Chapter 5
First and Second-Order Circuits
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First-Order Circuits
Electrical circuits with resistors and a single energy storage element - a capacitor or inductor are called first-order circuits.
They are described by a ...
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RC Circuit without Source
When a DC source is removed abruptly from an RC circuit, the circuit becomes source-free.
Assuming the fully charged capacitor's initial voltage is ...
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RC Circuit with Source
When a DC source is applied abruptly to an RC circuit, its voltage is represented as a unit step function.
The voltage across the capacitor is the step ...
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RL Circuit without Source
When a DC source is suddenly disconnected from an RL circuit, it becomes source-free.
Assuming the inductor has an initial current i0, the initial energy ...
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RL Circuit with Source
When an RL circuit is connected to a DC source, its complete response is divided into transient and steady-state responses.
The transient response is the ...
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Design Example: Frog Muscle Response
A student uses an RL circuit to study the muscle response of a frog's leg to electrical stimulation.
Closing the switch causes a brief muscle ...
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Second-Order Circuits
An electrical circuit comprising two irreducible energy storage elements is called a second-order circuit.
Some examples include RLC circuits as well as ...
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Series RLC Circuit without Source
A source-free RLC circuit a composed of a resistor, an inductor, and a capacitor in series without an external energy source.
Here, the initial energy ...
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Types of Responses of Series RLC Circuits
A source-free series RLC circuit is represented by a second-order differential equation.
Its complete solution is a linear combination of two distinct ...
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Series RLC Circuit with Source
Consider an automobile ignition system that produces high voltage from the battery essential for generating a spark.
This system can be modeled as a ...
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Parallel RLC Circuits
Consider a street lamp with an RLC surge protector to protect its components from sudden voltage spikes.
This setup can be approximated by the simplest ...
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Second-order Op Amp Circuits
Consider an audio system that utilizes a second-order low-pass filter to eliminate the undesirable high-frequency noise in the audio signal.
This setup ...
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Design Example: Underdamped Parallel RLC Circuit
Underdamped parallel RLC circuits can sustain oscillations at a resonant frequency, making them suitable for use in oscillators.
An electrical engineer is ...
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