# The OP AMP -, Figure 1

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1 The OP AMP Amplifiers, in general, taking as input, one or more electrical signals, and produce as output, one or more variations of these signals. The most common use of an amplifier is to accept a small electrical signal and increase the voltage or power, for example the amplifiers inside of a stereo. OP AMP s ( Operational Amplifiers) are a fundamental building block for handling analog electrical signals. Typically an OP AMP has two inputs called + and -, ( or V IN + and V IN -) and a single output. The output depends only on the difference of the voltage on the two inputs. If the difference of the two input voltages is V IN, the output voltage is V Out, then V Out = V IN G V. This defines the (voltage) gain, G V. Figure 1 The drawing on the left is the standard diagrammatical representation of an OP AMP with two inputs and one output. The drawing on the right indicates the conceptual operation of an OP AMP by displaying an idealized equivalent circuit. An ideal OP AMP would have the following characteristics: 1. The input resistance R IN would be infinite 2. The output resistance R OUT would be zero 3. The voltage gain, G V would be infinite 4. The bandwidth (how quickly the output will follow the input) would be infinite. 5. If the voltages on the two inputs are equal than the output voltage is zero ( If the output is not zero it is said to have an offset.) These characteristics lead to a couple of secondary s characteristics, which often are considered to be the core of the axiomatic definition of an OP AMP A. Because R IN is infinite, there is no current through the two input leads. B. Because the gain is infinite, the voltage difference between the two inputs must be vanishing small, i.e., ZERO. ( Usually a feedback resistor is used to insure this. If there is a non-zero difference between the voltages on V IN + and V IN -, V OUT will be drive to its positive or negative extreme. This clipping limits the functional gain of the device.) These two derived characteristics seem strange, but usually they are enough to figure out how an OP AMP should work in a circuit. This will be show in the first circuit below.

3 Figure 3 Using a potentiometer to produce a variable voltage from a dual power supply. Be aware that the output of an OP AMP is limited to the range of -V POWER to +V POWER. If you have setup a circuit in which the amplifier gain is 10, then the range of the input signal should be limited to -V POWER /10 to +V POWER / 10, otherwise OP AMP will saturate and clipping will occur. For high gain amplifiers it is possible that the usable input range is so small ( like a few millivolts) that you might miss it as you turn the potentiometer knob and the output will jump from full negative to full positive. Voltmeters or DMM s are the best measuring devices for many of the circuits built in this lab. One on the output and one across the two input leads should be enough. If you use a fast varying signal from a function generator on the input, you probably will need to use an oscilloscope to make measurements. It is assumed you have a basic familiarity with the operation of an oscilloscope from your introductory E&M lab. But you should consult your TA or instructor concern the operation of the specific oscilloscope that you are using. As always be aware of grounding loops, unintentional loops, and incomplete circuits when connecting external function generators or oscilloscopes to your circuit. You will be using a 741 or equivalent OP AMP for your work. Sometimes these come in a package that contains two or four identical OP AMP s in a single DIP. The full manufacturer s data sheet is available at From this one can compare the LM741 against the ideal OP AMP Characteristic Ideal Typical for real Input Resistance 6 M 2 Output Resistance Voltage Gain 50,000 to 100,000 4 Bandwidth 1 MHz, changes at 0.7 V / s 5 Offset voltage 0 1 mv A Input Current 0 30 nanovolts ( 3 X 10-8 volts ) B Voltage difference of inputs 0????

4 Unity Gain Inverting Amplifier The Circuits Figure 4 An circuit for a Unity Gain Inverting Amplifier using a 741 OP AMP. Note the two resistors have the same resistance. R 2 is a FEEDBACK RESISTOR. Let s try to analyze this circuit. Note that + input which is pin # 3 is connected to ground. Characteristic B this implies that the voltage applied to the - input or pin # 2 must also be zero. Note the current into pin # 2 is zero by Characteristic A. For a given input V IN what can V OUT be so that this condition is satisfied. Think about the circuit from V IN through the two resistors to V OUT. If V OUT = - V IN then the wire between the two resistors will be a zero potential, thus satisfying characteristic B. Note the function of the feedback resistor R 2. Inverting Amplifier Figure 5 An circuit for a Inverting Amplifier using a 741 OP AMP. The Gain defined as V OUT / V IN = R 2 / R 1. Try to analyze this circuit. First find the current between V IN and V OUT, and then the voltage drop across, R 1 and/or R 2. This should be enough to let you solve for V OUT in terms of V IN, R 1, and R 2.

5 Level Detector or comparator Figure 6 In this Level Detector, the potentiometer R 1 set the trigger level and when the voltage at V IN ( here controlled by R 2 ) equals that the LED goes on ( or off.) Some other more interesting source of a voltage level could be used rather than a potentiometer. Note the absence of any feedback. Using the OP AMP Characteristics A and B analyze this circuit. The Summing Amplifier Figure 7 This is a Summing Amplifier. V OUT = - ( V IN 1 + V IN 2 ) Using the OP AMP Characteristics A and B analyze this circuit. In the circuit for the Summing Amplifier, could the value of the 330 k resistor be halved without changing the function of the rest of the circuit?

6 The Difference Amplifier Figure 8 This is a Difference Amplifier. V OUT = V IN 2 - V IN 1 Using the OP AMP Characteristics A and B analyze this circuit. Could the value of the resistor between ground and pin # 3 be halved without affecting the operation of the rest of the circuit? The Basic Integrator You will need to Figure 9 This is a basic Integrator circuit using an OP AMP. Use a function generator for the input and make measurements of the input and the output with an oscilloscope. Using the OP AMP Characteristics A and B analyze this circuit. This time you will need to write down some time dependant equations for each half of the input cycle. Try changing the value of the capacitor or R1 or R2 and see what happens. Try changing the frequency of the input and see what happens.

7 The Basic Differentiator Figure 10 This is a basic Differentiator circuit. You will need to use a function generator for the input and make measurements of the input and the output with an oscilloscope. Using the OP AMP Characteristics A and B analyze this circuit. This time you will need to write down some time dependant equations for each half of the input cycle. Try changing the value of the capacitor or R1 or R2 and see what happens. Try changing the frequency of the input and see what happens. The Function Generator (The diagram is on the next page) This circuit is rather complex, but the first trick is to note that it can be broken down into four stages that interact only a little. NOTE: Neatness and order are very important to get the circuit wired correctly. First let us pretend that each of the four stages operates independent of each other, except that the output of one is the input for the next stage. If that is true, then while constructing this circuit, you could just wire the first stage and see if it is operating correctly before wiring the next stage. As is often the case, it is easier to analyze some part circuit other than the beginning. Doing this often lets you get started on the analysis that might otherwise seem overwhelming and reduces the remain problem to something a bit more manageable. The fourth stage is just an inverting amplifier. What is the gain of the fourth stage?

8 Figure 11 This Function Generator is designed to produce a frequency of 1 khz and have the power supply set at ±9 volts. It should produce a square wave, a triangle wave, and a sine wave. Analyzing the second stage is easy, it is an integrator. The second stage accepts a square wave as its input and outputs a triangle wave. The third stage is also an integrator, but its input is a triangle wave. Well the integral of a triangle wave is not really quite a sine wave. But note how much smaller C3 is compared to C2. This suggests that something odd might occur. With a short RC time constant, an integrator is more like a smoother, and a smoothed triangle wave is similar to a sine wave. You should try to determine how accurate of a sine wave this unit produces. The first stage is bit trickier to understand. Note that the center of an RC circuit element connects to pin 2 ( the - input) of the first OP AMP. Pretend momentarily that the tops of R1 and R3 are not attached to the output of the first OP AMP, but rather are being driven by an external square wave that varies between ± 7 V. Think of the OP AMP in this first stage as a level detector with the trigger voltage set to about 0.2 times the driving voltage because R3 and R2 form a voltage divider. The output of this first OP AMP is a square wave because, as the capacitor is charged in one direction, at some point, V IN exceeds the trigger level and the output voltage goes to its maximum negative voltage. As the capacitor charges with the opposite polarity, at some point,

9 V IN becomes smaller than the trigger level and the output voltage goes to its maximum positive voltage. This causes the output of the first OP AMP to be a square wave. If R1 is driven at the correct frequency the output voltage of the first OP AMP will match in frequency and phase the assumed square wave that was driving R1 and R3. Thus, the square wave will be selfperpetuating. Set up and solve the time dependant equations for the charging ( or discharging) of the capacitor during each half of the driving square wave. You should get something like: Try doubling and halving the value of C1 and observe the changes in the output of the circuit. Make two additional OP AMP circuits chosen from the one of the references below. Good general references include:.forrest M. Mims III, Engineer s NoteBook II, ( Radio Shack 1982.) PP This is the source of most of the circuits that are presented here. This book shows many other useful OP AMP circuits. Walter G. Jung, IC Op-Amp Cookbook, 3 rd ed. (Howard W Sams and Co, Indianapolis, In, 1986.) This book is all about OP AMP s, both understanding them and using them. J.H. Moore, C.C. Davis and M.A.Coplan, Building Scientific Apparatus, A Practical Guide to Design and Construction, 2 nd ed. ( Perseus Books, Cambridge, MA, 1991.) This is a good practical text. Paul Horowitz and Winfield Hill, The Art of Electronics, 2 nd ed. (Cambridge University Press, Cambridge, 1989.) Many consider this the bible of applied electronics. This text is very complete, very dense, and very long.

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