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Goals

To become familiar with operational amplifiers (op-amp) and to use the op amp in various types of feedback circuits.

Background

An operational amplifier (op-amp) is one of the most important and versatile electronic components. It is extensively used in a variety of electronics circuits, from audio systems, filters, and engine control to appliances.

The op-amp symbol is given in Figure 1. The device has two input terminals, i.e. a non-inverting and an inverting terminal, v_p and v_n, respectively. An interesting property of the op-amp is that the output voltage is only a function of the difference of the two input terminals, as follows:
 

 

In addition, the device is characterized by a very large amplification (or gain) A_v, a large input resistance and small output resistance. A typical value of the gain A_v is 200,000. As a result of the large amplification A_v, the required input voltage difference (v_p - v_n) to obtain a finite output voltage is very small and often assumed to be zero. The input terminals are said to be virtually short-circuited. This is an important property that we will make use of extensively to analyze op-amp circuits. Also, because the input resistance is very large the input current will be very small. This leads to two important rules we have to remember when working with op-amp circuits:

1. The input current is zero.
2. The two input terminals are virtually shorted together (or the voltage difference between the inverting and non-inverting amplifier is zero) when the amplifier is used with negative feedback.

Another aspect of the op-amp is that the maximum output voltage is always limited to a certain value determined by the power supplies, as schematically indicated in Figure 2. The corresponding input voltage range to keep the op-amp in the active region is than given by,
 

It is clear from the figure that the input should be kept very small in order to stay in the active (or linear region). This makes it difficult to use op-amps by itself (also called in an open loop configuration). It is for this reason that op-amps are rarely used in open loop. However, a much more useful way to use op-amps is in a negative feedback configuration. This involves connecting the output back to the inverting input of the op-amp. The feedback will keep the differential input voltage (v_p – v_n) close to zero. With feedback, the overall gain is called the closed-loop gain, which will be drastically reduced as compared to the open-loop gain. A major advantage of using feedback is that the gain is now a function of the resistors only and is independent of the op-amp gain A_v, which can vary from device to device. Two popular feedback configurations are the inverting and non-inverting op-amp circuits as shown in Figure 3.
 

Notice that in both cases the output voltage is fed back to the negative input terminal. The only difference is the connection of the input voltage to the inverting or non-inverting input terminal.

An op-amp comes in a DIP (dual in-line package) as shown in Figure 4. Pins 1 and 5 are used for nulling the offset voltage. We will not use these pins in this lab. Pin 8 is not connected (NC) to the internal circuits of the op-amp. One of the more popular op-amps is the LM741.

Pre-lab assignment

1. Review the section on op-amp circuits in the textbook (pp. 87 in Basic Circuit Engineering Analysis, by D. Irwin).
2. Consider the circuit of Figure 3a with R₁ = 1kW and R₂ = 5 kW. Find the value of the amplification A=v_o/v_i. Indicate how you got your result. Make use of the two op-amp rules given above.
3. a. Derive the expression of the amplification for the non-inverting amplifier of Figure 3b, using the rules given above.

b. What value of feedback resistor R₁ is needed to give an amplification equal to 2 when R₂=10 kW.

4. Figure 5 shows the circuit schematic of a summing amplifier. Prove that the output voltage is given by,

 
V_o = -[(R_F/R₁).V₁ + (R_F/R₂).V₂ +(R_F/R₃).V₃]
  Figure 5: Summing amplifier  
5. An interesting circuit is shown in Figure 6 that can be used as an inverting or non-inverting amplifier by changing a switch position. Prove that the voltage gain is either +1 or –1, depending on the switch position.
  Figure 6: Amplifier that can be used as a follower (i.e. an amplifier with gain =1)or as an inverting amplifier with gain –1.  
6. For which circuits of figure 7 do the op-amp rules given above apply? If they do not, explain. What is the output voltage of each circuit? Note that the circuit of Fig. 7b is called a follower.

In-lab assignment

1. Equipment

1. Digital multimeter (HP 34401A)
2. Triple output programmable power supply (HP E3631A)
3. Protoboard
4. Blue box with cables and connectors
5. One 10-turn 10 kohm potentiometer
6. Resistors: One 5 kohm , two 10kohm and 22 kohm
7. One buzzer

1. Procedure

1. Non-inverting amplifier circuit.

a. Build the circuit of figure 8. Notice that this is the same non-inverting amplifier as the one in figure 3b. The input voltage is derived from the power supply by a potentiometer, used as a voltage divider. Measure the actual values of the resistors R1 and R2 and record them in your lab notebook
 

Figure 8: non-inverting amplifier   Before placing the components on the protoboard and wiring them up, it is helpful to sketch the physical layout in your notebook. An example of a possible protoboard layout is shown in Figure 9.     Figure 9: Protoboard layout of the circuit in Fig. 8

b. When you finish building the circuit set the power supply to 10 and –10V (from the +/- 25V). It is important that the Vcc and –Vcc are exactly equal in magnitude. Set the current limiter to 100 mA. Double check the connection of the protoboard before connecting and switching on the power supply to your protoboard.

c. Measure the input-output characteristic of the op-amp circuit: vary the input voltage Vin between –6V and +6V in steps of about 1V by adjusting the potentiometer. Measure the actual value of Vin and the corresponding output voltage Vo with the HP multimeter. Make a table with as entries Vin, Vo (measured), and Vo (calculated). Note that the output voltage saturates above a certain input voltage.

If you get unexpected results, you need to debug your circuit. Check the voltages at the Vcc and -Vcc pins of the op-amp; make sure the output is fed back to the inverting input of the op-amp (neg. feedback), etc.

d. At Vin=2V, measure v_p, v_n and the difference (v_p - v_n). Use a sensitive voltage scale so that the very small difference between v_p and v_n can be measured. Notice that this difference should be small because the inputs are virtually short-circuited as explained in the background section.

e. For you report, complete the table above with the calculated values of the output voltage. Make a plot of the measured and calculated output voltage versus the input voltage. You can use a spreadsheet or Matlab to make the plot. Indicate on the graph the transition between the active and saturated regions of the circuit. Find the slope of the graph (i.e. the amplification) and compare it with the calculated one, based on measured resistance values. Note also the maximum and minimum output voltage (i.e. the saturation levels).

2. Summing Amplifier

1. Build the summing amplifier of figure 10. First, sketch how you will layout the circuit on your protoboard. For voltage source V2 use the 6V supply of the HP triple output power supply.
    Figure 10: Summing amplifier  
2. Measure the actual values of the resistors.
3. Write the expression of the output voltage as a function of the input voltages V₁ and V₂.
4. Make the voltage V₁=1V and V₂=2V and measure the output voltage. Next, change the voltage V₁=3V and measure the output voltage. How do the measured values compare to the calculated ones?
5. For V₁=1V and V₂=2V measure v_n to verify that the inverting input terminal is virtually shorted to ground.

1. The Op-amp as a buffer

One of the main advantages of an op-amp is that it draws very little input current (ideally zero current – see rule 1). This implies that the op-amp can be used as a buffer. An example where such a buffer is used is a voltage divider shown in figure 11a. The voltage V₁ is given by V_CC.R1/(R1+R2). However, as soon as one applies a load resistance R_L to the terminal V₁ the voltage will drop (Fig. 11b). Suppose that R1=R2=22kOhm and R_L=5kOhm, the voltage V₁ will drop from 5V to 1.56V after connecting the load resistor R_L! Clearly, this is not a very useful voltage divider circuit. One way to keep the voltage V₁ constant is by inserting a buffer amplifier between the voltage divider and the load, as shown in figure 11c. Because the op-amp has an infinite input resistance the voltage divider is undisturbed and the voltage V₁ remains equal to 5V. The op-amp, used as a follower, ensures that the voltage V_o over the load R_L is equal to 5V.
 
  a. Build the circuit of Figure 11b with R1=R2=22 kOhm, and Vcc=10V. Before connecting the load to the voltage divider measure the voltage V₁. Next, connect a "buzzer" to the output of the voltage divider and measure V₁ again. What do you notice? Does the buzzer buzz? Find the equivalent resistor of the buzzer (based on the measured V1 voltage).
  Figure 11: The op-amp as a buffer . Figure 12: The buzzer, connect with correct polarity..   b. Insert a follower between the voltage divider and the buzzer. Does the buzzer buzz? Measure V₁ and V_o. What do you notice? Explain briefly.

References:

1. J. D. Irwin, "Basic Circuit Engineering Analysis", Prentice-Hall, 1996.
2. P. Horowitz and W. Hill, "The Art of Electronics", Cambridge University Press, Cambridge, 1989.
3. J. Getty, "The Analysis and Design of Linear Circuits – Lab manual", Prentice-Hall, 1993.

Created by J. Van der Spiegel, Feb. 12, 1998; updated by Sid Deliwala, Nov 1. 2009.

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