PLL Demodulator

The Phase Locked Loop (PLL) demodulator is one of the most elegant and high-performance approaches to FM demodulation. Unlike traditional LC-based detectors such as the ratio detector or Foster-Seeley discriminator, the PLL uses feedback control theory to track the instantaneous frequency of an FM signal and extract the modulating information from the error signal generated during that tracking process.

Core Concept Explanation

A Phase Locked Loop consists of three fundamental building blocks: a phase detector, a low pass filter, and a voltage controlled oscillator. In the locked state, the VCO output frequency exactly matches the input FM carrier frequency. The phase detector continuously compares the phase of the incoming FM signal with the phase of the VCO output and generates an error voltage proportional to their phase difference.

When the FM signal frequency deviates above or below the carrier, the VCO must change its frequency to track the deviation. The only way the VCO frequency can change is if the control voltage at its input changes. This control voltage is the output of the low pass filter that processes the phase detector error signal. Since the control voltage must change to track frequency deviations, and the frequency deviations themselves follow the modulating signal, the VCO control voltage is directly proportional to the original audio message. This control voltage is the demodulated output.

The PLL achieves demodulation entirely through feedback. No tuned transformer, no alignment, no amplitude-dependent detection. Because of this, PLL demodulators have superior linearity and noise performance compared to traditional detectors. They are also easily integrated into CMOS chips, making them the standard choice in modern FM receiver ICs.

Mathematical Expression

Let the input FM signal be represented as s(t) equals A cos of (2 pi fc t plus 2 pi kf integral of m(tau) d tau), where kf is the frequency sensitivity in Hz per volt and m(t) is the message signal. The instantaneous frequency deviation is delta f(t) equals kf times m(t). In the locked state, the VCO output phase tracks the input phase, so the phase error phi_e(t) approaches zero. The VCO control voltage v_c(t), which is the LPF output, must satisfy the VCO equation: f_VCO equals f_c plus k_v times v_c(t), where k_v is the VCO gain constant in Hz per volt.

For perfect lock, f_VCO must equal instantaneous input frequency, giving k_v times v_c(t) equals kf times m(t), so v_c(t) equals (kf divided by k_v) times m(t). The demodulated output is thus linearly proportional to m(t). The proportionality constant kf divided by k_v is the overall demodulator gain. This linear relationship is what gives PLL demodulators their excellent fidelity.

Practical Understanding

The capture range and lock range are two critical parameters of a PLL demodulator. The lock range, also called the hold-in range, is the range of input frequencies over which the PLL can maintain lock once it is locked. The capture range, or pull-in range, is the range of frequencies from which the PLL can acquire lock starting from an unlocked state. Typically, the capture range is narrower than the lock range. For FM broadcast, the PLL must have a lock range wider than the maximum frequency deviation, which is plus or minus 75 kHz for broadcast FM.

The LPF bandwidth determines the maximum audio frequency that can pass to the output. For FM broadcast applications, the LPF cutoff is typically set at 15 kHz to pass the full audio bandwidth. The VCO free-running frequency must be preset close to the FM carrier frequency. In integrated PLL chips like the NE565, this is done using an external resistor and capacitor connected to the VCO terminals.

Numerical Example

In a PLL FM demodulator, the VCO gain constant k_v is 50 kHz per volt and the frequency sensitivity of the FM transmitter kf is 25 kHz per volt. A message tone m(t) produces a frequency deviation of 25 kHz. The demodulated output voltage can be calculated from the VCO control voltage in the locked condition.

Given:
VCO gain: k_v = 50 kHz/V
FM frequency sensitivity: k_f = 25 kHz/V
Message amplitude: m(t) causes Δf = 25 kHz

Why this formula applies:
In locked state, VCO must produce exactly Δf to match input.
Control voltage v_c drives VCO to produce this deviation.

Formula:
v_c(t) = Δf / k_v

Substitution:
v_c = 25 × 10³ / (50 × 10³)

Calculation:
v_c = 0.5 V

Demodulator output = v_c = 0.5 V

Alternatively: v_c = (k_f / k_v) × m(t)
If m(t) = 1V: v_c = 25/50 × 1 = 0.5 V

Final Answer:
Demodulated output voltage = 0.5 V for 25 kHz frequency deviation.

Exam Tip: In PLL FM demodulator, the output is taken from the VCO control voltage (LPF output), NOT from the phase detector output. The phase detector output still contains high frequency components. The demodulator gain is k_f / k_v. GATE may give k_v and k_f and ask for output amplitude — use v_c = Δf / k_v directly.

Quick Revision

• PLL demodulator uses a phase detector, low pass filter, and VCO in a feedback loop to track the instantaneous frequency of the FM signal.
• Demodulated output is the VCO control voltage v_c(t), which is proportional to the original modulating signal m(t).
• Key formula: v_c(t) = (k_f / k_v) × m(t), where k_f is FM modulator sensitivity and k_v is VCO gain in Hz/V.
• Lock range must exceed the maximum frequency deviation of the FM signal (75 kHz for broadcast FM).
• PLL demodulator has better linearity and noise performance than ratio detector or Foster-Seeley discriminator.
• Exam trap: Output is taken at LPF output (VCO control input), not directly at phase detector output.
• IC example: NE565 is a standard PLL chip used for FM demodulation in lab setups.