Phase Lock Loop

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Phase Lock Loop
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Phase Lock Loop

• An extremely versatile circuit used extensively
  in modern electronic communications systems for
  providing a wide variety of functions, including
  modulation, demodulation, etc.
• The PLL consist of four primary blocks
• Phase Comparator
• Low Pass Filter
• Low Gain Operational Amplifier
• Voltage Control Oscillator

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Phase Lock Loop
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Phase Lock Loop

• The PLL uses phase lock to perform its intended
  function.
• Before phase lock can occurs it must have
  frequency lock.
• After frequency lock has occurred, the phase
  comparator produces an output voltage that is
  proportional to the difference in the phase
  between the VCO output frequency and the external
  input frequency.

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Phase Lock Loop

• When there is no external input signal or when
  the feedback loop is open, the VCO operates at a
  preset frequency called its natural or
  free-running frequency (fn) .
• The natural frequency is the VCOs output
  frequency when the PLL is not lock.

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Operation of the Phase Lock Loop

• When an external frequency (fi) is initially
  applied to the PLL, the phase comparator compares
  the frequency of the external input to the
  frequency of the VCO output signal. The phase
  comparator produces an error voltage (vd) that is
  proportional to the difference in the frequency
  between the two signals.
• The error voltage is filtered and amplified and
  then applied to the VCO input.
• If the external signal is sufficiently close to
  the VCO natural frequency, the feedback nature of
  the PLL causes the VCO to synchronize or lock
  onto the external input signal.

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Operation of the Phase Lock Loop

• The PLL has three operating states.
• Free Running
• In the free running state, either there is no
  external signal or the feedback loop is open.
• Capture
• To be in the capture state their must be an
  external signal and the feedback loop must be
  closed.
• In the capture state the PLL is in the process of
  acquiring a lock.
• Lock
• In the lock state, the VCO output frequency is
  lock onto the (equal to) the frequency of the
  external input signal.
• In the lock state, the VCO output frequency
  tracks (follows) changes in the frequency of the
  external input in the external signal.

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Loop Acquisition
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Loop Acquisition

• When an external signal enters the phase
  comparator it mixes with the VCO output signal.
• Initially the two frequencies are not equal and
  the loop is unlock.
• Because the phase comparator is a non-linear
  device, the external and VCO output signals mix
  and produces cross-products frequencies (i.e sum
  and differences).
• The low pass filter blocks the two input
  frequencies and the sum of their frequencies. The
  only signal allowed to pass is the difference of
  the two signal. This signals is sometimes called
  the beat frequency.

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Loop Acquisition

• The beat frequency is amplified and then inputted
  to the VCO, where it changes the output frequency
  of the VCO by an amount proportional to its
  polarity and amplitude.
• As the VCO output frequency changes the, the
  amplitude and frequency of the beat frequency
  changes proportionately.
• After several cycles around the loop, the VCO
  output frequency equals the external frequency,
  and the loop is said to acquire a lock.

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Loop Acquisition

• Once frequency lock has occurred, the beat
  frequency at the output of the LPF is 0Hz (a dc
  voltage), and its magnitude and polarity is
  proportional to the difference in phase between
  the external signal and the VCO output signal.
• The dc voltage provides an input bias to the VCO,
  keeping it locked onto the frequency of the
  external input signal.
• In essence the phase comparator is a frequency
  comparator until frequency acquisition is
  achieved, then it becomes a phase comparator.

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PLL Capture and Lock Ranges

• Capture range is defined as the band of
  frequencies centered around the VCO natural
  frequency where the PLL can initially establish
  or acquire frequency lock with an external input
  signal from an unlocked condition.
• Lock range is defined as the band of frequencies
  centered on the VCOs natural frequency over
  which a PLL can maintain frequency lock with an
  external input signal.

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Capture Range

• The capture range is generally between 0.5 and
  1.7 times the VCOs natural frequency.
• Capture rage is sometimes called the acquisition
  range.
• Pull-in range is the capture range expressed as a
  peak value.
• The lowest frequency the PLL can lock onto is
  called the lower capture limit (fcl), and the
  highest frequency the PLL can lock onto is called
  the upper capture limit (fcu).

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Capture Range
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Lock Range

• Lock range is also known as tracking range.
• Lock range of frequencies over which the PLL will
  accurately track of follow the frequency of the
  external input signal after lock has occurred.
• Hold-hold range is the lock range expressed as a
  peak value.
• The lowest frequency a PLL will track is called
  the lower lock limit (fll), and the highest
  frequency that a PLL will track is called the
  upper lock limit (flu).

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Lock Range
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Capture and Lock Ranges
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Voltage Controlled Oscillator

• A VCO is an oscillator (more specifically, a
  free-running multi-vibrator) with a stable
  frequency of oscillation that depends on external
  bias voltage.
• The output from the VCO is a frequency, an its
  input and its input a bias or control signal that
  may be a dc or an ac voltage.
• When a dc or slow changing ac voltage is applied
  to the VCO input, the output frequency changes or
  deviates proportionally.

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Transfer Curve of a VCO
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Transfer Curve of a VCO

• The output frequency (fo) with 0-V input bias is
  the VCOs natural frequency (fn).
• The Change in the output frequency caused by a
  change in the input voltage is called the
  frequency deviation (?f).
• So we have fo fn ?f

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Transfer Function of a VCO
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Phase Comparator

• A phase comparator, sometimes called a phase
  detector, is a nonlinear device with two input
  signals
• An external input frequency.
• The VCO output signal.
• The output is the product of the two signals of
  frequencies fi and fo and therefore contains
  their sum and differences (fi fo).

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PLL FM Demodulator