## RC Oscillator

### Principle of RC Oscillator Or Phase Shift Oscillator

Good frequency stability and waveform can be obtained from oscillators employing resistive and capacitive elements. Such oscillators are called R-C or phase shift oscillators.

These oscillators have additional advantage of being used at a very low frequencies.

In a phase shift oscillator, a phase shift of 180^{0 }is obtained with a phase shift circuit instead of inductive or capacitive coupling.

A further phase shift of 180^{0 }is introduced due to the transistor properties. Thus energy supplied back to the tank circuit is of correct phase.

**Phase shift Circuit:**

A phase shift circuit consists of an R-C network. Fig.1 (i) shows a single section of RC network.

Fig.1 (i)

As we know the alternating voltage V’_{1} across R leads the applied voltage V_{1 }by Φ^{0}. The value of Φ depends upon the value of R and C. If resistance R is varied, the value of Φ also changes.

If R were reduced to zero, V’_{1 }will lead V_{1 }by 90^{0 }i.e Φ=90^{0}.

However, adjusting R to zero would be impracticable because it would lead to no voltage across R. Therefore, in practice, R is varied to such a value that makes V’_{1} to lead V_{1} by 60^{0} .

Fig.1 (ii) shows the three sections of RC network. Each section produces a phase shift of 60^{0}. Consequently, a total phase shift of 180^{0 }is produced.

Fig.1 (ii)

### Phase shift Oscillator

Fig.2 shows the circuit of a phase shift oscillator.

Fig.2

It consists of a conventional single transistor amplifier and a RC phase shift network.

The phase shift network consists of three sections of R_{1}C_{1} , R_{2}C_{2 }and R_{3}C_{3}.

At some particular frequency f_{0}, the phase shift in each RC section is 60^{0 }so that the total phase shift produced by the RC network is 180^{0}.

The frequency of oscillation is given by:

Where,

#### Circuit Operation:

When the circuit is switched on, it produces oscillations of frequency determined by exp.(i) .

The output E_{0 }of the amplifier is fed back to RC feedback network. This network produces a phase shift of 180^{0} and a voltage E_{i }appears at its output which is applied to the transistor amplifier.

The feedback fraction m =E_{i }/ E_{0}.

The phase shift of 180^{0 }is produced by the transistor amplifier and a further phase shift of 180^{0 }is produced by the RC network. As a result, the phase shift around the entire loop is 360^{0}.

#### Advantages

- It does not require transformers or inductors.
- It can be used to produce very low frequencies.
- The circuit provides good frequency stability.

#### Disadvantages

- It is difficult for the circuit to start oscillations as the feedback is generally small.
- The circuit gives small output.

## Wien Bridge Oscillator

The wien-bridge oscillator is the standard oscillator circuit for all frequencies in the range of 10 Hz to about 1 MHz.

It is the most widely frequently used type of audio oscillator as the output is free from circuit fluctuations and ambient temperature.

Fig.3 shows the circuit of a wien-bridge oscillator.

Fig.3

It is essentially a two stage amplifier with R-C bridge circuit.

The bridge circuit has the arms R_{1}C_{1} , R_{3}, R_{2}C_{2} and tungsten lamp L_{p}.

Resistances R_{3 }and L_{p }are used to stabilise the amplitude of the output.

The transistor T_{1 }serves as an oscillator and amplifier while the other transistor T_{2 }serves as an inverter to produce 180^{0} phase shift.

The circuit uses positive and negative feedback. The positive feedback is through R_{1}C_{1} , C_{2}R_{2}_{ }to the transistor T_{1}. The negative feedback is through the voltage divider to the input of transistor T_{2}.

The frequency of oscillation is determined by the series element R_{1}C_{1} and parallel element C_{2}R_{2 }of the bridge.

If ,

and

then,

#### Circuit Action

When the circuit is started, bridge circuit produces oscillations of frequency determined by exp.(i).

The two transistors produce a total phase shift of 360^{0 }so that proper positive feedback is ensured.

The negative feedback in the circuit ensures constant output. This is achieved by the temperature sensitive tungsten lamp L_{p}. Its resistance increases with current. So when the amplitude of the output tend to increase, more current would provide more negative feedback. The result is that the output would return to original value. A reverse action would take place if the output tends to decrease.

### Advantages of Wien Bridge Oscillator

- It gives constant output.
- The circuit works quite easily.
- The overall gain is high because of two transistors.
- The frequency of oscillations can be easily changed by using potentiometer.

### Disadvantages of Wien Bridge Oscillator

- The circuit requires two transistors and a large number of components.
- It can not generate very high frequencies

## Quartz Crystal Oscillator

Quartz crystals are generally used in crystal oscillators because of their great mechanical strength and simplicity in manufacture.

The natural frequency *f *of a crystal is given by:

Where *K* = a constant that depends upon the cut

*t* = the thickness of the crystal

In order to use crystal in an electronic circuit, it is placed between two metal plates. The arrangement then forms a capacitor with crystal as the dielectric as shown in fig.4.

Fig.4

If an a.c. voltage is applied across the plates, the crystal will start vibrating at the frequency of applied voltage.

However, if the frequency of the applied voltage is made equal to the natural frequency of the crystal , resonance takes place and crystal vibration reach a maximum value. This natural frequency is almost constant.

### Equivalent Circuit of Crystal Oscillator

When the crystal is not vibrating, it is equivalent to capacitance C_{m}_{ }because it has two metal plates separated by a dielectric as shown in fig.5(i). This capacitance is known as mounting capacitance.

Fig.5 (i) Fig.5 (ii)

When a crystal vibrates, it is equivalent to R-L-C- series circuit.

Therefore, the equivalent circuit of a vibrating crystal is R-L-C series circuit shunted by the mounting capacitance C_{m }as shown in fig.5 (ii).

## Transistor Crystal Oscillator

Fig.6 shows the transistor crystal oscillator.

Fig.6

It is a Collpit’s oscillator modified to act as a crystal oscillator. Th only change is the addition of the crystal (Y) in the feedback network.

The crystal will act as a parallel-tuned circuit.

As we can see in this circuit that instead of resonance caused by L and (C_{1}+C_{2}), we have the parallel resonance of the crystal.

At parallel resonance, the impedance of the crystal is maximum. This means that there is a maximum voltage drop across C_{1}. This in turn will allow the maximum energy transfer through the feedback network at the parallel resonant frequency *f*_{p }which is given by:

Where,

Note that feedback is positive. A phase shift of is produced by the transistor. A further phase shift of is produced by the capacitor voltage divider.

This oscillator will oscillate only at *f _{p}* . Even a small deviation from

*f*will cause the oscillator to act as an effective short. Consequently, we have an extremely stable oscillator.

_{p }### Advantages of Crystal Oscillator

- They have a high order of frequency stability.
- The quality factor (Q) of the crystal is very high. The Q factor of the crystal may be as high as 10,000 compared to about 100 of L-C tank.

### Disadvantages of Crystal Oscillator

- They are fragile and consequently can only be used in low power circuit.
- The frequency of oscillations can not be changed appreciably.