Unit 4 Sinusoidal Oscillators PDF

UNIT 4: Sinusoidal Oscillators Sinusoidal oscillator: what is feedback? Positive feedback and oscillators. Condition for transistor oscillators – Barkhausen criterion. Types of transistor oscillators: tuned RC and crystal oscillators. Tuned oscillators – Colpitts oscillator, Hartley Oscil...

UNIT 4: Sinusoidal Oscillators Sinusoidal oscillator: what is feedback? Positive feedback and oscillators. Condition for transistor oscillators – Barkhausen criterion. Types of transistor oscillators: tuned RC and crystal oscillators. Tuned oscillators – Colpitts oscillator, Hartley Oscillator RC oscillators – Phase shift oscillator, Wien-bridge RC oscillator Crystal Oscillator BY - PROF. SUSHANT SATISH SAWANT 1 Sinusoidal Oscillator An electronic device that generates sinusoidal oscillations of desired frequency is know as a sinusoidal oscillator. An oscillator generates a frequency it does not create energy, but acts as an energy converter. It receives dc energy and changes it into ac energy of desired frequency. The frequency of oscillations depends upon the constants of the device. BY - PROF. SUSHANT SATISH SAWANT 2 advantages An oscillator is a non-rotating device. Consequently, there is little wear and tear and hence longer life. Due to the absence of moving parts, the operation of an oscillator is quite silent. An oscillator can produce waves from small (20 Hz) to extremely high frequencies (100 MHz). The frequency of oscillations can be easily changed when desired. It has good frequency stability i.e. frequency once set remains constant for a considerable period of time. It has very high efficiency. BY - PROF. SUSHANT SATISH SAWANT 3 feedback The process of injecting a fraction of output energy of some device back to the input is know as feedback. There are two types of feedback: Positive feedback: when the feedback energy (voltage or current) is in phase with the input signal and thus aids it is called positive feedback. The positive feedback increases the gain of amplifier but also increases distortion and instability. Positive feedback is mostly used in oscillators. Negative feedback: when the feedback energy (voltage or current) is out of phase with the input signal and thus opposes it is called negative feedback. Negative feedback reduces gain of amplifier but it reduces distortion, stability in gain increased bandwidth and improved input and output impedance. BY - PROF. SUSHANT SATISH SAWANT 4 Positive Feedback Amplifier - Oscillator A transistor amplifier with proper positive feedback can act as an oscillator i.e. it can generate oscillations without any external signal source. A positive feedback amplifier is one that produces a feedback voltage 𝑉𝑓 that is in phase with original input signal. A phase shift of 1800 is produced by the amplifier and a further phase shift of 1800 is introduced by feedback network. The signal is shifted by 3600 and fed to the input i.e. feedback voltage is in phase with the input signal. BY - PROF. SUSHANT SATISH SAWANT 5 BY - PROF. SUSHANT SATISH SAWANT 6  Points to be noted: A transistor amplifier with proper positive feedback will work as an oscillator. The circuit needs only a quick trigger signal to start the oscillations. Once the oscillations have started, no external signal source is needed. To get continuous undamped output from the circuit, the following condition must be met: 𝑚𝑣 𝐴𝑣 = 1 𝐴𝑣 = voltage gain of amplifier without feedback 𝑚𝑣 = feedback fraction BY - PROF. SUSHANT SATISH SAWANT 7 Barkhausen criterion This criterion is required to produce continuous undamped oscillations at the output of an amplifier, the positive feedback should be such that: 𝐴𝑣 𝑚𝑣 = 1 Once this condition is set in the positive feedback amplifier, continuous undamped oscillations can be obtained at output immediately after connecting the necessary power supplies. BY - PROF. SUSHANT SATISH SAWANT 8  The voltage gain of a positive feedback amplifier is given by: 𝐴𝑣 𝐴𝑣𝑓 = , if 𝑚𝑣 𝐴𝑣 = 1, then 𝐴𝑣𝑓 → ∞. 1−𝑚𝑣 𝐴𝑣 This means that a vanishing small input voltage would give rise to finite output voltage even when the input signal is zero. Thus once the circuit receives the input trigger, it would become an oscillator, generating oscillations with no external signal source. BY - PROF. SUSHANT SATISH SAWANT 9 Different types of transistor oscillators Tuned collector oscillator Colpitt’s oscillator Hartley oscillator Phase shift oscillator Wien Bridge oscillator Crystal oscillator BY - PROF. SUSHANT SATISH SAWANT 10 Tuned Collector Oscillator BY - PROF. SUSHANT SATISH SAWANT 11  It contains tuned circuit 𝐿1 − 𝐶1 in the collector. The feedback coil 𝐿2 in base circuit magnetically coupled to the tank circuit coil 𝐿1. The biasing is provided by potential divider arrangement. The capacitor C connected in the base circuit provides low reactance path to the oscillations. The frequency of oscillation is given by: 1 𝑓= 2𝜋 𝐿1 𝐶1 BY - PROF. SUSHANT SATISH SAWANT 12 operation When switch S is closed, collector current starts increasing and charges the capacitor 𝐶1. When this capacitor is fully charged, it discharges through coil 𝐿1 , setting up oscillations of frequency. These oscillations induce some voltage in coil 𝐿2 by mutual induction. The frequency of voltage in coil 𝐿2 is same as that of tank circuit but its magnitude depends upon the number of turns of 𝐿2 and coupling between 𝐿1 and 𝐿2. The voltage across 𝐿2 is applied between base and emitter and appears in the amplified form in the collector circuit, thus overcoming the losses occurring in the tank circuit. The number of turns of 𝐿2 and coupling between 𝐿1 and 𝐿2 are so adjusted that oscillations across 𝐿2 are amplified to a level just sufficient to supply losses to the tank circuit. BY - PROF. SUSHANT SATISH SAWANT 13  The phase of feedback is in phase with generated oscillations. A phase shift of 180° is created between the voltages of 𝐿1 and 𝐿2 due to transformer action (transformer introduces a phase shift of 180° between input and output). A further phase shift of 180° takes place between the base emitter and collector circuit due to transistor properties. As a result, the energy feedback to the tank circuit is in phase with the generated oscillations. BY - PROF. SUSHANT SATISH SAWANT 14  The tuned collector oscillator circuit used in the local oscillator of a radio receiver makes use of an LC tuned circuit with 𝐿1 = 58.6𝜇𝐻 and 𝐶1 = 300𝑝𝐹. Calculate the frequency of oscillations. BY - PROF. SUSHANT SATISH SAWANT 15  𝐿1 = 58.6𝜇𝐻 = 58.6 × 10−6 𝐻 𝐶1 = 300𝑝𝐹 = 300 × 10−12 𝐹 1 1 3 𝑓= = 𝐻𝑧 = 1199 × 10 𝐻𝑧 = 2𝜋 𝐿1 𝐶1 2𝜋 58.6×10−6 ×300×10 −12 1199𝑘𝐻𝑧 BY - PROF. SUSHANT SATISH SAWANT 16  Find the capacitance of the capacitor required to build an LC oscillator that uses an inductance of 𝐿1 = 1𝑚𝐻 to produce a sine wave of frequency 1𝐺𝐻𝑧. BY - PROF. SUSHANT SATISH SAWANT 17  1 𝑓= 2𝜋 𝐿1 𝐶1 1 1 𝐶1 = = = 2.53 × 10−17 𝐿1 2𝜋𝑓 2 1×10−3 2𝜋×1×109 2 = 2.53 × 10−5 𝑝𝐹 BY - PROF. SUSHANT SATISH SAWANT 18 Colpitt’s Oscillator BY - PROF. SUSHANT SATISH SAWANT 19  It uses two capacitors and placed across a common inductor L and the center of the two capacitors is tapped. The tank circuit is made up of 𝐶1 , 𝐶2 and 𝐿. 1 𝐶1 𝐶2 𝑓= , 𝐶𝑇 = 2𝜋 𝐿1 𝐶1 𝐶1 +𝐶2 𝐶1 − 𝐶2 − 𝐿 is also the feed back circuit that produces a phase shift of 180°. BY - PROF. SUSHANT SATISH SAWANT 20 operation When the circuit is turned on, the capacitors 𝐶1 𝑎𝑛𝑑 𝐶2 are charged. The capacitors discharge through L, setting up oscillations of frequency as per the equation. The output voltage of the amplifier appears across 𝐶1 and feedback voltage of the amplifier appears across 𝐶1 and feedback voltage is developed across 𝐶2. The voltage across it is 180° out of phase with voltage developed across 𝐶1. A phase shift of 180° is produced by the transistor and further phase shift of 180° is produced by 𝐶1 − 𝐶2 voltage divider. BY - PROF. SUSHANT SATISH SAWANT 21 Feedback fraction 𝑚𝑣 The amount of feedback voltage in Colpitt’s oscillator depends upon feedback fraction 𝑚𝑣 of the circuit. 𝑉𝑓 𝑋𝑐2 𝐶1 Feedback fraction, 𝑚𝑣 = = = 𝑉𝑜𝑢𝑡 𝑋𝑐1 𝐶2 𝐶1 𝑚𝑣 = 𝐶2 BY - PROF. SUSHANT SATISH SAWANT 22  Determine the operating frequency and feedback fraction for Colpitt’s oscillator for given figure. BY - PROF. SUSHANT SATISH SAWANT 23  𝐶1 𝐶2 0.001×0.01 𝐶𝑇 = = = 9.09 × 10−4 𝜇𝐹 = 0.909𝑛𝐹 𝐶1 +𝐶2 0.001+0.01 𝐿 = 15𝜇𝐻 = 15 × 10−6 𝐻 1 1 𝑓= = = 1361𝑘𝐻𝑧 2𝜋 𝐿1 𝐶𝑇 2𝜋 15×10−6 ×0.909×10−9 𝐶1 0.001 𝑚𝑣 = = = 0.1 𝐶2 0.01 BY - PROF. SUSHANT SATISH SAWANT 24  A 1mH inductor is available. Choose the capacitor values in a Colpitts oscillator so that f = 1MHz and 𝑚𝑣 = 0.25. BY - PROF. SUSHANT SATISH SAWANT 25  𝐶1 𝐶1 𝑚𝑣 = ,∴ 0.25 = ,∴ 𝐶2 = 4𝐶1 𝐶2 𝐶2 1 𝑓= 2𝜋 𝐿1 𝐶𝑇 1 1 𝐶𝑇 = = = 25.3 × 10−12 𝐹 = 25.3𝑝𝐹 𝐿 2𝜋𝑓 2 1×10−3 2𝜋×1×106 2 𝐶1 𝐶2 𝐶𝑇 = = 25.3pF 𝐶1 +𝐶2 𝐶2 𝐶2 = 25.3pF 1+ ൗ𝐶1 𝐶2 = 25.3pF, ∴ 𝐶2 = 25.3 × 5 = 126.5𝑝𝐹 1+4 𝐶1 = 𝐶2ൗ4 = 126.5Τ4 = 31.6𝑝𝐹 BY - PROF. SUSHANT SATISH SAWANT 26 Hartley Oscillator BY - PROF. SUSHANT SATISH SAWANT 27  It is similar to Colpitt’s instead of using tapped capacitor, two inductors 𝐿1 and 𝐿2 are placed across a common capacitor C and the centre of inductors. The tank circuit is made up of 𝐿1 , 𝐿2 and C. the frequency of oscillations is determined by the values of: 1 𝑓= , where 𝐿 𝑇 = 𝐿1 + 𝐿2 + 2𝑀 2𝜋 𝐶𝐿𝑇 M = mutual inductance between 𝐿1 and 𝐿2 𝐿1 − 𝐿2 − 𝐶 also is the feedback network which produces a phase shift of 180°. BY - PROF. SUSHANT SATISH SAWANT 28 Operation When circuit is turned on the capacitor is charged. When it is fully charged it discharges through coils 𝐿1 and 𝐿2 setting up oscillations of frequency given in equation. The output voltage of the amplifier appears across 𝐿1 and feedback voltage across 𝐿2. The voltage across 𝐿2 is 180° out of phase with the volage developed across 𝐿1. A phase shift of 180° produced by transistor and further phase shift of 180° is produced by 𝐿1 − 𝐿2 voltage divider. In this way, feedback is properly phased to produce continuous undamped oscillations. BY - PROF. SUSHANT SATISH SAWANT 29 Feedback fraction 𝑚𝑣 𝑉𝑓 𝑋𝐿2 𝐿2 𝑚𝑣 = = = 𝑉𝑜𝑢𝑡 𝑋𝐿1 𝐿1 𝐿2 𝑚𝑣 = 𝐿1 BY - PROF. SUSHANT SATISH SAWANT 30  Calculate the operating frequency and feedback fraction for Hartley oscillator for given figure. The mutual inductance between coils, 𝑀 = 20𝜇𝐻. BY - PROF. SUSHANT SATISH SAWANT 31  𝐿1 = 1000𝜇𝐻; 𝐿2 = 100𝜇𝐻; 𝑀 = 20𝜇𝐻; Total inductance, 𝐿 𝑇 = 𝐿1 + 𝐿2 + 2𝑀 = 1000 + 100 + 2 × 20 = 1140𝜇𝐻 = 1.14𝑚𝐻 𝐶 = 20𝑝𝐹 1 1 𝑓= = 𝐻𝑧 = 1052𝑘𝐻𝑧 2𝜋 𝐶𝐿𝑇 2𝜋1.14×10−3 ×20×10−12 𝐿2 100 𝑚𝑣 = = = 0.1 𝐿1 1000 BY - PROF. SUSHANT SATISH SAWANT 32  A 1pF capacitor is available. Choose the inductor values in Hartley oscillator so that f=1MHz and 𝑚𝑣 = 0.2. Consider M=0. BY - PROF. SUSHANT SATISH SAWANT 33  𝐿2 𝐿2 𝑚𝑣 = ,∴ 0.2 = ,∴ 𝐿1 = 5𝐿2 𝐿1 𝐿1 1 𝑓= 2𝜋 𝐿𝑇 𝐶 1 1 𝐿𝑇 = = = 25.3 × 10−3 𝐻 = 25.3𝑚𝐻 𝐶 2𝜋𝑓 2 1×10−12 2𝜋×1×106 2 𝐿 𝑇 = 𝐿1 + 𝐿2 = 25.3pF 5𝐿2 + 𝐿2 = 25.3pF 6𝐿2 = 25.3pF, ∴ 𝐶2 = 25.3/6 = 4.22mH 𝐿1 = 5𝐿2 = 5 × 4.22 = 21.1𝑚𝐻 BY - PROF. SUSHANT SATISH SAWANT 34 Phase shift oscillator BY - PROF. SUSHANT SATISH SAWANT 35  It consists of single transistor amplifier and a RC phase shift network. The phase shift network consists of three sections 𝑅1 𝐶1 , 𝑅2 𝐶2 and 𝑅3 𝐶3. At some particular frequency 𝑓0 the phase shift in each RC section is 60° so that total phase-shift produced by the RC network is 180°. The frequency of oscillations is given by: 1 𝑓0 = , where 𝑅1 = 𝑅2 = 𝑅3 = 𝑅, 𝐶1 = 𝐶2 = 𝐶3 = 𝐶 2𝜋𝑅𝐶 6 BY - PROF. SUSHANT SATISH SAWANT 36 Operation Good frequency stability and waveform can be obtained from oscillators employing resistive and capacitive elements. Such amplifier are called R-C or phase shift oscillators and have additional advantages that they can be used for very low frequencies. When the circuit is switched on, it produces oscillations of frequency given by the equation. The output of amplifier is fed back to RC feedback network. This network produces a phase shift of 180° and a voltage appears at its output is applied to the transistor amplifier. BY - PROF. SUSHANT SATISH SAWANT 37  Advantages: It does not require transformers or inductors. It can be used to produce very low frequencies. The circuit provides good frequency stability. Disadvantages It is difficult for the circuit to start oscillations as the feedback is generally small. The circuit gives small output. BY - PROF. SUSHANT SATISH SAWANT 38  In phase shift oscillator 𝑅1 = 𝑅2 = 𝑅3 = 1𝑀Ω 𝑎𝑛𝑑 𝐶1 = 𝐶2 = 𝐶3 = 68𝑝𝐹. At what frequency does the circuit oscillate? BY - PROF. SUSHANT SATISH SAWANT 39  1 1 𝑓0 = = 𝐻𝑧 = 954𝐻𝑧 2𝜋𝑅𝐶 6 2𝜋×106 ×68×10−12 6 BY - PROF. SUSHANT SATISH SAWANT 40  A phase shift oscillator uses 5pF capacitors. Find the value of R to produce a frequency of 800kHz. BY - PROF. SUSHANT SATISH SAWANT 41  1 𝑓0 = 2𝜋𝑅𝐶 6 1 1 𝑅= = = 16.2𝑀𝐻𝑧. 2𝜋𝑓0 𝐶 6 2𝜋×800×103 ×5×10−12 × 6 BY - PROF. SUSHANT SATISH SAWANT 42 Wien Bridge Oscillator BY - PROF. SUSHANT SATISH SAWANT 43  The Wien-bridge oscillator is the standard oscillator circuit for all frequencies in the range of 10 Hz to about 1 MHz. It is the most frequently used type of audio oscillator as the output is free from circuit fluctuations and ambient temperature. It is essentially a two-stage amplifier with R-C bridge circuit. The bridge circuit has the arms 𝑅1 𝐶1 , 𝑅3 , 𝑅2 𝐶2 and tungsten lamp 𝐿𝑃. Resistance 𝑅3 and 𝐿𝑃 are used to stabilise the amplitude of the output. The transistor 𝑇1 serves as an oscillator and amplifier while the other transistor 𝑇2 serves as an inverter (phase shift 180°). The circuit uses positive and negative feedbacks. The positive feedback is through 𝑅1 𝐶1 , 𝐶2 𝑅2 to the transistor 𝑇1. The negative feedback is through the voltage divider to the input of transistor 𝑇2. 1 1 𝑓=. If 𝑅1 = 𝑅2 = 𝑅 and 𝐶1 = 𝐶2 = 𝐶 then 𝑓 = 2𝜋 𝑅1 𝐶1 𝑅2 𝐶2 2𝜋𝑅𝐶 BY - PROF. SUSHANT SATISH SAWANT 44 Operation When the circuit is started, bridge circuit produces oscillations of frequency given in the equation. The two transistors produce a total phase shift of 360° so that proper positive feedback is ensured. The negative feedback in the circuit ensures constant output. This is achieved by the temperature sensitive tungsten lamp 𝐿𝑃. Its resistance increases with current. Should the amplitude of output tend to increase, more current would provide more negative feedback. The result is that the output would return to original value. A reverse action would take place if the output tends to decrease. BY - PROF. SUSHANT SATISH SAWANT 45  Advantage: It gives constant output. The circuit works quite easily. The overall gain is high because of two transistors. The frequency of oscillations can be easily changed by using a potentiometer. Disadvantage: The circuit requires two transistors and a large number of components. It cannot generate very high frequencies. BY - PROF. SUSHANT SATISH SAWANT 46  In the Wien bridge oscillator 𝑅1 = 𝑅2 = 220𝑘Ω and 𝐶1 = 𝐶2 = 250𝑝𝐹. Determine the frequency of oscillations. BY - PROF. SUSHANT SATISH SAWANT 47  𝑅1 = 𝑅2 = 220𝑘Ω 𝐶1 = 𝐶2 = 250𝑝𝐹 1 1 𝑓 = = = 2892𝐻𝑧 2𝜋𝑅𝐶 2𝜋×220×103 ×250×10−12 BY - PROF. SUSHANT SATISH SAWANT 48 Limitations of LC and RC Oscillators Due to change in temperature the values of resistors and inductors will change and hence change in frequency of oscillator will take place. If any component in the feedback network is changed, it will shift operating frequency of the oscillator. BY - PROF. SUSHANT SATISH SAWANT 49 Piezoelectric Crystals Certain crystalline materials, Rochelle salt, quartz and tourmaline exhibit the piezoelectric effect, i.e. when we apply an AC voltage across them, they vibrate at the frequency of the applied voltage. Conversely, when they are compressed or placed under mechanical strain to vibrate, they produce an AC voltage. Such crystals which exhibit piezoelectric effect are called piezoelectric crystals. BY - PROF. SUSHANT SATISH SAWANT 50 Transistor Crystal Oscillator BY - PROF. SUSHANT SATISH SAWANT 51  It is a Collpit’s oscillator modified to act as a crystal oscillator. The only change is the addition of the crystal (Y) in the feedback network. The crystal will act as a parallel-tuned circuit. At parallel resonance, the impedance of the crystal is maximum. This means that there is a maximum voltage drop across 𝐶1. This in turn will allow the maximum energy transfer through the feedback network at 𝑓𝑃. Even the smallest deviation from 𝑓𝑃 will cause the oscillator to act as an effective short. Consequently, we have an extremely stable oscillator. BY - PROF. SUSHANT SATISH SAWANT 52  Advantage: They have a high order of frequency stability. The quality factor Q of the crystal is very high. The Q factor of the crystal may be as high as 10000 compared to about 100 of L-C tank. Disadvantage: They are fragile and consequently can only be used in low power circuits. The frequency of oscillations cannot be changed appreciably. BY - PROF. SUSHANT SATISH SAWANT 53