#### RC Oscillators, Physics tutorial

RC Oscillators:

An example of oscillator circuit which follows basic development of feedback circuit is RC or phase shift oscillator. The requirements for oscillation are that loop gain, βA, is greater than unity and that phase shift around the feedback network is 1800 (providing positive feedback).

Phase Shift Principle:

LC or Tuned circuits are not necessary requirement for oscillation. There must be a 180° phase shift around feedback network (Total phase shift required is 360°. Though, balance of 180° is provided by active device of amplifier itself) and loop gain must be greater than unity. 180° phase shift in feedback signal can be attained by using suitable R-C network consisting of three or four R-C sections. Sine wave oscillators that use R-C feedback network are known as phase-shift oscillators.

RC or Phase Shift Oscillator:

Transistor phase-shift oscillator that uses three- section RC feedback network for producing total phase shift of 180° (i.e. 60° per section) in signal fed back to base. As CE amplifier produces phase reversal of input signal, total phase shift becomes 360° or 0° that is necessary for regeneration and therefore for sustained oscillations.

Values of R and C are so selected that each RC section generates phase advance of 60°. Addition of fourth section improves oscillator stability. It is found that phase shift of 180° takes place only at one frequency that becomes oscillator frequency.

Circuit Action:

Circuit is set into oscillations by any random or chance variation caused in base current by noise inherent in transistor or minor variation in voltage of dc source. This variation in base current

• is amplified in collector circuit
• is then fed back to RC network R1C2, R2C2 and R3C3
• is reversed in phase by RC network
• is next applied to base in phase with initial change in base current
• And therefore is utilized to sustain cycles of variations in collector current between saturation and cut-off values.

Obviously, circuit will stop oscillating moment phase shift differs from 180°. As is case with such transistor circuits

(i) voltage divider R5 - R5 provides dc emitter-base bias,

(ii) R6 controls collector voltage and

(iii) R4, C4 give temperature stability and prevent ac signal degeneration. Oscillator output voltage is capacitively coupled to load by C3.

Frequency of Oscillation:

Frequency of oscillation for three-section RC oscillator when three R and C components are equal is roughly given by

f0 = 1/2π√6.RC Hz = 0.065/RC HZ

1. As they don't need any bulky and expensive high-value inductors, such oscillators are well-suited for frequencies below 10 kHZ.

As only one frequency can fulfill Barkhausen phase-shift requirement, positive feedback takes place only for one frequency. Therefore, pure sine wave output is possible. It is not suited to variable frequency procedure since a large number of capacitors will have to be varied. Moreover, gain adjustment would be essential every time frequency change is made. It produces distortion level of nearly 5% in output signal. It necessitates use of high β transistor to overcome losses in network.

Wien Bridge Oscillator:

It is low-frequency (5Hz - 500 kHz), low-distortion, tunable, high- purity sine wave generator, frequently utilized in laboratory work. This oscillator utilizes two - connected RC coupled transistor amplifiers and one RC-bridge (known as Wien Bridge) network to give feedback. Here, Q1 acts as amplifier- oscillator and Q2 gives phase reversal and additional amplification. Bridge circuit is utilized to control phase of feedback signal at Q1.

Phase Shift Principle:

Any input signal at base of Q1 appears in amplified but phase- reversed form across collector resistor R6. It is further inverted by Q2 to give total phase reversal of 360° for positive feedback. Obviously, signal at R10 is amplified replica of input signal at Q1 and is of same phase as it has been inverted twice. We could feed this signal back to base of Q1 directly to give regeneration required for oscillator operation. But because Q1 will amplify signals over wide range of frequencies, direct coupling would result in poor frequency stability. By adding Wien bridge, oscillator becomes sensitive to the signal of only one particular frequency. Therefore, we get oscillator of good frequency stability.

Bridge Circuit Principle:

It is found that Wien bridge would become balanced at signal frequency for which phase shift is exactly 0° (or 360o),

Balance conditions are

R4/R3 = R1/R2 + C2/C1 and ωo = 1/√R1C1R2C2 or fo = 1/2π√R1C1R2C2

If R1 = R2 = R and C1 = C2 = C then f0 = 1/2πRc and R4/R3 = 2

Circuit Action:

Any random change in base current of Q1 can start oscillations. Assume, base current of Q1 is increased because of some reason; it is equivalent to applying the positive going signal to Q1. Following sequence of events will occur:

1. Amplified but phase-reversed signal will appear at collector of Q1.

2. Still further amplified and twice phase-reversed signal will appear at collector of Q2. Having been inverted twice, this output signal will be in phase with input signal at Q1;

3. Part of output signal at Q2 is fed back to input points of bridge circuit (point A-C). A part of this feedback signal is applied to emitter resistor R3 where it generates degenerative effect. Likewise, a part of feedback signal is applied across base-bias resistor R2 where it generates regenerative effect.

At rated frequency f0, effect of regeneration is made slightly more than that of degeneration to maintain continuous oscillations. By replacing R3 with a thermistor, amplitude stability of oscillator output voltage can be increased.

1. Highly stabilized amplitude and voltage amplification,

2. Exceedingly good sine wave output,

3. Good frequency stability.

Non-Sinusoidal Waveforms:

Any waveform whose shape is different from that of standard sine wave is known as non-sinusoidal waveform. Examples are: rectangular, square, triangular waveforms, saw-tooth, and pulses

a) Pulses:

A pulse may, in general, be stated as voltage or current which changes rapidly from one level of amplitude to another i.e. it is the abrupt discontinuity in voltage or current. These pulses are widely utilized in digital electronics.

1. Mark-to-Space Ratio (MSR) = Pulse width/ time between pulse = 1µs/4µs = 0.25

Therefore, mark-to-space ratio of the pulse is 1 : 4. This name has come from early Morse-code transmission systems where pulse was used to cause pen to mark paper.

2. Pulse Repetition Time (PRT) It may be stated as time between beginning of one pulse and that of other.

PRT = 5µs

3. Pulse Repetition Frequency (PRF)

It is given by number of pulses per second.

PRT = 1/PRT = 1/5µs = 106/5 = 200,000Hz = 200Hz

Pulse circuits find applications in almost all electronic- based industries. Different kinds of pulse code modulations are used in communication systems while radars use pulses to track targets. Digital computers need circuits which can be switched very rapidly between two states by using suitable pulses.

b) Square Wave:

A pulse waveform with mark-to-space ratio of 1:1. Such square waves or pulses are utilized:

1. For audio frequency note generation

2. For digital electronic switching as in computers

4. As synchronizing pulses in TV

5. For switching of high-power electronic circuits like thyristor circuits.

c) Saw-tooth Wave:

Such waves are used:

1. In scanning circuits of cathode-ray tubes (CRT),

2. In timing circuits where time for wave to proceed from one level to another is estimated, such as that produced in integrating circuit.

d) Triangular Wave:

Such waves are frequently used in scanning circuits where the uniform left-to-right scan is required as in computer displays, for audio frequency note generation,  in timing circuits for electronic applications.

Multivibrators (MV):

These devices are very helpful as pulse generating, storing and counting circuits. They are essentially two-stage amplifiers with positive feedback from output of one amplifier to input of the other. This feedback is supplied in such a manner that one transistor is driven to saturation and other to cut-off. It is followed by new set of conditions in which saturated transistor is driven to cut-off and cut-off transistor is driven to saturation. There are three basic kinds of MVs distinguished by kind of coupling network used. 1. Astable multivibrator (AVM), 2. Monostable multivibrator (MMV), 3. Bistable multivibrator (BMV).

First one is non-driven type while other two are driven type (also known as triggered oscillators).

Astable Multivibrator (AMV):

It is also known as free-running relaxation oscillator. It has no stable state but only two quasi-stable (half-stable) states between which it keeps oscillating constantly of its own accord without any external excitation.

Multivibrator: In this circuit, neither of the two transistors reaches the stable state. When one is ON, other is OFF and they continuously switch back and forth at the rate depending on RC time constant in circuit. Therefore, it oscillates and produces pulses of certain mark-to-space ratio. Moreover, two outputs (180° out of phase with each other) are available. It has two energy-storing elements i.e. two capacitors.

Monostable Multivibrator (MMV):

It is also known as a single-shot or single swing or one-shot multivibrator. Other names are: delay multivibrator and univibrator. It has: (i) one absolutely stable (stand-by) state and (ii) one quasi-stable state. It can be switched to quasi-stable state by the external trigger pulse but it returns to stable condition after the time delay determined by value of circuit components. It supplies the single output pulse of the desired duration for every input trigger pulse. It has one energy-storing element i.e. one-capacitor.

Bistable Multivibrator (BMV):

It is also known as Eccles-Jordan or flip-flop multivibrator. It has two absolutely stable states. It can remain in either of these two states unless external trigger pulse switches it from one state to other. Obviously, it doesn't oscillate. It has no energy storage element.

Uses of Multivibrators:

• Some of their uses are:
• As frequency dividers.
• As saw tooth generators
• As square wave and pulse generators.
• As a standard frequency source when synchronized by the external crystal oscillator
• For several specialized uses in radar and TV circuits, as memory elements in computers.

Tutorsglobe: A way to secure high grade in your curriculum (Online Tutoring)