## Inverting & Non-Inverting Operational Amplifier Basics

An operational amplifier (op-amp) is an integrated circuit (IC) that contains a large number of microscopic electrical and electronic components integrated on a single silicon wafer. An op-amp can be used in conjunction with other common components to create circuits that perform amplification and filtering, as well as mathematical operations, such as addition, subtraction, …

## Enhancement Mode MOSFET

Figure 1 depicts the circuit symbol and the construction of a typical n-channel enhancement-mode MOSFET. The device has four regions: the gate, the drain, the source, and the bulk. Each of these regions has its own conducting terminal. The bulk and source terminals are often electrically connected, in which case the bulk terminal is not shown in the …

## Bipolar Junction Transistor (BJT) Theory

A Bipolar Junction Transistor (BJT) is formed by joining three sections of alternating p- and n-type material. An NPN transistor is a BJT with a thin, lightly doped p-type base region sandwiched between a heavily doped n-type emitter region and a large, lightly doped n-type collector region. The Bipolar Junction Transistor (BJT) counterpart to the NPN is the PNP transistor, which utilizes the same doping scheme …

## Voltage and Currents in Star (Wye) and Delta Connected Loads

Most of the AC power used today is generated and distributed as three-phase power, which implies three sinusoidal sources, each out of phase with the other. The primary benefit is efficiency: The weight of the conductors and other components in a three-phase system is much lower than that in a single-phase …

## Instantaneous and Average Power Formula

When a linear electric circuit is excited by a sinusoidal source, all voltages and currents in the circuit are also sinusoids of the same frequency as the source. Figure 1 depicts the general form of a linear AC circuit. Figure 1 Time and frequency domain representations of an AC circuit. …

## Low Pass and High Pass Filter Bode Plot

Frequency response plots of linear systems are often displayed in the form of logarithmic plots, called Bode plots after the mathematician Hendrik W. Bode, where the horizontal axis represents frequency on a logarithmic scale (base 10) and the vertical axis represents either the amplitude or phase of the frequency response …

## Band Pass Filter Frequency Response

Using the same principles and procedures in the case of low and high pass filters, it is possible to derive a band pass filter frequency response for particular types of circuits. Such a filter passes the input to the output at frequencies within a certain range. The analysis of a …

## Low Pass and High Pass Filter Frequency Response

There are many practical applications that involve filters of one kind or another. Modern sunglasses filter out eye-damaging ultraviolet radiation and reduce the intensity of sunlight reaching the eyes. The suspension system of an automobile filters out road noise and reduces the impact of potholes on passengers. An analogous concept …

## Fourier Series

The aim of this article is to introduce the concept of frequency domain analysis of signals, and specifically the Fourier series. Later in this article, we explain how it is possible to represent periodic signals by means of the superposition of various sinusoidal signals of different amplitude, phase, and frequency. …

## Second Order System Transient Response

In general, a second-order circuit has two irreducible storage elements: two capacitors, two inductors, or one capacitor and one inductor. The latter case is the most important in terms of new fundamentals; however, the important aspects of all second-order system responses are discussed in this section. Since second-order circuits have …

## First Order System Transient Response

First-order systems are important in all engineering disciplines and occur frequently in nature. Such systems are characterized by a single state variable, where the system energy is proportional to the square of the state variable. That energy is dissipated by the system such that the rate of change of the …

## Resistance and Impedance in an AC Circuit

The i -v relationships of resistors, capacitors, and inductors can be expressed in phasor notation. As phasors, each i-v relationship takes the form of a generalized Ohm’s law: $\text{V=IZ}$ where the phasor quantity Z is known as impedance. For a resistor, inductor, and capacitor, the impedances are, respectively: \$\begin{matrix}{{Z}_{R}}=R & …

## Maximum Power Transfer Theorem

Maximum Power Transfer Theorem Definition Maximum power transfer theorem states that maximum power output is obtained when the load resistance Ro is equal to Thevenin resistance RT as seen from load Terminals. The reduction of any linear resistive circuit to its Thevenin or Norton equivalent form is a very convenient conceptualization, …

## Superposition Theorem

The principle of superposition is a valid and frequently used, analytic tool for any linear circuit. It is also a powerful conceptual aid for understanding the behavior of circuits with multiple sources. For any linear circuit, the principle of superposition states that each independent source contributes to each voltage and …

## Node Voltage Method

Node voltage analysis is the most general method for the analysis of electric circuits. Its application to linear resistive circuits is illustrated in this article. The node voltage method is based on defining the voltage at each node as an independent variable. One of the nodes is freely chosen as …

## Mesh Current Analysis

Another method of circuit analysis employs mesh currents. The objective, similar to that of node analysis, is to generate one independent equation for each independent variable in a circuit. In this method, each mesh in a circuit is assigned a mesh current variable and Kirchhoff’s voltage law (KVL) is applied …

## Characteristics of Network and Electric Circuit

The Oxford online dictionary defines a network as “a group or system of interconnected people or things”. In an electric network, elements, such as resistors, are connected by wires. The same dictionary defines a circuit as “a complete and closed path around which a circulating electric current can flow” or …

## Inverter Harmonic Distortion

It has been found that any periodic (repeating), the non-sinusoidal waveform can be produced by adding a series of sine waves at frequencies other than the fundamental. The fundamental frequency of a waveform is also called the first harmonic. AC voltage and current waveforms consist of frequencies, called harmonics that …