6. A simple RL network is shown in the following figure. The input of this system is x(t) and output y(t) is voltage across the resistor, R₂. Initial condition is given as, i, (0¯)= 1 x(t) R1 = 1 ohm L1 = 1 H R2 = 1 ohm y(t) Output a) For the system described above, i. Determine the input-output relation in terms of differential equation. ii. Determine Laplace domain Transfer function, H(s) from differential equation. [assume i, (0-) = 0] iii. Determine ROC from H(s) and comment on 'Stability' of the system.

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6. A simple RL network is shown in the following figure. The input of this system is x(t) and output y(t) is voltage
across the resistor, R₂. Initial condition is given as, i, (0¯)= 1
x(t)
R1 = 1 ohm
L1 = 1 H
R2 = 1 ohm
y(t)
Output
a) For the system described above,
i. Determine the input-output relation in terms of differential equation.
ii. Determine Laplace domain Transfer function, H(s) from differential equation. [assume i, (0-) = 0]
iii. Determine ROC from H(s) and comment on 'Stability' of the system.
Transcribed Image Text:6. A simple RL network is shown in the following figure. The input of this system is x(t) and output y(t) is voltage across the resistor, R₂. Initial condition is given as, i, (0¯)= 1 x(t) R1 = 1 ohm L1 = 1 H R2 = 1 ohm y(t) Output a) For the system described above, i. Determine the input-output relation in terms of differential equation. ii. Determine Laplace domain Transfer function, H(s) from differential equation. [assume i, (0-) = 0] iii. Determine ROC from H(s) and comment on 'Stability' of the system.
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