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CHAPTER 5 - OSCILLATORS

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**Oscillators Objectives Describe the basic concept of an oscillator**

Discuss the basic principles of operation of an oscillator Analyze the operation of RC, LC and crystal oscillators Describe the operation of the basic relaxation oscillator circuits

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**Oscillators Introduction**

An oscillator is a circuit that produces a periodic waveform on its output with only the dc supply voltage as an input. A repetitive input signal is not required except to synchronize oscillations in some applications The output voltage can be sinusoidal or nonsinusoidal, depending on the type of oscillator.

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Oscillators

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Oscillators Two major classifications for oscillators are feedback oscillators and relaxation oscillators. The feedback oscillator returns a fraction of the output signal to the input with no net phase shift, resulting in a reinforcement of the output signal. The relaxation oscillator makes use of an RC timing circuit to generate a waveform that is generally square wave or other nonsinusoidal waveform.

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Oscillators Feedback Oscillators

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**Feedback Oscillators Positive feedback:**

is characterized by the condition wherein the portion of the output voltage of an amplifier is fed to the input with no net phase shift, resulting in a reinforcement of the output signal. This is called “oscillation”. If the feedback circuit returns the signal out of phase, an inverting amplifier produces positive feedback.

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**Feedback Oscillators Conditions for oscillation:**

1. The phase shift around the feedback loop must be 0°. 2. The voltage gain ACL, around the closed feedback loop (loop gain) must equal to 1 (unity).

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**Feedback Oscillators Start-Up Conditions:**

When oscillation starts at t0, the condition ACL > 1 causes the sinusoidal output voltage amplitude to build up to a desired level. Then ACL decreases to 1 and maintains the desired amplitude.

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**Oscillators with RC Feedback Circuits**

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RC Feedback Circuits Three types of feedback oscillators that use RC circuits to produce sinusoidal outputs are: Wien-bridge oscillator – most widely used type Phase-shift oscillator Twin-T oscillator

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**The Wien-Bridge Oscillator**

RC Oscillators – Wien–bridge oscillator The Wien-Bridge Oscillator Wien-Bridge Oscillator is a lead-lag circuit. R1 and C1 form the lag portion and R2 and C2 form the lead portion At lower frequencies, the lead circuit dominates due to the high reactance of C2. As the frequencies increases, XC2 decreases, thus allowing the output voltage to increase.

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**RC Oscillators – Wien-bridge**

The lead-lag circuit of a Wien-bridge oscillator reduces the input signal by 1/3 and yields a response curve as shown. The resonant frequency can be determined by the formula below. Below fr, the lead circuit dominates and the output leads the input. Above fr, the lag circuit dominates and the output lags the input.

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**RC Oscillators – Wien-bridge**

It is a low frequency oscillator which ranges from a few kHz to 1 MHz. Structure of this oscillator is shown below; Voltage-divider Lead-lag network

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**RC Oscillators – Wien-bridge**

The lead-lag circuit is in the positive feedback loop of Wien-bridge oscillator. The voltage divider limits the gain. The lead lag circuit is basically a band-pass with a narrow bandwidth.

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**RC Oscillators – Wien-bridge**

Since there is a loss of about 1/3 of the signal in the positive feedback loop, the voltage-divider ratio must be adjusted such that a positive feedback loop gain of 1 is produced. This requires a closed-loop gain of 3. The ratio of R1 and R2 can be set to achieve this.

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**RC Oscillators – Wien-bridge**

To start the oscillations an initial loop gain greater than 1 must be achieved.

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**RC Oscillators – Wien-bridge oscillator using back-to-back zener diode**

The back-to-back zener diode arrangement is one way of achieving this.

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**RC Oscillators – Wien-bridge**

When dc is first applied the zeners appear as opens. This allows the slight amount of positive feedback from turn on noise to pass. The lead-lag circuit narrows the feedback to allow just the desired frequency of these turn transients to pass. The higher gain allows reinforcement until the breakover voltage for the zeners is reached.

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**RC Oscillators – Wien-bridge oscillator using a JFET negative feedback loop**

Automatic gain control is necessary to maintain a gain of exact unity. The zener arrangement for gain control is simple but produces distortion because of the nonlinearity of zener diodes. A JFET in the negative feedback loop can be used to precisely control the gain. After the initial startup and the output signal increases, the JFET is biased such that the negative feedback keeps the gain at precisely 1.

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**RC Oscillators – Wien-bridge**

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**RC Oscillators – Wien-bridge**

EXAMPLE What is fr for the Wien bridge shown in figure below? 4.7 nF 10 kW 680 W = 48.9 kHz 680 W 4.7 nF 1.0 kW 10 kW 1.0 mF

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**RC Oscillators – Phase-shift**

The attenuation, B of the three-section RC feedback circuit is: Where,

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**RC Oscillators – Phase-shift**

Each of the three RC circuits in the feedback loop can provide a maximum phase shift approaching 90o. Oscillation occurs at the frequency where the total phase shift through the three RC circuits is 180o. The frequency of oscillation is shown in the following equation: where R1 = R2 = R3 = R and C1 = C2 = C3 = C

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**RC Oscillators – Phase-shift - EXAMPLE**

Determine the value of Rf necessary for the circuit below to operate as an oscillator. (b) Determine the frequency of oscillation Answer: Rf = 290 kOhm, fr = 6.5 kHz

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**RC Oscillators – Twin-T Oscillator**

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**RC Oscillators – Twin-T Oscillator**

Two T-type RC filters used in the feedback loop One of the twin-T filters has a low-pass response, and the other has a high-pass response The combined parallel filters produce a band-stop response with a center frequency equal to frequency of oscillation, fr.

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