Circuits with feedback and sine wave oscillators
Feedback signal is a signal in which the output signal is sampled then fed back to the input to form error signal that drives the signal. The response gotten in the absence of feedback is different from the one gotten when feedback is present; this is because the feedback is made of some sub circuits which allow a certain percentage of the output signal to modify the effective input signal. There are two types of feedback which include positive feedback and negative feedback. In positive feedback the output signal is sampled then fed back to the input signal this in turn increases the input signal to make it more than it was. The signal fed back to the input signal is in phase with it hence it modifies it positively. This is done to produce oscillation and it can also be referred to as regenerative feedback .Positive feedback is used in oscillator circuits.
In positive feedback the output voltage is routed back to the non inverting terminal of the op-amp. When the inverting input is maintained at zero volts the output voltage will be determined by the polarity and magnitude of the voltage at the non inverting input terminal. If that voltage is positive the op-amp will drive out positive too, feeding that positive voltage back to the non inverting terminal which will result in a positive output. Likewise when the voltage at the non inverting terminal is negative the op-amp will drive out negative too feeding that negative back to the non inverting input and the result will be positive output (Boyce et al. 2010).
In negative feedback the output signal is sampled then fed back to the input signal this in turn decreases the input signal to make it less than it was. The signal fed back to the input signal is out of phase with it hence it dampens the input signal thus modifies it negatively. This can be referred to as degenerative feedback. Negative feedback is used in amplifier circuits.
The op-amp has two inputs; the inverting (-) and the non inverting (+) and one output. The input resistance is very high and the output resistance is very low. The op-amp amplifies the difference in voltages between the two which is called differential input voltage. If we connect the output of an op-amp to the inverting input and apply a voltage signal to the non inverting input we note that as
V input increases V output increases but as V output increases the output signal will be fed back to the inverting input hence decreasing the voltage difference between the inputs which in turn brings
the output down
Q2;
closed loop gain Acl= Vout = A(w)
Vin 1+FA(w)
where F = feedback coefficient=B(beta)
A(w)= frequency dependent gain.
Acl=Av1+Av2+Av3
1+B.A(w)
a)the required feedback factor
Acl =1
B
B= 1
30
=0.05
b)Av1+Av2+Av3 =50db
3
50db=100%
? =150%
=50*150
100
=75%
Q 3)
- a) Acl= A(w)
1+B.A(w)
B= A(w) * 1 – 1
Acl. A(w) A(w)
=1 – 1
Acl A(w)
=1 – 1
20 150
=0.043
b)
input resistance R with feedback= R + R*B
=(2 + 2*0.043)K ohms
=2.086K ohms
- c) The applied negative feedback improves performance of the op-amp by making it gain stability, linearity, frequency response ,step response etc and it reduces sensitivity to parameters variation due to manufacturing or environment. Positive feedback latches in the state it’s either saturated positive state or saturated negative state. This is known as Hysteresis which can be very useful in comparators. Comparators can be used to produce any square wave from any sort of ramping wave input.
Q5)
The above shows a 2 stage amplifier
Task 2
Q1) An example of a positive feedback is an oscillator. An op-amp consist of two inputs and one output. The positive input is also known as the regenerative input. The feedback circuit in positive feedback is between the positive terminal of the operational amplifier and the output of the amplifier .A positive feedback amplifier consist of a gain A and a feedback circuit with a feedback factor of B. in oscillators part of the output is fed back to the to the input through the feedback circuit. The fed back signal is added to the input by a summer as illustrated above and the summer output acts as the input signal of the amplifier. The difference between a positive (regenerative )and a negative (degenerative ) operational amplifiers is the positive feedback is achieve when the feed back circuit is between the positive terminal of the op amp and the output while that of negative feedback is when that feed back circuit is between the negative terminal and the output.
Q2) Feedback oscillator
Electronic amplifiers are examples of feedback oscillators. They include transistors and
op-amps which is usually connected in a feedback loop with its output fed back to the input through the loop to produce positive or negative feed back. Feedback oscillators can be classified according to the type of frequency selective filter they use in their feedback loop. In RC oscillators the filter is a network of resistors and capacitors. They are mostly used to generate lower frequencies like the audio range. In LC oscillator circuits the filters are a series of inductors and capacitors (Boyce et al. 2010).
Voltage controlled oscillators (VCO)
They are designed so that the oscillation frequency can be varied over some range by an input voltage or current. They are mostly used in phase locked loops in which the oscillator frequency can be locked to the frequency of another oscillator. They are used in modulators, filters and demodulators and forming the basis of frequency synthesizers’ circuits which are used to tune radios and television. The radio frequency VCO’s are usually made by adding the varactor diode to the turned circuit or resonator in an oscillator.
Q3)
The wien bridge is a two stage coupled RC coupled amplifier circuit that has a good stability at its resonant frequency.
Resonant frequency Fr= 1
2pie RC
The wien bridge oscillator uses a series RC circuit connected with a parallel RC of same component values producing phase delay or phase advance circuit depending upon the frequency.
Q4) a).
Fr= 1
2pie RC
R=R1 + R2 = 200+200=400ohms
1 = 1 + 1
Ceqq C1 C2
C= 1 = 1 = 1.06micro ohms
2pieFr 2pie * 150k ohms
b)
gain Gc=GR= 1
SQ ROOT 2
=0.7071
Feedback factor B= R
( 1/jwc) + R
= 200
(1/150k* 1.06*10^-6)+ 200
=0.97
- c) Vin=150mVL45Degrees
=0.15(sin 45 + jcos 45)
=0.1061+j 0.1061
R=0.1061
2pie FL=0.10601
L=1.13*10^-7
Vout =2pie FL
=2pie*150k*1.13*10^-7
=106.50mV
Q5)
A crystal oscillator is an electronic oscillator that uses the mechanical resonance of a vibrating to create an electric signal with very precise frequency. This frequency is used to keep track of time ,
to provide a stable clock signal for digital integrated circuit and to stabilize frequency for radio transmitters and receiver. Crystal oscillators can be manufactured for oscillation over a wide range of frequencies. Many application calls for a crystal oscillator frequency conveniently related to some other desired frequencies. Comparing crystal oscillators to other oscillators and starting first with the Wien bridge oscillator. It is an electronic oscillator which generates sine waves. The oscillator is based on a bridge circuit ,the bridge consist of four resistors and two capacitors .the oscillator can also be seen as a positive feedback oscillator .it has a resonance frequency given by
1/2pieRC. Transistor phase oscillator uses an N-P-N junction transistor. In the case of phase shift oscillator the output of the feedback network is loaded appreciably by a relatively small resistance of the transistor and hence instead of employing voltage series feedback ,voltage shunt is used for transistors phase shift oscillators .LC oscillators inductors and capacitors are combined in resonating circuits that produces a very good shape and has a quite good frequency stability that is the frequency does not alter so much for changes in the DC supply voltage or ambient temperature. LC oscillators are extensively used in RF signal where variable frequency is required (Boyce et al. (2010). In sweep oscillator this has a linearly changing voltage for almost the whole one cycle .a fast return to the waves original value .This wave shape is useful for changing the frequency of the voltage control oscillator which is an oscillator that can have its frequency varied over a set range by having a variable sweep voltage applied to its control input.
References
Boyce A, Cooke E, Jones R and Weatherill (2010). B –BTEC Level 3 National Engineering Student Book Pearson.
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