Transcript IC Technology and Device Models

Oscillator Circuits
1.
2.
3.
4.
5.
6.
CMOS inverter relaxation oscillator
Operational amplifier based relaxation oscillators
Voltage to frequency converter
Sinusoidal oscillators
Amplitude and frequency stabilization
Signal generator, frequency synthesizers and swept frequency
oscillators
Introduction
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An oscillator is a circuit that generates a repetitive waveform of fixed amplitude and
frequency without any external input signal. Oscillators are used in radio, television,
computers, and communications.
Oscillators: Tuned and Untuned
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Tuned: RC, LC, Crystal
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Untuned: Square wave, Triangular wave -> Sinusoidal oscillator
Tuned Oscillators
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RC oscillators most suitable for IC technology
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Crystal oscillators are often used with the crystal external to the IC.
Untuned Oscillators
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Untuned oscillators typically have only two stable states.
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Untuned oscillator can create sinusoid by applying the triangle wave to a sineshaping circuit
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Untuned oscillators are very compatible with IC technology.
Oscillator Principle
An oscillator is a type of feedback amplifier in which part of the output is fed back
to the input via a feedback circuit. If the signal fed back is of proper magnitude and
phase, the circuit produces alternating currents or voltages.
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vo
Av
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vi 1  Av B
vin = 0 and vo  0 implies that
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AvB = 1
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Expressed in polar form,
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AvB = 1  00
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In order to satisfy the above criterion, the oscillator must be able to achieve positive
feedback at some frequency w0 where the magnitude of the loop gain is exactly
unity. <Barkhausen Criterion>
The oscillation criterion should be satisfied at one frequency only for the circuit to oscillate at
one frequency, otherwise the resulting waveform will not be a simple sinusoid.
Frequency Stability
The ability of the oscillator circuit to oscillate at one exact frequency is
called frequency stability. Although a number of factors may cause
changes in oscillator frequency, the primary factors are temperature
changes and changes in the dc power supply. Temperature and power
supply changes cause variations in the op-amp's gain, in junction
capacitances and resistances of the transistors in an op-amp, and in
external circuit components. In most cases these variations can be kept
small by careful design, by using regulated power supplies, and by
temperature control.
LC circuits and crystals are generally used for the generation of highfrequency signals, while RC components are most suitable for audiofrequency applications.
6.1 CMOS Inverter Relaxation Oscillator
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An astable multivibrator which is capable of producing sustained
square wave oscillations is shown in figure. The time period of the
oscillation is determined by the time constant RC.
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The operation of the multivibrator can be analyzed by supposing it to begin in a state with
the output of gate 2 high (vout=vDD), output of the gate 1 low (v1=0), and the capacitor
voltage precharged to the negative value vC=vIC-VDD, where vIC, which is less than VDD, is
the logic transition level of gate 2. Under these conditions, the status of the capacitor
appears as in the first figure.
With v1 low, the input v2 to gate 2, given by v1+vC=0+vIC-VDD, will be initially negative and
will indeed force the output of gate 2 high. The capacitor will charge toward VDD, causing vC
to increase. When v2 reaches v1C, the output of gate 2 will be forced low, in turn causing
the output v1 of gate 1 to be forced high. Just prior to this switching operation, the
capacitor will have been charged to the value vC=vIC.
With v1 now equal to VDD and vOUT equal to zero, vC will begin to charge in the opposite
direction toward –vDD, thereby causing v2 to fall. When v2 falls below the logic transition
level vIC, the output of gate 2 will switch high, forcing v1 low. With v2 equal to VDD+vC, the
value v2=vIC will be reached in this second case when vC=vIC-VDD. After the switching
operation, the circuit will again appear as originally assumed. The cycle will thus repeat
itself, continuing indefinitely.
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The circuit will produce a square wave output at vOUT and its logical complement
at v1. Plots of the four principal voltages in the circuit are shown in figure.
The period of square wave produced by the circuit can be computed by
determining the time required for v2 to charge from vIC-VDD to vIC.
Derivation for Time Period
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vC= vF+(vi-vF)e-t/RC
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= VDD+(vIC-VDD –VDD) e-t/RC
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= vIC e-t/RC + VDD(1-2 e-t/RC)
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Where t=0 is defined as the point where the output of gate 2 just switches
high.
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At t=T/2, vC=v2=vIC, which, on substitution into above equation gives
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T = 2 RC ln [(2VDD-vIC)/(VDD-vIC)]
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For a symmetrical CMOS gate with vIC=VDD/2,
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T = 2 RC ln [(2VDD-VDD/2)/(VDD-VDD/2)] = 2 RC ln [(3/2)/(1/2)]
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T = 2.2 RC
6.2 Square Wave Generator
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Square wave outputs are generated when the op-amp is forced to
operate in the saturated region. That is, the output of the op-amp is
forced to swing repetitively between positive saturation +Vsat and
negative saturation –Vsat, resulting in the square wave output. One
such circuit is shown here. This square wave generator is also called
an astable multivibrator. The output of the op-amp in this circuit will
be in positive or negative saturation depending on whether the
differential voltage vid is negative or positive, respectively.
Operation
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Assume that the voltage across capacitor C is zero volts at the instant the dc supply
voltages +VCC and -VEE are applied. This means that the voltage at the inverting terminal is
zero initially. At the same instant, however, the voltage v1 at the noninverting terminal is a
very small finite value that is a function of the output offset voltage and the values of R1
and R2 resistors. Thus the differntial input voltage vid is equal to the voltage v1 at the
noninverting terminal. Although very small, voltage v1 will start to drive the op-amp into
saturation. For example, suppose that the output offset voltage is positive and that,
therefore, voltage v1 is also positive. Since initially the capacitor C acts as a short circuit, the
gain of the op-amp is very large; hence v1 drives the output of the op-amp to its positive
saturation +Vsat. With the output voltage of the op-amp at +Vsat, the capacitor C starts
charging toward +Vsat through resistor R. However, as soon as the voltage v2 across
capacitor C is slightly more positive than v1, the output of the op-amp is forced to switch to
a negative saturation, -Vsat. With the op-amp's output voltage at negative saturation, -Vsat,
the voltage v1 across R1 is also negative, since
Operation Contd.
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Thus the differential voltage vid = v1 – v2 is negative, which
holds the output of the op-amp in negative saturation. The
output remains in negative saturation until the capacitor C
discharges and then recharges to a negative voltage slightly
higher than –v1. Now, as soon as the capacitor's voltage v2
becomes more negative than –v1, the net differntial voltage vid
becomes positive and hence drives the output of the op-amp
back to its positive saturation +Vsat. This completes one cycle.
With output at +Vsat, voltage v1 at the noninverting input is
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The time period of the output waveform is given by
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If R2=1.16 R1,
Practical Consideration
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The highest frequency generated by the square wave generator is
set by the slew rate of the op-amp. An attempt to operate the
circuit at relatively higher frequencies causes the oscillator's output
to become triangular. In practice, each inverting and noninverting
terminal needs a series resistance Rs to prevent excessive
differential current flow because the inputs of the op-amp are
subjected to large differential voltages. A reduced peak-to-peak
output voltage swing can be obtained in the square wave
generator by using back-to-back zeners at the output terminal.
Voltage to Frequency Converter
A voltage to frequency converter produces an output signal whose instanteneous frequency is
a function of an external control voltage.
A voltage to frequency converter is also known as a voltage controlled oscillator (VCO). The
Signetics NE/SE556 VCO is a circuit that provides simultaneous square wave and triangle wave
outputs as a function of input voltage. The frequency of oscillation of the circuit is determined
by an external resistor R1, capacitor C1, and the voltage VC applied to the control terminal 5.
The control voltage at terminal 5 is set by the voltage divider formed with R2 and R3. The
initial voltage VC at terminal 5 must be in the range ¾(+V)  VC  +V
where +V is the total supply voltage. The input signal is ac coupled with the capacitor C and
must be < 3V p-p. The frequency of the output waveform is approximated by
f0  2 (+V-VC)/[R1C1(+V)]
where R1 should be in the range 2 k < R1 < 20 k
A small capacitor of 0.001 F should be connected between pins 5 and 6 to eliminate
possible oscillations in the control current source. The ideal conversion characteristics of a
voltage to frequency converter is linear.
Note: A frequency to voltage converter produces an output voltage whose amplitude is a
function of the frequency of the input signal.
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+V = 12V, R2 = 1.5k
R1 = R3 = 10k, C1 = 0.001F
Determine the nominal
frequency of the output
waveforms.
Compute the modulation in the
output frequency if VC is varied
between 9.5 V and 11.5 V.
Draw the square wave output
waveform if the modulating
input is a sine wave.
VC = 10k.12/11.5k = 10.43 V
f0 = 2 (12 - 10.43) /
(104.10-9.12)
= 26.17kHz
f0 (9.5) = 41.67 kHz
f0 (11.5) = 8.33 kHz
6.4 Sinusoidal Oscillators
LC Tuned Oscillators
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If we neglect the transistor capacitances (i.e., low frequency operation), the frequency
of oscillation will be determined by the resonance frequency of the parallel tuned circuit
(also known as tank circuit because it behaves as a reservoir for energy storage). Thus
for Colpitts oscillator (fig. a) and Hartley oscillator (fig. b), we respectively have
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The divider ratio determines the feedback factor and must be adjusted in conjunction
with the transistor gain to ensure that oscillations will start.
Derivation
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I’ = (1/r + sC2) V
V’ = v + v sL(sC2 + 1/ r ) = v [(1 + sL(sC2 + 1/ r )]
Substituting in I’ + gm v + sC1V’ = 0
[gm + 1/ r – (w2LC1/ r )] + j [ w(C1 + C2) – w3LC1C2] = 0
Equating imaginary part to zero
Equating the real part to 1 and substituting L, and taking gm r = B0,
C1/C2 = B0
to ensure that the loop gain at w0 is unity.
Phase Shift Oscillator
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The phase shift oscillator consists of an amplifier stage and three RC cascaded
networks as the feedback circuit. The amplifier provides a phase shift of 1800 and an
additional 1800 phase shift required for oscillation is provided by the cascaded RC
networks.
F = 1/2RC (1/(6+4k)
(Refer Millman, Halkias, page 487 for details)
Wien Bridge Oscillator
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It is one of the most commonly used audio – frequency oscillators because of its
simplicity and stability.
Crystal Oscillator
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Crystal oscillator uses a piece of quartz that is cut and polished to
vibrate at a certain frequency. Quartz is piezo-electric (a strain generates
a voltage, and vice versa), so acoustic waves in the crystal can be driven
by an applied electric field and in turn can generate a voltage at the
surface of the crystal.
RC oscillators can easily attain
stabilities approaching 0.1%. That’s
good enough for many applications. LC
oscillators can do a bit better, with
stabilities of 0.01% over reasonable
periods of time. That’s good enough
for oscillators in radio frequency
receivers and television sets. Crystal
oscillators do provide stabilities of a
few parts per million over normal
temperature ranges.
Signal Sources
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Signal Generators: Signal generators are sine-wave oscillators, usually equipped to give a wide
range of frequency coverage (50kHz to 50MHz is typical), with provision for precise control of
amplitude (using resistive divider network called an attenuator).
Sweep Generator: It is a signal generator that can sweep its output frequency repeatedly over
some range. These are handy for testing circuits whose properties vary with frequency in a
particular way, e.g. “tuned circuits” or filters. Nowadays these devices as well as many test
instruments, are available in configurations that allow you to program the frequency, amplitude,
etc., from a computer or other digital instrument.
Frequency Synthesizer: It is a device that generates sine waves whose frequencies can be set
precisely. The frequency is set digitally, often to eight significant figures or more and is internally
synthesized from a precise standard (a quartz crystal oscillator) by digital methods.
Function Generators: These are the most flexible signal sources of all. You can make sine,
triangle, and square waves over an enormous frequency range (0.01 Hz to 10 MHz is typical), with
control of amplitude and dc offset (a constant dc voltage added to the signal). Many of them have
provision for frequency sweeping, often in several modes (linear or logarithmic frequency
variations versus time).
HP8116A: Sine, square, and triangle waves from 0.001 Hz to 50 MHz (programmable), 10 mV to
16 V pp (programmable), linear and logarithmic sweeps, also provides trigger, FM, AM, voltage
controlled frequency, and single cycle.