Oscillators Study Notes for GATE & Other Electrical Engineering Exams

Oscillators

• Oscillators generate AC output without any external AC input by using noise AC signal generated in switching.
• DC power from V_CC or V_DD is converted to AC power.
• The range of frequency signals generated by the circuit can be high and output power will be small.

Bakhausen Criterion

• For sustained oscillations, the conditions known as Barkhausen criterion to be satisfied are as given

|K A_V|≥1

• Total loop phase shift must be 0^o or 360^oC or phase shift of feedback network must be 180^o when the amplifying device produces another 180^o.
• The introduction of positive feedback in the amplifier causes an increase in the voltage gain. If the loop gain, |K A_V|≥1, the Barkhausen criterion for oscillation is satisfied and an output remains after the input is removed.

For linear oscillations, in which the output is sinusoidal with small distortion, the loop gain (K A_V ) should only be slightly greater than unity.

Phase-shift Oscillator

A phase-shift oscillator relies upon the R-C phase shift circuit for providing the necessary phase relationship between output. The frequency of oscillation is given by:

For the loop gain (βA) to be greater than unity, the gain of the amplifier stage will be greater than 1/β or 29.

A > 29

FET Phase-shift Oscillator

|A| = g_mR_L

Where R_L, in this case, is parallel to the resistance of R_D and r_d.

Transistor Phase Shift Oscillator

At low frequencies (somewhere 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_C network produces and addition 180^o phase shift.

For the loop gain to be greater than unity, the requirement on the current gain of the transistor is found to be

IC Phase Shift Oscillator

Wien Bridge Oscillator

• A Wien bridge oscillator uses a frequency selective bridge circuit to provide low distortion sinusoidal oscillation.
• Neglecting the loading effect of the operational Amplifier input and output impedances, the analysis of the bridge circuit results as

• If, in particular, the values are R₁ = R₂ = R and C₁ = C₂ = C, the resulting oscillator frequency will be

• Therefore, a ratio of R₃ to R₄ greater than 2 will provide sufficient loop gain for the circuit to oscillate at the frequency calculated using:

Wien Bridge Oscillator

• For Wien bridge oscillator network, the minimum gain of the amplifier must be 3.
• The oscillator can produce variations in f₀ in the ratio of 10: 1 compared to a variation of 3: 1 in other types of oscillator circuits.

Tuned Oscillator Circuit

• Tuned-Input, Tuned-Output Oscillator Circuits
• A variety of networks can be built by providing tuning in both the input and output sections of the circuit.

Colpitts Oscillator

• The Colpitts oscillator is an example of a resonant network oscillator that is characterized by a split capacitor in its tank circuit.
• For Colpitts oscillator circuits with two capacitors and one inductor in the feedback network,

Hartley Oscillator

• The Hartley oscillators have a tapped coil in its tank network. As in the Colpitts oscillator, the Hartley is also used to generate RF (Radio Frequencies), and both have a frequency given by

• A thermistor with (NTCR) and sensistor with Positive Temperature Coefficient of Resistance (PTCR) are used for frequency stability in oscillator circuits.

The specification parameters of oscillator circuits are

• Amplitude stability
• Frequency stability
• Frequency range
• Distortion in output waveform etc.

Astable Multivibrator

• An astable multivibrator is an example for a square wave Relaxation Oscillator. The collector of each of the two transistors in which is capacitively coupled to the other’s base.
• The period of oscillation of a symmetrical multivibrator depends upon the discharging times constant and is given by

where R in Ohms, and C in Farads.

• To ensure saturation:

Crystal Oscillator

Crystal oscillator produces very highly stable output waveform in the high-frequency range of MHz. The maximum frequency of oscillation of a transistor f_max is dependent upon the transistors f_T as shown by the following relation in the given equation:

Undesired oscillation may occur in cascaded amplifier stages that operate from the same power supply by signals feedback along the power supply leads to earlier stages. The problem is usually overcome by RC decoupling filters that can reduce the amount of feedback.

Key Points

• The transistor may be used as a switch so that when it is in the saturated state its on-resistance is very low or in the cut-off state its off resistance is very high.
• When a transistor is switched on and off, its total high turn-on T_on = t_d+t_r time and its turn-off time, T_off = t_s+t_f where these times are due to capacitive delays in the transistor.

Harmonic Oscillator

• One feedback type harmonic oscillator circuit is shown in the following figure.

• The DC equivalent circuit also is shown in the figure.
• The DC operating point can be set by selecting V_CC, R_B and R_E
• The AC equivalent circuit is also shown in the below figure.

• The load is in parallel with capacitor C₂ and the transformer.
• If the load is resistive, generally it is, the Q of the tuned circuit and the loop gain are both affected, this must be taken into account when determining the minimum gain required for oscillation.
• If the load has a capacitive component, then the value of C₂ should be reduced in the same manner.

The detailed introduction and the study notes on the Oscillator are important for the GATE EE, SSC JE EE, ESE IES EE, ISRO EE, and other electrical engineering exam preparation.

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