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PHYSICS COURSE NAME LAB 09 THE OPERATIONAL AMPLIFIER Lab format: This lab is performed via an internet connection with the Remote Web-based Science Laboratory (RWSL). Relationship to theory: This lab corresponds to the study of operational amplifiers (Op Amps). OBJECTIVES To examine the use of operational amplifiers in inverting and non-inverting amplifier applications. To prepare for further explorations of operational amplifier circuits using simulations such as with NI Multisim. To develop further skills for working with oscilloscopes through additional practice. EQUIPMENT LIST Operational Amplifier Test Circuit for RWSL Non-inverting Operational Amplifier Board for RWSL Inverting Operational Amplifier board for RWSL. Oscilloscope – NI ELVIS II Function Generator – NI ELVIS II two Digital Multimeters (DVM) – NI ELVIS II INTRODUCTION Overview The modern operational amplifier (op amp) is an integrated circuit linear amplifier demonstrating high gain, high input impedance and low output impedance. They are used as filters, peak detectors, signalfunction generators, small signal rectifiers, instrumentation amplifiers and many other applications. Operational Amplifiers An amplifier is a device which takes an input signal of voltage Vin and generates an output signal of voltage Vout . If Vout is directly proportional to Vin , the amplifier is said to be “linear” as in Equation 1. 𝑉𝑜𝑢𝑡 = 𝐴 𝑉𝑖𝑛 Equation 1 or 𝐴= 𝑉𝑜𝑢𝑡 ⁄𝑉 𝑖𝑛 Creative Commons Attribution 3.0 Unported License 1 PHYSICS COURSE NAME LAB 09 where A is called the voltage gain of the amplifier. The op amp has two inputs and one output. (The physical unit of the op amp has other terminals as well as power inputs. See Figure 5.) The circuit symbol is a triangle as shown in Figure 1. The two inputs are labelled – and + and are called the inverting input and the non-inverting input, respectively. The inverting and non-inverting inputs do what their names imply. Compare input and output signals in Figure 2. Note that linear amplifiers preserve the shape of the input waveform (if not the amplitude). Vin inverting non-inverting Vout Figure 1. The schematic symbol for an op amp (a) (b) Figure 2. Action of (a) inverting and (b) non-inverting inputs The voltage gain for various amplifying circuits can be predicted from the characteristics of the ideal op amp, without actually delving into the workings of the op amp’s internal circuitry. The two essential principles of the ideal op amp are: The impedance between the inverting and non-inverting input terminals approaches infinity. Therefore, any current flowing between the inputs produces a negligible voltage drop. As a result, input potentials are approximately equal. The gain is determined by a feedback resistor RF which feeds some of the amplified signal from the output back to the inverting input. If this resistor were absent, the “open circuit” gain would be something in the range of 50,000 ~ 200,000. The presence of RF reduces the amplitude of the output signal and hence the gain. The smaller the feedback resistor, the smaller the gain. Creative Commons Attribution 3.0 Unported License 2 PHYSICS COURSE NAME LAB 09 The Non-Inverting Amplifier Circuit I RF R + Vout Vin Figure 3. Non-inverting amplifier circuit. Figure 3 shows the non-inverting amplifier circuit. The potential appearing at the inverting terminal equals the potential at the non-inverting terminal. Therefore, the voltage across R is equal to Vin . The current through R can be expressed as 𝐼= 𝑉𝑖𝑛 𝑅 Equation 2 All the current through R also passes through RF . The voltage across RF is 𝑉𝑜𝑢𝑡 − 𝑉𝑖𝑛 = 𝐼 𝑅𝐹 Substituting for I from Equation 2, 𝑉𝑜𝑢𝑡 − 𝑉𝑖𝑛 = 𝑉𝑖𝑛 𝑅𝐹 𝑅 Finally, we can solve for the gain of the ideal non-inverting amplifier circuit as 𝐴= 𝑉𝑜𝑢𝑡 𝑉𝑖𝑛 =1+ 𝑅𝐹 𝑅 Equation 3 Creative Commons Attribution 3.0 Unported License 3 PHYSICS COURSE NAME LAB 09 The Inverting Amplifier Circuit I Vin RF R + Vout Figure 4. Inverting amplifier circuit Figure 4 shows the inverting amplifier circuit. Note that both inputs sit at ground potential. As a result, the voltage across R is equal to Vin . The current through R can again be expressed as 𝐼= 𝑉𝑖𝑛 𝑅 Equation 4 All this current flows through RF as well. The potential across 𝑅𝐹 can be shown as 𝑉− − 𝑉𝑜𝑢𝑡 = 𝐼 𝑅𝐹 where 𝑉− represents the potential at the inverting terminal and is equal to zero. Substituting Equation 4 for I gives us the gain of the inverting amplifier (Equation 5). −𝑉𝑜𝑢𝑡 = 𝐴= 𝑉𝑜𝑢𝑡 𝑉𝑖𝑛 𝑉𝑖𝑛 𝑅𝐹 𝑅 =− 𝑅𝐹 𝑅 Equation 5 WARNINGS There are no special safety concerns associated with this lab. If connecting your own instruments rather than RWSL, keep in mind that many instruments are connected to each other through a common ground. Unintentionally creating a ground loop is a common rookie mistake. Creative Commons Attribution 3.0 Unported License 4 PHYSICS COURSE NAME LAB 09 PROCEDURE Part I: The op amp exterior Go to the Operational Amplifier Test Circuit for RWSL (Figure 6). Using the pin-out diagram as a guide (Figure 5), use the RWSL camera and zoom in to confirm that the circuit is the one shown in the schematic Figure 6. [Note: The power connections to the chip are implied but not shown in the schematic. This is customary for op amps.] This circuit takes a signal at the non-inverting input and returns the same signal at the output. Set the function generator for a 1.0 kHz sine wave of amplitude 1.0 V. Observe the input and output signals on the oscilloscope (see sample, Figure 7). Verify that the gain is equal to +1. OFFSET 1 - IN 2 8 UNUSED 7 +15 V + + IN 3 6 OUT -15 V 4 5 OFFSET Figure 5. 741C op amp terminal layout (“pin-out” diagram) signal generator Vin + Vout + _ - oscilloscope Figure 6. Test circuit Creative Commons Attribution 3.0 Unported License 5 PHYSICS COURSE NAME LAB 09 Figure 7: Op amp test circuit composite image showing oscilloscope display and controls. Note the RMS and peak-topeak voltages are displayed for each channel. Creative Commons Attribution 3.0 Unported License 6 PHYSICS COURSE NAME LAB 09 Part II: Non-inverting amplifier Go to the Non-inverting Operational Amplifier Board for RWSL (Figure 8). This circuit is similar to that shown in Figure 3 but the single RF has been replaced by a relay switch connection to a selection of resistors so that we can select RF1 through RF5 for RF. We are using RF = R = 10 k (or as specified) to start. Set the function generator for a 1.0 kHz sine wave of amplitude 1.0 V. Observe the input and the output signals on the oscilloscope. How do they compare? Change RF (using the relay) such that your gain will be about 2. While varying Vin using the function generator output control, record Vin and Vout pairs using the RMS voltages displayed on the oscilloscope. Plot a graph of Vout against Vin such that the amplifier gain can be obtained from the slope of the graph. Compare the measured gain with the ideal gain from Equation 3. Change RF to make the gain about 3 and repeat. Figure 8. Non-inverting operational amplifier board for RWSL Creative Commons Attribution 3.0 Unported License 7 PHYSICS COURSE NAME LAB 09 Part III: Inverting amplifier Go to the Inverting Operational Amplifier Board for RWSL (Figure 9). This circuit is similar to that shown in Figure 4 but the single RF has been replaced by a relay switch connection to a selection of resistors so that we can select RF1 through RF5 for RF. We are using RF = R = 10 k (or as specified) to start. Set the function generator for a 1.0 kHz sine wave of amplitude 1.0 V. Observe the input and the output signals on the oscilloscope. How do they compare? Repeat as in Part II, this time using gains of about ¼ and 2 by selecting the appropriate resistances using the relay. Compare the resulting gains with Equation 4. Figure 9. Inverting operational amplifier board for RWSL Original lab manual by John Wonghen and David Everitt Adapted for Remote Delivery by T. Sato under the Remote Science Labs for Second Year Physics Project (2012 – 2013) funded by BCcampus. Creative Commons Attribution 3.0 Unported License 8