need help Consider the 2nd -order RLC circuit shown below. Determine the transfe

Question

need help

Consider the 2nd -order RLC circuit shown below. Determine the transfer function, H(s) = Set C = 1 mu F and design the circuit (that is, select values for R and L) so that the natural frequency is omega n = 1,000pi r rad/sec, and the damping constant is xi = . Determine the resulting rise time, settling time, and percent overshoot of the unit step response. Use Matlab to plot the unit step response for your design in part b). Verify that the response has the correct rise time, settling time, and percent overshoot.

Explanation / Answer

let current through circuit be I(s)

I(s)=Vi(s)/Z

Z=R+sL+1/sC

Vo(s)=I(s)*(1/sC)

Vo(s)/Vi(s)=1/(s^2LC+sRC+1)

b) T(s)=Wn^2/(s^2+zeta*Wn*s+Wn^2)

natural frequency=Wn=1/sqrt(LC).................1

zeta*Wn=L/R.......................2

from 1 L value can be calculated

substituting value of L in 2 we get the value of R as values of Wn=1000*pi radian/sec and C=1uF and zeta=1/sqrt(2).

Related Questions

Navigate

• Browse (All)
• Browse N
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.