LECTURE 8: OSCILLATORS NOISE IN ELECTRONIC SYSTEMS
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Oscillators Wien-Bridge Relaxation Oscillator Noise Type of
Noise Noise Sources Noise Analysis
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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
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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 resulting in a
re-inforcement of the output signal.
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FEEDBACK OSCILLATORS Conditions of Oscillations: i.The phase
shift around the feedback loop must be 0 degree. ii.Closed feedback
loop gain A cl must be 1.
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FEEDBACK OSCILLATORS V f 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
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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
amplifiers input.
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WIEN-BRIDGE OSCILLATORS RC feedback is used in various lower
frequency (up to 1 MHz) sine- wave oscillators. At resonant
frequency f r 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.
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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 R 1 and R 2 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. Voltage- divider Lead-lag network
Basic Circuit Wien Bridge Oscillator
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WIEN-BRIDGE OSCILLATION CONDITIONS The phase shift around the
positive feedback loop must be 0 o and the gain around the loop
must be 1. The 0 o phase-shift condition is met when the frequency
is f r.
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WIEN-BRIDGE OSCILLATOR STARTUP The loop gain should be greater
than 1 at startup to build up output.
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WIEN-BRIDGE OSCILLATOR STARTUP
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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 R 2 and R 3. The capacitor
charges and discharges between these levels: The period of the
waveform is given by:
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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. Noise is a fundamental parameter to
be considered in an electronic design as it typically limits the
overall performance of the system.
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Noise is a purely random signal, the instantaneous value and/or
phase of the waveform cannot be predicted at any time. The
amplitude of the signal has very nearly a Gaussian probability
density function.
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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. EXTERNAL AND INTERNAL NOISE
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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. 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.
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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.
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THERMAL NOISE The RMS voltage due to thermal noise, generated
in a resistance R (ohms) over bandwidth f (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
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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.
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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
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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.
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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)
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BURST NOISE Burst noise consists of sudden step-like
transitions between two or more levels. is related to imperfections
in semiconductor material and heavy ion implants. 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.
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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 junctions 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.
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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.
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MEASURING NOISE RMS, P-P or PDF Instantaneous noise voltage
amplitudes are as likely to be positive as negative. Noise values
form a random pattern centered on zero. Since amplitudes vary
randomly with time, they can only be specified by a probability
density function, most commonly by Gaussian density function. is
the standard deviation of the Gaussian distribution and the rms
value of the noise voltage and current. The instantaneous noise
amplitude is within 1 68% of the time, is within 3 of the mean
99.7% of the time and within 3.4 99.94% of the time.
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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).
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MULTIPLE NOISE SOURCES When there are multiple noise sources in
a circuit, the total root-mean- square (rms) noise signal is the
square root of the sum of the average mean-square values of the
individual sources: 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:
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NOISE UNIT Internal noise is normally specified as a noise
spectral density in rms volts or amps per root Hertz, V/Hz or A /
Hz. In datasheet it is often expressed with a plot: 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
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EQUIVALENT NOISE EIN Noise characteristic for TLE2027
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CALCULATING SNR If the output signal is of 1V SNR = 1V/ 35.3 uV
= 28328 SNR dB = 20log(28328) = 89 dB Noise characteristic for
TLE2027
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CORNER FREQUENCY NOISE IN SPECTRAL DENSITY Usually a plot for
Noise Spectral Density is given in op-amp datasheets. These graphs
usually show two distinct regions: o Lower frequencies where pink
noise is the dominant effect o Higher frequencies where white noise
is the dominant effect The point in the frequency spectrum where
1/f noise and white noise are equal is referred to as the noise
corner frequency, f nc
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CORNER FREQUENCY IN NOISE SPECTRAL DENSITY The point in the
frequency spectrum where 1/f noise and white noise are equal is
referred to as the noise corner frequency, f nc The f nc can be
determined visually from the graph: Take the white noise portion of
the curve, and extrapolate it down to 10 Hz as a horizontal line.
White noise Take the portion of the pink noise from 10 Hz to 100
Hz, and extrapolate it as a straight line. The point where the two
intercept is f nc, the point where the white noise and pink noise
are equal in amplitude. Pink noise
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CORNER FREQUENCY Once the corner frequency is known, the
individual noise components can be added together (if the bandwidth
includes corner frequency): If f nc is not included in bandwidth,
all of the contribution will be from either the 1/f noise or the
white noise. Similarly, if the bandwidth is very large, and extends
to three decades or so above f nc, the contribution of the 1/f
noise can be ignored.
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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.
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INVERTING OP-AMP CIRCUIT NOISE MODEL e1 R1 e2 R2 E0 e3 Sources
e1, e2 and e3 represent the thermal noise contribution from the
resistors. Note : Noise current sources are missing here.
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NONINVERTING OP AMP CIRCUIT NOISE MODEL Sources e1, e2 and e3
represent the thermal noise contribution from the resistors. Note:
Noise current sources are missing here.
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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.
Input Noise expression:
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NON-INVERTING NOISE MODEL Output Noise expression: Adding input
noise from signal source at non- inverting input:
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INVERTING NOISE MODEL Output Noise expression: Adding input
noise from signal source at inverting input:
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REDUCING RESISTANCE VALUES Reducing resistance value can help
in reducing thermal noise.