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Solved: Design a circuit with one input, x(t), and one output, y(t), that are related by
Chapter 7, Problem P7.9-4(choose chapter or problem)
Design a circuit with one input, x(t), and one output, y(t), that are related by this differential equation:
\(\frac{d^3}{d t^3} y(t)+16 \frac{d^2}{d t^2} y(t)+8 \frac{d}{d t} y(t)+10 y(t)=4 x(t)\)
Questions & Answers
QUESTION:
Design a circuit with one input, x(t), and one output, y(t), that are related by this differential equation:
\(\frac{d^3}{d t^3} y(t)+16 \frac{d^2}{d t^2} y(t)+8 \frac{d}{d t} y(t)+10 y(t)=4 x(t)\)
ANSWER:Step 1 of 9:
For first order circuit, voltage of the capacitor equals:
In this case the output voltage is known, and equals:
When comparing these two equations we can conclude the following:
(1)
(2)
(3)
We can solve equations 2 and 3 to find and :
= (4)
= (5)
For the switch is closed, the capacitor is at steady state, meaning it acts as an open loop. The circuit looks as shown below.