1. UNIT II OSCILLATORS

2. Topics to be covered Classification, Barkhausen Criterion
Mechanism for start of oscillation and stabilization of amplitude,
General form of an Oscillator,
Analysis of LC oscillators –
Hartley, Colpitts
Clapp
Franklin
Armstrong
Tuned collector oscillators,

3. Topics to be covered RC oscillators phase shift Wienbridge
Twin-T Oscillators
Frequency range of RC and LC Oscillators,
Quartz Crystal Construction,
Electrical equivalent circuit of Crystal,
Miller and Pierce Crystal oscillators,
frequency stability of oscillators

4. THE OSCILLATOR
Oscillators are electronic circuits that generate an output signal without the necessity of an input signal.
It produces a periodic waveform on its output with only the DC supply voltage as an input.
The output voltage can be either sinusoidal or nonsinusoidal, depending on the type of oscillator.
Different types of oscillators produce various types of outputs including sine waves, square waves, triangular waves, and sawtooth waves
A basic oscillator :

5. Oscillator classification
Oscillators can be of 2 types
Feedback Oscillators
Relaxation Oscillators

6. Feedback Oscillators
One type of oscillator is the feedback oscillator, which returns a fraction of the output signal to the input with no net phase shift, resulting in a reinforcement of the output signal.
After oscillations are started, the loop gain is maintained at 1.0 to maintain oscillations.
A feedback oscillator consists of an amplifier for gain (either a discrete transistor or an op-amp) and a positive feedback circuit that produces phase shift and provides attenuation,

7. Basic elements of a feedback oscillator.

8. Relaxation Oscillators
A second type of oscillator is the relaxation oscillator.
Instead of feedback, a relaxation oscillator uses an RC timing circuit to generate a waveform that is generally a square wave or other nonsinusoidal waveform.
Typically, a relaxation oscillator uses a Schmitt trigger or other device that changes states to alternately charge and discharge a capacitor through a resistor.

9. FEEDBACK OSCILLATORS
Feedback oscillator operation is based on the principle of positive feedback.
In this section, we will look at the general conditions required for oscillation to occur.
Feedback oscillators are widely used to generate sinusoidal waveforms.
Positive Feedback
In positive feedback, a portion of the output voltage of an amplifier is fed back to the input with no net phase shift, resulting in a strengthening of the output signal.

10. The in-phase feedback voltage is amplified to produce the output voltage, which in turn produces the feedback voltage.
That is, a loop is created in which the signal maintains itself and a continuous sinusoidal output is produced.
This phenomenon is called oscillation.
In some types of amplifiers, the feedback circuit shifts the phase and an inverting amplifier is required to provide another phase shift so that there is no net phase shift.

11. Conditions for Oscillation
Two conditions are required for a sustained state of oscillation: 1. The phase shift around the feedback loop must be effectively . 2. The voltage gain, ,around the closed feedback loop (loop gain) must equal 1 (unity).

12. The voltage gain around the closed feedback loop, , is the product of the amplifier gain, , and the attenuation, B , of the feedback circuit.
If a sinusoidal wave is the desired output, a loop gain greater than 1 will rapidly cause the output to saturate at both peaks of the waveform, producing unacceptable distortion.
To avoid this, some form of gain control must be used to keep the loop gain at exactly 1 once oscillations have started.
For example, if the attenuation of the feedback circuit is 0.01, the amplifier must have a gain of exactly 100 to overcome this attenuation and not create unacceptable distortion .
An amplifier gain of greater than 100 will cause the oscillator to limit both peaks of the waveform

13. Start-Up Conditions
- The unity-gain condition must be met for oscillation to be maintained. - For oscillation to begin, the voltage gain around the positive feedback loop must be greater than 1 so that the amplitude of the output can build up to a desired level. - The gain must then decrease to 1 so that the output stays at the desired level and oscillation is sustained. - The voltage gain conditions for both starting and sustaining oscillation are illustrated

14. Analysis of LC oscillators
LC oscillator is a type of oscillator where a LC (inductor-capacitor) tank circuit is used for giving the required positive feedback for sustaining the oscillations.
The LC tank circuit is also termed as LC resonant circuit or LC tuned circuit.
According to the Barkhausen criterion for sustained oscillations, a circuit will sustain stable oscillations only for frequencies at which the loop gain of the system is equal to or greater than 1 and the phase shift between input and output is 0 or an integral multiple of 2π.
LC oscillators can realized using BJT, FET, MOSFET, opamp etc.
Typical applications of LC oscillators include RF signal generators, frequency mixers, tuners, sine wave generators, RF modulators etc.
In a practical LC oscillator, in addition to the Barkahusen criterion there must be some means to compensate for the energy lost in the tank circuit.
Application of active elements like BJT, FET, opamp etc in the LC oscillator is a way for meeting all these requirements.
The active element in an LC oscillator circuit has three essential jobs.
To give necessary gain.
Help in attaining the required positive feedback conditions.
Compensate the energy lost in the tank circuit.

15. The Colpitts Oscillator
One basic type of resonant circuit feedback oscillator is the Colpitts.
This type of oscillator uses an LC circuit in the feedback loop to provide the necessary phase shift and to act as a resonant filter that passes only the desired frequency of oscillation.

16. The approximate frequency of oscillation is the resonant frequency of the LC circuit and is established by the values of C1, C2 and L according to the formula:
Where is the total capacitance.
Because the capacitors effectively appear in series around the tank circuit, the total capacitance ( ) is
Conditions for Oscillation and Start-Up
The attenuation, B , of the resonant feedback circuit in the Colpitts oscillator is basically determined
by the values of C1 and C2.

17. The circulating tank current is through both C1 and C2 (they are effectively in series).
The voltage developed across C2 is the oscillator’s output voltage Vout and the voltage developed across C1 is the feedback voltage (Vf) as indicated.

18. The expression for the attenuation (B) is:
As you know, a condition for oscillation is
Since , so
where Av is the voltage gain of the amplifier
For the oscillator to be self-starting, must be greater than 1.
Therefore, the voltage gain must be made slightly greater than

19. Loading of the Feedback Circuit Affects the Frequency of Oscillation
The input impedance of the amplifier acts as a load on the resonant feed-back circuit and reduces the Q of the circuit.
Zin of the amplifier loads the feed-back circuit and lowers its Q , thus lowering the resonant frequency.
A basic FET Colpitts oscillator.

20. The resonant frequency of a parallel resonant circuit depends on the Q, according to the following formula:
As a rule of thumb, for a Q>10 , the frequency is approximately
When Q<10 , however, fr is reduced significantly.
A FET can be used in place of a BJT to minimize the loading effect of the transistor’s input impedance.

21. Advantages:
The one big advantage of this oscillator is that it's performance remains very good even the high frequency.
It has wide operation range from 1 to 60 MHz.
This type of oscillator have the capacity to produce more purer waves.
This oscillator generally also have the wide range of operation capacity .
Disadvantage:
The one main disadvantage is it's hard to construct .
Whenever the capacitor value change it becomes more difficult to adjust feedback.
Because of the circuit bulkiness the cost increases also
It has poor isolation property.

22. The Clapp Oscillator
The Clapp oscillator is a variation of the Colpitts.
The basic difference is an additional capacitor, in series with the inductor in the resonant feedback circuit.
Since is in series with and around the tank circuit, the total capacitance is
and the approximate frequency of oscillation(Q>10) is
If is much smaller than and then almost entirely controls the resonant frequency
Clapp provides a more accurate and stable frequency of oscillation.

23. A basic Clapp oscillator.

24. Advantages of Clapp Oscillator
The Clapp Oscillator possesses high-frequency stability than other oscillators.
Moreover, the effect of transistor parameters in Clapp oscillators is very less as compared to other oscillators. Therefore, the problem of stray capacitance is not severe in case of Clapp oscillator.
We can increase the frequency stability of Clapp oscillator by enclosing the entire circuit of the oscillator in a constant temperature zone.
Besides, the supply of voltage should be provided by a voltage regulator such as zener diode.

25. The Hartley Oscillator
The Hartley oscillator is similar to the Colpitts except that the feedback circuit consists of two series inductors and a parallel capacitor

26. In this circuit, the frequency of oscillation for (Q>10) is,
The inductors act in a role similar to in the Colpitts to determine the attenuation, B, of the feedback circuit.
To assure start-up of oscillation, must be greater than 1/B.
Loading of the tank circuit has the same effect in the Hartley as in the Colpitts; that is, the Q is decreased and thus decreases.

27. Advantages of the Hartley oscillator :
The frequency may be adjusted using a single variable capacitor, one side of which can be
earthed
The output amplitude remains constant over the frequency range
Either a tapped coil or two fixed inductors are needed, and very few other components
Easy to create an accurate fixed-frequency Crystal oscillator variation by replacing the
capacitor with a (parallel-resonant) quartz crystal or replacing the top half of the tank circuit
with a crystal and grid-leak resistor (as in the Tri-tet oscillator).
Disadvantages :
Harmonic-rich output if taken from the amplifier and not directly from the LC circuit (unless amplitude- stabilisation circuitry is employed).

28. The Armstrong Oscillator
This type of LC feedback oscillator uses transformer coupling to feed back a portion of the signal voltage.
The transformer secondary coil provides the feedback to keep the oscillation going.
The Armstrong is less common than the Colpitts, Clapp, and Hartley, mainly because of the disadvantage of transformer size and cost.
The frequency of oscillation is set by the inductance of the primary winding in parallel with
The Armstrong Oscillator is used to produce a sine-wave output of constant amplitude and of fairly constant frequency within the radio frequency range.
It is generally used as a local oscillator in receivers, as a source in signal generators, and as a radio-frequency oscillator in the medium- and high-frequency range.

29. A basic Armstrong oscillator.

30. RC oscillators The Phase-Shift Oscillator
The above figure shows a sinusoidal feedback oscillator called the phase-shift oscillator

31. Each of the three RC circuits in the feedback loop can provide a maximum phase shift approaching 90°.
Oscillation occurs at the frequency where the total phase shift through the three RC circuits is 180°.
The inversion of the op-amp itself provides the additional 180° to meet the requirement for oscillation of a 360° (or 0°) phase shift around the feedback loop.
The attenuation, B , of the three-section RC feedback circuit is
To meet the greater-than-unity loop gain requirement, the closed-loop voltage gain of the op-amp must be greater than 29 (set by )
The frequency of oscillation fr is given as

32. Advantages of RC Phase Shift Oscillator:
This circuit is very simple and cheap as it comprises resistors and capacitors (not bulky and expensive high- value inductors).
It provides good frequency stability.
The output of this circuit is sinusoidal that is quite distortion free.
The phase shift oscillator circuit is simpler than the Wein bridge oscillator circuit because it does not need negative feedback and the stabilization arrangements.
They have a wide range of frequency (from a few Hz to several hundred of kHz).
They are particularly apt for low frequencies, say of the order of 1 Hz, so these frequencies can be easily gained by using R and C of large values.
Disadvantages of RC Phase Shift Oscillator:
The output is small and It is due to smaller feedback.
The frequency stability is not as good as that of the Wien bridge oscillator.
It is difficult for the circuit to start oscillations as the feedback is usually small.
It needs high voltage (12 V) battery so as to develop a sufficiently large feedback voltage.

33. Applications of RC Phase Shift Oscillator:
FET phase-shift oscillator is used for generating signals over a wide frequency range. The frequency may be varied from a few Hz to 200 Hz by employing one set of resistor with three capacitors ganged together to vary over a capacitance range in the 1 : 10 ratio. Similarly the frequency ranges of 200 Hz to 2 kHz, 2 kHz to 20 kHz and 20 kHz to 200 kHz can be obtained by using other sets of resistors.
RC Phase Shift Oscillators are used in musical instruments, voice synthesis and in GPS units since they work at all audio frequencies.

34. The Twin-T Oscillator
Another type of RC feedback oscillator is called the twin-T because of the two T-type RC filters used in the feedback loop.

35. One of the twin-T filters has a low-pass response, and the other has a high-pass response.
The combined parallel filters produce a band-stop response with a center frequency equal to the desired frequency of oscillation,
Oscillation cannot occur at frequencies above or below because of the negative feedback through the filters.
At however, there is negligible negative feedback; thus, the positive feedback through the voltage divider
allows the circuit to oscillate.

36. Wein Bridge Oscillator
Due to the advantages like good frequency stability, very low distortion and ease of tuning, a Wien bridge oscillator becomes the most popular audio frequency range signal generator circuit. 
This type of oscillator uses RC feedback network so it can also be considered as RC oscillator.
The main difference between the general oscillator and Wien bridge oscillator is that in an oscillator, amplifier stage introduces 180 degrees phase shift and additional 180 degrees phase shift is introduced by feedback network so as to obtain the 360 degrees or zero phase shift around the loop to satisfy the Barkhausen criteria.
But, in case of the Wien bridge oscillator, a non inverting amplifier used in amplifier stage does not introduce any phase shift. 
Hence there is no need of phase shift through feedback network is required in order to satisfy the Barkhausen criteria. 

37. A Wien bridge oscillator produces sine waves which uses RC network as the frequency determining portion of the circuit. 

38. The output of the amplifier is applied between the terminals 1 and 3 while the input to the amplifier stage is supplied from terminals 2 and 4 hence the amplifier output becomes input voltage of the bridge whilst the output of the bridge becomes the input voltage of the amplifier.
When the bridge is balanced the input voltage to the amplifier becomes zero, so in order to produce the sustained oscillations input to the amplifier must be non-vanishing. Therefore the bridge is unbalanced by adjusting the proper values of the resistors.
As we mentioned above the RC network is responsible for determining the frequency of the oscillator.
This RC network consists of two frequency sensitive arms namely series R1C1 and parallel R2, C2. This network is also called as lead-lag circuit.

39. The output voltage across the capacitor lags behind the input voltage by an angle between 0 to – 90 degrees in the lag circuit. In the lead circuit, the output voltage across the resistor leads the input voltage by an angle between 0 and 90 degrees.
At very low frequencies the output voltage becomes zero since the series capacitor behaves as an open circuited and also there is no output at very high frequencies since the parallel capacitor acts as shorted circuited path to the input voltage.
Therefore in-between these two extreme conditions, the output voltage reach to the maximum value.
The resonant frequency is the frequency at which the output voltage is maximum. At this frequency, feedback fraction K reaches to a maximum value of 1/3.
The feedback will be maximum when Xc = R and hence the resonant frequency is given by
f = 1 / 2πRC

40. The above figure indicates the output voltage at resonant frequency
The above figure indicates the output voltage at resonant frequency. At the resonant frequency the phase shift through the circuit is zero and the attenuation V1/V0 is 1/3. Therefore, in order to maintain oscillations, the amplifier must have a gain greater than 3.
The different frequency ranges can be provided by the Wien bridge oscillator by mounting the two capacitors on the shaft and by varying their values simultaneously.

41. Advantages
Because of the usage of two stage amplifier, the overall gain of this oscillator is high.
By varying the values of C1 and C2 or with use of variable resistors, the frequency of oscillations can be varied.
It produces a very good sine wave with less distortion
The frequency stability is good
Due to the absence of inductors, no interference occurs from external magnetic fields.
Disadvantages
More number of components is needed for two stage amplifier type of Wien bridge oscillators.
Very high frequencies cannot be generated.

42. Quartz Crystal Oscillators
Some of the factors that affect the frequency stability of an oscillator generally include: variations in temperature, variations in the load, as well as changes to its DC power supply voltage to name a few.
Frequency stability of the output signal can be greatly improved by the proper selection of the components used for the resonant feedback circuit, including the amplifier.
But there is a limit to the stability that can be obtained from normal LC and RC tank circuits.
To obtain a very high level of oscillator stability a Quartz Crystal is generally used as the frequency determining device to produce another types of oscillator circuit known generally as a Quartz Crystal Oscillator, (XO).
When a voltage source is applied to a small thin piece of quartz crystal, it begins to change shape producing a characteristic known as the Piezo-electric effect.
This Piezo-electric Effect is the property of a crystal by which an electrical charge produces a mechanical force by changing the shape of the crystal and vice versa, a mechanical force applied to the crystal produces an electrical charge.

43. Then, piezo-electric devices can be classed as Transducers as they convert energy of one kind into energy of another (electrical to mechanical or mechanical to electrical).
This piezo-electric effect produces mechanical vibrations or oscillations which can be used to replace the standard LC tank circuit in the previous oscillators.
The quartz crystal used in a Quartz Crystal Oscillator is a very small, thin piece or wafer of cut quartz with the two parallel surfaces metallised to make the required electrical connections.
The physical size and thickness of a piece of quartz crystal is tightly controlled since it affects the final or fundamental frequency of oscillations. The fundamental frequency is generally called the crystals “characteristic frequency”.
Once cut and shaped, the crystal can not be used at any other frequency. In other words, its size and shape determines its fundamental oscillation frequency.

44. The crystals characteristic or characteristic frequency is inversely proportional to its physical thickness between the two metallized surfaces.
A mechanically vibrating crystal can be represented by an equivalent electrical circuit consisting of low resistance R, a large inductance L and small capacitance C as shown below.
Quartz Crystal Equivalent Model

45. The equivalent electrical circuit for the quartz crystal shows a series RLC circuit, which represents the mechanical vibrations of the crystal, in parallel with a capacitance, Cp which represents the electrical connections to the crystal. Quartz crystal oscillators tend to operate towards their “series resonance”.
The equivalent impedance of the crystal has a series resonance where Cs resonates with inductance, Ls at the crystals operating frequency.
This frequency is called the crystals series frequency, ƒs. As well as this series frequency, there is a second frequency point established as a result of the parallel resonance created when Ls and Cs resonates with the parallel capacitor Cp.
Series Resonant Frequency
Parallel Resonant Frequency

46. Miller Oscillator The Miller is a parallel-resonant circuit.
The crystal is used as a shunt impedance element to ground.
The voltage across the crystal is amplified and inverted by the transistor and fed back to the crystal through a small capacitance C2.
The collector tank circuit L1C1 is tuned to a frequency above resonance, so that the net impedance of L1C1, is inductive at the frequency of oscillation.
The tank circuit L1C1 must be inductive at the frequency of oscillation, or the circuit will not oscillate.
C1 is not necessary for the circuit to oscillate, but it cleans up the waveform across L1 considerably, which is absolutely awful without the capacitor across it

47. Miller circuit: (a) transistor version and (b) FET version
The circuit operates as follows.
The transistor provides a 180” phase reversal.
The tank circuit L1C1 is inductive at the oscillation frequency, and together with the collector’s output resistance provides a nominal 90” phase lead.
And C2, together with the crystal operating above resonance as an inductance, provides 90” more phase lead, so that the total phase shift around the loop is zero.

48. This is not a good oscillator circuit because the waveforms across the crystal are very poor and the frequency is unstable.
It turns out that the frequency of oscillation is quite sensitive to the value of the series feedback capacitor C2, which is about 5-40 pF.
The transistor version of the Miller circuit will operate at high or . medium frequencies, but not at low frequencies.
At low frequencies, the resistive loading of the transistor’s base input resistance across the high-impedance crystal is so great that the crystal will not oscillate.
The FET version of the Miller circuit can be used at any frequency: low, medium, or high.
The crystal voltage waveform is much better with a FET than with a transistor.
The frequency is still unstable and for the same reason: variability in the effective feedback capacitance C2 due to changes in the FET’s gain.

49. Pierce Crystal oscillators
The Pierce oscillator is a type of electronic oscillator particularly well-suited for use in piezoelectric crystal oscillator circuits.
The Pierce oscillator is a derivative of the Colpitts oscillator.
Virtually all digital IC clock oscillators are of Pierce type, as the circuit can be implemented using a minimum of components: a single digital inverter, one resistor, two capacitors, and the quartz crystal, which acts as a highly selective filter element.
The low manufacturing cost of this circuit, and the outstanding frequency stability of the quartz crystal, give it an advantage over other designs in many consumer electronics applications.
Biasing resistor
R1 acts as a feedback resistor, biasing the inverter in its linear region of operation and effectively causing it to function as a high gain inverting amplifier.
Assume the inverter is ideal, with infinite input impedance and zero output impedance.

50. Simple Pierce oscillator
The resistor forces the input and output voltages to be equal. Hence the inverter will neither be fully on nor fully off, but will operate in the transition region where it has gain.
Resonator
Extremely low cost applications sometimes use a piezoelectric PZT crystal ceramic resonator rather than a piezoelectric quartz crystal resonator.
The crystal in combination with C1 and C2 forms a pi network band-pass filter, which provides a 180 degree phase shift and a voltage gain from the output to input at approximately the resonant frequency of the crystal.

51. Note that at the frequency of oscillation, the crystal appears inductive.
Thus, the crystal can be considered a large, high Q inductor.
The combination of the 180 degree phase shift (i.e. inverting gain) from the pi network, and the negative gain from the inverter, results in a positive loop gain (positive feedback), making the bias point set by R1 unstable and leading to oscillation.
Isolation resistor
In addition to the biasing resistor R1, a series resistor Rs between the output of the inverter and the crystal.reduces the chance of overtone oscillation and can improve start-up time.
This second resistor Rs isolates the inverter from the crystal network. This would also add additional phase shift to C1.
Pierce oscillators above 4 MHz should use a small capacitor rather than a resistor for Rs.

52. Load capacitance
The total capacitance seen from the crystal looking into the rest of the circuit is called the "load capacitance".
When a manufacturer makes a "parallel" crystal, a technician uses a Pierce oscillator with a particular fixed load capacitance (often 18 or 20 pF) while trimming the crystal to oscillate at exactly the frequency written on its package.
Increasing the "load capacitance" slightly decreases the frequency generated by a Pierce oscillator, but never enough to reduce it all the way down to the series resonant frequency.

53. Barkhausen Criterion or Conditions for Oscillation
The circuit will oscillate when two conditions, called as Barkhausen’s criteria are met. These two conditions are:
The loop gain must be unity or greater
The feedback signal feeding back at the input must be phase shifted by 360 degrees (which is same as zero degrees). In most of the circuits, an inverting amplifier is used to produce 180 degrees phase shift and additional 180 degrees phase shift is provided by the feedback network.
At only one particular frequency, a tuned inductor-capacitor (LC circuit) circuit provides this 180 degrees phase shift.
Let us know how these conditions can be achieved.
The amplifier is a basic inverting amplifier and it produces a phase shift of 180 degrees between input and output.

54. The input to be applied to the amplifier is derived from the output Vo by the feedback network. Since the output is out of phase with Vi.
So the feedback network must ensure a phase shift of 180 degrees while feeding the output to the input. This is nothing but ensuring positive feedback.

55. Let us consider that a fictitious voltage, Vi is applied at the input of amplifier, then
Vo = A Vi
The amount of feedback voltage is decided by the feedback network gain, then
Vf = – β Vo
This negative sign indicates 180 degrees phase shift.
Substituting Vo in above equation, we get
Vf = – A β Vi
In oscillator, the feedback output must drive the amplifier, hence Vf must act as Vi. For achieving this term – A β in the above expression should be 1, i.e.,
Vf = Vs when – A β = 1.
This condition is called as Barkhausen criterion for oscillation.

56. Frequency Stability of Oscillators
In oscillators, the frequency of oscillations remains constant over a long interval of time.
Frequency stability is a measure of the degree to which the desired frequency is achieved.
The closure will be the output to a constant frequency if the frequency stability is better.
The oscillation frequency depends on various features of the circuit such as various components, supply voltages, stray elements, characteristic parameters of active devices, etc.
Frequency instability or variations of the desired output frequency may be caused by variations in the external circuit elements or by device characteristics.
In transistor oscillators such as a Hartley oscillator or Colpitts oscillators, the frequency of oscillations is not stable during long time operation.
This is because the capacitance existing at the base-collector junction in reverse biased condition is dominated at high frequencies and hence it affects the capacitor in tank circuit.
Also, due to change in temperature, the values of frequency dominating components like transistor, inductor, resistor, and capacitor also changes.

57. The variation of the frequency with temperature is given by
S wo T = (Δw / wr) (ΔT / Tr)
Where wr and Tr are the desired frequency and the operating temperature respectively. Δw and ΔT are change in frequency and change in temperature respectively.
The frequency stability can be given as
Sw = dθ/dw
A small frequency change in a desired frequency introduces the phase shift which is indicated as dθ.
Hence the oscillator will be more stable if the circuit gives a larger value of dθ/dw.
The frequency stability can be improved by enclosing the oscillator circuit in a constant temperature chamber and by using zener diodes in the circuit to maintain the constant voltage.
A loading effect is reduced by coupling the oscillator circuit to the load loosely, or with the use of a circuit having a low output impedance and a high input impedance.