real-world numbers: what actually reaches your antenna?

Free space, both antennas vertical, same elevation angle as the receiver in the 3D view. In real life, buildings, trees and the ground often cost another 10–40 dB.

Field strength E—
Received power—
Voltage at 50 Ω receiver input—
Gain needed to reach 0.3 V (diode)—
E = √(30·P·G) / d  ·  Pr = P·Gt·Gr·(λ / 4πd)²  ·  G = 1.64 × pattern(angle)

Why there's a hole on top

Radio waves are made by electrons accelerating. Stand directly above the antenna and look down: the electrons move straight toward you and away from you, with no sideways motion at all, so nothing is radiated your way. From the side you see the full up-and-down motion: maximum. Field strength ∝ sin(angle from the rod), power ∝ sin².

Near field vs. far field

Close to the rod (within about λ/2π ≈ 12 cm at 400 MHz), the field mostly sloshes back and forth between the two tips and stores energy, like the capacitor in Part 3. Further out, each loop of field pinches off and travels away on its own. That's the far field, the actual radio wave. A new loop leaves every half cycle: every 1.25 ns at 400 MHz.

From above, it's circles

Switch the slice to Horizontal: the ripples spread out evenly like a stone dropped in a pond. A vertical antenna is omnidirectional in the horizontal plane, which is why phones and walkie-talkies don't need to be pointed. The spacing between two same-coloured rings is exactly one wavelength: 75 cm.

Why Part 2 shows a flat wave

By the time the shell reaches you it is enormous. At 1 km, your 35 cm antenna sees a patch of a sphere 2 km across, which is essentially flat. So the receiving view in Part 2 correctly shows parallel field arrows (a plane wave) sweeping past. It's the same donut, zoomed way in.

The 1/d rule

Energy spreads over an ever-bigger sphere. Field strength falls as 1/d and power as 1/d². Double the distance → −6 dB. 1 W over 1 km arrives as about 7 mV/m, which is ~0.7 mV at the receiver: 400× too small for a diode. That's why every real receiver starts with an amplifier.

Shaping the donut

A half-wave dipole's donut is a little flatter than a tiny dipole's (gain 2.15 dBi vs 1.76 dBi). Stack several dipoles vertically (a "collinear", like on repeater towers) and the donut squashes into a pancake that throws more energy along the horizon, where the users are. A dish or Yagi squeezes it into one direction.

Part 2 · The receiving antenna

A wave pushes electrons in a wire, and that motion is the signal

A radio wave is an electric field (and a magnetic field) flipping direction 400 million times per second as it flies past. When that field passes a metal rod, it shoves the rod's free electrons up, then down, then up. Electrons moving back and forth are an alternating current. That tiny current is everything the receiver will ever get.

Slow-mo ~10⁹× · drag to orbit · scroll to zoom
E-field (pushes electrons)
B-field
electrons
current glow
/+ / − charge at tips
The 3D view needs WebGL and an internet connection (it loads three.js from a CDN).
The rest of the page still works.

Scope (bottom-left): faint = the passing E-field, bright = current at the antenna's centre (feed point), which goes down the cable to the receiver.

Wavelength λ = c / f75.0 cm
Ideal dipole ≈ 0.95 × λ/235.6 cm
This antenna resonates at400 MHz
Induced current100 %
Perfect length: electrons slosh in step with the wave.

Why length matters

Electrons pushed toward the tip bunch up there and push back, like water sloshing in a bathtub. The slosh has a natural rhythm set by the rod's length. When the rod is about half a wavelength long, that rhythm matches the wave and each push lands at the right moment, so the current is largest. The antenna itself is a resonator.

The 400 MHz numbers

λ = 300,000,000 m/s ÷ 400,000,000 Hz = 0.75 m. Half of that is 37.5 cm. Real rods have thickness, so the field "spills" past the ends and the rod acts a bit longer than it is. Trimming ~5% gives ≈ 35.6 cm tip to tip (two 17.8 cm arms). A walkie-talkie's single 17.8 cm whip is the same idea (a quarter-wave), with the ground or your hand acting as the missing half.

Current is biggest in the middle

Look at the electrons: the ones near the centre move the most and the ones at the tips barely move (they have nowhere to go). Charge piles up at the tips instead, + on one end and − on the other, and it swaps each half-cycle. That's why the cable connects at the centre, where the current is strongest (~73 Ω feed impedance).

Polarization

The E-field here points up and down, so only a vertical rod gets pushed along its length. Tilt the antenna: coupling falls as cos(angle). At 90° the field pushes electrons across the rod instead of along it, so there's almost no current.

How small is the signal?

A typical field of 1 mV/m acting on a half-wave dipole (effective length λ/π ≈ 24 cm) gives only ≈ 0.24 mV. Microvolts to millivolts is normal. Remember this for Part 7: a diode needs ~0.2–0.6 V before it conducts at all.

The antenna isn't picky enough

A dipole is a broad resonator (low Q). Set the frequency to 385 or 415 MHz and it still catches over 90%. So the antenna catches the whole neighbourhood of stations, and the LC tuner (Part 4) has to do the real picking.

Part 3 · What is a resonant frequency?

Every "springy" system has one rhythm it loves

Push a child on a swing. Push at random moments and nothing much happens. Push exactly once per swing and the swing goes higher and higher from tiny pushes. That special rhythm is the resonant frequency. In electronics, a capacitor + inductor make an electrical swing, called an LC tank.

Top: the tank. Charge on the capacitor plates, electrons flowing in the wire, magnetic field around the coil. Right: where the energy is right now. Bottom: the tank voltage over time.

The electrical swing

  1. Capacitor full. All the energy is stored as an electric field between the plates (like the swing at its highest point).
  2. The capacitor discharges through the coil. Current builds up slowly, because an inductor resists changes in current.
  3. Capacitor empty, current at maximum. All the energy is now in the coil's magnetic field (the swing at the bottom, moving fastest).
  4. The magnetic field collapses and keeps the current flowing, so it charges the capacitor again the other way round. Then everything repeats in reverse.
f₀ = 1 / ( 2π · √(L · C) )

A bigger C (more charge to move) or a bigger L (more sluggish current) means a slower swing and a lower frequency.


In step: every push adds energy.

Try this

Leave the ratio at 1.00× and press Reset: the amplitude grows over many cycles. Now set it to 0.80× and reset: the pushes are sometimes with the motion and sometimes against it, so it never gets big. That difference is how a radio picks a station.

Where do the losses come from?

Real wires and coils have resistance (R), which turns some energy into heat each cycle. Uncheck "driven" and pluck: the oscillation dies away. High Q (low loss) rings for a long time and responds only to a very narrow band of rhythms.

Q in one line

Q ≈ energy stored ÷ energy lost per cycle (×2π). Bandwidth = f₀ / Q. At 400 MHz with Q = 40, the tank passes roughly a 10 MHz-wide slice. That number matters in the next part.

Part 4 · Tuning

Tuning = sliding the tank's resonance onto 400 MHz

Your antenna is delivering three stations at once: 385 MHz, your target 400 MHz, and 415 MHz. The neighbours are even stronger than your target. The antenna current flows into a parallel LC tank. Only the frequency matching the tank's natural rhythm builds up a big voltage; the others barely register. Turning the tuning knob changes C (a variable capacitor), which moves f₀.

Resonance curve: how much voltage the tank builds for each frequency (1 = maximum). Shaded = bandwidth (−3 dB).

Oscilloscope over 100 ns. Top: what the antenna delivers (all three mixed into a mess). Bottom: the tank voltage (what the next stage sees), with the target alone in faint green for comparison.

Resonant freq f₀—
Q = R·√(C/L)—
Bandwidth f₀/Q—
C needed for 400 MHz—
—
—

Why the tank "prefers" f₀

An inductor's opposition to AC is XL = 2πfL, which grows with frequency. A capacitor's is XC = 1/(2πfC), which shrinks with frequency. At exactly one frequency they are equal and cancel: energy just swings between L and C and the tank looks like a huge resistance, so the voltage across it is big. At any other frequency, L or C acts like a short circuit and drains the signal to ground.

The Q trade-off

Low R, low Q: a wide curve, and neighbouring stations leak through. High R, high Q: a razor-sharp curve, great rejection. But go too sharp and you also cut off the sidebands that carry the audio (Part 5), which makes the sound muffled. Real receivers choose Q to match the signal's bandwidth.

Electronic tuning (varactor)

Modern radios have no knob-driven capacitor. They use a varactor diode: a reverse-biased diode whose insulating gap widens with voltage, so its capacitance changes with a DC voltage. A microcontroller sets that voltage, and C sets f₀. At 400 MHz you need only ~16 pF with a 10 nH coil (about 2 turns of wire on a 3 mm drill bit!).

Part 5 · Modulation (the transmitter's trick)

A pure 400 MHz wave carries no message. You have to wiggle it.

You can't send audio (20 Hz–20 kHz) through the air directly: the antenna would need to be kilometres long, and every station would overlap. So the transmitter makes a fast carrier (400 MHz) and uses the audio to vary one of its properties. Vary its height and you get AM. Vary its speed (frequency) and you get FM.

Drawn with ~30 carrier cycles per audio cycle. In reality, a 1 kHz tone on a 400 MHz carrier is 400,000 carrier cycles per audio cycle: far too many to draw.

Spectrum: what frequencies the modulated wave actually contains (horizontal axis in kHz away from 400 MHz).

s(t) = [1 + m·audio(t)] · sin(2π·400MHz·t)

Inside the transmitter, part by part

The block view is below. For the real, clickable circuits with part values, see Part 6.

1 · Oscillator = tank + transistor

The same LC tank from Part 3 (10 nH + 15.8 pF → 400 MHz) would ring and die out because of R. A transistor gives it a small push every cycle, taken from the battery at exactly the right moment (feedback). That makes a steady 400 MHz sine: the carrier. It's the swing plus a person who never stops pushing.

2 · AM modulator

The carrier goes through a second transistor amplifier. The audio is added to that transistor's supply voltage, so when the audio goes up the amplifier has more voltage to swing with and the carrier comes out taller. When the audio goes down, it comes out shorter. The outline (envelope) of the carrier now is the audio waveform.

2 · FM modulator (varactor)

Put a varactor diode across the oscillator's tank. Audio voltage changes its capacitance slightly, and f₀ = 1/(2π√LC) follows. Changing C by only 0.01 pF (out of 15.8) shifts the frequency by ~127 kHz. So a tiny audio voltage is enough to make the carrier run slightly faster and slower.

Part 6 · Build a real transmitter

Real transmitter circuits: how AM and FM are actually made

Part 5 showed the idea. These are the real circuits, with realistic parts for 400 MHz. Click any component to see what it physically does. Every number on the right is calculated from the component physics: the varactor's capacitance curve, the tank formula, and class-C amplifier behaviour. Probes 1–4 show the signal at each point.

1Microphone audioafter C1
2Voltage on the varactorDC bias + tiny audio
3Oscillator frequency vs timered = 12.5 kHz channel edges
4RF to antennaswing hugely exaggerated

Click a component

Every part of this 1-transistor FM transmitter has a specific job. Click one to read it.

Varactor C (at bias)—
Total tank C—
Carrier frequency—
Deviation Δf—
Index β = Δf / faudio—
Bandwidth (Carson)—
—

What happens, step by step

  1. Sound hits the mic, giving ~8 mV of audio at probe 1.
  2. C1 strips off the mic's DC. Ra/Rb shrink the audio to under 1 mV.
  3. The varactor sees 2 V DC ± that audio, so its capacitance wobbles by a few thousandths of a pF (probe 2).
  4. The tank's f₀ = 1/(2π√LC) wobbles by a few kHz around 400 MHz (probe 3).
  5. Q1 + Cf keep the tank ringing at whatever f₀ is right now. That's an FM carrier (probe 4).
  6. Co passes a little of it to the antenna, which launches the donut from Part 1.

Why it oscillates by itself

An oscillator is an amplifier that feeds its own output back to its input in phase, with a loop gain ≥ 1 (the Barkhausen criterion). The tank decides the frequency; Q1 and Cf provide the gain and the "push at the right moment". It starts from nothing: random thermal noise at 400 MHz gets amplified around the loop billions of times within microseconds, until the transistor saturates and the amplitude settles.

Real-world build notes

At 400 MHz, 1 cm of wire ≈ 7–10 nH: as much as the whole coil! So use SMD parts, keep leads under 2 mm, and put a solid ground plane under everything. Parts: BFR92A transistor, BB135 or SMV1233 varactor, L1 = 2 turns of 0.8 mm wire on a 3 mm drill bit, a 2–10 pF trimmer. Power it from a 78L05 regulator, because the frequency moves when the battery sags. Check your carrier with a €25 RTL-SDR dongle.

The drift problem → PLL

A free-running LC oscillator drifts by hundreds of kHz with temperature, battery voltage, even your hand nearby, and that's many channels. Real radios lock it with a PLL: a divider counts the output, compares it with a crystal (e.g. a 12.8 MHz TCXO), and slowly corrects the varactor's bias. The correction is slower than audio, so the average is crystal-accurate while the audio wiggles still pass. Chips like the CC1101, Si4463 or ADF7021 do all of this internally.

Pre-emphasis & limiting

Real FM transmitters boost the treble before modulating (pre-emphasis, a simple RC filter), and the receiver cuts it back (de-emphasis), which cuts hiss too. An audio limiter (clipping diodes!) makes sure shouting can't push the deviation beyond the channel, e.g. ±2.5 kHz for 12.5 kHz channels.

Legal note

400–406 MHz belongs to weather balloons and satellites, so don't transmit there. For experiments, use the 433.05–434.79 MHz ISM band (typically ≤10 mW; check your country's rules) or get an amateur radio licence for the 70 cm band (430–440 MHz). Retuning is just a small change to L or C.

Part 7 · AM demodulation (receiver)

Getting the audio back with one diode, two capacitors, and a resistor

This is the classic AM envelope detector, the heart of a crystal radio. Click any part of the circuit to see what it does. The four scopes show the signal at probe points A–D. The tank uses your tuning from Part 4, so if you mistuned it, you'll see (and "hear") the neighbours here.

AAntennaall stations, mixed
BAfter LC tankmostly the 400 MHz station
CAfter diode + R1 + C2envelope + DC
DAfter C3 → earphonepure audio

Click a component

Each part of the schematic above does exactly one job. Click it to read what it does, physically, and why it's there.

—
loops the waveform at probe D as sound

Real-world scale: R1 = 10 kΩ, C2 = 100 pF → τ = 1 µs. That's 400× longer than one 400 MHz cycle (2.5 ns) and 1000× shorter than one 1 kHz audio cycle (1 ms). The simulation squeezes these ratios so you can see them.

Why the diode is essential

The carrier goes + and − equally, so its average is zero. A speaker can't follow 400 MHz, so it would only feel that average: silence. The diode lets current through in one direction only and chops off the negative halves. Now the average is no longer zero. It's proportional to the carrier's height, which is the audio.

The RC "bucket with a hole"

Each positive peak pours charge into C2 through the diode (fast). Between peaks, C2 slowly drains through R1 (the hole). If the hole is too small (τ too long), the level can't drop when the audio goes down and the output clips diagonally. If it's too big (τ too short), it drops between every carrier peak and you get ripple. The sweet spot is Tcarrier ≪ R1·C2 ≪ Taudio.

C3 blocks DC

The envelope sits on top of a constant (DC) level, the carrier's average height. That DC would just push the earphone diaphragm to one side and waste its travel. A capacitor passes changes but blocks steady voltage, so C3 passes the audio wiggle and removes the offset.

Part 8 · FM demodulation (receiver)

Turning frequency wiggles back into a voltage

An FM signal always has the same height, so the AM diode detector from Part 7 hears only silence. We need a circuit whose output voltage depends on frequency. An LC tank does exactly that on the side of its resonance curve. Two tanks, two diodes and a few resistors make the classic balanced slope discriminator. Put a two-diode limiter in front of it and you get FM's famous noise immunity.

400 MHzfrom antenna + RF amp→ Mixer 1× LO 389.3 MHz→ 10.7 MHz1st IF filter→ Mixer 2× LO 10.245 MHz→ 455 kHz2nd IF (this circuit ↓)→ Limiter→Discriminator→Audio

Why convert down first? A mixer (a diode or transistor fed with two frequencies) outputs their difference: 400 − 389.3 = 10.7 MHz. The FM deviation survives unchanged. At 455 kHz, cheap LC tanks can resolve a few kHz of deviation; at 400 MHz they can't (see Part 4's bandwidth numbers).

AIF inputFM + noise & fading
BAfter limiterheight flattened
CUpper tankloud when f is high
DLower tankloud when f is low
EAudio outupper − lower

Click a component

Two AM detectors on two tanks, wired against each other. Click a part to see why it works.

The discriminator curve: output voltage vs frequency. The green dot is the incoming signal swinging ±Δf.

Tank bandwidth 455/Q—
Audio amplitude—
Distortion + noise—
—

Try this

  1. Press Listen, then turn the limiter off. The noise crackles straight through. Turn it back on: silence behind the tone.
  2. Switch to Single slope with the limiter off: fading goes straight into the audio. Balanced cancels much of it.
  3. Push deviation above the tank spacing: the dot runs past the S-curve's peaks and the tone distorts.

Why the limiter kills noise

Noise and fading mostly change the wave's height. The FM information is only in the timing of the zero crossings. Two diodes that clip everything above ±0.6 V throw away the height and keep the timing. Real receivers use several limiting amplifier stages, but it's the same principle.

Why balanced beats single

With one tank, the output is a curved slope sitting on a big DC level, and any amplitude change leaks straight through. With two tanks subtracted, the S-curve is straight through the middle (low distortion), is exactly zero at the centre frequency, and amplitude changes hit both tanks equally, so they cancel.

Quadrature detector (inside most FM chips)

Chips like the MC3361, SA605 or CD2003 use one tank that shifts the phase by 90° at the centre frequency, and a transistor "multiplier" compares the shifted and unshifted signals. Above centre the phase shift grows, below it shrinks, so the product's average follows the frequency: an S-curve again, built from the same L, C and transistors.

PLL detector

A voltage-controlled oscillator (varactor + LC, like the transmitter in Part 6) is locked onto the incoming signal by a phase comparator. To stay locked, its control voltage must follow the incoming frequency, so that control voltage is the audio. It's the transmitter run backwards: very linear, with great weak-signal performance.

Capture effect

If two FM stations share a channel, the limiter and discriminator lock onto the stronger one and almost completely suppress the weaker one, even if it's only a few dB weaker. That's great for broadcast and walkie-talkies, and it's why aviation stays on AM (Part 6).

Cheat sheet

The low-level parts and their one job each

Resistor (R)

Opposes current equally at every frequency and turns electrical energy into heat. V = I·R.

In the radio: sets Q (losses) in the tank; the "drain hole" (R1) in the envelope detector.

Capacitor (C)

Two plates with a gap. It stores energy in an electric field. It blocks DC, and passes AC more easily the higher the frequency: XC = 1/(2πfC).

In the radio: half of the tuning tank (C1), holds the peaks (C2), blocks DC (C3).

Inductor (L)

A coil of wire. It stores energy in a magnetic field and resists changes in current. It passes DC easily and opposes high frequencies: XL = 2πfL.

In the radio: the other half of the tank. At 400 MHz, 10 nH is only ~2 turns of wire.

Diode (D)

A one-way valve for current. It conducts when the anode is more positive than the cathode by its turn-on voltage (0.25–0.7 V), and blocks the other way.

In the radio: the rectifier (detector) that makes the carrier's average non-zero.

Varactor diode

A diode used backwards (reverse-biased). Its insulating depletion layer is a capacitor gap. More reverse voltage makes the gap wider and the capacitance lower.

In the radio: electronic tuning (receiver), and making FM (transmitter).

Transistor

A valve controlled by a small signal: a tiny current or voltage at its input controls a big current from the battery. That's an amplifier.

In the radio: keeps the oscillator going, performs AM modulation, amplifies weak µV signals before the diode.

Antenna

A conductor sized to the wavelength. It converts a passing EM wave into an AC current (receive), or an AC current into a wave (transmit). The same physics works both ways.

In the radio: ~35.6 cm dipole or 17.8 cm whip for 400 MHz.

Earphone / speaker

A coil in a magnet's field attached to a diaphragm. Current through the coil makes it move, which pushes air as sound. It's far too heavy to follow 400 MHz, but it follows audio fine.

In the radio: turns the demodulated voltage into sound.