En. Rosemizi Bin Abd Rahim EMT212 – Analog Electronic II Chapter 4 Oscillator By En. Rosemizi Bin Abd Rahim

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

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.

The Oscillator 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. Fig 16-1 Oscillator

Types of Oscillator RC Oscillator - Wien Bridge Oscillator - Phase Shift Oscillator 2. LC Oscillator - Hartley Oscillator - Colpitts Oscillator - Clapp Oscillator - Crystal Oscillator Fig 16-1 Oscillator 3. Relaxation Oscillator

Feedback Oscillator Principles An oscillator is an amplifier with positive feedback. Ve = Vi + Vf (1) Vo = Ave (2) Vf = Vo (3) From (1), (2) and (3), we get

Feedback Oscillator Principles Hence the closed loop gain, Vo/Vi = A/(1 - A) The closed loop gain can be very large if (1 - A)= 0 A small signal value at the input can produce an output of reasonable magnitude. Thus the amplifier will be unstable when (1 - A) = 0, or when the loop gain A = 1 In polar form, A = 1 0° or 1 360°

Feedback Oscillator Principles 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. Fig 16-3 Pos. Feedback

Design Criteria for oscillators 1) |A| equal to unity or slightly larger at the desired oscillation frequency. - Barkhaussen criterion, |A|=1 2) Total phase shift, of the loop gain must be 0° or 360°.

Factors that determine 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 sin wave at frequencies of 100 kHz to 100 MHz. Crystals generate a square or sin wave over a wide range,i.e. about 10 kHz to 30 MHz.

1. RC Oscillators

Oscillators With RC Feedback Circuits 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.

Wien-Bridge Oscillator It is a low frequency oscillator which ranges from a few kHz to 1 MHz. Structure of this oscillator is

Wien-Bridge Oscillator

Wien-Bridge Oscillator Multiply the top and bottom by jωC1, we get Divide the top and bottom by C1 R1 C2 R2

Wien-Bridge Oscillator Now the amp gives Furthermore, for steady state oscillations, we want the feedback V1 to be exactly equal to the amplifier input, V1’. Thus

Wien-Bridge Oscillator Hence Equating the real parts,

Wien-Bridge Oscillator If R1 = R2 = R and C1 = C2 = C - Gain > 3 : growing oscillations - Gain < 3 : decreasing oscillations

Wien-Bridge Oscillator 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. fr = 1/2RC Fig 16-6a&b

Wien-Bridge Oscillator The lead-lag circuit is in the positive feedback loop of Wien-bridge oscillator. The voltage divider limits gain. The lead lag circuit is basically a band-pass with a narrow bandwidth. Fig. 16-7b Wien-bridge

Wien-Bridge Oscillator 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. Fig 16-8a&b

Wien-Bridge Oscillator To start the oscillations an initial gain greater than 1 must be achieved. The back-to-back zener diode arrangement is one way of achieving this. When dc is first applied the zeners appear as opens. This allows the slight amount of positive feedback from turn on noise to pass. Fig 16-10 Wien-bridge w/zeners

Wien-Bridge Oscillator 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.

Wien-Bridge Oscillator 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. Fig 17-11 JFET AGC

Phase Shift Oscillator 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. fr = 1/26RC Fig 16-13 phase shift osc.

Phase Shift Oscillator The transfer function of the RC network is Fig 16-13 phase shift osc.

Phase Shift Oscillator If the gain around the loop equals 1, the circuit oscillates at this frequency. Thus for the oscillations we want, Putting s=jω and equating the real parts and imaginary parts, we obtain Fig 16-13 phase shift osc.

Phase Shift Oscillator From equation (1) ; Substituting into equation (2) ; Fig 16-13 phase shift osc. # The gain must be at least 29 to maintain the oscillations.

Phase Shift Oscillator – Practical The last R has been incorporated into the summing resistors at the input of the inverting op-amp. Fig 16-13 phase shift osc.

2. LC 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 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 With LC Feedback Circuits Using the small signal equivalent circuit this becomes Applying KVL around loop (1), and let ZT = Z1 + Z2 + Z3

Oscillators With LC Feedback Circuits Using KVL in loop (2) ; Substituting (2) into (1) ;

Oscillators With LC Feedback Circuits If the Z’s are purely imaginary and hie is real, then Substituting (3) into the expression ZT = Z1 + Z2 + Z3 = 0 ; Z2 and Z1 are the same type of component

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

Oscillators With LC Feedback Circuits

Colpitts Oscillators The Colpitts oscillator utilizes a tank circuit (LC) in the feedback loop. The resonant frequency can be determined by the formula below. Fig 16-19 BJT Colpitts

Colpitts Oscillators Conditions for oscillation and start up Fig 16-19 BJT Colpitts

Hartley Oscillators The Hartley oscillator is similar to the Colpitts. The tank circuit has two inductors and one capacitor. The calculation of the resonant frequency is the same. Fig 16-23 Hartley osc.

Crystal Oscillators 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. Fig 16-25 abc&d crystal

Oscillators With LC Feedback Circuits 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. Fig 16-26a xtal osc.

3. Relaxation Oscillators

Relaxation Oscillators 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 Fig 16-28 2 op-amp gen Fig 16-29 output waveforms

Triangular-wave Oscillator Triangular-wave oscillator circuit is a combination of a comparator and integrator circuit. Fig 16-28 2 op-amp gen Fig 16-29 output waveforms

Square-wave Oscillator 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. Fig 16-34 basic square wave Fig 16-35 waveforms

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

Sawtooth Voltage-Controlled Oscillator (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.

Sawtooth Voltage-Controlled Oscillator (VCO) Operation When Vout = VP Vanode > VG , PUT turn ‘ON’ The capacitor rapidly discharges. Vout drop until Vout = VF. Vanode < VG , PUT turn ‘OFF’ VP-maximum peak value VF-minimum peak value

Sawtooth Voltage-Controlled Oscillator (VCO) Oscillation frequency is

Sawtooth Voltage-Controlled Oscillator (VCO) Example Let VF = 1V, find Amplitude Frequency Sketch the output waveform

Sawtooth Voltage-Controlled Oscillator (VCO) Solution Amplitude So, peak – to- peak Amplitude is

Sawtooth Voltage-Controlled Oscillator (VCO) ii) Frequency

Sawtooth Voltage-Controlled Oscillator (VCO) iii) Output Waveform

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. Fig 16-37 555 timer

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 % Duty Cycle <50 %

The 555 Timer As An Oscillator Fig 16-40 555 w/diode

The 555 Timer As An Oscillator The 555 timer by be operated as a VCO with a control voltage applied to the CONT input (pin 5). Fig 16-42 555 VCO

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.

Summary 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.