Discussion
Consider the following network, impedance of this network as a function of the complex frequency 'S' consists of a certain number of zeros and poles. What is the location of poles ?
Answer: B
The poles are at s = -2 and s = ∞.
Looking into the input, the 2 H inductor is in series with the 1 Ω shunt resistor in parallel with the branch of the 1 H inductor and the second 1 Ω resistor:
\[ \begin{aligned} Z(s) &= 2s + \frac{1 \cdot (s + 1)}{1 + s + 1} \\ &= 2s + \frac{s + 1}{s + 2} \\ &= \frac{2s^{2} + 5s + 1}{s + 2} \end{aligned} \]
The denominator gives a finite pole at s = -2. The numerator is of higher degree than the denominator, so Z(s) also grows without limit as s goes to infinity, which is a pole at infinity. Options without ∞ miss that pole, and +2 has the wrong sign: an RL network has its poles in the left half-plane.
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