FM Demodulation

The goal of FM demodulation is to recover the original message signal from the frequency variations of the received carrier. Unlike AM demodulation (where a simple diode and RC circuit suffice), FM demodulation requires circuits that convert frequency changes into amplitude changes — and several elegant approaches have been developed over the decades.

What We Need to Recover

Recall the FM signal: s(t) = A cos(2πf_c·t + 2πk_f·∫x(τ)dτ). The message x(t) appears inside a cosine argument as an integral. Demodulation requires us to extract the instantaneous frequency deviation f_i(t) − f_c = k_f·x(t), then scale appropriately.

Any FM demodulator must perform two functions:

1. Frequency-to-amplitude conversion: turn frequency variations into proportional amplitude variations
2. Limiting/filtering: remove amplitude noise before (or during) demodulation

Method 1: Slope Detector

The simplest FM demodulator is the slope detector: a bandpass filter tuned slightly off the carrier frequency, so that the FM signal rides on the slope of the filter's frequency response. As instantaneous frequency shifts, the filter output amplitude changes proportionally.

• Advantage: Extremely simple — just a mistuned filter + AM envelope detector
• Disadvantage: Poor linearity (filter slope isn't perfectly linear), very sensitive to carrier drift, almost never used in practice
• The slope detector is a useful pedagogical tool but rarely built in real systems

Method 2: Foster-Seeley Discriminator

The Foster-Seeley discriminator (1936) solves the linearity problem of the slope detector. It uses a transformer with a center-tapped secondary and two diode detectors. The circuit is tuned so that at the carrier frequency, both diodes detect equal amplitude — their outputs cancel to zero. As frequency deviates above or below the carrier, the balance tips and a proportional output voltage appears.

• Output is positive for frequencies above carrier, negative for frequencies below
• Good linearity over a wide deviation range
• Requires a limiter stage before it (sensitive to amplitude variations)
• Was the standard FM demodulator in analog radios for decades

Method 3: Phase-Locked Loop (PLL)

The most widely used FM demodulator today is the Phase-Locked Loop (PLL). A PLL contains three components in a feedback loop:

The VCO (Voltage Controlled Oscillator) tracks the FM signal's frequency. The control voltage that drives the VCO is exactly what we want — it's proportional to the instantaneous frequency of the input, which is proportional to the original message. The loop filter's output IS the demodulated audio.

PLL advantages over analog discriminators:

• Excellent noise performance (can track weak signals)
• Easily integrated onto a single chip
• Automatic frequency control (AFC) built in — tracks carrier drift
• Naturally limits amplitude variations in its phase detector output
• Used in virtually all modern FM receivers (radio, cell phones, satellite)

Method 4: Digital FM Demodulation

In software-defined radios and digital receivers, FM is demodulated mathematically after digitizing the signal:

This approach is used in RTL-SDR dongles, GNU Radio, and all modern digital radio receivers. It's essentially free in computation (a handful of multiplications per sample) and has excellent performance.

FM Receiver Block Diagram

A complete FM broadcast receiver chains these stages together:

The intermediate frequency (IF) of 10.7 MHz is a standard in FM radio — chosen to be above the AM broadcast band (to avoid image interference) and far enough from the carrier to allow good filtering. The limiter before the demodulator removes amplitude variations (noise) before they reach the frequency detector.