An FM discriminator converts frequency modulation back into the original audio: instantaneous deviation from the carrier becomes an output voltage. The transfer characteristic — output voltage vs frequency offset — is the iconic S-curve: zero output at exact carrier, linearly rising slope through the passband, and saturating at the band edges. Anything that perturbs this curve (component tolerance, supply drift, temperature) shows up as distortion or DC offset in the recovered audio.
Foster-Seeley discriminator
Invented at RCA in 1936, the Foster-Seeley uses a centre-tapped IF transformer with a phase-shift network. The two diode envelope detectors see the vector sum of the primary and secondary voltages: at exact carrier the two are equal and the diode currents cancel. Off-carrier, one diode current grows while the other shrinks, generating a differential output proportional to frequency offset. Pros: highest sensitivity of any analog FM detector, very linear in-band. Cons: zero inherent AM rejection — without a hard limiter stage in front, any amplitude noise modulates straight through.
Ratio detector
Patented by Seeley & Avins (1948) as an improvement: same topology with a large stabilising capacitor across the diode output. The capacitor holds the sum of the diode currents nearly constant, so amplitude variations divide between the two diodes instead of being passed through. The output becomes a ratio rather than a difference — hence the name. Pros: ~20 dB inherent AM rejection, often used without a limiter (saves a stage). Cons: half the sensitivity of Foster-Seeley for the same transformer, slightly more curvature in the S-shape (this tool models that as the same tanh but with half Vpeak).
Why Δ / BW matters
The S-curve is well-approximated as Vout = Vpeak · tanh(Δf / BW). Modulating the frequency sinusoidally with peak deviation Δ gives output ≈ Vpeak · tanh(a · sin ωt) where a = Δ / BW. Expanding the tanh in a Taylor series shows a sin³ term that becomes a third-harmonic component with amplitude ratio ≈ a² / 12. Translation: keeping Δ / BW < 0.3 gets you under 1% THD, the conventional design target. Going past Δ / BW = 1 saturates the detector and the recovered audio becomes obviously distorted.
Why both topologies became obsolete
Modern FM receivers — DSP-based or quadrature-detector ICs (CXA1064, MC3361, …) — bypass both Foster-Seeley and ratio designs entirely. The quadrature detector uses an LC resonator to produce a 90° phase shift, then multiplies the FM signal by its own phase-shifted version: the product is a DC voltage proportional to frequency offset, with no transformer required. PLL-based detectors and direct-sampling SDRs offer even better performance. The classic discriminators still appear in vintage and amateur equipment and remain in every RF curriculum.
Why is the S-curve "S" shaped and not just a straight line?
A real tuned-circuit detector has a finite Q (bandwidth). At small offsets, the phase shift between primary and secondary voltages is nearly linear in frequency — so Vout is linear in Δf. As the offset grows the resonator response rolls off and the phase saturates near ±90°, so the output saturates as well. The hyperbolic tangent is the simplest function with this exact behaviour: zero at zero, linear slope at the origin, asymptoting to ±1.
What sets the discriminator bandwidth BW in a real design?
BW is the loaded-Q bandwidth of the tuned secondary: BW = f₀ / Q_loaded. So for a 10.7 MHz IF and Q = 40, BW ≈ 270 kHz — comfortably wider than the 75 kHz broadcast-FM deviation. Lower Q gives wider BW (more linear range, lower sensitivity); higher Q narrows the band (more sensitive, less headroom for deviation). The choice is set by the receiver's allowed RF channel spacing and the desired peak deviation.
Why does the ratio detector get half the sensitivity?
Because the stabilising capacitor splits the output into two halves: one half stays constant (carrying the rejected AM), the other half supplies the recovered audio. The output is taken differentially across only half the network, hence half the voltage swing for the same input. The trade-off — half sensitivity for 20 dB of free AM rejection — was a winning bet in mid-century radios where limiter stages were expensive vacuum tubes.
Why doesn't this tool show real component values (capacitors, transformers)?
Because the S-curve only depends on f₀, BW and Vpeak — once you've chosen those, the LC values follow from the IF design (transformer Q, coupling factor, diode load resistor). For a step-by-step component selection you need the actual receiver IF frequency, the choice of detector type, and the desired loaded Q — generally a paper design or a SPICE simulation, not a single calculator. This tool focuses on the behaviour: pick the operating point on the S-curve, see what happens to your signal.
My estimated THD reads way higher than what I measure in real receivers — why?
Two reasons. (1) Real receivers nearly always run with Δ / BW well under 0.3 — broadcast FM at 75 kHz deviation typically passes through a 250 – 280 kHz IF discriminator, giving a = 0.27 → THD ≈ 0.6%. (2) De-emphasis (50 µs in Europe, 75 µs in the US) attenuates the high-frequency harmonics by 6–20 dB after the discriminator, so measured-at-output THD is significantly lower than the raw discriminator THD. The tool reports the raw figure.
What's "AM rejection" and why do I care?
Pure FM has constant amplitude; the only information lives in the frequency. But real signals pick up amplitude variations from fading, multipath and noise. A perfect FM detector ignores those and only responds to frequency. A Foster-Seeley does not — it's an amplitude-sensitive envelope detector underneath, so amplitude noise modulates the output unless killed by a hard limiter in front. A ratio detector reduces AM modulation in the output by about 20 dB — usable without a limiter for ordinary noise, but professional receivers still add limiting for hard-fading conditions.
Can the test offset go past ±BW?
Yes — the slider covers ±3·BW so you can see where the S-curve rolls over. Past the linear region the output approaches ±Vpeak and stops responding to further frequency change. Real receivers occasionally see this on weak signals during fading or strong interferers; the result is hard clipping in the recovered audio.
Does the centre frequency f₀ actually affect anything in this model?
No — the S-curve depends only on offset from carrier (Δf), bandwidth (BW) and peak output (Vpeak). The centre frequency exists in the UI purely for context — picking a preset gives you a realistic carrier (broadcast FM at 100 MHz, NBFM at 146 MHz) so the numbers feel concrete. Internally the math is centre-frequency-agnostic.