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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.