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## Über dieses Buch

This textbook explains the fundamentals of electric circuits and uses the transfer function as a tool to analyze circuits, systems, and filters. The author avoids the Fourier transform and three phase circuits, since these topics are often not taught in circuits courses. General transfer functions for low pass, high pass, band pass and band reject filters are demonstrated, with first order and higher order filters explained in plain language. The author’s presentation is designed to be accessible to a broad audience, with the concepts of circuit analysis explained in basic language, reinforced by numerous, solved examples.

## Inhaltsverzeichnis

### Chapter 1. Introduction to Electric Circuits

Abstract
Electric circuits are a method to demonstrate how an electric device receives power and operate. For instance, a flashlight has batteries to provide power to a light bulb, wires to bring the power from batteries to the bulb, and a switch to control the on-off action. The operation of this flashlight can be modeled by its electric circuit. Of course, it has mechanical components to hold the batteries, wires, the switch, and the bulb in place and make the entire unit waterproof. The wires and the switch have electric insulators to protect the flow of electric current in the wires. Nevertheless, these components have no electrical importance when it comes to the distribution of the power and modeling of the circuit. Figure 1.1 shows a flashlight with its internal components and its equivalent circuit.

### Chapter 2. Component Voltage and Current Laws

Abstract
Electric circuit analysis is the collection of methods and tools to determine the voltages and currents as well as the power consumption and generation in electric circuits and components. The relations among the electric elements depend on the elements of the circuit and their configuration or topology. That is how the circuit elements are connected together.

### Chapter 3. Waveform and Source Analyses

Abstract
Electric circuits consist of several components that form a certain topology. The drivers of the circuit can be voltage sources and/or current source. They force the current pass through the circuit by generating voltage drops across elements. A circuit performs certain tasks and has a certain output as well. The sources which are considered as input to the circuit can generate various waveforms. These waveforms excite the circuit and cause different effects.

### Chapter 4. Circuit Response Analysis

Abstract
The flow of current in the circuit branches and drop of voltage across circuit elements depend on their behavior and their ability to store energy. For instance, the voltage drop across a resistor is in phase with its current passing through. But that is not the same in a capacitor or an inductor. This makes the circuit KVL and KCL equations integrodifferential equations. The order of these equations depends on the number of energy-storing elements. In this chapter, the circuit elements are introduced and their equations are discussed. The order of a circuit is discussed, and responses of first- and second-order circuits to their initial condition and to external sources are analyzed.

### Chapter 5. Steady-State Sinusoidal Circuit Analysis

Abstract
Sinusoidal waveforms as explained in Chap. 3 have an amplitude r, a frequency ω, and a phase shift or phase angle ϕ and are expressed as:

### Chapter 6. Mutual Inductance

Abstract
Electric circuits specifically when they are excited by AC sources can transfer energy either by direct electric connection or through magnetic coupling. Consider an inductor with N turns of winding. The current i passing through this inductor generates a magnetic flux ϕ around the windings. This flux creates a magnetic field that starts from the North Pole and ends at the South Pole. When the direction of current changes, the location of north and south poles changes which causes a change in direction of flux but still from the North Pole to the South Pole (Fig. 6.1). The time variations in the flux generates a voltage in the coil that is measured by:

### Chapter 7. Laplace Transform and Its Application in Circuits

Abstract
Most of the circuits introduced so far have been analyzed in time domain. This means that the input to the circuit, the circuit variables, and the responses have been presented as a function of time. All the input functions such as unit step, ramp, impulse, exponential, sinusoidal, etc. have been introduced as a time-dependent variable, and their effects on circuits have been identified directly as a function of time. This required utilization of differential equations and solutions in time domain. However, high-order circuits result in high-order differential equations, which, considering the initial conditions, sometimes are hard to solve. In addition, for circuits which are exposed to a spectrum of frequencies such as filters, the time domain analysis is a limiting factor.

### Chapter 8. Transfer Functions

Abstract
Linear physical system with one or multiple set of input and output can be represented by mathematical functions that relate any of the outputs to any of the inputs. These functions are unique and are defined based on the systems governing equations. The transfer function of a system is defined as the Laplace transform of the output response over the Laplace transform of the input excitation. Transfer functions are defined for any desired set of input and output functions that may relate the input and output together. Considering the Laplace transform of the input function as X(s) and the output as Y(s), the transfer function H(s)can be defined as:

### Chapter 9. Passive Filters

Abstract
Frequency-selective circuits or “filters” are circuits that either pass or attenuate signals at a specific frequency or a range of desired frequencies. These filters can be implemented in hardware to be programmed in software that runs on a processor and can accomplish similar tasks. For instance, consider old cassette players, or video players, in which several set of filters are required to make the quality of sound or video expected from high-quality sets, whereas consider a modern MP3 player, or a digital satellite receiver, in which the same or even better quality of signal processing is expected, but the sets have no actual hardware to accomplish the signal filtration. In this chapter, both hardware circuits and methods to implement the filters in software are discussed.

### Chapter 10. Operational Amplifiers

Abstract
Years before microcontrollers and digital computers were introduced, control system operations, industrial computations, and even simulation of dynamical systems were made possible by use of analog computers. The heart of an industrial analog computer is a device called operational amplifier or “opamp.” These amplifiers consist many transistors to accomplish a theoretical infinite gain to either inputs.

### Chapter 11. Active Filters

Abstract
Filters are frequency selective circuits. This means that they deliberately allow or block a range of frequencies while passing from input to output. Passive filters were circuits that accomplish this task by utilization of passive circuit elements such as R,L, and C. The maximum gain of the output signal is 100% of the input signal when operated at the resonant or at a frequency with orders of magnitude higher or lower than the cutoff frequency.