Download Op Amp Circuits - دانشگاه آزاد اسلامی واحد زنجان

3030 ‫ فروردين‬03 ‫تمرينات سري اول اندازه گيري دانشگاه آزاد اسالمي واحد زنجان موعد تحويل‬
First practice of electrical measurement Islamic azad zanjan university
Date=30/1/93
Op Amp Circuits
This problem set is designed to step the student through the basics of op amp circuit analysis
and design. The analysis questions will present a number of basic op amp circuits and will
ask the reader to calculate the transfer function (ratio of output voltage to input voltage(s)).
The student will first be asked to calculate a number of intermediate voltages and currents
necessary to achieve the final result, to give them an idea of the methods by which such
systems can be analyzed.
Analysis Questions
The following laws/rules are necessary to complete the following problems:
Kirchoff’s First Law: The voltages in any closed loop sum to zero.
Kirchoff’s Second Law: The currents into and out of any node sum to zero.
Ohm’s Law: The voltage drop across a resistor is equal to the current flowing through it
times the resistance.
First Ideal Op Amp Rule: No current flows into the inputs of an ideal op amp.
More rules will be added as we continue.
1. We want to calculate the transfer function (Vo/Vi) of the circuit shown in Figure 1.
Figure 1: Inverting Op Amp Configuration
a) Calculate the current I1 running through resistor R1.
b) How does that current relate to the current (I2) running through R2?
c) Using I2, find another expression for Vo in terms of V- and Vi.
d) Express Vo in terms of the voltage at the inverting terminal (V-) using the via the intrinsic op amp
gain (Av). (Remember: Vo= Av(V+ - V-) )
e) Using c) and d), find the transfer function in terms of Av. Then take the limit as Av goes to
infinity to find the ideal transfer function for the inverting op amp configuration.
f) Given the ideal transfer function, find the ideal value of V-.
Figure 2: Another Inverting Op Amp Configuration
g) Now consider the circuit in Figure 2. Using the technique of parts a)-c), and assuming V=0, find Vo in terms of V1 and V2. For R0 = R1, what mathematical operation does the input
stage implement?
[email protected]
http://www.iauz.ac.ir/faculties/90498
3030 ‫ فروردين‬03 ‫تمرينات سري اول اندازه گيري دانشگاه آزاد اسالمي واحد زنجان موعد تحويل‬
First practice of electrical measurement Islamic azad zanjan university
Date=30/1/93
2. We will now calculate the ideal transfer function of an instrumentation amplifier, as shown
in Figure 2. To do so, we will use the Second Ideal Op Amp Rule: an ideal op amp with
negative feedback works to make the voltage at the two inputs terminals equal.
Figure 3: Instrumentation Amplifier
a) What are the voltage at the inverting terminals of op amps 1 and 2.
b) Use those voltages to find the voltages at the output of op amps 1 and 2, Vo1 and Vo2
respectively.
We will calculate the gain of the third stage using the superposition principle.
c) For op amp 3, find Vo in terms of Vo1 for Vo2 grounded. What op amp configuration is
this?
d) For op amp 3, find Vo in terms of Vo2 for Vo1 grounded. What op amp configuration does
this resemble?
e) By superposition, the total output Vo of op amp 3 is the sum of the above two results.
Find the complete input/output relationship of op amp 3. Using that relationship and the
values of Vo1 and Vo2 found above, find Vo in terms of V1 and V2.
[email protected]
http://www.iauz.ac.ir/faculties/90498
3030 ‫ فروردين‬03 ‫تمرينات سري اول اندازه گيري دانشگاه آزاد اسالمي واحد زنجان موعد تحويل‬
First practice of electrical measurement Islamic azad zanjan university
Date=30/1/93
3. We now consider a non-inverting configuration op amp, but with a small change. We
replace the ground in the feedback path with an arbitrary voltage reference Vref. Find the
new transfer function by considering the voltage difference between the output and the
voltage reference.
Figure 4: Biased Non-Inverting Op Amp Configuration
This technique, known as biasing an amplifier, is essential for use with single supply op
amps, those for which there is only a positive saturation voltage. It is also useful for
amplifying sensor signals which are produced relative to a voltage reference, as described in
class. The transfer function will bear this out.
4. Our final circuit is very similar to the one above, but with one difference: the output feeds
back to the non-inverting terminal instead of the inverting terminal. This system therefore has
positive feedback instead of negative, meaning that it is unstable, and the output will rapidly
increase until it saturates (reaches the maximum voltage provided to the op amp). Further, the
second ideal op amp rule no longer applies, as we now have positive feedback. We will
analyze the operation of this circuit.
Figure 5: Comparator with Hysteresis
a) What is the voltage at the non-inverting input (V+) if the output is in positive saturation (Vo
= Vsat)?
b) What is the voltage at the non-inverting input (V+) if the output is in negative saturation
(Vo=-Vsat)?
c) Assuming that the op amp is currently in positive saturation, at what input voltage (Vi) will
it switch to negative saturation?
d) This circuit has hysteresis, meaning that the current transfer function is based on the
previous voltage inputs. For Vref=0, draw a graph of Vo versus Vi, showing how to achieve
the various output voltage states.
[email protected]
http://www.iauz.ac.ir/faculties/90498