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elec_inclass - Resistors, Inductors, and Capacitors...

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Resistors, Inductors, and Capacitors Operational Ampliﬁers Unit 2: Modeling in the Frequency Domain Part 4: Modeling Electrical Systems Engineering 5821: Control Systems I Faculty of Engineering & Applied Science Memorial University of Newfoundland January 23, 2009 ENGI 5821 Unit 2, Part 4: Modeling Electrical Systems

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Resistors, Inductors, and Capacitors Operational Ampliﬁers 1 Resistors, Inductors, and Capacitors First Example: Via DE Stating the Problem in the Freq. Domain First Example: In the Freq. Domain Second Example: Mesh Analysis Pattern of Impedances 1 Operational Ampliﬁers Inverting Op-Amp Noninverting Op-Amp ENGI 5821 Unit 2, Part 4: Modeling Electrical Systems
Resistors, Inductors, and Capacitors The following table gives the relevant relationships between voltage, current, and charge for resistors, inductors, and capacitors:

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Resistors, Inductors, and Capacitors The following table gives the relevant relationships between voltage, current, and charge for resistors, inductors, and capacitors: Voltage-current Current-voltage Voltage-charge Resistor v ( t ) = Ri ( t ) i ( t ) = 1 R v ( t ) v ( t ) = R dq dt Inductor v ( t ) = L di ( t ) dt i ( t ) = 1 L R t 0 v ( τ ) d τ v ( t ) = L d 2 q ( t ) dt 2 Capacit. v ( t ) = 1 C R t 0 i ( τ ) d τ i ( t ) = C dv ( t ) dt v ( t ) = 1 C q ( t ) These components are considered both passive and linear .
Resistors, Inductors, and Capacitors The following table gives the relevant relationships between voltage, current, and charge for resistors, inductors, and capacitors: Voltage-current Current-voltage Voltage-charge Resistor v ( t ) = Ri ( t ) i ( t ) = 1 R v ( t ) v ( t ) = R dq dt Inductor v ( t ) = L di ( t ) dt i ( t ) = 1 L R t 0 v ( τ ) d τ v ( t ) = L d 2 q ( t ) dt 2 Capacit. v ( t ) = 1 C R t 0 i ( τ ) d τ i ( t ) = C dv ( t ) dt v ( t ) = 1 C q ( t ) These components are considered both passive and linear . Passive because they involve no internal source of energy (although inductors and capacitors can store energy).

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Resistors, Inductors, and Capacitors The following table gives the relevant relationships between voltage, current, and charge for resistors, inductors, and capacitors: Voltage-current Current-voltage Voltage-charge Resistor v ( t ) = Ri ( t ) i ( t ) = 1 R v ( t ) v ( t ) = R dq dt Inductor v ( t ) = L di ( t ) dt i ( t ) = 1 L R t 0 v ( τ ) d τ v ( t ) = L d 2 q ( t ) dt 2 Capacit. v ( t ) = 1 C R t 0 i ( τ ) d τ i ( t ) = C dv ( t ) dt v ( t ) = 1 C q ( t ) These components are considered both passive and linear . Passive because they involve no internal source of energy (although inductors and capacitors can store energy). We consider them linear because their behavior is well-described using linear DE’s.
First Example: Via DE e.g. Find the transfer function for the circuit below.

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First Example: Via DE e.g. Find the transfer function for the circuit below. Consider the output to be the capacitor voltage and the input to be v ( t ),
First Example: Via DE e.g. Find the transfer function for the circuit below. Consider the output to be the capacitor voltage and the input to be v ( t ),

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First Example: Via DE e.g. Find the transfer function for the circuit below. Consider the output to be the capacitor voltage and the input to be v ( t ), Apply KVL around the loop:
First Example: Via DE e.g. Find the transfer function for the circuit below. Consider the

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This note was uploaded on 09/07/2009 for the course ENGINEERIN 5821 taught by Professor Andrewvardy, during the Spring '09 term at Memorial University.

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elec_inclass - Resistors, Inductors, and Capacitors...

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