Detailed Notes for Practical 3: PLL Applications

Practical 3: PLL Applications

Submission Details

• Final report due: Wednesday 14/05/2025 @ 23:59.
  • Submission methods:
  • Turnitin (no plagiarism form).
  • AMS (with signed plagiarism form).

Amplitude Modulation (AM)

• Reference: Practical 1 and Chapter 4 of Lathi's textbook.
• Key points:
  • Understanding the mechanisms of transmission.

Key Components of the Practical

• DSB-SC (Double Sideband Suppressed Carrier):
  • Focus on synchronous/coherent demodulation techniques.

Challenges with DSB-SC

• Recovering the carrier signal when the original signal is missing.

Synchronous Demodulation

• Input Signal: $m(t) cos( heta)$
• Demodulation Process:
  • Received Signal: $m(t) cos(2\pi f_c t)$
  • Coherent demodulation signal: cos(2 \pi f_e t)
  • Equations:
  • Equation (1): $m(t) cos(2\pi fc t) = rac{1}{2}(M(f + fc) + M(f - f_c))$
  • Equation (3): $e(t) = m(t) cos(we t) cos(we t)$
  • Utilize cosine identity: $cos^2( heta) = rac{1}{2}(1 + cos(2 heta))$
  • Final result: $e(t) = rac{1}{2}(m(t) + m(t) cos(2w_c t))$

Received Signal Dynamics

• Address phase distortions and Doppler shifts:
  • Received signal: $m(t) cos((w_e + Aw)t + \phi)$
  • Filter high frequency components to retrieve the original message signal, $e(t) = m(t)$ when phase delays approach zero.

Square Law Device (Full Wave Rectifier)

• Purpose of square law devices in demodulation processes.

Phase Locked Loop (PLL) Components

• Basic Elements:
  • Multiplier
  • Loop Filter
  • Voltage-Controlled Oscillator (VCO)

Phase Detection Mechanism

• Loop filter and multiplier combine for phase detection, outputting a voltage proportional to phase difference.
• Example:
  • Input signal: $cos(4\pi ft + \phi)$.
  • XOR function as a phase detector.

Characteristics of PLL

• Locking Mechanism:
  • Pull-in range ensures PLL will synchronize, but may involve cycle slipping in cases of sudden reference frequency changes.

Loop Filter Details

• Role:
  • Removes high harmonics and averages phase detection via integration.
  • Ensures stability, affects loop performance, and affects locking characteristics:
  • H(s) representation shows influence on stability:
    • $F(s) = \frac{Vin}{s(R1+R2)}$ and further derived forms.

Voltage Controlled Oscillator (VCO)

• VCO generates a sinusoidal output based on input voltage, defined as:
  • Instantaneous phase from the VCO provided, where output phase represents carrier phase estimate.

Practical Implementation Considerations

• Simulation hardware and layout in software such as OrCAD and LTspice, demonstrating modulation before/after bandpass filtering.
• Components of application include:
  • Modulation (Chopper, BPF)
  • Demodulation (Full Wave Rectifier, BPF)
  • Phase Detector (XOR)
  • VCO Output and Divider Circuit

Practical Results Expectations

• Show all theoretical and design equations for PLL (in Amplitude Modulation context).
• Utilize simulations and demonstrate outcomes in terms of signal processing at various stages.

Design Steps

• Step-by-step calculations of critical parameters:
  • $w_n$ and $K'$, resistor and capacitor calculations informed by established design equations.
• Example values:
  • Carrier frequency $Fc = 10 kHz$ (square wave), modulating frequency $Fm = 1 kHz$ (sine wave).

CD4046 Chip Utilization

• Overview of PLL chip connections and functionalities including signal inputs and outputs relevant to demodulation and phase comparison outcomes.