Question 6.3.5: Differentiation with Op Amps Design an op-amp circuit that d...
Differentiation with Op Amps
Design an op-amp circuit that differentiates the input voltage.
In theory, a differentiator can be created by interchanging the resistance and capacitance in the integrator circuit. The result is shown in Figure 6.3.9, where Z_{i}(s) = 1/Cs and Z_{f} (s) = R. The input-output relation for this ideal differentiator is
\frac{V_{o}(s)}{V_{i}(s)} = − \frac{Z_{f} (s)}{Z_{i}(s)} = − RCs
The model in the time domain is
v_{o}(t) = − RC \frac{d v_{i}(t)}{d t}
The difficulty with this design is that no electrical signal is “pure.” Contamination always exists as a result of voltage spikes, ripple, and other transients generally categorized as “noise.”
These high-frequency signals have large slopes compared with the more slowly varying primary signal, and thus they will dominate the output of the differentiator. Example 8.1.5 in Chapter 8 shows an improved differentiator design that does not have this limitation.
