OSCILLATORS

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

Oscillators Introduction Oscillators are circuits that produce a continuous signal of some type without the need of an input. These signals serve a variety of purposes. Communications systems, digital systems (including computers), and test equipment make use of oscillators.

Oscillators An oscillator is a circuit that produces a repetitive signal from a dc voltage. The feedback oscillator relies on a positive feedback of the output to maintain the oscillations. The relaxation oscillator makes use of an RC timing circuit to generate a nonsinusoidal signal such as square wave.

Oscillators

Oscillators Types of oscillators 1. RC oscilators 2. LC oscillators - Wien Bridge - Phase Shift 2. LC oscillators - Hartley - Colpitts 3. Relaxation oscilators

Oscillators Basic principles for oscillation An oscillator is an amplifier with positive feedback.

Oscillators

Oscillators The closed loop gaind is;

Oscillators In general A and  are functions of frequency and thus may be written as; is known as loop gain

Oscillators Writing the loop gain becomes; Replacing s with j; and

Oscillators At a specific frequency f0; At this frequency, the closed loop gain; will be infinite, i.e. the circuit will have finite output for zero input signal - oscillation

Oscillators Thus, the condition for sinusoidal oscillation of frequency f0 is; This is known as Barkhausen criterion. The frequency of oscillation is solely determined by the phase characteristic of the feedback loop – the loop oscillates at the frequency for which the phase is zero.

Oscillators The feedback oscillator is widely used for generation of sine wave signals. The positive (in phase) feedback arrangement maintains the oscillations. The feedback gain must be kept to unity to keep the output from distorting.

Oscillators

Oscillators Design Criteria for Oscillators 1. The magnitude of the loop gain must be unity or slightly larger i.e. – Barkhaussen criterion 2. Total phase shift, of the loop gain must be 0° or 360°.

Oscillators Factors determining the frequency of oscillation Oscillators can be classified into many types depending on the feedback components, amplifiers and circuit topologies used. RC components generate a sinusoidal waveform at a few Hz to kHz range. LC components generate a sine wave at frequencies of 100 kHz to 100 MHz. Crystals generate a square or sine wave over a wide range,i.e. about 10 kHz to 30 MHz.

Oscillators 1. RC Oscillators

Oscillators 1. RC Oscillators RC feedback oscillators are generally limited to frequencies of 1 MHz or less. The types of RC oscillators that we will discuss are the Wien-bridge and the phase-shift.

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;

Oscillators – Wien-bridge The loop gain for the oscillator is where; and;

Oscillators – Wien-bridge Hence; Substituting for s;

Oscillators – Wien-bridge For oscillation frequency f0; Since at the frequency of oscillation, T(j) must be real (for zero phase condition), the imaginary component must be zero i.e.;

Oscillators – Wien-bridge Which gives us;

Oscillators – Wien-bridge From the previous equation; the magnitude condition is; or; To ensure oscillation, the ratio R2/R1 must be slightly greater than 2.

Oscillators – Wien-bridge With the ratio; then; K = 3 ensures the loop gain of unity – oscillation. - K > 3 : growing oscillations - K < 3 : decreasing oscillations

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 frequency of resonance can be determined by the formula below.

Oscillators – Wien-bridge

Oscillators – Wien-bridge

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.

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.

Oscillators – Wien-bridge

Oscillators – Wien-bridge To start the oscillations an initial gain greater than 1 must be achieved.

Oscillators – Wien-bridge The back-to-back zener diode arrangement is one way of achieving this.

Oscillators – Wien-bridge

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.

Oscillators – Wien-bridge 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.

Oscillators – Wien-bridge 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.

Oscillators – Wien-bridge

Oscillators – Phase-shift

Oscillators – Phase-shift The phase shift oscillator utilizes three RC circuits to provide 180º phase shift that when coupled with the 180º of the op-amp itself provides the necessary feedback to sustain oscillations. The gain must be at least 29 to maintain the oscillations. The frequency of resonance for the this type is similar to any RC circuit oscillator.

Oscillators – Phase-shift The transfer function of the RC network is

Oscillators – Phase-shift If the gain around the loop equals 1, the circuit oscillates at this frequency. Thus for the oscillations we want, or;

Oscillators – Phase-shift Putting s = j and equating the real parts and imaginary parts, we obtain; (1) (2)

Oscillators – Phase-shift From equation (1); Substituting into equation (2); The gain must be at least 29 to maintain the oscillations

Oscillators – Phase-shift The last R has been incorporated into the summing resistors at the input of the inverting op-amp.

Oscillators – Phase-shift

Oscillators 2. LC Oscillators

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.

Oscillators Oscillators With LC Feedback Circuits Employs BJTs (or FETs) instead of op-amps and are therefore useful at high frequencies. Consider the general BJT circuit:

Oscillators Oscillators With LC Feedback Circuits Using the small signal equivalent circuit this becomes;

Oscillators Oscillators With LC Feedback Circuits (1) Applying KVL around loop (1), and let we will have; or; (1)

Oscillators Oscillators With LC Feedback Circuits (2) Applying KVL around loop (2); (2)

Oscillators Oscillators With LC Feedback Circuits Substituting (2) into (1);

Oscillators Oscillators With LC Feedback Circuits If the Z’s are purely imaginary and hie is real, then; Substituting (3) into the expression

Oscillators Oscillators With LC Feedback Circuits Z2 and Z1 are the same type of component Z3 is the opposite type (-ve). If Z2 and Z1 are inductors, then Z3 is a capacitor and vice versa.

Oscillators Oscillators With LC Feedback Circuits

Oscillators Oscillators With LC Feedback Circuits

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

Oscillators – Colpitts

Oscillators – Colpitts The resonant frequency can be determined by the formula below.

Oscillators – Colpitts Conditions for oscillation and start up

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

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

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. We can better understand the use of a crystal in the operation of an oscillator by viewing its electrical equivalent.

Oscillators – Crystal

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

Oscillators 3. Relaxation Oscillators

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

Oscillators – Relaxation Triangular-wave oscillator Triangular-wave oscillator circuit is a combination of a comparator and integrator circuit.

Oscillators – Relaxation Triangular-wave oscillator

Oscillators – Relaxation Triangular-wave oscillator

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.

Oscillators – Square-wave

Oscillators – Square-wave

Oscillators – Sawtooth voltage controlled oscillator (VCO) Sawtooth VCO circuit is a combination of a Programmable Unijunction Transistor (PUT) and integrator circuit.

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.

Oscillators – Sawtooth VCO OPERATION

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

Oscillators – Sawtooth VCO OPERATION Oscillation frequency

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

Oscillators – Sawtooth VCO EXAMPLE (cont’d)

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

Oscillators – Sawtooth VCO EXAMPLE – Solution a) (ii) Frequency

Oscillators – Sawtooth VCO EXAMPLE – Solution a) (ii) Frequency

Oscillators – Sawtooth VCO EXAMPLE – Solution b) Output waveform

Oscillators The 555 timer as an oscillator

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.

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 %

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

Oscillators The 555 Timer As An Oscillator

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).

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.

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.