# Electric Circuit II

#### Course Information

Catalog Description:

First & Second-Order Circuits: Source free for series and parallel RC, RL, and RLC circuits.Step response of series and parallel RC, RL and RLC circuits. AC Circuits Analysis Theorems and Techniques. AC Steady state power calculation and power factor correction. Magnetically-Coupled circuits and mutual inductance: Transformers. Series and Parallel Resonance: Passive filters. Fourier analysis: Response of electric circuits to non-sinusoidal signals. Average RMS, and power values for non-sinusoidal signals. Laplace transform and its application to First & Second Order circuit analysis. Two-port networks: Different representations of two-port networks, interconnections of two-port networks. Operational Amplifiers and Filters.

Course Objectives:

The objective of this course is to continue with electric circuits analysis. This course is mainly

intended to develop an understanding of sinusoidal steady state (AC) circuit analysis. Step

responses of first order and second order circuits are studied. The course introduces phasor,

sinusoidal steady state analysis, ac power, RMS values, three-phase systems, and RC, RL and

RLC circuits. The last part of this course is devoted to advanced topics. It provides students

with solid introduction to Laplace and Fourier analysis and two-port network analysis and Amplifiers.

Course Learning Outcomes:

At the end of this course, the students are expected to be able to solve RC, RL and RLC circuits and find the transient response this circuits. Also, will be able to solve AC circuits using different techniques, analyze balanced and unbalanced three phase AC circuits.

The student can understand mutual inductance and transformers.

The student when studying this course, can apply Laplace and Fourier techniques for circuits to simplify and solve the problems, understand Two-port networks technique.

Finally, the student will have a good idea about Amplifiers for different types and its Equations.

Detailed content of course:

Series and parallel circuit:

in this section, we’ll first discuss the difference between series circuits and parallel circuits, using circuits containing the most basic of components – resistors and batteries capacitors and inductors-and who to use this component to make filters.

Series and parallel component:

• Series Resistor • Parallel Resistor • Series inductor • Parallel inductor
• Series capacitor • Parallel capacitor Series RLC circuit:

we have seen that the three basic passive components of: Resistance, Inductance, and Capacitance have very different phase relationships to each other when connected to a sinusoidal alternating supply. In a pure ohmic resistor the voltage waveforms are “in-phase” with the current. In a pure inductance the voltage waveform “leads” the current by 90o, In a pure capacitance the voltage waveform “lags” the current by 90o.

For the series RLC circuit above, this can be shown as: Finally, when working with a series RLC circuit containing multiple resistances, capacitance’s or inductance’s either pure or impure, they can be all added together to form a single component. For example, all resistances are added together, RT = (R1 + R2 + R3) …etc. or all the inductance’s LT = (L1 + L2 + L3) …etc. this way a circuit containing many elements can be easily reduced to a single impedance.

Parallel RLC circuit:

the analysis of a parallel RLC circuits can be a little more mathematically difficult than for series RLC circuits. in the above parallel RLC circuit, we can see that the supply voltage, VS is common to all three components whilst the supply current IS consists of three parts. The current flowing through the resistor, IR, the current flowing through the inductor, IL and the current through the capacitor, IC.

so, for both series and parallel AC or Dc circuit will we analyze and solve it to find the steady state and transient response, calculate Average RMS, and power values.

Filter:

filter circuits pass to the output only those input signals that are in a desired range of frequencies (called pass band). The amplitude of signals outside this range of frequencies (called stop band) is reduced (ideally reduced to zero). Typically, in these circuits, the input and output currents are kept to a small value and as such, the current transfer function is not an important parameter. The main parameter is the voltage transfer function in the frequency domain, ,As is complex number, it has both a magnitude and a phase, filters in general introduce a phase difference between input and output signals.

We have four types of filter: Low-pass, High-pass, Stop-band and Pass-band. These filters can be constructed using an appropriate combination of elements R, L and C.

Low-Pass Filter High-Pass Filter  Mutual Inductance and Transformers

When two inductors (or coils) are in a close proximity to each other, the magnetic flux caused by current in one coil links with the other coil, thereby inducing voltage in the latter. This phenomenon is known as mutual inductance. With two coils near each other we can forming a so-called transformer Laplace Transform:

The Laplace Transform is a powerful tool that is very useful in Electrical Engineering. The transform allows equations in the “time domain” to be transformed into an equivalent equation in the Complex S Domain.

The mathematical definition of the Laplace transform is as follows:

For R, L and C, the Laplace transform for its voltage with a zero-initial condition: Operational Amplifiers:

The term operational amplifier was introduced in 1947 by John Ragazzini and his colleagues, in their work on analog computers for the National Defense Research Council after World War II. The first op amps used vacuum tubes rather than transistors.

The op amp is an electronic unit that behaves like a voltage-controlled voltage source. It can also be used in making a voltage- or current-controlled current source. An op amp can sum signals, amplify a signal, integrate it, or differentiate it. The ability of the op amp to perform these mathematical operations is the reason it is called an operational amplifier. Summary:In this course we introduced basic of series and parallel R, L, C, and how to make a series or parallel circuit form this component, the student will have a good idea about filters and Amplifiers and introduce the Laplace transform to analysis circuit and solve problem.

At the end of electric circuit, I and II, the student will have a basic low to understand and solve a circuit problem.

References