UNIT - IV FEEDBAK AMPLIFIES & OSILATTOS OBJETIVES i)the basics of feedback. ii)the properties of negative feedback. iii)the basic feedback topologies. iv)an example of the ideal feedback case. v)some realistic circuit examples and how to analyze them. INTODUTION TO FEEDBAK There are two types of feedback: regenerative (positive feedback) and degenerative (negative feedback). Unless you want your circuit to oscillate, we usually use NEGATIVE FEEDBAK... This idea came about in the late 90 s when they were able to build amplifiers with reasonable gains, but with gains that were difficult to control from amplifier to amplifier... One day, while riding the Staten Island Ferry, Harold Black invented negative feedback... DEFINITION By building an amplifier whose gain is made deliberately, say 40 decibels higher than necessary (0,000-fold excess on an energy basis) and then feeding the output back to the input in such a way as to throw away the excess gain, it has been found possible to effect extraordinary improvement in constancy of amplification and freedom from nonlinearity. Harold Black, inventor of negative feedback, 94 70
POPETIES OF NEGATIVE FEEDBAK The gain of the circuit is made less sensitive to the values of individual components. Nonlinear distortion can be reduced. The effects of noise can be reduced (but not the noise itself). The input and output impedances of the amplifier can be modified. The bandwidth of an amplifier can be extended. All you have to do to get some feedback (of the negative kind) is to supply a scaled replica of the amplifier s output to the inverting (negative) input (more on this below) and presto! Of course, if you use negative feedback, overall gain of the amplifier is always less than the maximum achievable by the amplifier without feedback. THE BASI FEEDBAK IUIT 7
With an input signal xs, an output signal xo, a feedback signal xf, and an amplifier input signal xi, let s look at the basic feedback circuit illustrated above. The amplifier has a gain of A and the feedback network has a gain of The input to the amplifier is, xi = xs - xf The output of the amplifier is, xo = Axi So we can obtain an expression for the output signal in terms of the input signal and the feedback gain... xo = A xs - xf = A xs - β xo earranging, xo = Axs - A β xo β o + A β s 7
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FOM BASI BLOK DIAGAM TO ATUALDIFFEENT TYPES OF FEEDBAK IUITS 75
The comparison of parameters of different types of amplifiers is given in the form of tabular column which is shown below. OMPAISON TABLE 76
BASI STUTUE OF THE IUIT Here we have assumed that there was an input comparator or mixer and an output sampler that provided us with a copy of the output signal for use as a feedback signal. The form these devices take depends upon whether the amplifier s input and output are current or voltage based... 77
SEIES-SHUNT FEEDBAK - VOLTAGE AMPLIFIE 78
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SHUUNT-SEIES FEEDBAK - UENT AMPLIFIE SEIES-SEIES FEEDBAK -TANSONDUTANE AMPLIFIE VOLTAGE -IN, UENT -OUT (SHUNT [VOLTAGE] MIXING, UENT -SAMPLING) 80
SHUNT-SHUNT FEEDBAK -TANSESISTANE AMPLIFIE UENT-IN, VOLTAGE-OUT (SHUNT [UENT] MIXING, VOLTAGE-SAMPLING) 8
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SUMMAY OF STEPS YOU WILL USE 84
LINEA OSILLATOS A linear oscillator ideally produces a pure sinusoidal output at a single frequency (hopefully). To achieve linear oscillation, a linear amplifier must oscillate without external stimuli (other than a start-up transient to get it going, perhaps). In order to understand this type of oscillator, a minor excursion into theory will be required (it s worth it, since a little bit of intuitive understanding goes a long way!). What is required to make a linear oscillator (that works, that is!) is the arrangement shown below (this is just POSITIVE feedback)... 85
Actually, it is a necessary condition for this type of oscillator (linear) to work. Intuitively, however the fact that the overall gain is infinity means that the output of the circuit is some signal (to be determined!), even with NO input at all! If one can arrange it so that the Barkhausen riterion is met at only a single frequency, 86
it is possible to obtain a very pure sinewave output (if it is met at multiple frequencies, you might get an interesting mix of frequencies). TYPES OF OSILLATOS. Non-sinusoidal Oscillator These Oscillators produce other than sine wave. (eg.) Triangular wave, square wave,sawtooth wave They are generated by using relaxation oscillator circuits. In this type of circuit, the V or I change abruptly one or more times during each cycle and thus result in a nonsinusoidal oscillation. Application Used as a timing circuit A few non-sinusoidal oscillators are, (i) Multivibrator (ii) Saw-tooth wave generator (iii) ectangular wave generator (iv) Triangular wave generator. Sinusoidal Oscillator (i) (ii) In a Sinusoidal Oscillator the voltage varies continuously with respect to time. They are generated using any one of the following property. Negative resistance Feedback 87
(iii) Heterodyne (iv) rystal (v) Magnetostriction (vi) Ultra high frequency (vii) Nature of sinusoidal oscillation. damped Oscillation The electrical oscillation whose amplitude goes on decreasing with time is known as damped Oscillation. Undamped Oscillation 88
The electrical oscillation whose amplitude remains constant with time is known as undamped Oscillation BAKHAUSEN ITEION The overall gain of a positive feedback amplifier is given by the relation A f =A/(-βA) Where, A f is the voltage gain with feedback βa is the loop gain (i) If βa is made equal to unity then A f is infinity. (i.e) the circuit had stopped amplifying and started oscillating. To provide positive feddedback the feedback network should produce a phase shift of 80º in addition to 80º phase shift produced by the amplifier. Therefore the total phase shift should be 60º. Hence the condition for oscillations is βa must be equal to one (ii) The total phase shift should be 60º. FEQUENY STABILITY The ability of the oscillator to maintain constant frequency is called Frequency stability Factors affecting Frequency stability. operating point. Parameters of active device. Power source 4. Temperature variation 89
5. Mechanical vibration A. OSILLATO. WEIN BIDGE OSILLATO It consists of two transistors connected in cascade and a bridge network used to provide positive feedback. Transistor Q provides amplifications and phase shift of 80º. Transistor Q provides further amplifications and a phase shift of 80º. Signals at base Q are amplified and they appear with a phase shift of 60º at the collector of Q. Though the signal at the output of Q is in phase with the input of Q it cannot be directly fed as a feedback signal; since it would affect the frequency stability. ircuit operation The bridge circuit consists of two arms, the resistive arm and reactive arm. The resistive arm consists of swamping resistor which introduces a negative feedback to Q. Thus it improves bias stability since the arm consists of only resistive components alone. The amount of feedback is determined only by voltage divider and 4. The reactive arm consists of two networks, out of which one is in shunt and another is in series. since capacitors are connected in this arm they are frequency sensitive. Hence the feedback signal from this arms changes w.r.to frequency and magnitude depends upon the voltage divider formed by -4. The bridge is said to be balanced if the voltage at point A equals to voltage at point D and this occurs only at one frequency. The circuit consists if two coupled amplifier, which provides phase shift of 60º.So the feedback network has no need to provide any additional phase shift. When the circuit is energized by switching on the supply a small random oscillations are produced at base. They are further amplified at ollector of Q.Since the oscillations at collector of Q have 90
been inverted twice, the input signal is in phase with the output signal, apart of output form the collector of Q is feedback to Wein Bridge which is further amplified. The process continues still a sustained oscillation is produced. Frequency calculation Impendence of series arm Z S (S) s s s Impendence of parallel arm Z (S) p S 9
9 S S x s (S) Z P Feedback Voltage (S) Z (S) Z (S) Z (S) V (S) V S p p 0 p 0 f s s s s (S) V (S) V WKT, (S) V (S) V 0 f feedback fraction ratio. s s s s s s s s s s s s Let &... s s s GAIN of op. amp... (S) V (S) V A i f f 0 WKT, for oscillation to start,
A Sub & in... f i s s s replace s = where f s j f is the frequency of oscillation j is the complex variable f i eal part, j 0 j j f f Imaginary part, f i f i j j Frequency ange 0Hz to MHz 9
Advantages. Good Frequency stability. Good amplitude stability. Application Audio signal generator.. PHASE SHIFT OSILLATO A fraction of output of a single stage amplifier is passed thro, a phase shift network, before feeding back to the input. The phase shift network provides a phase shift of 80º and another 80º phase shift is produced by the amplifier. Hence the total phase shift is 60º. ircuit Diagram. The feedback network consists of three identical section. Each section produces a phase shift of 60º. Therefore the total phase shift of the feedback network is80º and another 80º phase shift is produced by the amplifier. Therefore the total phase shift should be 60º. 94
ircuit operation When the circuit is energized by switching on the supply a small random oscillations are produced.the oscillation may start due to minor variation in d.c supply. The output form the collector is feedback to phase shift network and finally applied to the base. The oscillation will be maintained if loop gain is made equal to unity. frequency calculation Node I(S) I (S) I(S) V0 (S) V (S) V (S) V (S) V (S) s s V (S) V (S) V (S) 0 s s Node I(S) I4 (S) I5 (s)... V (S) V s (S) V (S) V (S) Vf (S) s 95
V (S) V0 (S) V (S) s s Node Since I (S) 0 i 7... I5(6) I6 (S) s V (S) V s Sub in f (S) s Vf (S) V0 (S) s V (S) s s V (S) V (S) s V (S) scv (S) Now Sub in Equating 4 & 5 V f (S) s s f s s V (S) scv (S) f s 0 0 s... s 6 5s V (S) s Vf (S) WKT,, feedback fraction ratio V (S) 0 0...4 s Put s j s 6s 5s j j 6 5j... 6 f Gain of op- amp, A... 7 WKT, condition for oscillation is A... 8 i 96
97 Sub 6, 7 in 8 5j 6 j j i f Equating real and imaginary part to zero, eal part, 0 6 6 6 6 f 6 f Imaginary part, 5j j j i f 5 i f 5 i f 9 i f Frequency ange 0Hz to MHz Advantages
4. Good Frequency stability 5. Good amplitude stability Application Audio signal generator. B. L Oscillators They are also known as tuned Oscillators or tank circuit oscillator. They are used to produce frequency in the range of MHz to 500MHz. Hence they are also known as.f oscillators. TYPES OF L OSILLATOS.TUNED OLLETO O AMSTONG OSILLATO It uses inductive feedback The L circuit is in collector of transistor Hartley Oscillator It uses inductive feedback olpitt s Oscillator It uses capacitive feedback lapp Oscillator It uses capacitive feedback. TUNED BASE OSILLATO It uses inductive feedback The L circuit is in base of transistor 98
.TUNED OLLETO OSILLATO It uses inductive feedback. The L circuit is in collector of transistor. The feedback signal is taken from the secondary winding Land fed back to the base terminal. There is phase shift of 80ºin the transformer and another 80º phase shift is produced by transistor amplifier. Hence the total phase shift is 60º. Hence the feedback fraction β=m/l M- Mutual inductance between primary and secondary winding. L- self inductance between primary and secondary winding. WKT, βa= A=/β For the oscillation to start, voltage gain must be greater than /β, e are used to produce d.c bias to the transistor. The capacitor ' and e act as a bypass capacitor to the resistor and e respectively. Operation When the circuit is energized by switching on the supply small random oscillations are produced, hence the collector current increase to quiescent value. These current charges the capacitor. when it is fully charged it discharges thro, the primary winding of L producing a magnetic field around it. When the capacitor I s fully discharged, magnetic field collapses and charges the capacitor in reverse direction. The process continues still a sustained oscillation is produced. HATLEY OSILLATO It uses inductive feedback. The tank circuit consists of two coils L and L. The L is inductively coupled to L and the combination works as 99
auto transformer. The feedback between output and input is accomplished thro; this autotransformer action which also introduces a phase shift of 80º and the transistor Q provides amplifications and a phase shift of 80º. Hence the total phase shift is 60º. Hence the feedback fraction β=l /L WKT, βa= A=/β For the oscillation to start, voltage gain must be greater than /β A= L /L, e are used to produce d.c bias to the transistor. The capacitor c permits only a.c current to pass thro, tank circuit.b acts as blocking capacitor, which blocks the d.c current reaching the base terminal. and e act as a bypass capacitor. Operation When the circuit is energized by switching on the supply small random oscillations are produced, hence the collector current increase to quiescent value. The oscillations are produced because of positive feedback from the tank circuit. The process continues still a sustained oscillation is produced. 00
OLPITTS OSILLATO It uses capacitive feedback. The tank circuit consists of two capacitor and connected in series with each other which introduces a phase shift of 80º and the transistor Q provides amplifications and a phase shift of 80º. Hence the total phase shift is 60º. Hence the feedback fraction β= / WKT, βa= A=/β For the oscillation to start, voltage gain must be greater than /β A= /, e are used to produce d.c bias to the transistor. The capacitor c permits only a.c current to pass thro, tank circuit.b acts as blocking capacitor, which blocks the d.c current reaching the base terminal. and e act as a bypass capacitor. Operation When the circuit is energized by switching on the supply a small random oscillation are produced, hence the collector current increase to quiescent value. The oscillations are produced because of positive feedback from the tank circuit. The process continues still a sustained oscillation is produced. 0
LAPP OSILLATO It uses capacitive feedback. The circuit differs from the colpitt only in one respect, that it contained one additional capacitor connected in series with inductor. This additional capacitor eliminates the effect of frequency stability and improves the frequency stability. The tank circuit consists of two capacitor and connected in series with each other which introduces a phase shift of 80º and the transistor Q provides amplifications and a phase shift of 80º. Hence the total phase shift is 60º. Hence the feedback fraction β= / WKT, βa= A=/β For the oscillation to start, voltage gain must be greater than /β A= /, e are used to produce d.c bias to the transistor. The capacitor c permits only a.c current to pass thro, tank circuit.b acts as blocking capacitor, which blocks the d.c current reaching the base terminal. and e act as a bypass capacitor. Operation When the circuit is energized by switching on the supply small random oscillations are produced, hence the collector current increase to quiescent 0
value. The oscillations are produced because of positive feedback from the tank circuit. The process continues still a sustained oscillation is produced..tuned BASE OSILLATO It uses inductive feedback. The L circuit is in base of transistor. The feedback signal is taken from the secondary winding Land fed back to the base terminal. Thers is phase shift of 80ºin the transformer and another 80º phase shift is produced by transistor amplifier. Hence the total phase shift is 60º. Hence the feedback fraction β=m/l M- Mutual inductance between primary and secondary winding. L- self inductance between primary and secondary winding. WKT, βa= A=/β 0
For the oscillation to start, voltage gain must be greater than /β, e are used to produce d.c bias to the transistor. The capacitor ' and e act as a bypass capacitor to the resistor and e respectively. Operation When the circuit is energized by switching on the supply small random oscillations are produced, hence the collector current increase to quiescent value. These current charges the capacitor. when it is fully charged it discharges thro, the primary winding of L producing a magnetic field around it. When the capacitor I s fully discharged, magnetic field collapses and charges the capacitor in reverse direction. The process continues still a sustained oscillation is produced.. YSTAL OSILLATO It is basically a tuned oscillator. It uses a piezoelectric crystal in the tank circuit. The crystal is usually made up of quartz crystal and provides a high frequency of stability and accuracy. Therefore the crystal oscillators are used in applications where frequency stability is very essential. They are widely used in digital watches and clocks. Quartz crystal It has a very peculiar property known as piezoelectric effect. When an a.c voltage is applied to the crystal, it stars vibrating at a frequency of applied voltage. onversely if a force is applied to the crystal, it generates the a.c voltage. Electric equivalent of a crystal 04
It consists of series -L- circuit in parallel with a capacitance.when the crystal is not vibrating, it is equivalent to capacitance. When the crystal is vibrating, it is equivalent to series -L- circuit. The series resonant frequency (fs) occurs when reactance of inductance equals to the reactance of capacitance. f s L The parallel resonant frequency occurs when reactance of inductance equals to the reactance of series -L- circuit. fp L where = * /( + ) Q=Factor of the crystal is given by Q=(* * f s *L)/ rystal Oscillator circuit The crystal is connected as a series element in the feedback path from collector to base., e are used to produce d.c bias to the transistor. The capacitor c permits only a.c current to pass thro, tank circuit.b acts as blocking capacitor, which blocks the d.c current reaching the base terminal and e act as a bypass capacitor. he coupling capacitor has a negligible impedance at the circuit operating frequency. 05
The circuit operating frequency of oscillation is set by series resonant frequency of crystal and its value is given by relation, OSILLATOS USING OP-AMP PHASE SHIFT OSILLATO An example of a sinewave generator is shown in Figure. This is a phase-shift oscillator, and amongst other things demonstrates that negative feedback becomes positive feedback if there is enough phase-shift around the feedback loop. Here, the opamp is connected as an inverting amplifier, but the connection between output and input of three sections in cascade introduces 80 phase shift at some particular frequency. If the gain of the amplifier section is sufficient to make up for the attenuation of the phase-shift network at that frequency, then the system will oscillate. If the gain is too high, the oscillations build up until the amplifier output reaches its maximum values and the system saturates (that is it becomes non-linear). If the gain is too low, the system may show resonance, but it will not oscillate. In fact, the diode network provides controlled nonlinearity to keep the overall loop gain at unity, and so provide stable oscillation. Note that at least three sections are required, since each section can produce only just under 90 phase-shift at most, so that two cannot provide the necessary 80 shift. This circuit is quite tricky to analyse, just because each section loads the preceding section. A sinewave oscillator based on the Wien bridge, somewhat easier to analyse and also rather better in performance, appears in the tutorial exercises. The 06
circuit in Figure was in fact designed by adjusting values in a PSpice model. _ + Sinewave V(Sinewave) Output (V) 0 0.06-0.07 0.08 0.09 0. - - Time (s) 07
Phase-shift oscillator voltages Waveforms (V) 0-0. 0.0 0.0 0.0 0.04 0.05 - - Time (s) V(Sinewave) V(:) V(:) Figure. Phase-shift oscillator. Waveforms are calculated for = 0 k, = = 00 k, = 0 nf. Note the initial exponential rise of oscillation amplitude, followed by levelling off as the diode limiter operates. Note also the phase-shifted waveforms at each stage of the phase-shift network. 08