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PHASE LOCKED LOOP SIMULATIONS

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### Talk Outline

### LOOP COMPONENTS variations on it, are used in frequency synthesis applications.

History

Introduction

PLL Basics

PLL Types

Loop Components

-Phase Detectors

-Voltage controlled Oscillators

-Loop Filters

Applications

History:

- Coincides with invention of “coherent communication” (DeBellescize, 1932).
- The earliest widespread use of PLLs was to the horizontal and vertical sweeps used in television, where a continuous clocking signal had to be synchronized with a periodic synch pulse.
- PLLs were critical to development of color television
- The first PLL IC arrived around 1965. This created an explosion in the use of PLLs.

PLLs Today

– PLLs in every cell phone, television, radio, pager, computer, all telephony, ...

– The most prolific feedback system built by engineers.

– At low end: all software PLLs implement entire PLL functionality on sampled data.

– At high end: optical PLLs used in clock recovery for 160 Gbps data (OFC 2002).

PLL Basics

- Definition:
A phase-locked loop (PLL) is an electronic circuit with a voltage- or current-driven oscillator that is constantly adjusted to match in phase (and thus lock on) the frequency of an input signal.

Components Of PLL

- Phase Detector (PD):A nonlinear device whose output contains the phase difference between the two oscillating input signals.
- Voltage controlled oscillator (VCO): Another nonlinear device which produces oscillations whose frequency is controlled by a lower frequency input voltage.
- Loop filter

- General sinusoid at reference input can be written as:
Vin=Einsin(ωt)…….(1)

- Assume VCO output signal is
Vosc=Eoscsin(ωt- Ød+90)

=Eosccos(ωot - Ød)……(2)

- Phase Detector output:
Vpd=KmVinVosc

where Km is the multiplication constant

- Vpd=KmEinEoscsin(ωt)cos(ωt-Ød)
- Using the familiar trigonometric identity in terms of the PLL:
Vpd=0.5KmEinEosc[sin(Ød) + sin(2ωt-Ød)]

- The output of the low pass filter :
Vcntl=0.5KlpKmEinEoscsin(Ød)

For small Ød

Vcntl=0.5KlpKmEinEoscØd

Capture Range:

- The maximum difference between the input signals frequency and oscillators free running frequency where lock can eventually be attained is defined as the capture range.
- The Phenomenon of “Beating”.

Lock Range:

- The maximum frequency excursions over which the output remains locked with the input is called the lock range.
- The maximum output of the low pass filter is given by
Vcntl-max=0.5 KlpKmEinEosc

when Ød=90.

Therefore lock range is given by

ωlck=KoscVcntl-max.

Types Of PLLs

- Analog or Linear PLL (LPLL)
• Digital PLL (DPLL)

• All digital PLL (ADPLL)

LPLL

- The LPLL (Best) or analog PLL is the classical form of PLL. All components in the LPLL operate in the continuous-time domain.

- The phase detector is typically some form of analog multiplier.
- The phase error function is of the form
φ(t) = KmK1Asin [θ(t) − θ^(t)]

≈ KD[θ(t) − θ^(t)]

- The loop filter may be active or passive, but it typically results in the loop being either first-order or second-order.
- The design/analysis of the loop filter makes use of the Laplace transform.

DPLL multiplier.

The digital PLL is just an analog PLL with a digital phase detector.

- The DPLL is a hybrid system
- The DPLL is very popular in synthesizer
applications

In the below figure the optional digital divider, and variations on it, are used in frequency synthesis applications.

- Popular types of digital phase detectors include: variations on it, are used in frequency synthesis applications.
– Exclusive or gate (EXOR)

– Edge-triggered JK-flip flop

– Phase frequency detector (PFD)

ADPLL variations on it, are used in frequency synthesis applications.

- The all-digital PLL (classical all-digital) is distinctly different from the other two PLLs
- The ADPLL is a digital loop in two senses:
– All digital components

– All digital (discrete-time) signals

- There are many ADPLL building blocks, and many variations on putting them together.

ADPLL variations on it, are used in frequency synthesis applications.

- The VCO is replaced by a Digitally Controlled Oscillator (DCO) or also called a Numerically Controlled Oscillator (NCO)

Phase Detector variations on it, are used in frequency synthesis applications.

- A phase detector is a circuit that normally has an output voltage with an average value proportional to the phase difference between the input signal and output of VCO.
Vpd=Kp∆Ф

- Phase detectors can be a simple EX-OR gate, a sample and hold, an analog multiplier or a combination of D-flip flops.

XOR variations on it, are used in frequency synthesis applications.

- The simplest phase detector is xor

- An exclusive OR gate gives a high output when the signals are of opposite sign and a low output when they are of the same sign.

Phase Frequency Detector are of opposite sign and a low output when they are of the same sign.

- It is a combination of tri state phase frequency detector and a charge pump.

Sample and Hold Phase Detector are of opposite sign and a low output when they are of the same sign.

- A sample and hold circuit samples an input signal and holds on to its last sampled value until the input is sampled again.

Analysis are of opposite sign and a low output when they are of the same sign.

Design Circuit: are of opposite sign and a low output when they are of the same sign.XOR (TTL Logic) gate:

EXCLUSIVE OR GATE are of opposite sign and a low output when they are of the same sign.

VCC 4 0 5V

VINA 1 0 PULSE(0V 5V 0US 0.1US 0.1US 2US 5US)

VINB 9 0 PULSE(0V 5V 0US 0.1US 0.1US 3US 5US)

RBA 4 3 4K

RBB 4 8 4K

RCSA 4 5 1.9K

RCSB 4 11 1.9K

RSDA 7 0 1.2K

RSDB 12 0 1.2K

RCX 4 14 3K

RC 4 15 1.6K

RCP 4 16 120

RX 18 0 1K

DCA 0 1 DIODE

DCB 0 9 DIODE

DSA 5 6 DIODE

DSB 11 13 DIODE

DX 17 19 DIODE

Q1A 2 3 1 QM

Q1B 10 8 9 QM

QS2A 5 2 7 QM

QS2B 11 10 12 QM

QSDA 6 7 0 QM

QSDB 13 12 0 QM

QX1 14 13 6 QM

QX2 14 6 13 QM

QS 15 14 18 QM

QP 16 15 17 QM

QO 19 18 0 QM

.MODEL DIODE D (RS=40 TT=0.1NS)

.MODEL QM NPN (IS=1E-14 BF=50 BR=1 RB=70 RC=4 TF=0.1NS TR=1NS)

.TRAN 0.1US 15US

.PLOT V(1) V(9) V(19)

.END

Voltage Controlled Oscillators (VCOs) are of opposite sign and a low output when they are of the same sign.

- The function of a VCO is to generate a stable and periodic waveform whose frequency can be varied with the applied control voltage.
- The actual clock from PLL is the VCO output.
- VCO’s frequency is modulated by the input voltage

Classification of VCO are of opposite sign and a low output when they are of the same sign.

Depending on the type of output waveform, VCOs are classified as

- Harmonic Oscillators
- Relaxation Oscillators

Some of the commonly used VCOs are of opposite sign and a low output when they are of the same sign.-Ring Oscillators:Common in monolithic topologies and it uses odd number of inverters connected in feedback loop.-Other forms of VCOs, such as crytal oscillators and resonant oscillators essentially run on the same principle

VCO Circuit Design: are of opposite sign and a low output when they are of the same sign.

- A simple design of VCO consists of a collector coupled astable multivibrator using n-p-n transistor with a control voltage.
Step 1

Step 2 are of opposite sign and a low output when they are of the same sign.f=1/2RCln (1+Vcc/V)

Step 3: are of opposite sign and a low output when they are of the same sign.

*Voltage controlled Oscillator are of opposite sign and a low output when they are of the same sign.

VCC 6 0 DC 5V

VI 7 0 PULSE(0 5 0US 30US 30US 30US 40US)

RC1 6 1 1K

RC2 6 2 1K

RE1 7 10 1K

RE2 7 11 1K

R3 7 8 2K

R4 7 9 2K

R5 8 0 4.7K

R6 9 0 4.7K

C1 1 4 150PF

C2 2 3 150PF

Q1 1 3 0 QM

Q2 2 4 0 QM

.MODEL QM NPN (IS=2E-16 BF=50 BR=1 RB=5 RC=1 RE=0 TF=0.2NS TR=5NS)

Q3 3 8 10 QM1

Q4 4 9 11 QM1

.MODEL QM1 PNP (IS=2E-16 BF=100 BR=1 RB=5 RC=1 RE=0 TF=0.2NS TR=5NS)

.IC V(1)=0 V(3)=0

.TRAN 0.1US 90US

.PLOT TRAN V(2) V(7)

.END

Loop filter: are of opposite sign and a low output when they are of the same sign.

- The loop filter may be active or passive, but it typically results.
- In the loop being either first-order or second-order.
- A 1st order filter having a low frequency pole and high frequency zero is recommended.
- Loop filter system functions, F(s), include:
Filter Type Filter F(s)

perfect integrator 1+sτ2/sτ1

imperfect integrator 1+sτ2/1+sτ1

lag or low pass 1/1+sτ

Filter Design are of opposite sign and a low output when they are of the same sign.

- Design circuit is a simple RC low-pass filter which can extract the average value from the output of the phase detector.
- This average value is used to drive the VCO

R1

out

in

C1

Hlp(s)=1+sR2C1/1+s(R1+R2)C1

R2

low pass filter are of opposite sign and a low output when they are of the same sign.

R1 1 2 86K

C1 2 3 5PF

R2 3 0 2K

VIN 1 0 PULSE(0V 9V 0US 0US 0US 2US 5US)

.TRAN 0.01US 15US

.PLOT TRAN V(2) V(1)

.END

PLL APPLICATIONS are of opposite sign and a low output when they are of the same sign.

- The earliest widespread use of PLLs was for the horizontal and
- vertical sweeps used in televisions.
- PLLs were critical to development of color televisions also.
- PLLs today:
- –Cell phones, televisions, radios, pagers, computers, all
- telephony,
- – At low end: all software PLLs implement entire PLL functionality
- on sampled data.
- – At high end: optical PLLs used in clock recovery for 160 Gbps
- data

- Phase-locked loops are widely used for synchronization purposes
- Space communications for coherent carrier tracking
- and threshold extension
- Bit and symbol synchronization
- They are also used for:
- Demodulation of frequency modulated signals
- To synthesize new frequencies which are multiples of a
- reference frequency, with the same stability as the
- reference frequency.

- Deskewing purposes
- the clock must be received and amplified
- finite delay dependent on process,temperature and voltage between detected clock edge and the received data
- delay limits the frequency at which data can be sent
- deskew PLL on the receiver side phase-matches the clock at each data flip-flop to the received clock.
- 2. Clock generation
- multiplies lower-frequency reference clock (usually 50 or 100 MHz) up to the operating frequency of the processor that operate at Gigahertz

- 3. Spread spectrum purposes
- All electronic systems emit some unwanted radio
- frequency energy
- limits on this emitted energy and any interference
- caused
- spreading the energy over a larger portion of the
- spectrum
- 4. Jitter and noise reduction
- reference and feedback clock edges can be brought into very
- close alignment
- phase and frequency of generated clock is unaffected by rapid
- changes in voltages of the power supply lines and of the
- substrate on which the PLL circuits are fabricated

1. Carrier Recovery purposes

• General block diagram of frequency recovery from a modulated

signal.

• When carrier has strong component in signal spectrum, PLL

can lock.

• When carrier is missing from signal spectrum, PLL must be

preceded by a nonlinear element.

2. Costas Loop purposes

- A Costas loop can both recover the carrier and demodulate the data from a
- signal.
- If there were no modulation, the upper arm is simply a PLL lock to a carrier.
- The effect of the lower arm of the loop is to lock to the modulation and cancel it
- out of the upper arm of the loop.
- Does the same thing as squaring loop, but down converts signal to baseband &
- does filtering there.

3. Clock distribution purposes

4. Frequency Synthesis purposes

In wireless applications, frequency synthesizers provide local oscillators ability for up and down conversion of modulated signals

A basic PLL synthesizer purposes

5. Disk Drive Control purposes

Amplitude encoded position error signal (PES) in a hard disk.

PLLs are used to time the acquisition

of the readback signal.

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