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# 5. Operational Amplifiers

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5. Operational AmplifiersIntroductionIn many electronic circuits, the signals (voltage differences) that are generated andmanipulated are very small. Therefore, amplification is often essential. When playing a CD forinstance, the signals generated in the CD player are quite small and will not adequately drive aspeaker system. The signals from the CD player are therefore passed into the stereo amplifier(which often comes as a tuner/amplifier combination in modern home stereo systems). The heartof the stereo amplifier is the operational amplifier, or op-amp, which takes low level voltagesignals as inputs and produces large output voltages that vary linearly with the input voltage.Operational AmplifiersThe op-amp is a simple example of an integrated circuit. The common 411 op-amp used inthis laboratory contains 24 transistors on a single silicon chip. Many integrated circuits are muchlarger: a computer's microprocessor can contain several million separate elements. Eachtransistor is a three terminal semiconductor device that controls a large current with a small one.If you later study electronics, you will learn about transistors. In this course, we will omit thatstage and show how the functioning of op-amp circuits can be understood without knowinganything about the individual transistors of which op-amps are composed. You need onlyunderstand a few basic principles (explained below) and Kirchoff's circuit laws. Our reason fordoing this lab is to show you how practical problems can be solved using electronic devices.These days, most scientists solve practical instrumentation problems using op-amps and otherintegrated circuits rather than discrete components.An op-amp has three main terminals. The circuit symbol for an op-amp is shown infigure 1. The V- input is called the inverting input, the V+ input is called the non-inverting input,and Vout is the output voltage. All voltages are measured relative to the ground line of the powersupply for the op-amp. All op-amps need a power supply in order to provide the amplification,since without a voltage higher than the input voltages it would be impossible to produceamplification. Generally the power supply is provided by connections at +15 V and -15 V to theop-amp. (Note that by convention, these power supply connections are not shown on the circuitsymbol for the op-amp. However, you must always connect them up in the lab.) The supplyvoltages determine the maximum output voltage range of the op-amp, and if Vout reaches one ofthe supply voltages the op-amp is said to be in "saturation". This situation is to be avoided sinceif the op-amp is in saturation, its output cannot be varying linearly with the inputs.5-15- 2 Operational AmplifiersVVVout+-+-Figure 1: Op-amp inputs and outputThe op-amp will amplify both AC and DC signals, although there is a high frequency f3dB(analogous to the f3dB or “cutoff frequency of a low-pass filter) determined by the type of op-amp;frequencies beyond this value will be amplified less and less as the frequency increases. Wedescribe the signal amplifying properties of the op-amp by giving its gain, the ratio between theoutput signal and the input signal. In the so-called "open loop" configuration shown in figure 1,the output voltage is given byVoutA0V V , (1)where the open loop voltage gain A0 characterizes the op-amp. Note that the voltage differencebetween the inputs is amplified and not the voltage between an input and ground. If you add 5volts to both inputs, this does not affect the output at all! Equation 1 makes it clear why V- iscalled the "inverting" input; it contributes negatively to the output signal.The input impedance of an op-amp is typically 106  although it can be as high as 1012  insome models. The output impedance is usually very small. The gain A0 is extraordinarily high,typically 106 at low frequencies, so that an op-amp hooked up solely with two inputs and itssupplies would almost certainly be in saturation (a voltage difference of only 15 microvoltsbetween the inputs would be sufficient to cause saturation). By using "feedback" (see below), thishigh gain can be controlled and made useful. FeedbackBecause the op-amp has such a huge open loop gain A0, it is always used with a feedbacknetwork that controls the inputs by returning some voltage from the output to the input. Thisreduces the effective gain, but it also causes the amplification to be nearly independent offrequency up to much higher frequencies than the open loop f3dB mentioned above. The term feedback refers to configurations in which a fraction of the output voltage isreturned (it is "fed back") to one of the inputs (see figure 2). Thus, the output Vout depends uponitself, as well as the input to the circuit, Vin. (If you find this idea confusing, you are not alone.Operational Amplifiers 5-3The US Patent Office refused to grant its inventor a patent for this extremely importantengineering concept because it didn't believe his idea would work!) Feedback can be positive(returned to the non-inverting input) or negative (returned to the inverting input), but negativefeedback is used primarily in analog circuits because it yields stable, controllable outputs, and wewill concentrate on it. For positive feedback, an increasing output Vout +-circuit componentscircuit components+- Negative feedback--stable Positive feedback --unstableFigure 2: Feedbackdrives the inputs even further positive, resulting in a still more positive Vout. (A similar argumentcan be made that once Vout swings negative, it will result in a large negative swing.) As a result,the device will always be in saturation. While this can be useful for some purposes (e.g. formaking oscillators and in digital circuits), we shall concentrate on "negative feedback" here. Tomake the idea more comprehensible, we will first consider some non-electronic examples offeedback. EXAMPLES OF FEEDBACKSteam engines were equipped with devices

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