a) Show that for large values of C, Eq. 16.67 can be approximated by the expression Note

Chapter 16, Problem 16.26

(choose chapter or problem)

a) Show that for large values of C, Eq. 16.67 can be approximated by the expression

\(v_{o}(t) \approx \frac{-V_{m} T}{4 R C}+\frac{V_{m}}{R C} t\).

Note that this expression is the equation of the triangular wave for \(0 \leq t \leq T / 2\). Hints:

(1) Let \(e^{-t / R C} \approx 1-(t / R C)\) and \(e^{-T / 2 R C} \approx 1-(T / 2 R C)\);

(2) put the resulting expression over the common denominator 2 - (T/2RC);

(3) simplify the numerator; and

(4) for large C, assume that T/2RC is much less than 2.

b) Substitute the peak value of the triangular wave into the solution for Problem 16.13 (see Fig. P16.13(b)) and show that the result is Eq. 16.59.