A
phase-locked loop or
phase lock loop (PLL) is a
control systemA control system is a device or set of devices to manage, command, direct or regulate the behavior of other devices or systems.There are two common classes of control systems, with many variations and combinations: logic or sequential controls, and feedback or linear controls...
that generates a
signalIn the fields of communications, signal processing, and in electrical engineering more generally, a signal is any time-varying or spatial-varying quantity....
that has a fixed relation to the
phaseThe phase of an oscillation or wave is the fraction of a complete cycle corresponding to an offset in the displacement from a specified reference point at time t = 0. Phase is a frequency domain or Fourier transform domain concept, and as such, can be readily understood in terms of simple harmonic...
of a "reference" signal. A phase-locked loop circuit responds to both the frequency and the phase of the input signals, automatically raising or lowering the frequency of a controlled oscillator until it is matched to the reference in both frequency and phase. A phase-locked loop is an example of a control system using
negative feedbackNegative feedback occurs when the output of a system acts to oppose changes to the input of the system; with the result that the changes are attenuated. If the overall feedback of the system is negative, then the system will tend to be stable.- Overview :...
.
Phase-locked loops are widely used in
radioRadio is the transmission of signals by modulation of electromagnetic waves with frequencies below those of visible light. Electromagnetic radiation travels by means of oscillating electromagnetic fields that pass through the air and the vacuum of space...
, telecommunications,
computerA computer is a machine that manipulates data according to a set of instructions.Although mechanical examples of computers have existed through much of recorded human history, the first electronic computers were developed in the mid-20th century . These were the size of a large room, consuming as...
s and other electronic applications. They may generate stable frequencies, recover a signal from a noisy communication channel, or distribute clock timing pulses in digital logic designs such as
microprocessorA microprocessor incorporates most or all of the functions of a central processing unit on a single integrated circuit . The first microprocessors emerged in the early 1970s and were used for electronic calculators, using binary-coded decimal arithmetic on 4-bit words...
s. Since a single
integrated circuitIn electronics, an integrated circuit is a miniaturized electronic circuit that has been manufactured in the surface of a thin substrate of semiconductor material...
can provide a complete phase-locked-loop building block, the technique is widely used in modern electronic devices, with output frequencies from a fraction of a cycle per second up to many gigahertz.
Analogy
TuningIn music, there are two common meanings for tuning:* Tuning practice, the act of tuning an instrument or voice.* Tuning systems, the various systems of pitches used to tune an instrument, and their theoretical basis.-Tuning practice:...
a string on a guitar can be compared to the operation of a phase-locked loop. Using a
tuning forkA tuning fork is an acoustic resonator in the form of a two-pronged fork with the prongs formed from a U-shaped bar of elastic metal . It resonates at a specific constant pitch when set vibrating by striking it against a surface or with an object, and emits a pure musical tone after waiting a...
or
pitchpipeA pitch pipe is a small device used to provide a pitch reference for musicians without absolute pitch. Although it may be described as a musical instrument, it is not typically used to play music as such.- Origins :...
to provide a reference frequency, the tension of the string is adjusted up or down until the
beatIn acoustics, a beat is an interference between two sounds of slightly different frequencies, perceived as periodic variations in volume whose rate is the difference between the two frequencies....
frequency is inaudible. This indicates that the tuning fork and guitar are vibrating at the same frequency. If we imagine the guitar could be tuned
perfectly to the reference tuning fork frequency, and maintained there, the guitar string would be said to be in phase-lock with the fork.
History
Earliest research towards what became known as the phase-locked loop goes back to 1932, when British researchers developed an alternative to
Edwin ArmstrongEdwin Howard Armstrong was an American electrical engineer and inventor. Armstrong was the inventor of frequency modulation radio, regeneration, and the superheterodyne....
's
superheterodyne receiverIn electronics, the superheterodyne receiver is a receiver which uses the principle of frequency mixing or heterodyning to convert the received signal to a lower "intermediate" frequency, that can be more conveniently processed than the original radio carrier frequency...
, the
HomodyneHomodyne detection is a method of detecting frequency-modulated radiation by non-linear mixing with radiation of a reference frequency, the same principle as for heterodyne detection....
or
direct-conversion receiverIn telecommunication, a direct-conversion receiver , also known as homodyne, synchrodyne, or zero-IF receiver, is a radio receiver design that demodulates the incoming signal by mixing it with a local oscillator signal synchronized in frequency to the carrier of the wanted signal...
. In the homodyne or synchrodyne system, a local
oscillatorAn electronic oscillator is an electronic circuit that produces a repetitive electronic signal, often a sine wave or a square wave.A low-frequency oscillator is an electronic oscillator that generates an AC waveform at a frequency below ≈20 Hz...
was tuned to the desired input frequency and multiplied with the input signal. The resulting output signal included the original modulation information. The intent was to develop an alternative receiver circuit that required fewer tuned circuits than the superheterodyne receiver. Since the local oscillator would rapidly drift in frequency, an automatic correction signal was applied to the oscillator, maintaining it in the same phase and frequency as the desired signal. The technique was described in 1932, in a paper by Henri de Bellescize, in the French journal
L'Onde Électrique.
In analog television receivers since at least the late 1930s, phase-locked-loop horizontal and vertical sweep circuits are locked to synchronization pulses in the broadcast signal.
When
SigneticsSignetics, once a major player in semiconductor manufacturing, made a variety of devices which included integrated circuits, bipolar and MOS, the Dolby circuit, logic, memory and analog circuits and Motorola clone CPUs, some of which were included in the first Atari video games.Signetics was...
introduced a line of monolithic integrated circuits that were complete phase-locked loop systems on a chip in 1969, applications for the technique multiplied. A few years later RCA introduced the "CD4046"
CMOSComplementary metal–oxide–semiconductor is a technology for making integrated circuits. CMOS technology is used in microprocessors, microcontrollers, static RAM, and other digital logic circuits. CMOS technology is also used for a wide variety of analog circuits such as image sensors, data...
Micropower Phase-Locked Loop, which became a popular integrated circuit.
Structure and function
Phase-locked loop mechanisms may be implemented as either analog or digital circuits. Both implementations use the same basic structure.
Both analog and digital PLL circuits include three basic elements:
- a phase detector
A phase detector is a frequency mixer or analog multiplier circuit that generates a voltage signal which represents the difference in phase between two signal inputs...
,
- a variable electronic oscillator
An electronic oscillator is an electronic circuit that produces a repetitive electronic signal, often a sine wave or a square wave.A low-frequency oscillator is an electronic oscillator that generates an AC waveform at a frequency below ≈20 Hz...
, and
- a feedback
Feedback describes the situation when output from an event or phenomenon in the past will influence the same event/phenomenon in the present or future....
path (which often includes a frequency dividerA frequency divider is an electronic circuit that takes an input signal with a frequency, , and generates an output signal with a frequency:where is an integer. Phase-locked loop frequency synthesizers make use of frequency dividers to generate a frequency that is a multiple of a reference...
).
Digital phase-locked loop (DPLL)
A digital phase-locked loop operates similarly to an analog phase-locked loop, but is implemented entirely using digital circuits. In place of a voltage-controlled oscillator (VCO), a DPLL uses local reference clock and a variable dividing counter under digital control to create the equivalent oscillator function.
DPLLs are easier to design and implement, and are less sensitive to voltage noise than analog PLLs, however they typically suffer from higher phase noise due to the
quantization errorThe difference between the actual analog value and quantized digital value due is called quantization error. This error is due either to rounding or truncation.-Quantization noise model of quantization error :...
of using a non-analog oscillator. For this reason digital phase locked loops are not well-suited to synthesizing higher frequencies or handling high frequency reference signals. DPLLs are sometimes used for data recovery.
Basic design
A PLL 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
voltage-controlled oscillatorA voltage-controlled oscillator or VCO is an electronic oscillator designed to be controlled in oscillation frequency by a voltage input. The frequency of oscillation is varied by the applied DC voltage, while modulating signals may also be fed into the VCO to cause frequency modulation or phase...
(VCO) which creates an output frequency. The output frequency is fed through a
frequency dividerA frequency divider is an electronic circuit that takes an input signal with a frequency, , and generates an output signal with a frequency:where is an integer. Phase-locked loop frequency synthesizers make use of frequency dividers to generate a frequency that is a multiple of a reference...
back to the input of the system, producing a negative feedback loop. If the output frequency drifts, the error signal will increase, driving the VCO frequency in the opposite direction so as to reduce the error. Thus the output is locked to the frequency at the other input. This input is called the reference and is often derived from a crystal oscillator, which is very stable in frequency.
Analog phase locked loops are generally built of a
phase detectorA phase detector is a frequency mixer or analog multiplier circuit that generates a voltage signal which represents the difference in phase between two signal inputs...
, low pass filter and
voltage-controlled oscillatorA voltage-controlled oscillator or VCO is an electronic oscillator designed to be controlled in oscillation frequency by a voltage input. The frequency of oscillation is varied by the applied DC voltage, while modulating signals may also be fed into the VCO to cause frequency modulation or phase...
(VCO) placed in a negative
feedbackFeedback describes the situation when output from an event or phenomenon in the past will influence the same event/phenomenon in the present or future....
closed-loop configuration. There may be a
frequency dividerA frequency divider is an electronic circuit that takes an input signal with a frequency, , and generates an output signal with a frequency:where is an integer. Phase-locked loop frequency synthesizers make use of frequency dividers to generate a frequency that is a multiple of a reference...
in the feedback path or in the reference path, or both, in order to make the PLL's output signal frequency an integer multiple of the reference. A non integer multiple of the reference frequency can be created by replacing the simple divide-by-N counter in the feedback path with a programmable
pulse swallowing counterA pulse swallowing counter is a component in an all-digital feedback system. The overall pulse swallowing system is used as part of a fractional-N frequency divider. The overall pulse swallowing system cancels beatnotes created when switching between N, N+1, or N−1 in a fractional-N...
. This technique is usually referred to as a fractional-N synthesizer or fractional-N PLL.
The oscillator generates a periodic output signal. Assume that initially the oscillator is at nearly the same frequency as the reference signal. Then, 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.
The block commonly called 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 or lock range), how fast the loop achieves lock (lock time or lock-up time) and
Overshoot (signal)In signal processing, control theory, electronics, and mathematics, overshoot is when a signal or function exceeds its steady-state value.It arises especially in the step response of bandlimited systems such as low-pass filters...
(damping). Depending on the application, this may require one or more of the following: a simple proportion (gain or attenuation), an
integralIntegration is an important concept in mathematics which, together with differentiation, forms one of the main operations in calculus. Given a function ƒ of a real variable x and an interval [a, b] of the real line, the definite integralis defined informally...
(low pass filter) and/or
derivativeIn calculus the derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much a quantity is changing at a given point; for example, the derivative of the position of a vehicle with respect to time is the instantaneous velocity...
(high pass filter). Loop parameters commonly examined for this are the loop's gain margin and
phase marginIn electronic amplifiers, phase margin is the difference, measured in degrees, between the phase of the amplifier's output signal and -180°. In feedback amplifiers, the phase margin is measured at the frequency at which the open loop voltage gain of the amplifier and the closed loop voltage gain...
. Common concepts in Control Theory are used to design this function and are covered in the
Control systemA control system is a device or set of devices to manage, command, direct or regulate the behavior of other devices or systems.There are two common classes of control systems, with many variations and combinations: logic or sequential controls, and feedback or linear controls...
section.
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. This frequency modulates the VCO and produces FM sidebands commonly called "reference spurious". The low pass characteristic of this block can be used to attenuate this energy, but at times a band reject "notch" may also be needed.
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.
Depending on the application, either the output of the controlled oscillator, or the control signal to the oscillator, provides the useful output of the PLL system.
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 VFO 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.
Phase detector
The two inputs of the
phase detectorA phase detector is a frequency mixer or analog multiplier circuit that generates a voltage signal which represents the difference in phase between two signal inputs...
(PD) are the reference input (Fi) and the feedback from the voltage controlled oscillator (VCO). The PD output controls the VCO such that the phase difference between the two inputs is held constant, making it a negative
feedbackFeedback describes the situation when output from an event or phenomenon in the past will influence the same event/phenomenon in the present or future....
system.
There are several types of phase detectors in the two main categories of analog and digital.
Analog
The analog phase detector takes the form of an ideal
frequency mixerIn telecommunications, a mixer is a nonlinear or time-varying circuit or device that accepts as its input two different frequencies and presents at its output a mixture of signals at several frequencies:# the sum of the frequencies of the input signals...
. This device produces an output that is the product of the two instantaneous input voltages. The multiplication process produces the classical sum and difference frequencies of mixers, but when used as a phase detector, a
Low-pass filterA low-pass filter is a filter that passes low-frequency signals but attenuates signals with frequencies higher than the cutoff frequency. The actual amount of attenuation for each frequency varies from filter to filter. It is sometimes called a high-cut filter, or treble cut filter when used in...
is required to attenuate the sum frequency. When the remaining difference frequency is low enough to pass through the filter with sufficient amplitude, it moves the VCO frequency closer to the reference frequency allowing the loop, after a transient period, to acquire lock. This process is called "capture" and the maximum frequency separation (between reference input and VCO) that allows lock is the "capture range". The loop is called "locked" when the VCO is on the same frequency as the reference and differs only in some amount of phase.
When the loop is locked, the sum and difference are still present, but the sum becomes a frequency twice that of the reference. The difference, which appears as the average value of the sum frequency, becomes, after the filter, a DC component proportional to the (cosine of the) phase difference. This then sets the VCO frequency.
The phase difference at the inputs, when in lock, is near 90 degrees for this type; the exact amount being determined by the loop gain. Though an additional integration can be added to bring it to 90, this is rarely required in simple loops.
The phase and amplitude characteristics of the low-pass filter are dominant factors in determining the capture range, lock time and transient performance of the loop.
Two common implementations are the
double balanced diode mixer and the
four-quadrant multiplier (which is also a double balanced mixer).
The presence of the sum frequency at the mixer output also adds complexity in applications where spectral purity of the VCO signal is important. This causes frequency modulation of the VCO at twice the reference frequency. The resulting unwanted (spurious) sidebands, also called "reference spurs" can dominate the filter requirements and reduce the capture range and lock time well below 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.
Digital
The simplest is an
XOR gateThe XOR gate is a digital logic gate that implements exclusive disjunction - it behaves according to the truth table above. A HIGH output results if one, and only one, of the inputs to the gate is HIGH . If both inputs are LOW or both are HIGH , a LOW output results.XOR gate is short for...
. It compares well to the analog mixer in that it locks near a 90° phase difference and has a square-wave output at twice the reference frequency. The average value of this square wave is the DC component that sets the VCO frequency. The square-wave changes duty-cycle in proportion to the phase difference resulting, after the filter, in the VCO control voltage. It requires inputs that are symmetrical square waves, or nearly so. The remainder of its characteristics are very similar to the analog mixer for capture range, lock time, reference spurious and low-pass filter requirements.
A more complex digital PD uses a simple state machine to determine which of the two signals has a zero-crossing earlier or more often. This brings the PLL into lock even when it is off frequency and is known as a
Phase Frequency DetectorA phase frequency detector , in electronics, is a device which compares the phase of two input signals. It has two inputs which correspond to two different input signals, usually one from a voltage-controlled oscillator and another from some external source...
.
A PLL with a
bang-bang charge pumpA charge pump is a kind of DC to DC converter that uses capacitors as energy storage elements to create either a higher or lower voltage power source. Charge pump circuits are capable of high efficiencies, sometimes as high as 90-95% while being electrically simple circuits.Charge pumps use some...
phase detector supplies current pulses with fixed total charge, either positive or negative, to the capacitor acting as an
integratorAn integrator is a device to perform the mathematical operation known as integration, a fundamental operation in calculus.The integration function is often part of engineering, physics, mechanical, chemical and scientific calculations....
. A phase detector for a bang-bang charge pump must always have a
dead band where the phases of the reference and feedback clocks are close enough that the detector fires either both or neither of the charge pumps, for no total effect. Bang-bang phase detectors are simple, but are associated with significant minimum peak-to-peak
jitterJitter is the time variation of a periodic signal in electronics and telecommunications, often in relation to a reference clock source. Jitter may be observed in characteristics such as the frequency of successive pulses, the signal amplitude, or phase of periodic signals...
, because once in lock the phase offset drifts inside the two extreme values of the dead band without triggering any corrections.
A
proportional phase detector employs a charge pump that supplies charge amounts in proportion to the phase error detected. Some have dead bands and some do not. A dead band is an area where small changes in phase difference produce no correction to the VCO. Specifically, some designs produce both "up" and "down" control pulses even when the phase difference is zero. These pulses are small, nominally the same duration, and cause the charge pump to produce equal-charge positive and negative current pulses when the phase is perfectly matched. If the inputs are slightly mismatched, either the up or down pulse will contain slightly more charge than the other and the PLL will be able to correct the offset. PLLs with this kind of control system don't exhibit a dead band and typically have lower minimum peak-to-peak jitter that is determined by other limiting factors.
These types, having outputs consisting of very narrow pulses at lock, are very useful for applications requiring very low VCO spurious outputs. The narrow pulses contain very little energy and are easy to filter out of the VCO control voltage. This results in low VCO control line ripple and therefore low FM sidebands on the VCO.
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.
Oscillator types
Inductive oscillators (
LC oscillators) are built of an LC "tank" circuit, which oscillates by charging and discharging a capacitor through an inductor. These oscillators are typically used when a tunable precision frequency source is necessary, such as with radio transmitters and receivers. Most LC oscillators use off-chip inductors. On-chip inductors suffer large resistive losses, so that the
QIn physics and engineering the quality factor or Q factor is a dimensionless parameter that describes how under-damped an oscillator or resonator is, or equivalently, characterizes a resonator's bandwidth relative to its center frequency....
of the resulting tank circuit is generally less than 10. As processes have made larger numbers of metal layers available (allowing designers to distance the inductor metal layer from the resistive substrate), on-chip inductors have become more useful.
A voltage-controlled capacitor is one method of making an LC oscillator vary its frequency in response to a control voltage. Any reverse-biased
semiconductorA semiconductor is a material that has an electrical resistivity between that of a conductor and an insulator, that is, generally in the range 10
3 Siemens/cm to 10
−8 S/cm. Devices made from semiconductor materials are the foundation of modern electronics, including radio,...
diodeIn electronics a diode is a two-terminal electronic component which conducts electric current asymmetrically or unidirectionally; that is, it conducts current more easily in one direction than in the opposite direction. The term usually refers to a semiconductor diode, the most common type today,...
displays a measure of voltage-dependent capacitance and can be used to change the frequency of an oscillator by varying a control voltage applied to the diodes. Special-purpose variable capacitance varactor diodes are available with well-characterized wide-ranging values of capacitance. Such devices are very convenient in the manufacture of voltage-controlled oscillators (a voltage-controlled inductor would be in principle as useful, but such devices are unsatisfactory at the frequencies usually desired).
Crystal oscillators are piezoelectric quartz crystals that mechanically vibrate between two slightly different shapes. Crystals have very high Q, and can only be tuned within a very small range of frequencies. Crystal oscillators are typically used as the frequency reference for PLLs, and can be found in nearly every consumer electronic device. Because the crystal is an off-chip component, it adds some cost and complexity to the system design, but the crystal itself is generally quite inexpensive.
- Surface acoustic wave
]A surface acoustic wave is an acoustic wave traveling along the surface of a material exhibiting elasticity, with an amplitude that typically decays exponentially with depth into the substrate.-Discovery:...
devices (SAWs) are a kind of crystal oscillator, but achieve much higher frequencies by establishing standing waves on the surface of the quartz crystal. These are more expensive than crystal oscillators, and are used in more specialized applications which require a direct and very accurate high frequency reference, for example, in cellular telephones.
For a PLL built into a microprocessor chip,
ring oscillatorA ring oscillator is a device composed of an odd number of NOT gates whose output oscillates between two voltage levels, representing true and false...
s can be used as
voltage-controlled oscillatorA voltage-controlled oscillator or VCO is an electronic oscillator designed to be controlled in oscillation frequency by a voltage input. The frequency of oscillation is varied by the applied DC voltage, while modulating signals may also be fed into the VCO to cause frequency modulation or phase...
s-a free running multivibrator (VCOs). They are built of a ring of active delay stages. Generally the ring has an odd number of inverting stages, so that there is no single stable state for the internal ring voltages. Instead, a single transition propagates endlessly around the ring. The frequency is controlled by varying either the supply voltage or the capacitive loading on each stage. VCOs generally have the lowest Q of the used oscillators, and so suffer more jitter than the other types. The jitter can be made low enough for many applications (such as driving an ASIC), in which case VCOs enjoy the advantages of having no off-chip components (expensive) or on-chip inductors (low yields on generic CMOS processes). These oscillators also have larger tuning ranges than the other kinds, which improves yield and is sometimes a feature of the end product (for instance, the dot clock on a graphics card which drives a wide range of monitors).
Feedback path and optional divider
Most PLLs also include a divider between the oscillator and the feedback input to the phase detector to produce a
frequency synthesizerA frequency synthesizer is an electronic system for generating any of a range of frequencies from a single fixed timebase or oscillator. They are found in many modern devices, including radio receivers, mobile telephones, radiotelephones, walkie-talkies, CB radios, satellite receivers, GPS systems,...
. 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. If this divider divides by , it allows the VCO to multiply the reference frequency by . 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 in a sense can also be attained by locking the PLL to the 'N'th harmonic of the signal.
Equations
The equations governing a phase-locked loop with an analog multiplier as the phase detector may be derived as follows. Let the input to the phase
detector be and the output of the
voltage-controlled oscillatorA voltage-controlled oscillator or VCO is an electronic oscillator designed to be controlled in oscillation frequency by a voltage input. The frequency of oscillation is varied by the applied DC voltage, while modulating signals may also be fed into the VCO to cause frequency modulation or phase...
(VCO) is with frequency , then the output of the phase detector is given by
the VCO frequency may be written as a function of the VCO input
as
where is the
sensitivity of the VCO and is expressed in Hz / V.
Hence the VCO output takes the form
where
The loop filter receives this signal as input and produces an output
where is the operator representing the
loop filter transformation.
When the loop is closed, the output from the loop filter becomes the input to
the VCO thus
We can deduce how the PLL reacts to a sinusoidal input signal:
The output of the phase detector then is:
This can be rewritten into sum and difference components using trigonometric identities:
As an approximation to the behaviour of the loop filter we may
consider only the difference frequency being passed with no phase change, which enables us to derive a small-signal model of the phase-locked loop. If we can make , then the can be approximated by its argument resulting in: . The phase-locked loop is said to be
locked if this is the case.
Control system analysis
Phase locked loops can also be analyzed as control systems by applying the
Laplace transformIn mathematics, the Laplace transform is a widely used integral transform. It has many important applications in mathematics, physics, optics, electrical engineering, control engineering, signal processing, and probability theory....
. The loop response can be written as:
Where
- is the output phase in radian
The radian is a unit of plane angle, equal to 180/π degrees, or about 57.2958 degrees, or about 57°17′45″. It is the standard unit of angular measurement in all areas of mathematics beyond the elementary level....
s
- is the input phase in radians
- is the phase detector gain in volt
The volt is the SI derived unit of electromotive force, commonly called "voltage". It is also the unit for the related but slightly different quantity electric potential difference...
s per radian
- is the VCO gain in radians per volt-second
The second , sometimes abbreviated sec., is the name of a unit of time, and is the International System of Units base unit of time...
- is the loop filter transfer function (dimensionless)
The loop characteristics can be controlled by inserting different types of loop filters. The simplest filter is a one-pole
RC circuitA resistor–capacitor circuit ', or RC filter or RC network, is an electric circuit composed of resistors and capacitors driven by a voltage or current source...
. The loop transfer function in this case is:
The loop response becomes:
This is the form of a classic
harmonic oscillatorIn classical mechanics, a harmonic oscillator is a system which, when displaced from its equilibrium position, experiences a restoring force, F, proportional to the displacement, x according to Hooke's law:where k is a positive constant....
. The denominator can be related to that of a second order system:
Where
- is the damping factor
- is the natural frequency of the loop
For the one-pole RC filter,
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 0.707 (critical damping). 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
This filter has two time constants
Substituting above yields the following natural frequency and damping factor
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 eg using higher order filters to reduce various types or source of phase noise. (See the D Banerjee ref below)
Applications
Phase-locked loops are widely used for
synchronizationSynchronization or synchronisation is timekeeping which requires the coordination of events to operate a system in unison. The familiar conductor of an orchestra serves to keep the orchestra in time....
purposes; in space
communicationsTelecommunication is transmission over a distance for the purpose of communication. In earlier times, this may have involved the use of smoke signals, drums, semaphore, flags or heliograph. In modern times, telecommunication typically involves the use of electronic devices such as the telephone,...
for
coherentIn physics, coherence is a property of waves, that enables stationary interference. More generally, coherence describes all properties of the electronic correlation between physical quantities of a wave....
carrierIn telecommunications, a carrier wave, or carrier is a waveform that is modulated with an input signal for the purpose of conveying information. This carrier wave is usually of much higher frequency than the input signal....
tracking and
threshold-Film and television:* Threshold , an adaptation of the 1958 science fiction film It! The Terror from Beyond Space* Threshold , an American science fiction drama series* "Threshold" , an episode of the TV series...
extension, bit synchronization, and symbol synchronization. Phase-locked loops can also be used to demodulate
frequency-modulatedIn telecommunications, frequency modulation conveys information over a carrier wave by varying its frequency . In analog applications, the instantaneous frequency of the carrier is directly proportional to the instantaneous value of the input signal...
signals. In radio transmitters, a PLL is used to synthesize new frequencies which are a multiple of a reference frequency, with the same stability as the reference frequency.
Clock recovery
Some data streams, especially high-speed serial data streams (such as the raw stream of data from the magnetic head of a disk drive), are sent without an accompanying clock. The receiver generates a clock from an approximate frequency reference, and then phase-aligns to the transitions in the data stream with a PLL. This process is referred to as
clock recoverySome digital data streams, especially high-speed serial data streams are sent without an accompanying clock signal. The receiver generates a clock from an approximate frequency reference, and then phase-aligns to the transitions in the data stream with a phase-locked loop...
. In order for this scheme to work, the data stream must have a transition frequently enough to correct any drift in the PLL's oscillator. Typically, some sort of redundant encoding is used; 8B10B is very common.
Deskewing
If a clock is sent in parallel with data, that clock can be used to sample the data. Because the clock must be received and amplified before it can drive the flip-flops which sample the data, there will be a finite, and process-, temperature-, and voltage-dependent delay between the detected clock edge and the received data window. This delay limits the frequency at which data can be sent. One way of eliminating this delay is to include a deskew PLL on the receive side, so that the clock at each data flip-flop is phase-matched to the received clock. In that type of application, a special form of a PLL called a
Delay-Locked LoopIn electronics, a delay-locked loop is a digital circuit similar to a phase-locked loop , with the main difference being the absence of an internal oscillator...
(DLL) is frequently used ;;.
Clock generation
Many electronic systems include processors of various sorts that operate at hundreds of megahertz. Typically, the clocks supplied to these processors come from clock generator PLLs, which multiply a lower-frequency reference clock (usually 50 or 100 MHz) up to the operating frequency of the processor. The multiplication factor can be quite large in cases where the operating frequency is multiple gigahertz and the reference crystal is just tens or hundreds of megahertz.
Spread spectrum
All electronic systems emit some unwanted radio frequency energy. Various regulatory agencies (such as the
FCCThe Federal Communications Commission is an independent agency of the United States government, created, directed, and empowered by Congressional statute , and with the majority of its commissioners appointed by the current President...
in the United States) put limits on the emitted energy and any interference caused by it. The emitted noise generally appears at sharp spectral peaks (usually at the operating frequency of the device, and a few harmonics). A system designer can use a spread-spectrum PLL to reduce interference with high-Q receivers by spreading the energy over a larger portion of the spectrum. For example, by changing the operating frequency up and down by a small amount (about 1%), a device running at hundreds of megahertz can spread its interference evenly over a few megahertz of spectrum, which drastically reduces the amount of noise seen on broadcast
FM radioFM broadcasting is a broadcast technology invented by Edwin Howard Armstrong that uses frequency modulation to provide high-fidelity sound over broadcast radio.-Terminology:...
channels, which have a bandwidth of several tens of kilohertz.
Clock distribution
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. From a control theory perspective, the PLL is a special case of the
Kalman filterThe Kalman filter is an efficient recursive filter that estimates the state of a linear dynamic system from a series of noisy measurements. It is used in a wide range of engineering applications from radar to computer vision, and is an important topic in control theory and control systems...
.
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.
JitterJitter is the time variation of a periodic signal in electronics and telecommunications, often in relation to a reference clock source. Jitter may be observed in characteristics such as the frequency of successive pulses, the signal amplitude, or phase of periodic signals...
and noise reduction
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 jitterJitter is the time variation of a periodic signal in electronics and telecommunications, often in relation to a reference clock source. Jitter may be observed in characteristics such as the frequency of successive pulses, the signal amplitude, or phase of periodic signals...
. Ideally, the static phase offset should be zero, and the tracking jitter should be as low as possible.
Phase noisePhase noise is the frequency domain representation of rapid, short-term, random fluctuations in the phase of a wave, caused by time domain instabilities . Generally speaking radio frequency engineers speak of the phase noise of an oscillator, whereas digital system engineers work with the jitter...
is another type of jitter observed in PLLs, and is mostly caused by the amplifier elements used in the circuit. Some technologies are known to perform better than others in this regard. The best digital PLLs are constructed with emitter-coupled logic (
ECLIn electronics, emitter-coupled logic, or ECL, is a logic family in which current is steered through bipolar transistors to prevent saturation...
) elements, at the expense of high power consumption. To keep phase noise low in PLL circuits, it is best to avoid saturating logic families such as transistor-transistor logic (
TTLTransistor–transistor logic is a class of digital circuits built from bipolar junction transistors and resistors. It is called transistor–transistor logic because both the logic gating function and the amplifying function are performed by transistors .TTL is notable for being a widespread...
) or
CMOSComplementary metal–oxide–semiconductor is a technology for making integrated circuits. CMOS technology is used in microprocessors, microcontrollers, static RAM, and other digital logic circuits. CMOS technology is also used for a wide variety of analog circuits such as image sensors, data...
.
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 supply and substrate noise rejection. The higher the noise rejection, the better.
To further improve the phase noise of the output oscillation, an injection locked oscillator can be employed following the voltage controlled oscillator in the PLL.
Frequency Synthesis
In digital wireless communication systems (GSM, CDMA etc), PLL's are used to provide the Local Oscillator (LO) for up-conversion during transmission, and down-conversion during reception. 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 LO modules are typically built with a
Frequency SynthesizerA frequency synthesizer is an electronic system for generating any of a range of frequencies from a single fixed timebase or oscillator. They are found in many modern devices, including radio receivers, mobile telephones, radiotelephones, walkie-talkies, CB radios, satellite receivers, GPS systems,...
integrated circuit, and discrete resonator VCO's.
Frequency Synthesizer manufacturers include Analog Devices, National Semiconductor and Texas Instruments. VCO manufacturers include Sirenza, Z-Communications, Inc. (Z-COMM)
Other applications include:
- Demodulation
Demodulation is the act of extracting the original information-bearing signal from a modulated carrier wave.A demodulator is an electronic circuit used to recover the information content from the modulated carrier wave....
of both FMIn telecommunications, frequency modulation conveys information over a carrier wave by varying its frequency . In analog applications, the instantaneous frequency of the carrier is directly proportional to the instantaneous value of the input signal...
and AMAmplitude modulation is a technique used in electronic communication, most commonly for transmitting information via a radio carrier wave. AM works by varying the strength of the transmitted signal in relation to the information being sent...
signals
- Recovery of small signals that otherwise would be lost in noise (lock-in amplifier
A lock-in amplifier is a type of amplifier that can extract a signal with a known carrier wave from extremely noisy environment . It is essentially a homodyne with an extremely low pass filter...
)
- Recovery of clock timing information from a data stream such as from a disk drive
- Clock multipliers in microprocessors that allow internal processor elements to run faster than external connections, while maintaining precise timing relationships
- DTMF decoders, modem
Modem is a device that modulates an analog carrier signal to encode digital information, and also demodulates such a carrier signal to decode the transmitted information. The goal is to produce a signal that can be transmitted easily and decoded to reproduce the original digital data...
s, and other tone decoders, for remote controlA remote control is a component of an electronics device, most commonly a television set, used for operating the device wirelessly from a short line-of-sight distance....
and telecommunications
See also
- Control theory
Control theory is an interdisciplinary branch of engineering and mathematics, that deals with the behavior of dynamical systems. The desired output of a system is called the reference...
- Numerically-controlled oscillator
A numerically controlled oscillator is an electronic system for synthesizing a range of frequencies from a fixed timebase. The name is an analogy with "voltage-controlled oscillator".- Capabilities and limitations :...
- also known as a Digitally-controlled oscillator (DCO). These are instances of direct synthesizers, which synthesize a digital waveform using a lookup table driven by a counter that is incremented at the reference frequency.
- Costas loop
A Costas loop is a phase-locked loop used for carrier phase recovery from suppressed-carrier modulation signals, such as from double-sideband suppressed carrier signals. It was invented by John P. Costas at General Electric in the 1950s...
- Kalman filter
The Kalman filter is an efficient recursive filter that estimates the state of a linear dynamic system from a series of noisy measurements. It is used in a wide range of engineering applications from radar to computer vision, and is an important topic in control theory and control systems...
- Direct conversion receiver
- Circle map
In mathematics, a circle map is a member of a family of dynamical systems on the circle first defined by Andrey Kolmogorov. Kolmogorov proposed this family as a simplified model for driven mechanical rotors . The circle map equations also describe a simplified model of the phase-locked loop in...
- a simple mathematical model of the phase-locked loop showing both mode-locking and chaotic behaviour.
- Carrier recovery
A carrier recovery system is a circuit used to estimate and compensate for frequency and phase differences between a received signal's carrier wave and the receiver's local oscillator for the purpose of coherent demodulation....