Given is the parallel connected RLC network as depicted in the figure below. L C R ↑ )I(t) The controllable current source (t) is the system input. The current ia(t) flowing through a resistive load is the system output. The constant system parameters are the resistance R, the capacitance C, and the inductance L. a) Using the Kirchhoff's current and voltage laws, derive and write down the linear differential equation which describes the input-output behavior of the RLC network. Based on that, derive the input-output transfer function. Calculate the poles and zeros of the system. Determine the parametric condition (i.e. relationship between R, L, and C values) for which the system has only the real poles and is, thus, not oscillatory.

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Given is the parallel connected RLC network as depicted in the figure below.
L
R
↑)I(t)
The controllable current source I(t) is the system input. The current ir(t) flowing
through a resistive load is the system output. The constant system parameters are
the resistance R, the capacitance C, and the inductance L.
a) Using the Kirchhoff's current and voltage laws, derive and write down the
linear differential equation which describes the input-output behavior of the
RLC network. Based on that, derive the input-output transfer function.
Calculate the poles and zeros of the system. Determine the parametric
condition (i.e. relationship between R, L, and C values) for which the system
has only the real poles and is, thus, not oscillatory.
Transcribed Image Text:Given is the parallel connected RLC network as depicted in the figure below. L R ↑)I(t) The controllable current source I(t) is the system input. The current ir(t) flowing through a resistive load is the system output. The constant system parameters are the resistance R, the capacitance C, and the inductance L. a) Using the Kirchhoff's current and voltage laws, derive and write down the linear differential equation which describes the input-output behavior of the RLC network. Based on that, derive the input-output transfer function. Calculate the poles and zeros of the system. Determine the parametric condition (i.e. relationship between R, L, and C values) for which the system has only the real poles and is, thus, not oscillatory.
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