Oscillator Circuits

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Oscillator Circuits

1. CMOS inverter relaxation oscillator
2. Operational amplifier based relaxation
   oscillators
3. Voltage to frequency converter
4. Sinusoidal oscillators
5. Amplitude and frequency stabilization
6. Signal generator, frequency synthesizers and
   swept frequency oscillators

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Introduction

• 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
• Tuned RC, LC, Crystal
• Untuned Square wave, Triangular wave -gt
  Sinusoidal oscillator
• Tuned Oscillators
• RC oscillators most suitable for IC technology
• Crystal oscillators are often used with the
  crystal external to the IC.
• Untuned Oscillators
• Untuned oscillators typically have only two
  stable states.
• Untuned oscillator can create sinusoid by
  applying the triangle wave to a sine-shaping
  circuit
• Untuned oscillators are very compatible with IC
  technology.

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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.

• vin 0 and vo ? 0 implies that
• AvB 1
•  Expressed in polar form,
• AvB 1 ? 00

• 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. ltBarkhausen
  Criteriongt
• 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.

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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 high-frequency signals, while
  RC components are most suitable for
  audio-frequency applications.

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6.1 CMOS Inverter Relaxation Oscillator

• 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 (voutvDD), output of
  the gate 1 low (v10), and the capacitor voltage
  precharged to the negative value vCvIC-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
  v1vC0vIC-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 vCvIC.
• 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 VDDvC, the value v2vIC
  will be reached in this second case when
  vCvIC-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.

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Derivation for Time Period

• vC vF(vi-vF)e-t/RC
• VDD(vIC-VDD VDD) e-t/RC
• vIC e-t/RC VDD(1-2 e-t/RC)
• Where t0 is defined as the point where the
  output of gate 2 just switches high.
• At tT/2, vCv2vIC, which, on substitution into
  above equation gives
• T 2 RC ln (2VDD-vIC)/(VDD-vIC)
• For a symmetrical CMOS gate with vICVDD/2,
• T 2 RC ln (2VDD-VDD/2)/(VDD-VDD/2) 2 RC ln
  (3/2)/(1/2)
• T 2.2 RC

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6.2 Square Wave Generator

• 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.

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Operation

• 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

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Operation Contd.

• 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

• The time period of the output waveform is given
  by
• If R21.16 R1,

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Practical Consideration

• 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.

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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 lt 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? lt R1 lt 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

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6.4 Sinusoidal Oscillators

• LC Tuned Oscillators
• 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

• The divider ratio determines the feedback factor
  and must be adjusted in conjunction with the
  transistor gain to ensure that oscillations will
  start.

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Derivation

• 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.

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Phase Shift Oscillator

• 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/?(64k)
• (Refer Millman, Halkias, page 487 for details)

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Wien Bridge Oscillator

• It is one of the most commonly used audio
  frequency oscillators because of its simplicity
  and stability.

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Crystal Oscillator

• 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. Thats good enough for many
  applications. LC oscillators can do a bit better,
  with stabilities of 0.01 over reasonable periods
  of time. Thats 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.

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Signal Sources

• 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.