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Unformatted text preview: (over) ----------------Problem 4.3: Consider the circuit containing a nonlinear element N as shown in Figure 4.3. The i-v relation for a ⎛ –-----v--⎞ the element N is given by i a = ( 10 A ) ⋅ ⎜ 1 – e 5 V ⎟ . ⎝ ⎠ 2 Ω N + -v i + -v a i a a) Write an equation relating the voltage v a to the input voltage v i . b) Solve for the voltage v a for v i = 10 volts. Note: This requires that you solve the equation in part a. itera-tively for v a . Hint: Use the exponential term to solve for v a as a function of v a and iterate. Δ v c) Find the incremental change in v a for a 2% increase in v i and calculate the ratio a . Δ v i d) Find the value for the incremental resistance of the nonlinear element N by linearizing the expression for i a about the operating point when v i = 10 volts. e) Draw the incremental circuit for the circuit in Figure 4.3. Δ v f) Find the ratio a from the incremental circuit and compare with your exact value from part c. Δ v i...
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