s13_ps09_fall03

# s13_ps09_fall03 - Uniﬁed Engineering I Fall 2003 Problem...

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Unformatted text preview: Uniﬁed Engineering I Fall 2003 Problem S13 (Signals and Systems) Consider the RLC circuit below: L1 + u(t) + – C2 R3 y(t) – This circuit is a notch ﬁlter, meaning that the output y (t) is almost the same as the input u(t), except that the circuit “ﬁlters out” frequencies in a narrow range, deter­ mined by the component values. For example, this circuit might be used to ﬁlter out 60 Hz noise caused by electrical wiring from the input to an audio system, to prevent 60 Hz “hum.” For this circuit, ﬁnd a state­space description of the system, in the form dx(t) = Ax(t) + B u(t) dt y (t) = C x(t) + Du(t) No component values are given, so just ﬁnd the matrices A, B , C , and D in symbolic form. ...
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