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Typically, the reference clock enters the chip and drives a phase locked loop PLL , which then drives the system's clock distribution.
The clock distribution is usually balanced so that the clock arrives at every endpoint simultaneously.
One of those endpoints is the PLL's feedback input. The function of the PLL is to compare the distributed clock to the incoming reference clock, and vary the phase and frequency of its output until the reference and feedback clocks are phase and frequency matched.
PLLs are ubiquitous—they tune clocks in systems several feet across, as well as clocks in small portions of individual chips. Sometimes the reference clock may not actually be a pure clock at all, but rather a data stream with enough transitions that the PLL is able to recover a regular clock from that stream.
Sometimes the reference clock is the same frequency as the clock driven through the clock distribution, other times the distributed clock may be some rational multiple of the reference.
The output of the multiplier contains both the sum and the difference frequency signals, and the demodulated output is obtained by low pass filtering.
Since the PLL responds only to the carrier frequencies which are very close to the VCO output, a PLL AM detector exhibits a high degree of selectivity and noise immunity which is not possible with conventional peak type AM demodulators.
One desirable property of all PLLs is that the reference and feedback clock edges be brought into very close alignment. The average difference in time between the phases of the two signals when the PLL has achieved lock is called the static phase offset also called the steady-state phase error.
The variance between these phases is called tracking jitter. Ideally, the static phase offset should be zero, and the tracking jitter should be as low as possible.
Phase noise is another type of jitter observed in PLLs, and is caused by the oscillator itself and by elements used in the oscillator's frequency control circuit.
Some technologies are known to perform better than others in this regard. The best digital PLLs are constructed with emitter-coupled logic ECL elements, at the expense of high power consumption.
Another desirable property of all PLLs is that the phase and frequency of the generated clock be unaffected by rapid changes in the voltages of the power and ground supply lines, as well as the voltage of the substrate on which the PLL circuits are fabricated.
This is called substrate and supply noise rejection. The higher the noise rejection, the better. To further improve the phase noise of the output, an injection locked oscillator can be employed following the VCO in the PLL.
In most cellular handsets this function has been largely integrated into a single integrated circuit to reduce the cost and size of the handset.
However, due to the high performance required of base station terminals, the transmission and reception circuits are built with discrete components to achieve the levels of performance required.
GSM local oscillator modules are typically built with a frequency synthesizer integrated circuit and discrete resonator VCOs.
A phase detector compares two input signals and produces an error signal which is proportional to their phase difference.
The error signal is then low-pass filtered and used to drive a VCO which creates an output phase. The output is fed through an optional divider back to the input of the system, producing a negative feedback loop.
If the output phase drifts, the error signal will increase, driving the VCO phase in the opposite direction so as to reduce the error. Thus the output phase is locked to the phase at the other input.
This input is called the reference. Analog phase locked loops are generally built with an analog phase detector, low pass filter and VCO placed in a negative feedback configuration.
A digital phase locked loop uses a digital phase detector; it may also have a divider in the feedback path or in the reference path, or both, in order to make the PLL's output signal frequency a rational multiple of the reference frequency.
A non-integer multiple of the reference frequency can also be created by replacing the simple divide-by- N counter in the feedback path with a programmable pulse swallowing counter.
The oscillator generates a periodic output signal. Assume that initially the oscillator is at nearly the same frequency as the reference signal.
If the phase from the oscillator falls behind that of the reference, the phase detector changes the control voltage of the oscillator so that it speeds up.
Likewise, if the phase creeps ahead of the reference, the phase detector changes the control voltage to slow down the oscillator. Since initially the oscillator may be far from the reference frequency, practical phase detectors may also respond to frequency differences, so as to increase the lock-in range of allowable inputs.
A phase detector PD generates a voltage, which represents the phase difference between two signals. The PD output voltage is used to control the VCO such that the phase difference between the two inputs is held constant, making it a negative feedback system.
For instance, the frequency mixer produces harmonics that adds complexity in applications where spectral purity of the VCO signal is important.
The resulting unwanted spurious sidebands, also called " reference spurs " can dominate the filter requirements and reduce the capture range well below or increase the lock time beyond the requirements.
In these applications the more complex digital phase detectors are used which do not have as severe a reference spur component on their output. Also, when in lock, the steady-state phase difference at the inputs using this type of phase detector is near 90 degrees.
In PLL applications it is frequently required to know when the loop is out of lock. The more complex digital phase-frequency detectors usually have an output that allows a reliable indication of an out of lock condition.
It can also be used in an analog sense with only slight modification to the circuitry. The block commonly called the PLL loop filter usually a low pass filter generally has two distinct functions.
The primary function is to determine loop dynamics, also called stability. This is how the loop responds to disturbances, such as changes in the reference frequency, changes of the feedback divider, or at startup.
Common considerations are the range over which the loop can achieve lock pull-in range, lock range or capture range , how fast the loop achieves lock lock time, lock-up time or settling time and damping behavior.
Depending on the application, this may require one or more of the following: Loop parameters commonly examined for this are the loop's gain margin and phase margin.
Common concepts in control theory including the PID controller are used to design this function. The second common consideration is limiting the amount of reference frequency energy ripple appearing at the phase detector output that is then applied to the VCO control input.
The design of this block can be dominated by either of these considerations, or can be a complex process juggling the interactions of the two.
Often also the phase-noise is affected. All phase-locked loops employ an oscillator element with variable frequency capability.
PLLs may include a divider between the oscillator and the feedback input to the phase detector to produce a frequency synthesizer.
A programmable divider is particularly useful in radio transmitter applications, since a large number of transmit frequencies can be produced from a single stable, accurate, but expensive, quartz crystal—controlled reference oscillator.
Some PLLs also include a divider between the reference clock and the reference input to the phase detector. It might seem simpler to just feed the PLL a lower frequency, but in some cases the reference frequency may be constrained by other issues, and then the reference divider is useful.
Frequency multiplication can also be attained by locking the VCO output to the N th harmonic of the reference signal. Instead of a simple phase detector, the design uses a harmonic mixer sampling mixer.
The harmonic mixer turns the reference signal into an impulse train that is rich in harmonics. Consequently, the desired harmonic mixer output representing the difference between the N harmonic and the VCO output falls within the loop filter passband.
It should also be noted that the feedback is not limited to a frequency divider. This element can be other elements such as a frequency multiplier, or a mixer.
The multiplier will make the VCO output a sub-multiple rather than a multiple of the reference frequency. A mixer can translate the VCO frequency by a fixed offset.
It may also be a combination of these. An example being a divider following a mixer; this allows the divider to operate at a much lower frequency than the VCO without a loss in loop gain.
The equations governing a phase-locked loop with an analog multiplier as the phase detector and linear filter may be derived as follows.
The star symbol is a conjugate transpose. Then the following dynamical system describes PLL behavior. The time-domain model takes the form. PD characteristics for this signals is equal  to.
Phase locked loops can also be analyzed as control systems by applying the Laplace transform. The loop response can be written as:.
The loop characteristics can be controlled by inserting different types of loop filters. The simplest filter is a one-pole RC circuit.
The loop transfer function in this case is:. This is the form of a classic harmonic oscillator. The denominator can be related to that of a second order system:.
The loop natural frequency is a measure of the response time of the loop, and the damping factor is a measure of the overshoot and ringing.
Ideally, the natural frequency should be high and the damping factor should be near 0. With a single pole filter, it is not possible to control the loop frequency and damping factor independently.
For the case of critical damping,. A slightly more effective filter, the lag-lead filter includes one pole and one zero. This can be realized with two resistors and one capacitor.
The transfer function for this filter is. The loop filter components can be calculated independently for a given natural frequency and damping factor.
Real world loop filter design can be much more complex e. See the D Banerjee ref below. Digital phase locked loops can be implemented in hardware, using integrated circuits such as a CMOS However, with microcontrollers becoming faster, it may make sense to implement a phase locked loop in software for applications that do not require locking onto signals in the MHz range or faster, such as precisely controlling motor speeds.
Software implementation has several advantages including easy customization of the feedback loop including changing the multiplication or division ratio between the signal being tracked and the output oscillator.
Furthermore, a software implementation is useful to understand and experiment with. As an example of a phase-locked loop implemented using a phase frequency detector is presented in MATLAB, as this type of phase detector is robust and easy to implement.
This example uses integer arithmetic rather than floating point, as such an example is likely more useful in practice.
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