**Study Notes on Oscillators**which will cover the topics such as

**Oscillators, Feedback Oscillators, Oscillation with RC Feedback Circuits, Wien Bridge Oscillator, Phase Shift Oscillator, Oscillation with LC Feedback Circuits, Colpitt's oscillator, and Clapp Oscillator.**

**1. Oscillators**

- 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.
- It produces a periodic waveform on its output with only the DC supply voltage as an input.
- Different types of oscillators produce various types of outputs including sine waves, square waves, triangular waves, and sawtooth waves.
The basic structure of a sinusoidal oscillator consists of an amplifier and a frequency-selective network connected in a positive feedback loop as shown in figure 1.

Formulas for GATE Electronics & Communication Engineering - Digital Circuits

In the block diagram of figure 1,

V_{d} = V_{f} + V_{in}

V_{0} = AV_{d}

V_{f} = βV_{0}

Using these relationships, the following equation is obtained:

Equation (i) & (ii) gives two requirements for oscillation:

- The magnitude of the loop gain Aβ must be at least 1, and
- The total phase shift of the loop gain Aβ must be equal to 0° or 360°.

The above conditions is known as the **Barkhausen** criterion.

In figure 1, if the amplifier causes a phase shift of 180°, the feedback circuit must provide an additional phase shift of 180° so that the total phase shift around the loop is 360°. The type of waveform generated by an oscillator depends on the components in the circuit hence may be sinusoidal, square or triangular. In addition, the frequency of oscillation is determined by the components in the feedback circuit.

Formulas for GATE Electronics & Communication Engineering - Electronic Devices

Oscillators can be of 2 types:

**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.

**Relaxation Oscillators:**

- Instead of feedback, a relaxation oscillator uses an RC timing circuit to generate a waveform that is generally a square wave or other non sinusoidal 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.

**2. Oscillation with RC Feedback Circuits**

- Three types of feedback oscillators that use RC circuits to produce sinusoidal outputs are the:
- Wien-bridge oscillator
- Phase-shift oscillator
- Twin-T oscillator

- Generally, RC feedback oscillators are used for frequencies up to about 1 MHz.
- The Wien-bridge is by far the most widely used type of RC feedback oscillator for this range of frequencies.

**3. Wien Bridge Oscillator**

Because of its simplicity and stability, one of the most commonly used audio-frequency oscillators is the wein bridge. Figure 2 shows the wein bridge oscillator in which the wein bridge circuit is connected between the amplifier input terminals and the output terminal. The bridge has a series RC network in one arm and a parallel RC network in adjoining arm. In the remaining two arms of the bridge, resistors R_{1} and R_{2} are connected.

The phase angle criterion for oscillation is that the total phase shift around the circuit must be 0°. This condition occurs only when the bridge is balanced, that is **at resonance. **the frequency of oscillation f_{0} is exactly the resonant frequency of the balanced wein bridge and is given by:

Assuming that the resistors are equal in value, and capacitors are equal in value in the reactive leg of the wein bridge. At this frequency the gain required for sustained oscillation is given by

**4. Phase-shift Oscillator**

- A phase-shift oscillator relies upon an
*R-C*phase shift network to provide the necessary phase relationship between output and input to a CE amplifier. The frequency of oscillation is given by and the phase shift is 180^{o}.

** 4.1** **Phase-shift Oscillator using Op-Amp:**

The op-amp is used in the inverting mode; therefore, any signal that appears at the inverting terminal is shifted by 180° at the output. An additional 180° phase sift required for oscillation is provided by the cascaded RC networks. Thus, the total phase shift around the loop is 360° (or 0°). At some specific frequency when the phase shift of the cascaded RC networks is exactly 180° and the gain of the amplifier is sufficiently large, the circuit will oscillate at the frequency. This frequency is called the frequency of oscillation f_{0} and is given by

- For the loop gain β
*A*to be greater than unity, the gain of the amplifier stage must be greater than 1/β or 29.

*A* > 29

**4.2 Phase-shift Oscillator using FET:**

Here an FET amplifier of conventional design is followed by three cascaded arrangements of a capacitor C and a resistor R, the output of the last RC combination being returned to the gate. If the loading of the phase-shift network on the amplifier can be neglected, the amplifier shifts by 180° the phase of any voltage which appears on the gate, and the network of resistors and capacitors shifts the phase by an additional amount. At some frequency the phase-shift introduced by the RC network will be precisely 180° and at this frequency the total phase-shift from the gate around the circuit and back to the gate will be exactly zero. This particular frequency will be the one at which the circuit will oscillate, provided that the magnitude of the amplification is sufficiently large.

The frequency of oscillation for this circuit is given by

In order that |βA| shall not be less than unity, it is required that |A| be at least 29. Hence and FET with μ < 29 cannot be made to oscillate in such a circuit.

**4.3 Phase Shift Oscillator using Transistor:**

- At low frequencies (around 100 kHz or less), resistors and capacitors are usually employed to determine the frequency of oscillation, if the phase shift through the common-emitter amplifier is 180
^{o}, then the oscillation may occur at the frequency, where the*R*network produces and addition 180_{C}^{o}phase shift.

The frequency of oscillation is given by

Where, K = R_{C}/R. The condition for sustaining of oscillation is given by

**(Note: **The value of K which gives the minimum h_{fe} turns out to be 2.7 and for this optimum value of R_{C}/R, we find h_{fe} = 44.5.**)**

**5. Oscillators with LC Feedback Circuits**

- Although the RC feedback oscillators, particularly the Wien bridge, are generally suitable for frequencies up to about 1 MHz, LC feedback elements are normally used in oscillators that require higher frequencies of oscillation.
- Also, because of the frequency limitation (lower unity-gain frequency) of most op-amps, transistors (BJT or FET) are often used as the gain element in LC oscillators.
- This section introduces several types of resonant LC feedback oscillators like the Colpitts, Clapp, Hartley & crystal-controlled oscillators.

### 6. The Colpitts Oscillator

- 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.

- The approximate frequency of oscillation is the resonant frequency of the LC circuit and is established by the values of C
_{1}, C_{2}and L, and according to the formula:

- Where C
_{T}is the total capacitance. Because the capacitors effectively appear in series around the tank circuit, the total capacitance C_{T}is

**Drawback of Colpitts oscillator**

f_{0} is unstable due to the effect of internal capacitances.

net input capacitance C_{i} appears in parallel with C_{1} and net output capacitance C_{0} appears in parallel with C_{2}. As a result.

Since, C_{i} and C_{0} vary with time and temperature, f_{0} becomes unstable. To eliminate this drawback an additional capacitance C_{3} can be connected in series with inductor. Such circuit is called clapp oscillator.

**7. The Clapp Oscillator**

- The Clapp oscillator is a variation of the Colpitts. The basic difference is an additional capacitor, C
_{3}in series with the inductor in the resonant feedback circuit. - Since C
_{3 }is in series with C_{1}and C_{2}around the tank circuit, the total capacitance is

- and the approximate frequency of oscillation is

- If C
_{3 }is much smaller than C_{1 }and C_{2}then C_{3 }almost entirely controls the resonant frequency - Clapp provides a more accurate and stable frequency of oscillation

Frequency of oscillation

If C_{3} is selected such that it is much smaller than then

f_{0} becomes independent of C_{1} and C_{2}.

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