Tuning: Picking a Station
Every broadcast in your city arrives at your antenna at once. A variable capacitor and one coil sort them out.
Builds on: 9.1 LC Resonance5.3 Impedance & RC Filters
The problem: everything, everywhere, all at once
An antenna is just a wire in which every passing radio wave induces a little voltage — simultaneously. News at 540 kHz, jazz at 760 kHz, rock at 1000 kHz: your antenna delivers their sum, a hopeless-looking scribble. The receiver’s first job is selectivity: amplify one, ignore the rest.
The solution: a tuned circuit
Connect an LC tank across the antenna. Signals at the tank’s resonant frequency drive it like a well-timed playground push — the response builds cycle upon cycle. Signals at other frequencies push out of time and average away to almost nothing. The tank is a band-pass filter with its peak at f₀, and Q sets how narrow the peak is:
Make C variable and f₀ moves — that is literally what the tuning knob on an old radio turns: a variable capacitor, interleaved metal plates whose overlap sets C from ~40 to ~400 pF. With a fixed coil of a couple hundred microhenries, that sweeps f₀ across the whole AM broadcast band. (Modern radios tune with voltage-controlled capacitors and synthesizers, but the physics is unchanged.)
Selectivity is a trade
Too low a Q and you hear two stations at once. Too high and you start shaving off the audio sidebands the station carries (more on those next lesson) — the sound gets muffled. Real receivers chain several tuned stages to get steep skirts without strangling the signal. But one LC, honestly, is enough to build a working radio — people have done it with a coil wound on a toilet-paper tube for a century.
At 1 MHz, one wave cycle is a microsecond — a thousand times faster than anything in your earlier labs, yet the same sine-wave mathematics from 5.1 applies without modification. Scales change; laws don’t.
⚡ Lab — The Crowded Air
Three stations on one antenna, one LC tank, one knob.
- Sweep the capacitor and watch each station rise and fall through the tank’s peak.
- At Q = 8, tune between Jazz and Rock: both leak through. Raise Q and separate them.
- Note the antenna trace never changes — selection happens entirely in your tank.