Conditions of Oscillator- Barkhausen Criterion

The phase shift around the feedback loop must be effectively 0°.

The voltage gain, Acl, around the closed feedback loop (loop gain) must equal 1 (unity).

Feedback oscillator operation is based on the principle of positive feedback.

>Positive feedback

: the condition wherein a portion of the output voltage an amplifier is feed back to the input with no net phase shift, resulting in a reinforcement of the output signal.

>The

in phase

feedback voltage, Vf is amplified to produce the output voltage, which in turn produces the feedback voltage.

That is, a loop is created in which the signal sustains itself and a continuous sinusoidal output is produced.

>If the feedback circuit returns the signal

out of phase

and an inverting amplifier is required to provide another 180° phase shift so that there is no net phase shift.

Learning Outcome

Describe the operating principles of an oscillator

Discuss feedback oscillators

Briefly describe a relaxation oscillator

Describe and analyze the operation of RC feedback oscillators

Wien-Bridge oscillator

Phase Shift oscillator

TWO CLASSIFICATIONS OF OSCILLATOR

RC feedback is used in various lower frequency sine-wave oscillators. This notes covers three: the Wien-bridge oscillator, the phase-shift oscillator, and the twin-T oscillator.

Oscillators with RC Feedback circuits

**Oscillator - Chapter 4**

What is oscillator?????

definition : move or swing back and forth in a regular rhythm

in term of electronic: a circuit that 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

Relaxation Oscillator

Feedback Oscillator

Feedback Oscillator

Basic element of feedback oscillator

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

After oscillations are started, the loop gain is maintained at 1.0 to maintain oscillations.

Returns a fraction of the output signal to the input with no net phase shift, resulting in a reinforcement of the output signal.

Feedback Oscillator

Computer simulations, such as Multisim, use digital signals, which do not have thermal noise. This often creates a problem for computer simulations of oscillators.

Wien-Bridge Oscillator

The feedback circuit in a Wien-bridge uses a lead-lag circuit. When the R’s and C’s have equal values, the output will be ⅓ of the input at only one frequency and the phase shift at this frequency will be 0 degree.

The basic Wien-bridge uses the lead-lag network to select a specific frequency that is amplified. The voltage-divider sets the gain to make up for the attenuation of the feedback network

The non-inverting amplifier must have a gain of exactly 3.0 as set by R1 and R2 to make up for the attenuation. If it is too little, oscillations will not occur; if it is too much the sine wave will be clipped.

To produce the precise gain required, the Wien bridge needs some form of automatic gain control (AGC). One popular method is shown here and uses a JFET transistor.

The key elements of the AGC circuit are highlighted in yellow. The diode charges C3 to the negative peak of the signal. This develops the gate bias voltage for the JFET that is related to the output level

example 1

example 1 -solution

The circuit is redrawn in Figure 16–7(b) to show that the op-amp is connected across

the bridge circuit. One leg of the bridge is the lead-lag circuit, and the other is the voltage

divider.

RC Phase Shift Oscillator

The phase-shift oscillator uses three RC circuits in the feedback path that have a total phase shift of 180 degree at one frequency – for this reason an inverting amplifier is required for this circuit.

Even with identical R’s and C’s, the phase shift in each RC circuit is slightly different because of loading effects. When all R’s and C’s are equal, the feedback attenuates the signal by a factor of 29, B = 1/29

fo = 1

[2πRC√2(N)]

N = Number of RC stages

Multisim can simulate the phase-shift oscillator, but has difficulty starting. In the Multisim file for Example given, a switch is provided to provide a voltage spike to start oscillations. This is not needed in the actual circuit.

Design a phase-shift oscillator for a frequency of 800 Hz. The capacitors are to be 10 nF.

example

Solution

Because the Rf is not precise, you will see the output “grow” in Multisim. In actual circuits, you can use a potentiometer to adjust a precise gain, but the circuit will be sensitive to temperature change.

You can also use back-to back zener diodes to limit the output. The output is limited to about 7 Vpp with 1N4372A (3.0 V) zeners.

Section checkup!

1.There are two feedback loops in the Wien-bridge oscillator. What is the purpose of each?

2. A certain lead-lag circuit has R1= R2 and C1 = C2. An input voltage of 5 V rms is applied.The input frequency equals the resonant frequency of the circuit. What is the rms output voltage?

3.Why is the phase shift through the RC feedback circuit in a phase-shift oscillator 180°?

Will be question on next class. Prepare the answer!

Section Checkup

1. What is an oscillator?

2. What type of feedback does a feedback oscillator require?

3. What is the purpose of the feedback circuit?

4. Name the two types of oscillators.

5. What are the conditions required for a circuit to oscillate?

6. Define positive feedback.

Answer in 10 min!

Pop Quiz

how many poles does a second order LPF have? How many resistors and capacitors are used in the frequency-selective circuit?

Why is the damping factor of a filter important?

What is the primary purpose of cascading LPF?

how many region in actual response graph?

what is roll-off rate?

how to determine the no of pole?no of order? are they the same thing?

how to limit the frequency above the fc of high pass filter?

what is the differences between passive and active filter?

Answer in 10 mins.

A = 1/B = 1/(1/29)

= 29 = Rf/Rs

Rf = 29Rs