4. Experiment D1: Operational Amplifier

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1 4. Experiment D1: Operational Amplifier 4.1. Aim The aim of this experiment is to investigate some properties of real op-amps which are not present in `ideal' op-amps, but which affect practical op-amp circuits significantly Preparation Note that an ideal op-amp has infinite gain, maintained over an infinitely large frequency range including zero frequency ( DC ), infinitely high input impedances, zero output impedance, zero input offset voltage and zero bias currents. The non-ideal values of these properties are what you will be concerned with in this two week experiment. You need to ensure that you read enough to understand these concepts: 1. input bias current 2. input offset current 3. input offset voltage 4. slew rate 5. common-mode rejection. It is important to study the Clayton book, as it contains a lot of information relevant to this experiment. Other points to remember for your preparation: Consider and draw the circuits that you need to perform the experiments, particularly for week 2; Briefly describe the steps you need to take for each part of the experiment some information is left out deliberately to make you think; Make predictions about the results that you expect to see for each part of the experiment; As part of your results, use the datasheet to get predicted values and sketch graphs. Feedback Op-amps are frequently used with a high degree of negative feedback. In the limit such an amplifier may be used as a unity-gain voltage follower, i.e. be subject to 100% feedback (in the sense of a direct connection from output to inverting input). Stability Any amplifier with negative feedback applied can become unstable (that is, oscillate on its own, without any external provocation). It will do this if, at a frequency at which the gain is greater than unity, the overall loop phase-shift is equal to 180 (equivalent to a sign change, i.e. converting the negative feedback into positive feedback). Since an op-amp has several stages of amplification, the possibility of such a large phase shift must always be present. If we consider a single stage of amplification within an op-amp, then if the stage load comprises a resistor, this will inevitably be shunted by stray capacitance (see Figure 4-1). At high frequencies, the load will degenerate into the capacitance alone, since the impedance of the capacitance will be much less than the impedance of the resistance. 15

2 Figure 4-1: Model of Amplifying Stage (at HF most of the current goes into the capacitance). At LF, (constant) At HF, Consequently the output voltage will exhibit 90 of phase lag over a wide range of frequencies, including a considerable range where the gain, even though falling at 6 db per octave, is still above unity. An op-amp incorporating several similar stages will therefore oscillate when even a limited amount of negative feedback is applied. Consider a specific example-an op-amp with four internal gain stages each with a stage load resistor (R) of 10 kω, with a stray capacity load (C) of 10 pf in parallel. Then simple circuit theory shows that the amplifier gain will have fallen to 0.7 of its low-frequency value (-3 db) when the frequency reaches f = 1/(2 π R C), viz 1.59 MHz. At this frequency the phase shift is 45, and hence four identical stages will have an overall phase shift of 180. The overall gain will have decreased only by a factor (0.7) 4, i.e or -12 db. For any operational amplifier with a reasonable amount of low-frequency gain, instability is almost certain with only the most modest degree of feedback. Internal Compensation To counteract this most practical op-amps are internally compensated, that is, constructed with one stage having a deliberately poor high-frequency response, i.e. one stage has a high equivalent shunt capacitance; the others have the minimum capacitance possible. Then from a very low frequency this stage provides 90 of phase shift with a rate of gain reduction of 6 db per octave (= 20 db per decade). If the overall gain falls to unity (0 db) before the phase shift due to other causes can equal 90, the amplifier will be unconditionally stable under all values of feedback. This makes the amplifier easy to use. The disadvantage is that amplifier gain is thrown away unnecessarily at HF if less feedback is used audio amplifiers are an example. Frequency Response It is this internal compensation which accounts for the characteristic frequency response of op-amps. The frequency at which the phase shift is 45 is of necessity that at which the gain is reduced from the DC value by 3 db. This is shown in Fig. 2 on a graph of gain (db) versus frequency, plotted on a logarithmic scale. This type of graph is known as a `Bode gain plot', and on it the high-frequency section is asymptotic to a straight line falling at 20 db per decade; the phase shift is close to 90 over this range. The high-frequency asymptote meets the flat low-frequency gain asymptote at the same frequency as the 3 db point, i.e. where the true gain is 3 db below the DC gain. 16

3 Figure 4-2: Bode Gain Plot of typical op-amp. Phase and Gain Margins There are two stability criteria which can be applied to the overall amplifier. The first is to measure the phase-shift at unity gain and determine the phase stability margin, i.e. the amount by which the phase shift is less than 180. The second is to measure the gain at the frequency at which the phase shift is 180, and determine the gain stability margin as the amount by which the gain is less than 0 db. Bibliography (Although some of these titles are currently out of print, most are available through the Library.) [1] Operational Amplifiers, 4th Edition, George Clayton and G. Burbridge, Butterworth-Heinemann, 2000, ISBN Library ref: [2] Op-amps and Linear Integrated Circuits, 3rd Edition, R A Gayakwad, Prentice Hall, 1993, ISBN [3] Operational Amplifiers and Linear Integrated Circuits, 5th Edition, Robert F Coughlin, Prentice Hall, 1998, ISBN [4] Reference Data for Radio Engineers, 6th Edition, International Telephone and Telegraph, 1975, ISBN [5] Analog Electronics, T E Price, Prentice Hall, 1997, ISBN [6] Operational amplifier characteristics and applications, 3rd Edition, Robert G. Irvine, Prentice-Hall, 1994, ISBN [7] Intuitive operational amplifiers: from basics to useful applications, Rev. Edition, Thomas M. Frederiksen, McGraw-Hill, 1988, ISBN [8] 17

4 4.3. Experiment D1 (741 op-amp) The circuit is first constructed on strip-board. The op-amp should be connected to a 15 V power supply. The centre terminal then becomes the system 0V. Do not connect the offset null potentiometer until the last part of the experiment (D2 part 5). 1. Measure the input offset voltage, input bias currents, and input offset current, using the circuits shown in Figure 4-3 and the associated formulae. Note signs of voltages and directions of currents. 18

5 Figure 4-3: Offset voltage and bias current. If in (a), R f = 50 kω, and R 1 = 100Ω, can the terms in I b- and I b+ be ignored, assuming the expected values from the 741 data sheet? If so, what is the value of V os? If in (b), R 1 = 100Ω, R 3 = 100 kω, which terms in the formula can be ignored? What is the value of I b+? If in (c), R 4 = 100kΩ, which terms in the formula can be ignored? What is the value of I b-? From the measured values find the input offset current and input bias current. Compare these measured values with those from the data sheet, and comment on any differences. NB: If V o > 12V, the gain is too high and R f should be reduced. 19

6 2. Measure the gain and frequency response of the circuit shown in Figure 4-4 for various values of feedback, in both inverting mode (as shown) and non-inverting mode. Suitable values for R f are 2k2, 22 k and 220 k. Plot the gain in db against log frequency, and comment on the curves found. If the bandwidth is defined as the frequency at which the gain has fallen by 3 db, is there any significance in the product of low-frequency gain and bandwidth? NB: check that the 3 db frequency is the same as the frequency where the sloping asymptote intersects the flat LF asymptote. NB: Is there any advantage in using log-linear graph paper? Figure 4-4: Inverting feedback amplifier. By extrapolation, determine the frequency at which the gain is 0 db. Measure the phase shift between input and output voltages, in the asymptotic sloping section. Check that the output (sign?) lags the input by close to 90. Updated K.N. Bateson Updated July 2008 S. Worrall 20

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