A phase-locked loop or phase lock loop (PLL) is a control system that generates a signal that has a fixed relation to the phase of a "reference" signal. A control system is a device or set of devices to manage command direct or regulate the behavior of other devices or systems In the fields of communications, Signal processing, and in Electrical engineering more generally a signal is any time-varying or spatial-varying quantity The 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 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. Oscillation is the repetitive variation typically in Time, of some measure about a central value (often a point of Equilibrium) or between two or more different states A phase-locked loop is an example of a control system using negative feedback. Feedback is a circular causal Process whereby some proportion of a system's output is returned (fed back to the Input.

Phase-locked loops are widely used in radio, telecommunications, computers and other electronic applications. Radio is the transmission of signals by Modulation of electromagnetic waves with frequencies below those of visible Light. A computer is a Machine that manipulates data according to a list of instructions. They may generate stable frequencies, recover a signal from a noisy communication channel, or distribute clock timing pulses in digital logic designs such as microprocessors. A microprocessor incorporates most or all of the functions of a Central processing unit (CPU on a single Integrated Since a single integrated circuit 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. Microchipsjpg|right|thumb|200px|Microchips ( EPROM memory with a transparent window showing the integrated circuit inside

## Analogy

Tuning a string on a guitar can be compared to the operation of a phase-locked loop. In Music, there are two common meanings for tuning: Tuning practice, the act of tuning an instrument or voice Using a tuning fork or pitchpipe to provide a reference frequency, the tension of the string is adjusted up or down until the beat frequency is inaudible. A tuning fork is an acoustic Resonator in the form of a two-pronged Fork with the tines formed from a U-shaped bar of elastic A pitch pipe is a small device used to provide a pitch reference for musicians without Absolute pitch. In Acoustics, a beat is an Interference between two Sounds of slightly different frequencies, perceived as periodic variations in volume whose 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 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 Armstrong's superheterodyne receiver, the Homodyne. Year 1932 ( MCMXXXII) was a Leap year starting on Friday of the Gregorian calendar. Edwin Howard Armstrong ( December 18, 1890 &ndash January 31, 1954) was an American Electrical engineer and Inventor In Electronics, the superheterodyne receiver (also known by its full name the supersonic heterodyne receiver, or by the abbreviated form superhet) is a Homodyne detection is a method of detecting Frequency-modulated Radiation by non-linear mixing with radiation of a reference frequency, the same principle In the homodyne or synchrodyne system, a local oscillator was tuned to the desired input frequency and multiplied with the input signal. An electronic oscillator is an Electronic circuit that produces a repetitive electronic signal often a Sine wave or a Square wave. The resulting output signal included the original audio 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 H. de Bellescise, in the French journal Onde Electrique. [1]

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. [2]

When Signetics introduced a line of monolithic integrated circuits that were complete phase-locked loop systems on a chip in 1969,[3] applications for the technique multiplied. Signetics, once a major player in semiconductor manufacturing made a variety of devices which included Integrated circuits bipolar and MOS, the Dolby Microchipsjpg|right|thumb|200px|Microchips ( EPROM memory with a transparent window showing the integrated circuit inside A few years later RCA introduced the "CD4046" CMOS Micropower Phase-Locked Loop, which became a popular integrated circuit. Complementary metal–oxide–semiconductor ( CMOS) (pronounced "see-moss" siːmɔːs ˈsiːmɒs is a major class of Integrated circuits CMOS technology

## 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 variable electronic oscillator, and
• a feedback path (which often includes a frequency divider). 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 An electronic oscillator is an Electronic circuit that produces a repetitive electronic signal often a Sine wave or a Square wave. Feedback is a circular causal Process whereby some proportion of a system's output is returned (fed back to the Input. A frequency divider is an Electronic circuit that takes an input signal with a Frequency, f_{in} and generates an output signal with a frequency

## Digital phase-locked loop

A Digital Phase-Locked Loop (DPLL) 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 a counter with a variable divisor. DPLLs are sometimes used for data recovery.

## Analog phase-locked loop

### Basic design

Phase-locked loop block diagram

Analog PLLs are generally built of a phase detector, low pass filter and voltage-controlled oscillator (VCO) placed in a negative feedback closed-loop configuration. Block diagram is a Diagram of a System, in which the principal parts or functions are represented by blocks connected by lines that show the relationships of 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 low-pass filter is a filter that passes low- Frequency signals but Attenuates (reduces the Amplitude of signals with frequencies A voltage-controlled oscillator or VCO is an Electronic oscillator designed to be controlled in Oscillation Frequency by a Voltage Feedback is a circular causal Process whereby some proportion of a system's output is returned (fed back to the Input. There may be a frequency divider 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 frequency divider is an Electronic circuit that takes an input signal with a Frequency, f_{in} and generates an output signal with a frequency 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 counter. 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. A low-pass filter smooths out abrupt changes in the control voltage; it can be demonstrated that some filtering is required for a stable system. 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.

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.

### Elements

#### Phase detector

The two inputs of the phase detector (PD) are the reference input and the feedback from the voltage controlled oscillator (VCO). 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 The PD output controls the VCO such that the phase difference between the two inputs is held constant, making it a negative feedback system. Feedback is a circular causal Process whereby some proportion of a system's output is returned (fed back to the Input.

There are several types of phase detectors in two main categories of analog and digital.

##### Analog

The analog phase detector takes the form of an ideal frequency mixer. In Telecommunication, a mixer is a Nonlinear or time-varying circuit or device that accepts as its Input two different frequencies and presents 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 filter is required to attenuate the sum frequency. A low-pass filter is a filter that passes low- Frequency signals but Attenuates (reduces the Amplitude of signals with frequencies 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 exclusive ORgate. 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 set 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 Detector. A phase frequency detector, in electronics is a device which compares the phase of two input signals

A PLL with a bang-bang charge pump phase detector supplies current pulses with fixed total charge, either positive or negative, to the capacitor acting as an integrator. A charge pump is an Electronic circuit that uses Capacitors as energy storage elements to create either a higher or lower Voltage power source An integrator is a device to perform the mathematical operation known as integration, a fundamental operation in Calculus. 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 jitter, because once in lock the phase offset drifts inside the two extreme values of the dead band without triggering any corrections. Jitter is an unwanted variation of one or more characteristics of a periodic signal in Electronics and Telecommunications.

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 Q of the resulting tank circuit is generally less than 10. For other uses of the terms Q and Q factor see Q value. In Physics and Engineering the quality As processes have made larger numbers of metal layers available, 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 semiconductor diode 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. A semiconductor' is a Solid material that has Electrical conductivity in between a conductor and an insulator; it can vary over that Dioden2jpg|thumb|right|150px|Figure 2 Various semiconductor diodes Special-purpose variable capacitance varactor diodes are available with well-characterized wide-ranging values of capacitance. In Electronics, a varicap diode, varactor diode, variable capacitance diode or tuning diode is a type of Diode which has a variable 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. Piezoelectricity is the ability of some materials (notably Crystals and certain Ceramics including bone to generate an Electric potential in response to 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 devices (SAWs) are a kind of crystal oscillator, but achieve much higher frequencies by establishing standing waves on the surface of the quartz crystal. A surface acoustic wave ( SAW) is an Acoustic wave traveling along the surface of a material having some elasticity, with an Amplitude that 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 oscillators can be used as voltage-controlled oscillators-a free running multivibrator (VCOs). A ring oscillator is a device composed of an odd number of NOT gates whose output oscillates between two voltage levels representing true and false A voltage-controlled oscillator or VCO is an Electronic oscillator designed to be controlled in Oscillation Frequency by a Voltage 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 synthesiser. A frequency synthesizer is an electronic system for generating any of a range of frequencies from a single fixed timebase or oscillator. 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 M, it allows the VCO to multiply the reference frequency by N / M. 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 xc(t) and the output of the voltage-controlled oscillator (VCO) is xr(t) with frequency ωr(t), then the output of the phase detector xm(t) is given by

$x_m(t) = x_c(t) \cdot x_r(t)$

the VCO frequency may be written as a function of the VCO input y(t) as

$\omega_r(t) = \omega_f + g_v y(t)\,$

where gv is the sensitivity of the VCO and is expressed in Hz/V. A voltage-controlled oscillator or VCO is an Electronic oscillator designed to be controlled in Oscillation Frequency by a Voltage

Hence the VCO output takes the form

$x_r(t) = A_r \cos\left( \int_0^t \omega_r(\tau)\, d\tau \right) = A_r \cos(\omega_f t + \varphi(t) )$

where

$\varphi(t) = \int_0^t g_v y(\tau)\, d\tau$

The loop filter receives this signal as input and produces an output

xf(t) = Ffilter(xm(t))

where FFilter 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

y(t) = xf(t) = Ffilter(xm(t))

We can deduce how the PLL reacts to a sinusoidal input signal:

xc(t) = Acsin(ωct).

The output of the phase detector then is:

$x_m(t) = A_c \sin( \omega_c t ) A_r \cos(\omega_f t + \varphi(t)).$

This can be rewritten into sum and difference components using trigonometric identities:

$x_m(t) = {A_c A_f \over 2} \sin( \omega_c t - \omega_f t - \varphi(t) ) + {A_c A_f \over 2} \sin( \omega_c t + \omega_f t + \varphi(t) )$

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. In Mathematics, trigonometric identities are equalities that involve Trigonometric functions that are true for every single value of the occurring variables If we can make $\omega_f \approx \omega_c$, then the $\sin(\cdot)$ can be approximated by its argument resulting in: $y(t)=x_f(t) \simeq - A_c A_f \varphi (t) / 2$. The phase-locked loop is said to be locked if this is the case.

Some parts of this article are derived from public domain parts of Federal Standard 1037C in support of MIL-STD-188. Federal Standard 1037C, entitled Telecommunications Glossary of Telecommunication Terms is a United States Federal Standard issued by the General Services Administration MIL-STD-188 is a series of US military standards relating to Telecommunications Purpose Faced with “past technical deficiencies in telecommunications

### Control system analysis

Phase locked loops can also be analyzed as control systems by applying the Laplace transform. In Mathematics, the Laplace transform is one of the best known and most widely used Integral transforms It is commonly used to produce an easily soluble algebraic The loop response can be written as:

$\frac{\theta_o}{\theta_i} = \frac{K_p K_v F(s)} {s + K_p K_v F(s)}$

Where

• θo is the output phase in radians
• θi is the input phase in radians
• Kp is the phase detector gain in volts per radian
• Kv is the VCO gain in radians per volt-second
• F(s) is the loop filter transfer function (dimensionless)

The loop characteristics can be controlled by inserting different types of loop filters. The radian is a unit of plane Angle, equal to 180/ π degrees, or about 57 The volt (symbol V) is the SI derived unit of electric Potential difference or Electromotive force. The second ( SI symbol s) sometimes abbreviated sec, is the name of a unit of Time, and is the International System of Units The simplest filter is a one-pole RC circuit. A resistor–capacitor circuit (RC circuit, or RC filter or RC network, is an Electric circuit composed of resistors and capacitors driven by The loop transfer function in this case is:

$F(s) = \frac{1}{1 + s R C}$

The loop response becomes:

$\frac{\theta_o}{\theta_i} = \frac{\frac{K_p K_v}{R C}}{s^2 + \frac{s}{R C} + \frac{K_p K_v}{R C}}$

$s^2 + 2 s \zeta \omega_n + \omega_n^2$

Where

• ζ is the damping factor
• ωn is the natural frequency of the loop

For the one-pole RC filter,

$\omega_n = \sqrt{\frac{K_p K_v}{R C}}$
$\zeta = \frac{1}{2 \sqrt{K_p K_v R C}}$

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,

$R C = \frac{1}{2 K_p K_v}$
$\omega_c = K_p K_v \sqrt{2}$

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

$F(s) = \frac{1+s C R_2}{1+s C (R_1+R_2)}$

This filter has two time constants

τ1 = C(R1 + R2)
τ2 = CR2

Substituting above yields the following natural frequency and damping factor

$\omega_n = \sqrt{\frac{K_p K_v}{\tau_1}}$
$\zeta = \frac{1}{2 \omega_n \tau_1} + \frac{\omega_n \tau_2}{2}$

The loop filter components can be calculated independently for a given natural frequency and damping factor

$\tau_1 = \frac{K_p K_v}{\omega_n^2}$
$\tau_2 = \frac{2 \zeta}{\omega_n} - \frac{1}{K_p K_v}$

## Applications

Phase-locked loops are widely used for synchronization purposes; in space communications for coherent carrier tracking and threshold extension, bit synchronization, and symbol synchronization. In Physics, coherence is a property of waves that enables stationary (i In Telecommunications, a carrier wave, or carrier is a Waveform (usually Sinusoidal) that is modulated (modified with an input signal In Telecommunications a self-synchronizing code is a Line code in which the symbol stream formed by a portion of one Code word, or by the overlapped Phase-locked loops can also be used to demodulate frequency-modulated signals. Demodulation is the act of removing the Modulation from an analog signal to get the original Baseband signal back 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 recovery. Some digital 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 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. In Telecommunications 8b/10b is a Line code that maps 8-bit symbols to 10-bit symbols to achieve DC-balance (see

### 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 Loop (DLL) is frequently used. In electronics a delay-locked loop (DLL is a digital circuit similar to a Phase-locked loop (PLL with the main difference being the absence of an internal Oscillator [4]

### 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.

All electronic systems emit some unwanted radio frequency energy. Various regulatory agencies (such as the FCC 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 by FM receivers which have a bandwidth of 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 filter. The Kalman filter is an efficient Recursive filter that estimates the state of a Dynamic system from a series of noisy measurements

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.

### Jitter 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. 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 mostly caused by the amplifier elements used in the circuit. Phase noise is the Frequency domain representation of rapid short-term random fluctuations in the phase of a Wave, caused by Time domain instabilities 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. In electronics emitter-coupled logic, or ECL, is a Logic family in which current is steered through bipolar transistors to implement Logic To keep phase noise low in PLL circuits, it is best to avoid saturating logic families such as transistor-transistor logic (TTL) or CMOS. Transistor–transistor logic ( TTL) is a class of Digital circuits built from Bipolar junction transistors (BJT and Resistors It is called Complementary metal–oxide–semiconductor ( CMOS) (pronounced "see-moss" siːmɔːs ˈsiːmɒs is a major class of Integrated circuits CMOS technology

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. A voltage-controlled oscillator or VCO is an Electronic oscillator designed to be controlled in Oscillation Frequency by a Voltage

### 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 basestation 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 Synthesizer 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:

• Control theory
• Numerically-controlled oscillator - also known as a Digitally-controlled oscillator (DCO). Demodulation is the act of removing the Modulation from an analog signal to get the original Baseband signal back Amplitude modulation ( AM) is a technique used in electronic communication most commonly for transmitting information via a Radio Carrier wave Lock-in amplifierjpg|thumb|250px|and one from Stanford Research Systems Disk storage is a general category of a Computer storage mechanisms in which data is recorded on planar round and rotating surfaces ( disks, discs, or A microprocessor incorporates most or all of the functions of a Central processing unit (CPU on a single Integrated Dual-tone multi-frequency ( DTMF) signaling is used for Telephone signaling over the line in the voice-frequency band to the call switching center Modem (from mo dulator- dem odulator is a device that modulates an analog carrier signal to encode Digital information A remote control is an electronic device used for the remote operation of a Machine. Control theory is an interdisciplinary branch of Engineering and Mathematics, that deals with the behavior of Dynamical systems The desired output A numerically controlled oscillator ( NCO) or digitally controlled oscillator ( DCO) is an electronic system for synthesizing a range of frequencies from 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
• Kalman filter
• Circle map - a simple mathematical model of the phase-locked loop showing both mode-locking and chaotic behaviour. In Telecommunication, a Costas loop is a Phase-locked loop used for carrier phase recovery from suppressed-carrier Modulation signals The Kalman filter is an efficient Recursive filter that estimates the state of a Dynamic system from a series of noisy measurements In Telecommunication, a direct-conversion receiver (DCR also known as homodyne, synchrodyne, or zero-IF receiver, is a Radio receiver In Mathematics, a circle map is a member of a family of dynamical systems on the circle first defined by Andrey Kolmogorov.
• Carrier recovery

## References

1. ^ Notes for a University of Guelph course describing the PLL and early history, including an IC PLL tutorial
2. ^ National Television Systems Committee Video Display Signal
3. ^ A. 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 B. Grebene, H. R. Camenzind, “Phase Locking As A New Approach For Tuned Integrated Circuits”, ISSCC Digest of Technical Papers, pp. 100-101, Feb. 1969.
4. ^ M Horowitz, C. Yang, S. Sidiropoulos (1998-01-01). Year 1998 ( MCMXCVIII) was a Common year starting on Thursday (link will display full 1998 Gregorian calendar) New Year See also New Year The Ancient Romans began their consular year on January 1st since 153 BC High-speed electrical signaling: overview and limitations. IEEE Micro.
• H. de Bellescise, La réception Synchrone, Onde Electrique, volume 11, 1932.
• William F. Egan, Phase-Lock Basics, John Wiley & Sons, 1998 (provides useful Matlab scripts for simulation)
• William F. Egan, Frequency Synthesis by Phase Lock (2nd ed. ), John Wiley and Sons, 2000 (provides useful Matlab scripts for simulation)
• Dan H. Wolaver, Phase-Locked Loop Circuit Design, Prentice Hall, 1991, ISBN-10: 0136627439
• Richard C. Dorf, The Electrical Engineering Handbook, CRC Press, Boca Raton 1993 ISBN 0-8493-0185-8
• R. E. Best, Phase-locked Loops: Design, Simulation and Applications, McGraw-Hill 2003, ISBN 0-07-141201-8
• Floyd M Gardner, Phaselock Techniques
• J. Klapper and J. T. Frankle, "Phase-Locked and Frequency-Feedback Systems", Academic Press 1972 (FM Demodulation)
• Predicting the Phase Noise and Jitter of PLL-Based Frequency Synthesizers
• Build a 1.5-V 2.4-GHz CMOS PLL — an article on designing a standard PLL IC for Bluetooth applications.
• PLL Performance, Simulation and Design Handbook by Dean Banerjee from National Semiconductor.

## phase-locked loop

### -noun

1. an electronic circuit used to lock an oscillator in phase with an arbitrary input signal
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