LECTURE 8:

OSCILLATORS

NOISE IN ELECTRONIC SYSTEMS

Oscillators

Wien-Bridge

Relaxation Oscillator

Noise Noise

Type of Noise

Noise Sources

OSCILLATORS

An oscillator is a circuit that produces a periodically

oscillating waveform on its output with dc input.

Two major classifications: o Feedback oscillators

o Relaxation oscillators

FEEDBACK OSCILLATORS

Feedback oscillator operation is based on the

principle of positive feedback.

A fraction of output signal is returned to input

with no net phase shift.

Conditions of Oscillations: i. The phase shift around the feedback loop must be 0 degree

ii. Closed feedback loop gain Acl must be 1

FEEDBACK OSCILLATORS

Vf is amplified to produce the output

voltage , which in turn produces the

feedback voltage.

A loop is created and signal sustain itself

and produces continuous oscillations.

In some types of oscillators feedback

shifts the phase by 180. inverting amplifier

are used there to produce another 180

degree

START-UP CONDITIONS

Feedback oscillators require a small disturbance such as that

generated by thermal noise to start oscillations. This initial voltage

starts the feedback process and oscillations.

The feedback circuit permits only a voltage with a frequency equal

to selected frequency to appear in phase on the amplifier’s input.

WIEN-BRIDGE OSCILLATORS

RC feedback is used in various lower frequency (up to 1 MHz) sine-

wave oscillators.

At resonant frequency fr the attenuation of the circuit is 1/3.

The lead-lag circuit is used in the feedback of Wien-Bridge

oscillator.

It gives 0 phase shift and 1/3 attenuation at resonant frequency.

WIEN-BRIDGE OSCILLATORS

The basic Wien-bridge uses the lead-lag network to select a

specific frequency that is amplified. The voltage-divider sets the

gain to make up for the attenuation of the feedback network.

The non-inverting amplifier must

have a gain of exactly 3.0 as set by

R1 and R2 to make up for the

attenuation.

If it is too little, oscillations will not

occur; if it is too much the sine

wave will be clipped.

Vout

–

+

R4

R3

R2

R1

C1

C2

Voltage-

divider

Lead-lag

network

Basic Circuit Wien Bridge Oscillator

WIEN-BRIDGE OSCILLATION

CONDITIONS

The phase shift around the positive feedback loop must be 0o and

the gain around the loop must be 1.

The 0o phase-shift

condition is met when

the frequency is fr.

RELAXATION OSCILLATOR

A simple relaxation oscillator that uses a Schmitt trigger is the basic

square-wave oscillator.

The two trigger points, UTP and LTP are set by R2 and R3. The

capacitor charges and discharges between these levels:

The period of the waveform is

given by:

31

2

22 ln 1

RT R C

R

3UTP

2 3

max

RV V

R R

3LTP

2 3

max

RV V

R R

Vout

–

+

R2

R3

R1

Vf

VC

C

NOISE

Noise is a random fluctuation in an electrical signal.

Noise in electronic devices varies greatly, as it can be

produced by several different effects.

It is not something most designers get excited

about. In fact, they probably wish the whole

topic would go away. It can, however, be a

fascinating study by itself. A good

understanding of the underlying principles can,

in some cases, be used to reduce noise in the

design.

Noise is a fundamental parameter to be

considered in an electronic design as it typically

limits the overall performance of the system.

Noise can either be generated internally in the

op amp, from its associated passive

components, or superimposed on the circuit by

external sources.

“External” refers to noise present in the signal

being applied to the circuit or to noise

introduced into the circuit by another means,

such as conducted on a system ground or

received on one of the many antennas formed

by the traces and components in the system.

TYPES OF INTERNAL NOISE

Thermal Noise

Shot Noise

Flicker Noise

Burst Noise

Avalanche Noise

Some or all of these noises may be present in a design,

presenting a noise spectrum unique to the system.

TYPES OF INTERNAL NOISES

Thermal Noise

Shot Noise

Flicker Noise

Burst Noise

Avalanche Noise

It is not possible in most cases to separate the effects, but

knowing general causes may help the designer optimize the

design, minimizing noise in a particular bandwidth of interest.

THERMAL NOISE

Generated by the random thermal motion of charge carriers

(usually electrons), inside an electrical conductor.

It happens regardless of any applied voltage.

Power Spectral Density is nearly equal throughout

the frequency spectrum, approximately white noise.

THERMAL NOISE

The amplitude of the signal has very nearly a

Gaussian probability density function.

The RMS voltage due to thermal noise , generated in a

resistance R (ohms) over bandwidth Δf (hertz), is given by:

The noise from a resistor is proportional to its resistance and

temperature.

Lowering resistance values also reduces thermal noise.

See example in section 10.3.2 ‘Op-amp for every one’

SHOT NOISE

The name ‘Shot Noise’ is short of Schottky noise, also called

quantum noise.

It is caused by random fluctuations in the motion of charge

carriers in a conductor.

SHOT NOISE

Some characteristics of shot noise:

Shot noise is always associated with current flow. It stops

when the current flow stops.

Shot noise is independent of temperature.

Shot noise is spectrally flat or has a uniform power density,

meaning that when plotted versus frequency it has a constant

value.

Shot noise is present in any conductor

FLICKER NOISE

Flicker noise is also called 1/f noise. Its origin is one of the

oldest unsolved problems in physics.

It is present in all active and many passive devices.

It may be related to imperfections in crystalline structure of

semiconductors, as better processing can reduce it.

FLICKER NOISE

Some characteristics of flicker noise:

It increases as the frequency decreases, hence the name 1/f

It is associated with a dc current in electronic devices

It has the same power content in each octave (or decade)

BURST NOISE

Burst noise consists of sudden step-like transitions between

two or more levels.

As high as several hundred microvolts.

Lasts for several milli-seconds.

Burst noise makes a popping sound at rates below 100 Hz

when played through a speaker — it sounds like popcorn

popping, hence also called popcorn noise.

Low burst noise is achieved by using clean device

processing, and therefore is beyond the control of the designer.

AVALANCHE NOISE

Avalanche noise is created when a PN junction is operated in

the reverse breakdown mode.

Under the influence of a strong reverse electric field within the

junction’s depletion region, electrons have enough kinetic

energy.

They collide with the atoms of the crystal lattice, to form

additional electron-hole pair.

These collisions are purely random and produce random

current pulses similar to shot noise, but much more intense.

AVALANCHE NOISE

When electrons and holes in the depletion region of a

reversed-biased junction acquire enough energy to cause the

avalanche effect, a random series of large noise spikes will be

generated.

The magnitude of the noise is difficult to predict due to its

dependence on the materials.

MEASURING NOISE

RMS, PPP or PDF

NOISE FLOOR

When all input sources are turned off and the output is properly

terminated, there is a level

of noise called the noise floor that determines the smallest

signal for which the circuit is useful.

The objective for the designer is to place the signals that the

circuit processes

above the noise floor, but below the level where the signals will

clip.

SIGNAL TO NOISE RATIO

The noisiness of a signal is defined as:

In other words, it is a ratio of signal voltage to noise voltage

(hence the name signal-to-noise ratio).

MULTIPLE NOISE SOURCES

When multiple sources of noise are present, their contributions add

in proportion to their noise powers, not the noise voltages.

Uncorrelated noise adds by the sum of the individual noise powers.

If there are two noise sources of equal amplitude in the circuit,

the total noise is not doubled (increased by 6 dB). It only

increases by 3 dB. Consider a very simple case, two noise

sources with amplitudes of 2 Vrms:

OP-AMP NOISE

OP-AMP CIRCUIT NOISE

MODEL

Noise in op-amp circuits can be modeled as

voltage noise source and current noise source.

Input voltage noise is always represented by a

voltage source in series with the non-inverting

input.

Input current noise is always represented by

current sources from both inputs to ground.

INVERTING OP-AMP

CIRCUIT NOISE

Sources e1, e2 and e3

represent the thermal noise

contribution from the resistors.

Reducing resistance value can

help in reducing thermal noise.

DIFFERENTIAL OP-AMP

CIRCUIT NOISE

NONINVERTING OP AMP

CIRCUIT NOISE

Reducing resistance value can

help in reducing thermal noise.

GENERAL NOISE MODEL

Figure describes the noise model for

the non-inverting amplifier

configuration showing all noise

sources.

In addition to the intrinsic input

voltage noise (en) and current noise

(in=in+=in-) sources, there also exists

thermal voltage noise (et 4 TR = k )

associated with each of the external

resistors.

GENERAL NOISE MODEL

Assume Rf||Rg = Rseq for bias current

cancellation.

NOISE SPECTRAL DENSITY

More on Noise

Noise is normally specified as a noise spectral density in rms volts

or amps per root Hertz, V/√Hz or A /√ Hz.

It gives measure of noise power per unit (Hertz) bandwidth.

In datasheet it is often expressed as

Noise Voltage

http://www.ti.com/lit/ds/symlink/tle2027.pdf

Sn = En2 / B

Sn = V / √Hz

NOISE BANDWIDTH

NOISE UNIT

More on Noise

In datasheet it is often expressed as:

Example:

An op-omp TLE2027 has noise specification of 2.5

nV/ √ Hz

Noise characteristic for TLE2027

http://www.ti.com/lit/ds/symlink/tle2027.pdf

EQUIVALENT NOISE EIN

More on Noise

TLE2027 is used in a system that operates

over an audio frequency range of 20 Hz to

20 kHz with a gain of 40db (100).

Equivalent noise over the whole bandwidth

is :

2.5nV * √(20,000 - 20)

2.5nV * 141.35

EIN = 353.38nV

If the gain of the system is 100

Eout= 353.38nV x 100 = 35.3 microV

Noise characteristic for TLE2027

CALCULATING SNR

More on Noise

If the output signal is of 1V

SNR = 1V/ 35.3 uV

= 28328

SNRdB= 20log(28328)

= 89 dB

Noise characteristic for TLE2027