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1214 Modify the gains of the coef cient multipliers in Example 127 if we wish to slow down the simulation by a factor of 10 (ie, if = 01) 1215 For the simulation of Example 127, what will the largest magnitude of the voltage analog of xM be for a road displacement xR = 001 sin (100t) [Hint: Use phasor techniques to compute the frequency response xM ( )/F ( ), where f (t) = B dxR /dt +
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KxR , and evaluate the output voltage by multiplying the input by the magnitude of the frequency response at = 100]
1216 Change the parameters of the analog computer simulation of Example 128 to simulate the differential equation d 2 x/dt 2 + 2x = 10f (t)
PHYSICAL LIMITATIONS OF OP-AMPS
Thus far, the operational ampli er has been treated as an ideal device, characterized by in nite input resistance, zero output resistance, and in nite open-loop voltage gain Although this model is adequate to represent the behavior of the op-amp in a large number of applications, practical operational ampli ers are not ideal devices but exhibit a number of limitations that should be considered in the design of instrumentation In particular, in dealing with relatively large voltages and currents, and in the presence of high-frequency signals, it is important to be aware of the nonideal properties of the op-amp In the present section, we examine the principal limitations of the operational ampli er Voltage Supply Limits As indicated in Figure 114, operational ampli ers (and all ampli ers, in general) are powered by external DC voltage supplies, VS+ and VS , which are usually symmetrical and of the order of 10 V to 20 V Some op-amps are especially designed to operate from a single voltage supply, but for the sake of simplicity we shall from here on consider only symmetrical supplies The effect of limiting supply voltages is that ampli ers are capable of amplifying signals only within the range of their supply voltages; it would be physically impossible for an ampli er to generate a voltage greater than VS+ or less than VS This limitation may be stated as follows: VS < vout < VS+ (1281)
For most op-amps, the limit is actually approximately 15 V less than the supply voltages How does this practically affect the performance of an ampli er circuit An example will best illustrate the idea
EXAMPLE 129 Voltage Supply Limits in an Inverting Ampli er
Problem
Compute and sketch the output voltage of the inverting ampli er of Figure 1242
RF VS+
Solution
Known Quantities: Resistor and supply voltage values; input voltage Find: vout (t) Schematics, Diagrams, Circuits, and Given Data: RS = 1 k ; RF = 10 k ; RL =
+ ~ vS + + vout RL
1k ;
= 15 V;
= 15 V; vS (t) = 2 sin(1,000t)
12
Operational Ampli ers
Assumptions: Assume supply voltage limited op-amp Analysis: For an ideal op-amp the output would be:
vout (t) =
RF vS (t) = 10 2 sin(1,000t) = 20 sin(1,000t) RS
However, the supply voltage is limited to 15 V, and the op-amp output voltage will therefore saturate before reaching the theoretical peak output value of 20 V Figure 1243 depicts the output voltage waveform
vout(t) 20 15 10 5 0 5 10 15 20
t Actual response Ideal response: vout(t) = 20 sin (2,000t)
Figure 1243 Op-amp output with voltage supply limit
Comments: In a practical op-amp, saturation would be reached at 15 V below the supply voltages, or at approximately 135 V Focus on Computer-Aided Solutions: An Electronics WorkbenchTM simulation of the
circuit of Figure 1242 can be found in the accompanying CD-ROM
Note how the voltage supply limit actually causes the peaks of the sine wave to be clipped in an abrupt fashion This type of hard nonlinearity changes the characteristics of the signal quite radically, and could lead to signi cant errors if not taken into account Just to give an intuitive idea of how such clipping can affect a signal, have you ever wondered why rock guitar has a characteristic sound that is very different from the sound of classical or jazz guitar The reason is that the rock sound is obtained by overamplifying the signal, attempting to exceed the voltage supply limits, and causing clipping similar in quality to the distortion introduced by voltage supply limits in an op-amp This clipping broadens the spectral content of each tone and causes the sound to be distorted One of the circuits most directly affected by supply voltage limitations is the op-amp integrator The following example illustrates how saturation of an integrator circuit can lead to severe signal distortion
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