Name: Partner(s): Desk #: Date: Purpose The Operational Amplifier This lab is adapted from the Kwantlen Lab Manual The purpose of this lab is to examine the functions of operational amplifiers (op amps) in two different circuits. Introduction and Theory Operational amplifier The modern operational amplifier (op amp) is an integrated circuit linear amplifier that demonstrates high gain, high input impedance, and low output impendence. They are used as filters, peak detectors, signal-function generators, small signal rectifiers, instrumentation amplifiers, and in many other applications. In general, an amplifier is a device which takes an input signal (V in ) and general an output signal ( ). If is directly proportional to V in, then the amplifier is said to be linear : = AVin or = A V in A is called the (voltage) gain of the amplifier. The op amp has two inputs and one output. (The op amp has other terminals as well for powering the circuit.) The symbol for the op amp is a triangle as shown in Figure 1. Figure 1 The two inputs are labelled and, which represent inverting and non-inverting, respectively. The inverting and non-inverting inputs do what their names imply (Figure 2). Note that the linear amplifiers preserve the shape of the input waveform (if not the amplitude). V in Figure 2 2409 The Operational Amplifier - 1 Saved: 2/19/16, printed: 2/19/16
When both inputs are connected, the is given by the difference of the two inputs: = AVin = A( V -V ) Typical ( open circuit ) gain A of op amps are in the range of 50,000 to 200,000, which tends to have high uncertainty and is limited by the maximum supply voltage to the op amp. Thus, simply hooking up 2 different inputs to an op amp does not make a reliable amplifier. Somewhat paradoxically, the behavior of the op amp becomes much more predictable when we connect the output back to the inverting input (known as negative feedback, see Figure 3). Without actually delving into the workings of the op amp s internal circuitry, we can analyse the voltage gain for various amplifying circuits involving the op amp can be predicted from the characteristics of the ideal op amp, with infinite open circuit gain A, infinite input impedance, and 0 output impedance. Horowitz & Hill provided two Golden ules in their book The Art of Electronics to analyse the behaviour of op amps: Golden rules for Op Amp (with negative feedback) Golden ule #1: The output attempts to do whatever is necessary to make the voltage difference between the inputs zero. Golden ule #2: The inputs draw no current. ule #1 is a result of the negative feedback. If there is any voltage difference between V and V -, the would be huge due to the large A, therefore making V - large and would be even larger. The only possible stable situation would require that is set to whatever voltage necessary for the ( V -V ) to be as close to 0 as possible. Note that = AVin = A( V -V ) can still be satisfied because A approaches (recall that in calculus, it is possible for 0 times can result in a finite number). ule #2 is a direct result of the infinite input impedance of the op amp. Based on these two rules, we can analyse the following two common amplifier circuits. F F (a) (b) Figure 3 2409 The Operational Amplifier - 2 Saved: 2/19/16, printed: 2/19/16
Non-inverting amplifier circuit Figure 3(a) shows the non-inverting amplifier circuit. The potential appearing at the inverting terminal equals the potential at the non-inverting terminal (rule #1). Since is connected to ground on the other side, the voltage across is equal to V in. Using Ohm s law, the current through can be expressed ΔV Vin 0 I = = This current flows towards the ground. This current must all passes through F (the feedback resistor) because no current can enter the inverting input of the op amp (rule #2). The voltage across F is V out Vin = IF Substituting I=V in /, F Vin = Vin Finally, solving for the gain F F = 1 or A = 1 (1) Vin Inverting amplifier circuit Figure 3(b) shows the inverting amplifier circuit. Note that the non-inverting input is connected to ground; therefore, the inverting input must also be at ground potential, or 0 V (rule #1). This is known as a virtual ground, because the input is at ground potential without being connected to ground. As a result, the voltage across is equal to V in. The current through can be expressed Vin I = All the current through also passes through F (rule #2). Being consistent with the direction of the current flow, the voltage across F is V out = I F Substituting I=V in /, F = Vin Finally, solving for the gain F F = or A = (2) V in 2409 The Operational Amplifier - 3 Saved: 2/19/16, printed: 2/19/16
Op amp setup The LM741CN op amp is packaged as an 8-pin IC chip. It has 8 external terminals for connections to the internal circuitry. The diagram below shows the configuration of these terminals around the case of the op amp. For simplicity, we use 12 V and 12 V from our bread board as the power supplies for the supply voltages of V and V (do not confuse these with the non-inverting and inverting inputs). NC stands for no connections (not even to ground), and we will not be using the offset null terminals. Apparatus LM741CN op amp, oscilloscope, function generator, DC power supply, multimeter, proto-board with power supply, decade resistance box, a 10 kω resistor, 4 identical resistors (between 10 and 100 kω ). Part A: Non-inverting amplifier F Vin 12 V (2) V (7) V- (4) (3) -12 V (6) Figure 3(a) 1. Set up the circuit in Figure 3(a) (also shown above with the pin numbers labelled) on the proto-board. Make connections to pin 2 (inverting input), 3 (non-inverting input) and 6 ( ) first, with = 10 kω, and decade resistor box F = 10 kω. Then connect pin 7 (V) and 4(V). Finally plug in the power cord of the breadboard. Set the function generator for a 1.0 khz sine wave of 2.0 V pp. Based on your and F values, what should the gain be for this amplifier? 2409 The Operational Amplifier - 4 Saved: 2/19/16, printed: 2/19/16
2. Observe the input and output signals on the oscilloscope. How do they compare in shape, amplitude and phase? 3. Vary the amplitude of V in (from 2 V pp to 10 V pp )and measure the V pp of V in and. Use Excel to make a plot of against V in. Calculate the voltage gain from the slope of your graph. Compare with the ideal gain. Attach the Excel graph at the end of this report. 4. Change the resistor box so that the gain is 3 and repeat Step 2. What happens when you set V in to 10 V pp? 2409 The Operational Amplifier - 5 Saved: 2/19/16, printed: 2/19/16
Part B: Inverting amplifier epeat Part B for the inverting amplifier circuit of Figure 3(b) (also shown below). Use gains of about 1/4 and 2. Answer all the questions and also attach the Excel graph at the end of this report. F V in Figure 3(b) 2409 The Operational Amplifier - 6 Saved: 2/19/16, printed: 2/19/16
Part C: Adder and subtractor Originally, operational amplifiers were vacuum tube DC amplifiers designed to perform mathematical functions such as addition, subtraction, differentiation, and integration. Op amps were the basic building blocks of analog computers. Modern solid state op amps can perform mathematical functions as well (though more useful circuit designs have been developed for computers). In the circuits below, the op amp is being used to perform a mathematical operation on the two DC inputs V 1 and V 2. For each circuit, set V 1 and V 2 between 1 and 6 V, and measure the input and output voltages using a multimeter. epeat for different input voltages and record the results in the data tables below. (All resistors are of equal value.) V 1 V 1 V 2 V 2 Figure 4(a) Figure 4(b) V 1 V 2 V 1 V 2 What mathematical operation is being performed for each circuit? Pick one circuit, use Kirchhoff s rules and the properties of ideal op amps to derive the relation between and V 1 and V 2. Does it agree with what you find experimentally? 2409 The Operational Amplifier - 7 Saved: 2/19/16, printed: 2/19/16