In this article we will discuss about:- 1. Meaning of Oscillator 2. Types of Oscillators 3. Conditions for Oscillation 4. Fundamental Oscillatory Circuit 5. Frequency Stability.
Contents:
- Meaning of Oscillator
- Types of Oscillators
- Conditions for Oscillation
- Fundamental Oscillatory Circuit
- Frequency Stability in Oscillator
1. Meaning of Oscillator:
An oscillator may be defined as an active device that generates sinusoidal or other repetitive waveforms. Important characteristics of an oscillator are its frequency and amplitude stability, harmonic content and output power. One group of oscillators is known as sinusoidal (or harmonic) oscillators as they are characterized by the generation of sinusoidal waveform of definite frequency.
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Relaxation oscillators, on the other hand, are active devices which generate non- sinusoidal waveforms like square and saw-tooth waveforms. Oscillators can further be classified as negative impedance or feedback oscillators which make use of an active device that possesses a negative impedance over a range of its operating characteristics.
Although an oscillator is required, in general, for producing a single frequency, non-linearities are sometimes present in the oscillator circuit and these give rise to other frequencies known as harmonics. Depending on the particular use an oscillator may be classified as class A, AB, B or C. For high quality laboratory instruments oscillators are operated in class A condition while for transmitters when efficiency is of greatest importance, class C operation might be used.
2. Types of Oscillators:
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Some oscillators can be readily converted to push-pull operation. The output power with a push- pull connection is increased and harmonics are decreased. A Hartley oscillator might be connected in push-pull. The feedback is achieved by capacitive coupling from the plate tank back to the input. The 180° phase shift can be obtained by tapping to opposite sides of the tank. For high frequencies the push-pull connection is found to be useful.
2. Transistor RC Oscillators:
A transistor phase shift or RC oscillator is shown in Fig 3.5. The three-stage, phase-lead network is designed for providing the required 180° phase shift.
It satisfies the criterion that the product Aβ = 1. A network of this type is a loss network (i.e., β < 1) so that there is a minimum amplifier gain A to ensure oscillation. The equivalent circuit of the amplifier is shown in Fig. 3.6.
In Fig. 3.6(a) the hybrid equivalent circuit of the transistor has been separated. Some approximations can be taken to simplify the number of terms in the equations.
Since 1/h0e is much larger than RL, so its effect can be neglected. Further hre is so small that its effect may be ignored for many practical circuits. The current source at the collector is replaced by a voltage source. The result of these changes is given in the equivalent circuit of Fig. 3.6(b).
The basic Wien bridge circuit is shown in Fig. 3.7. It is essentially an RC oscillator whose feedback network forms two arms of a Wien bridge. The phase shift of the bridge voltage is zero at balance in comparison to the bridge input voltage. As a result of the zero phase shift the amplifier must be non-inverting. Considering the figure we find that the voltage Vi is the input to the bridge and is also the output of the amplifier. The output of the bridge V0 is the input to the amplifier.
For balance, we have-
If A = k, then the Barkhausen criterion Aβ = 1 is satisfied. In this way, by adjusting the ratio of R4/R3, the bridge is unbalanced slightly for developing a feedback voltage. Typical transistor Wien bridge oscillator is shown in Fig. 3.7(a). Tuning to various frequencies is made by using ganged variable capacitors in the bridge arm.
4. Negative Resistance Oscillator:
We know that the oscillations in a simple oscillatory circuit are damped ultimately by the coil resistance and the associated losses unless energy is supplied to the circuit. By connecting a negative resistance across the terminals of the LC circuit the various losses could be eliminated.
A simple oscillatory circuit with a negative resistance connected in parallel and series resonant cases is shown in Fig. 3.8. If | RP | = | – Rn |, then the conductance of the parallel circuit Gp – Gn= 0.
For a series resonant circuit-
5. Crystal Oscillators:
A crystal oscillator is one where piezoelectric crystal is used as the frequency-determining component. The crystal takes the place of the inductor in the parallel resonant LC circuit and has the property that its resonant frequency is relatively constant.
Certain natural crystals like quartz, tourmaline and Rochelle salts exhibit a piezoelectric effect. When a voltage is applied to the faces of a piezoelectric crystal, the shape of the crystal is distorted. If an alternating voltage is applied to the faces of a piezoelectric crystal, it produces mechanical vibration showing a maximum amplitude at the natural resonant frequency of the crystal.
Quartz Crystal and its Characteristics:
In Fig. 3.9(a) we have illustrated the form of the natural quartz crystal while in Fig. 3.9(b) the relation between the various axes is shown. The axis joining the pointed ends of the crystal is called the Z-axis or the optical axis. If any stress is applied in this direction, it will not produce a piezo-electric effect.
The cross-section here is hexagonal in shape. Axes through the corners of the hexagon are called electrical axes and are labelled x, x’ and x”. On the other hand, the three axes perpendicular to the faces of the crystal are known as the mechanical axes and are label y, y’ and y”.
If a section is cut from the crystal in such a manner that the flat sides of longer dimension are perpendicular to one of the electrical axes, mechanical stresses along the edges in the y-direction will produce an electric potential in the direction of X-axis. This section as shown in Fig. 3.10(a) is referred to as an X-cut.
Again, when the direction of cut is changed by 30° so that the flat side is perpendicular to the mechanical axis, then the section as revealed in Fig. 3.10(b) is called a Y-cut. A mechanical force applied to the flat sides in the y-direction produces an electric potential across the edges.
Electrical equivalent circuit of a quartz or other piezoelectric crystal. The crystal is represented by a series resonant circuit LCR shunted by a capacitance CM. The inductance L represents the electrical equivalent of crystal mass, C is the electrical equivalent of crystal compliance and R is an electrical equivalent of the internal friction of the crystal structure. The shunt capacitance CM represents the capacitance between the mounting electrodes with the crystal as a dielectric.
One of the frequencies ƒ1 can be expressed as-
At this series resonant frequency, the crystal impedance presented to the circuit is very low.
An electrical equivalent circuit of a crystal at frequency greater than the series resonant frequency is shown in Fig. 3.12.
In the circuit, Lx represents the equivalent inductance of the series arm. The resonant frequency ƒ2 can be obtained by using the equation-
Variation of reactance of a crystal with frequency is shown in Fig. 3.13(a) while Fig. 3.13(b) illustrates the low impedance at series resonance ƒ1 and high impedance at parallel resonance ƒ2.
With the variation of temperature, the resonant frequency of a quartz crystal is affected, causing minute changes in dimensions, compliance and density. With an increase of temperature, the frequency of oscillation may either increase or decrease. One of the methods of frequency stabilization is to keep the crystal in an oven whose temperature is properly regulated.
An alternative method is to use crystal cuts whose temperature coefficient approaches zero. The frequency stability depends, in fact, on the amplitude of mechanical vibrations. This vibration is a function of the current through the crystal whose flow depends on the voltage across the crystal and the ratio of mounting capacitance CM to internal capacitance C. The greater is the amplitude of vibration, the poorer is the frequency stability.
3. Conditions for Oscillation
:
Before attaining the steady state, an oscillator must build up oscillations.
For the oscillations to be self-sustaining the following items are required:
i. An amplifying device,
ii. Regenerative feedback,
iii. Some circuit non-linearity, and
iv. Some energy storage system.
Basically the four-terminal or feedback oscillator is a regenerative feedback amplifier. Positive feedback results when the feedback factor βA is positive and less than unity. If βA is increased to unity, the gain with feedback becomes infinite and then the amplifier functions as an oscillator.
The condition βA = 1 is known as the Barkhausen criterion and this is true at a single and precise frequency at which the feedback signal appearing at the input is exactly in phase with the input signal. Oscillations occur even if βA > 1 and the amplitude of oscillation increases without limit. For all practical purposes, non-linearity limits the theoretically infinitive gain to some finite value for both βA = 1 and βA > 1.
4. Fundamental Oscillatory Circuit
:
A fundamental oscillatory circuit is the ICR circuit. In Fig. 3.1(a), Rs is the series resistance while in Fig. 3.1(b), RP is the parallel resistance connected with L and C as shown.
We may now define resonance as a condition in which the current and voltage in a reactive circuit are in phase with each other. If the resistance Rs becomes zero, then the resonant frequency ƒ0 can be defined as-
Fig. 3.2 shows that if some initial energy is given in an ideal LC circuit it will oscillate indefinitely at the resonance frequency as given by equation (3.1). The analysis of the circuit with an initial current I0 in the inductor involves a differential equation, the solution of which leads to three possible conditions. The oscillatory or underdamped condition results when-
When L/C = 4R2P, we get the critical damping. The critically damped circuit does not oscillate but within a very short time it dissipates the circuit energy.
If L/C > 4R2P, the over-damped condition.
It is to be noted that in an oscillator the underdamped condition is desirable. If additional energy is periodically supplied to the circuit, then the amplitude of oscillation remains constant.
The logarithmic decrement is an important factor in many oscillator circuits. This is nothing but the natural logarithm of the ratio of amplitudes of two successive peaks of the underdamped waveform. If i1 and i2 are the successive peaks of the underdamped waveform, then the logarithmic decrement δ is given by-
5. Frequency Stability
in Oscillator:
Changes in transistor parameters, power supply voltages and in the passive circuit elements cause a change from the required frequency value. This change is called as the drift. In general, both active and passive oscillator circuit parameters change due to temperature and aging. The variations of temperature of transistor parameters cause a very great problem.
Use of emitter resistor stabilizes the operating point against changes in transistor parameters or bias voltages. Additional stabilization can also be realized using a thermistor (Rth) in the base bias network of the oscillator. This is shown in Fig. 3.4. The thermistor Rth a temperature sensitive resistance with negative temperature coefficient, tends to reduce the base-forward bias with increasing temperature.
For the compensation of the temperature, semiconductor diodes are also very useful. For a good frequency stability, a piezoelectric crystal is used as the frequency-determining element.