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Practical Op-Amp Design Considerations The results presented in the preceding pages suggest that operational ampli ers permit the design of rather sophisticated circuit in a few very simple steps, simply by selecting appropriate resistor values This is certainly true, provided that the circuit component selection sati es certain criteria Here we summarize some important practical design criteria that the designer should keep in mind when selecting component values for op-amp circuits Section 126 explores the practical limitations of op-amps in greater detail 1 Use standard resistor values While any arbitrary value of gain can in principle be achieved by selecting the appropriate combination of resistors, the designer is often constrained to the use of standard 5 percent resistor values (see Table 21) For example, if your design requires a gain of 25, you might be tempted to select, say, 100-k and 4-k resistors to achieve RF /RS = 25 However, inspection of Table 21 reveals that 4 k is not a standard value; the closest 5 percent tolerance resistor value is 39 k , leading to a gain of 2564 Can you nd a combination of standard 5 percent resistors whose ratio is closer to 25 2 Ensure that the load current is reasonable (do not select very small resistor values) Consider the same example given in 1 Suppose that the maximum output voltage is 10 V The feedback current required by your design with RF = 100 k and RS = 4 k would be IF = 10/100,000 = 01 mA This is a very reasonable value for an op-amp, as you will see in Section 126 If you tried to achieve the same gain using, say, a 10- feedback resistor and a 039- source resistor, the feedback current would become as large as 1 A This is a value that is generally beyond the capabilities of a general-purpose op-amp, so the selection of exceedingly low resistor values is not acceptable On the other hand, the selection of 10-k and 390- resistors would still lead to acceptable values of current, and would be equally good As a general rule of thumb, you should avoid resistor values lower than 100 in practical designs 3 Avoid stray capacitance (do not select excessively large resistor values) The use of exceedingly large resistor values can cause unwanted signals to couple into the circuit through a mechanism known as capacitive coupling This phenomenon is discussed in 15 Large resistance values can also cause other problems As a general rule of thumb, you should avoid resistor values higher than 1 M in practical designs 4 Precision designs may be warranted If a certain design requires that the ampli er gain be set to a very accurate value, it may be appropriate to use the (more expensive) option of precision resistors: for example, 1 percent tolerance resistors are commonly available, at a premium cost Some of the examples and homework problems explore the variability in gain due to the use of higher and lower tolerance resistors.

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Naturally, some difficulties with analogy-based estimation offset its advantages Its accuracy relies on three factors: The availability of an appropriate analog The soundness of the strategy for selecting the analog The manner in which differences between the analog and target are allowed for when deriving an estimate There may be no appropriate analog project within an available data set for the project that you want to estimate One danger is that an analog may be selected and used regardless of its appropriateness An old project could be selected as an analog because it appears similar to the target project, even though factors affecting effort have changed over time

and using Table 61, we compute f (t) = e 2t + e 3t u(t)

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621 Find the inverse Laplace transform of each of the following functions:

s 1 s(s + 2) 3s (s 2 + 1)(s 2 + 4) 1 (s + 2)(s + 1)2

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Transfer Functions, Poles, and Zeros It should be clear that the Laplace transform can be quite a convenient tool for analyzing the transient response of a circuit The Laplace variable, s, is an extension of the steady-state frequency response variable j already encountered in this chapter Thus, it is possible to describe the input-output behavior of a circuit using Laplace transform ideas in the same way in which we used frequency response ideas earlier Now, we can de ne voltages and currents in the complex frequency domain as V(s) and I(s), and denote impedances by the notation Z(s), where s replaces the familiar j We de ne an extension of the frequency response of a circuit, called the transfer function, as the ratio of any input variable to any output variable, ie: H1 (s) = Vo (s) Vi (s) or H2 (s) = Io (s) Vi (s) etc (653)

As an example, consider the circuit of Figure 632 We can analyze it using a method analogous to phasor analysis by de ning impedances Z1 = R1 1 ZC = sC ZL = sL Z2 = R2 (654)

Summary

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