### Lecture 10

```Phase Locked Loop
Ayman Khattab
Mohamed Saleh
Mostafa El-Khouly
Tarek El-Rifai
Outline
• PLL Overview
• Type (I) PLL
• Phase detector
• Low Pass Filter
• Voltage Controlled Oscillator
• Type (II) PLL
• Phase/Frequency Detector
• Charge Pump PLL
• Drawbacks of PLL
• Applications
What is PLL ?!
• PLL is an electronic circuit that locks the phase
of the output to the input.
Vin
Phase Locked Loop
Vout
Locking Condition
• Locking equation:
• Minimum difference between the two phases is called the
static phase error.
• Hence ,
Simple PLL
• PLL is a negative feedback system that detects the phase error
ΔΦ and then adjusts the phase of the output.
Phase detector
• The Phase detector (PD),acts an comparator that detects ΔΦ
between the output and the input through feedback system.
• Phase detector can be implemented using 2 different
methods :
1.
2.
XOR gate.
Signal multiplier
PD as an XOR gate
PD as a signal multiplier
•
Assume the input signal and the feedback signal are given by :
•
Multiplying both signals will give:
•
The output of this block will be fed to the low pass filter.
Low Pass Filter
• The output signal of the PD (shown in figure) cannot be
directly fed to the VCO
• We need to feed the VCO with DC voltage signal that
corresponds to the phase difference (ΔΦ)
• Thus we need a LPF to smoothen the PD output signal (turns
it into DC voltage signal) that corresponds to (ΔΦ)
LPF output
• The output voltage from the PD(multiplier) is
• The LPF will eliminate this term
Which represents high frequency
• The output from the LPF will be
which is (ΔΦ)
Voltage Controlled Oscillator
• The output from the LPF which is the phase difference (ΔΦ) is
the input to the VCO
• The VCO output is proportional to the input phase difference
(ΔΦ)
• The output of the VCO is given by:
Alignment of the VCO’s phase
• The VCO oscillates at the same frequency as an ideal
reference but with a finite phase error.
• It is required to eliminate the phase error by adjusting the
phase of the VCO.
• But the phase does not change instantaneously so the
frequency of the VCO must be changed, allowing it to
accumulate phase faster or slower than the reference
eventually eliminating the phase error.
• After the phase is eliminated the frequency of the VCO is
returned to its initial value.
Alignment of the VCO’s phase(cont’d)
• The output of the VCO exhibits the following trend during
locking process
• As shown below, the Vcont is stepped at t=to and remains at
the new value till t=t1, when the phase error goes to zero.
• Therefore the 2 signals have the same frequency and phase at
last.
Type(II) PLL
Phase/Frequency Detector (PFD)
• The PFD is different from the normal phase detector in a way
that it generates two outputs, QA and QB.
• QA and QB reflect not only the phase shift, but also reflects
which input has a higher frequency.
Phase/Frequency Detector (PFD)
• To understand output QA and QB, the
following state machine is presented
Now you can easily map the state
diagram to the output response diagram

Phase/Frequency Detector (PFD)
• At this point, we have 2 outputs QA and QB , these two
outputs are then fed to a low pass filter. Afterwards, the
output signals are subtracted and fed to the VCO.
Phase/Frequency Detector (PFD)
• The PFD is composed of two D-flip flops , in this example A
leads B, hence QA=1.
• B rises to 1, therefore QB rises to 1(QA is still 1) activating the
reset, resetting QA and QB.
PD vs. PFD
• In case of the PD, if the VCO frequency and the input frequency
are very different at the startup, the loop may never acquire lock,
since the low pass filter will not be able to process the fast
changes in the phase shift at its input.
• In case of PFD, The first rising edge on +IN sends the output high
and this is maintained until the first rising edge occurs on –IN.
• In a practical system this means that the output, and thus the
input to the VCO, is driven higher, resulting in an increase in
frequency at –IN.
Charge Pump
• The charge pump replaces the low pass filter and the
differential amplifier in the original model of the PLL
• The two switches are MOSFETs the controlled by the 2 signals
QA(Up) and QB(Down).
• If A leads B then QA is high,
turning S1 on, charging the
output capacitance hence Vcont increases.
• If QB is high, S2 is on
discharging the capacitance
to ground, hence Vcont decreases.
Why do we use CP?!
• In Type I PLL, as the frequency difference between the VCO
running frequency and the input increases, the phase error
increases from 0 to π, to acquire an output frequency from
the VCO same as that of the input.
• In CP, the phase difference is translated to voltage that
accumulate on the output capacitance, hence the phase error
can be reduced to the static phase error.
Charge pump drawbacks
• A small phase difference between the 2 signals A and B still
turns one switch on, charging or discharging the capacitance
driving Vout towards ∞ or - ∞ slowly.
• The circuit exhibits an infinite gain.
CP Modified design
• Adding resistance in series to the output C1 stabilizes the
circuit, as the resistance increases the time constant,
decreasing the accumulated charge on the output.
Advantages of CP
1.
2.
3.
4.
Consume less power than active filters.
Have less noise than active filters.
Do not have offset voltage of the Op amp.
More compatible with the objective of
putting the filter on chip.
Drawbacks of PLL
• Clock Jitter:
– PLL components do not have zero response time.
– Reference clock jitter being multiplied by the PLL.
• Inherently noise sensitive.
• Some PLLs can require expensive, high-quality
external components to implement the loop-filter
design.
PLL Applications
1. FM Demodulator.
2. Frequency synthesizer.
FM Demodulator
• when an FSK waveform is applied to a PLL, the PLL acts as a
frequency Demodulator.
• The input frequency toggles between two values and so does
the output frequency.
• The control voltage must also toggle between two values.
• At each input frequency jump the control voltage begins to
change in the opposite direction.
• The final control voltage signal is the demodulated signal.
FM Demodulator(cont’d)
FM Demodulator Example:
• For the FM modulator, If  = 10 / and
= 5 , find  for  = 2.5   10
solution
=  =  +

−
=

2.5  =

2.5−5
10
= −0.25
10 − 5
10  =
= 0.5
10
Frequency Synthesizer
• Frequency synthesizer generates multiple
signals at different frequencies by adding
dividers, using only one oscillator (VCO).
Any Questions ?!
References
•
RF microelectronics, Behzad Razavi, 2nd version, chapter 9
•
PLL Phase Detector / Comparator, http://www.radio-electronics.com/info/rftechnology-design/pll-synthesizers/phase-locked-loop-detector.php
•
Introduction to PLL,
http://www.digitavid.net/VirtualUniveristy/Presentations/IntroductiontoPLL.pdf
•
LECTURE 170 – APPLICATIONS OF PLLS AND FREQUENCY DIVIDERS (PRESCALERS),
http://users.ece.gatech.edu/pallen/Academic/ECE_6440/Summer_2003/L170FreqSyn-I(2UP).pdf
•
Introduction to Phase Locked Loops, Kenneth Finnegan,
https://www.youtube.com/watch?v=0jzLDe950AY
Thank You ! =)
```