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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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).
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.
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.
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.
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.
A bigger C (more charge to move) or a bigger L (more sluggish current) means a slower swing and a lower frequency.
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.
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 ≈ 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.
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.
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.
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.
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!).
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).
The block view is below. For the real, clickable circuits with part values, see Part 6.
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.
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.
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 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.
Every part of this 1-transistor FM transmitter has a specific job. Click one to read it.
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.
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.
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.
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.
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.
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.
Each part of the schematic above does exactly one job. Click it to read what it does, physically, and why it's there.
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.
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.
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.
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.
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.
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).
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.
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.
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.
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.
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.
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).
Opposes current equally at every frequency and turns electrical energy into heat. V = I·R.
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).
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.
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.
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.
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.
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.
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.