Oscillator Circuits

1. CMOS inverter relaxation oscillator2. Operational amplifier based relaxation oscillators3. Voltage to frequency converter4. Sinusoidal oscillators5. Amplitude and frequency stabilization6. Signal generator, frequency synthesizers and swept

frequency oscillators

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 -> 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.

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

BA

A

v

v

v

v

i

o

1

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

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.

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.

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

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 t=0 is defined as the point where the output of gate 2 just switches high.

At t=T/2, vC=v2=vIC, which, on substitution into above equation gives

T = 2 RC ln [(2VDD-vIC)/(VDD-vIC)]

For a symmetrical CMOS gate with vIC=VDD/2,

T = 2 RC ln [(2VDD-VDD/2)/(VDD-VDD/2)] = 2 RC ln [(3/2)/(1/2)]

T = 2.2 RC

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.

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

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 R2=1.16 R1,

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.

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 byf0 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.

+V = 12V, R2 = 1.5k R1 = R3 = 10k, C1 = 0.001F 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 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.

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.

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 = 1/2RC (1/(6+4k) (Refer Millman, Halkias, page 487 for details)

Wien Bridge Oscillator

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

Crystal Oscillator

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.

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.

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.