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Oscillators 2. LC Oscillators

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**Oscillators Oscillators With LC Feedback Circuits**

For frequencies above 1 MHz, LC feedback oscillators are used. We will discuss the Colpitts, Hartley and crystal-controlled oscillators. Transistors are used as the active device in these types.

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Oscillators Oscillators With LC Feedback Circuits

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**Oscillators – Colpitts**

The Colpitts oscillator utilizes a tank circuit (LC) in the feedback loop as shown in the figure.

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**Oscillators – Colpitts**

LC feedback oscillators use resonant circuits in the feedback path. A popular LC oscillator is the Colpitts oscillator. It uses two series capacitors in the resonant circuit. The feedback voltage is developed across C1. The effect is that the tank circuit is “tapped”. Usually C1 is the larger capacitor because it develops the smaller voltage.

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Oscillators Oscillators With LC Feedback Circuits If ZT = 0; Colpitts

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**Oscillators – Colpitts**

Total capacitance (CT ) is ; The resonant frequency can be determined by the formula below.

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**Oscillators – Colpitts**

Conditions for oscillation and start up

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**Oscillators – Colpitts**

If Q > 10, this formula gives good results. Recall that the total capacitance of two series capacitors is the product-over-sum of the individual capacitors. Therefore, For Q < 10, a correction for Q is

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Oscillators – Hartley The Hartley oscillator is similar to the Colpitts. The tank circuit has two inductors and one capacitor

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Oscillators – Hartley The Hartley oscillator is similar to the Colpitts oscillator, except the resonant circuit consists of two series inductors (or a single tapped inductor) and a parallel capacitor. The frequency for Q > 10 is One advantage of a Hartley oscillator is that it can be tuned by using a variable capacitor in the resonant circuit.

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Oscillators Oscillators With LC Feedback Circuits If ZT = 0; Hartley

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Oscillators – Hartley The calculation of the resonant frequency is the same.

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Oscillators – Crystal The crystal-controlled oscillator is the most stable and accurate of all oscillators. A crystal has a natural frequency of resonance. Quartz material can be cut or shaped to have a certain frequency.

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Oscillators – Crystal Since crystal has natural resonant frequencies of 20 MHz or less, generation of higher frequencies is attained by operating the crystal in what is called the overtone mode

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Oscillators 3. Relaxation Oscillators

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**Oscillators – Relaxation**

Relaxation oscillators make use of an RC timing and a device that changes states to generate a periodic waveform (non-sinusoidal). 1. Triangular-wave 2. Square-wave 3. Sawtooth

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**Oscillators – Relaxation**

Triangular-wave oscillator Triangular-wave oscillator circuit is a combination of a comparator and integrator circuit. A square wave can be taken as an output here.

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**Oscillators – Relaxation**

Triangular-wave oscillator

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**Oscillators – Relaxation**

Triangular-wave oscillator

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**Oscillators – Relaxation**

For the triangular wave generator, the frequency is found from: Example: What is the frequency of the circuit shown here? Solution: 10 nF 82 kW 22 kW = 671 Hz 10 kW

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**Oscillators – Relaxation**

Normally, the triangle wave generator uses fast comparators to avoid slew rate problems. For non-critical applications, a 741 will work nicely for low frequencies (<2 kHz). The circuit here is one you can construct easily in lab. (The circuit is the same as Example 16-4 but with a larger C.) The waveforms are: Both channels: 5 V/div 250 ms/div

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**Oscillators – Square-wave**

A square wave relaxation oscillator is like the Schmitt trigger or Comparator circuit. The charging and discharging of the capacitor cause the op-amp to switch states rapidly and produce a square wave. The RC time constant determines the frequency.

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**Oscillators – Square-wave**

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**Oscillators – Square-wave**

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**Oscillators – Sawtooth voltage controlled oscillator (VCO)**

Sawtooth VCO circuit is a combination of a Programmable Unijunction Transistor (PUT) and integrator circuit.

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**Oscillators – Sawtooth VCO**

OPERATION Initially, dc input = VIN Vout = 0V, Vanode < VG The circuit is like an integrator. Capacitor is charging. Output is increasing positive going ramp.

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**Oscillators – Sawtooth VCO**

OPERATION

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**Oscillators – Sawtooth VCO**

OPERATION When Vout = VP Vanode > VG , PUT turns ‘ON’ The capacitor rapidly discharges. Vout drop until Vout = VF. Vanode < VG , PUT turns ‘OFF’ VP – maximum peak value VF – minimum peak value

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**Oscillators – Sawtooth VCO**

OPERATION Oscillation frequency

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**Oscillators – Sawtooth VCO**

EXAMPLE In the following circuit, let VF = 1V. a) Find; (i) amplitude; (ii) frequency; b) Sketch the output waveform

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**Oscillators – Sawtooth VCO**

EXAMPLE (cont’d)

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**Oscillators – Sawtooth VCO**

EXAMPLE – Solution a) (i) Amplitude and So, the peak-to-peak amplitude is;

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**Oscillators – Sawtooth VCO**

EXAMPLE – Solution a) (ii) Frequency

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**Oscillators – Sawtooth VCO**

EXAMPLE – Solution a) (ii) Frequency

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**Oscillators – Sawtooth VCO**

EXAMPLE – Solution b) Output waveform

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Oscillators The 555 timer as an oscillator

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**Oscillators The 555 Timer As An Oscillator**

The 555 timer is an integrated circuit that can be used in many applications. The frequency of output is determined by the external components R1, R2, and C. The formula below shows the relationship.

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**Oscillators The 555 Timer As An Oscillator**

Duty cycles can be adjusted by values of R1 and R2. The duty cycle is limited to 50% with this arrangement. To have duty cycles less than 50%, a diode is placed across R2. The two formulas show the relationship; Duty Cycle > 50 %

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Oscillators The 555 Timer As An Oscillator Duty Cycle < 50 %

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Oscillators The 555 Timer As An Oscillator

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**Oscillators The 555 Timer As An Oscillator**

The 555 timer may be operated as a VCO with a control voltage applied to the CONT input (pin 5).

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Oscillators Summary Sinusoidal oscillators operate with positive feedback. Two conditions for oscillation are 0º feedback phase shift and feedback loop gain of 1. The initial startup requires the gain to be momentarily greater than 1. RC oscillators include the Wien-bridge, phase shift, and twin-T. LC oscillators include the Colpitts, Clapp, Hartley, Armstrong, and crystal.

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**Oscillators Summary (cont’d)**

The crystal actually uses a crystal as the LC tank circuit and is very stable and accurate. A voltage controlled oscillator’s (VCO) frequency is controlled by a dc control voltage. A 555 timer is a versatile integrated circuit that can be used as a square wave oscillator or pulse generator.

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END CHAPTER 5

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