Question 6.4.3: Design an op-amp circuit that differentiates the input volta......
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 6.4.7, where Z_{i}(s)=1/C s\;\mathrm{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)}=-R C sThe model in the time domain is
v_{o}(t)=-R C{\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 6.4.4 shows an improved differentiator design that does not have this limitation.
