PLL Loop Filter Designer

Design a type-2 second-order PLL passive loop filter. Calculates time constants, capacitor and resistor values for target loop bandwidth and phase margin.

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Formula

\tau_2 = \frac{\sin \phi}{\omega_c}, \quad \tau_1 = \frac{1}{\omega_c^2 \tau_2}

ωc — Loop crossover frequency (2π × f_BW) (rad/s)

φ — Phase margin (rad)

τ1 — Zero time constant (s)

τ2 — Pole time constant (s)

How It Works

Phase-Locked Loop (PLL) loop filters are critical circuit elements in frequency synthesis and signal processing systems. A Type-2 passive loop filter provides essential feedback control for frequency and phase synchronization in communication and electronic systems. The filter's design involves calculating time constants and component values that determine the loop's dynamic performance, including lock time, stability, and noise characteristics.

Worked Example

Problem: Design a Type-2 PLL loop filter with a bandwidth of 10 kHz and phase margin of 45 degrees Solution: 1. Calculate ωc: ωc = 2π * 10,000 = 62,832 rad/s 2. Compute τ1: τ1 = 1 / (ωc²·τ2) 3. Calculate τ2: τ2 = sin(45°) / ωc = 0.707 / 62,832 4. Select R1 = 10 kΩ 5. Determine C1: C1 = τ1 / R1 6. Determine C2: C2 = τ2 / R1

Practical Tips

✓Always verify loop stability through simulation or experimental testing
✓Consider temperature coefficients of capacitors in critical designs
✓Use precision resistors to maintain accurate time constants

Common Mistakes

✗Neglecting the relationship between phase margin and loop stability
✗Incorrectly calculating time constants
✗Overlooking component tolerances that affect filter performance

Frequently Asked Questions

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