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### Relate the Current and Voltage of a Capacitor

Capacitors store energy for later use. The voltage and current of a capacitor are related. The relationship between a capacitor’s voltage and current define its capacitance and its power. To see how the [more…]

### Apply the Impulse Function to Circuit Analysis

The impulse function, also known as a Dirac delta function, helps you measure a spike that occurs in one instant of time. Think of the spiked impulse function [more…]

### Apply the Unit Step Function to Circuit Analysis

The unit step (Heavyside) function models the behavior of a switch (off/on). The unit step function can describe sudden changes in current or voltage in a circuit. The unit step function looks like, well [more…]

### Apply the Exponential Function to Circuit Analysis

The *exponential function* is a step function whose amplitude *V** _{k}* gradually decreases to 0. Exponential functions are important to circuit analysis because they’re solutions to many problems in which a circuit [more…]

### Sinusoidal Functions and Circuit Analysis

The sinusoidal functions (sine and cosine) appear everywhere, and they play an important role in circuit analysis. The sinusoidal functions provide a good approximation for describing a circuit’s input [more…]

### How to Perform Complex Processing with Op Amps

If you understand the basic building blocks of op amp circuits, you’re ready to tackle complex processing actions with op amps. Using op amp circuits, you can analyze an instrumentation amplifier, solve [more…]

### Op Amp Circuits and Circuit Analysis

The op amp circuit is a powerful took in modern circuit applications. You can put together basic op amp circuits to build mathematical models that predict complex, real-world behavior. Commercial op amps [more…]

### Analyze Noninverting Op Amp Circuits

Use op amp circuits to build mathematical models that predict real-world behavior.The mathematical uses for signal processing include noninverting and inverting amplification. One of the most important [more…]

### Analyze Inverting Op Amp Circuits

An inverting amplifier takes an input signal and turns it upside down at the op amp output. When the value of the input signal is positive, the output of the inverting amplifier is negative, and vice versa [more…]

### Analyze a Unique Inverting Op Amp: A Summing Amplifier

You can extend an inverting amplifier to more than one input to form a summer, or summing amplifier. An inverting amplifier takes an input signal and turns it upside down at the op amp output. [more…]

### Analyze a Unique Inverting Op Amp: An Op Amp Subtractor

There’s a special op amp circuit —a *differential amplifier*, or subtractor — that is actually a combination of a noninverting amplifier and inverting amplifier. A differential amplifier multiplies the difference [more…]

### Linear Dependent Sources and Circuit Analysis

Dependent sources are used to model transistors and the operational amplifier IC. A *dependent source* is a voltage or current source controlled by either a voltage or a current at the input side of the [more…]

### Find Thévenin’s and Norton’s Equivalents for Complex Source Circuit

A Thévenin or Norton equivalent circuit is valuable for analyzing the source and load parts of a circuit. Thévenin’s and Norton’s theorem allow you to replace a complicated array of independent sources [more…]

### Gauge Maximum Power Transfer Using Thévenin’s and Norton’s Theorems

Thévenin’s and Norton’s theorems can be used to analyze complex circuits by focusing on the source and load circuits. One application of Thévenin’s and Norton’s theorems is to calculate the maximum power [more…]

### Find Thévenin and Norton Equivalent Circuits Using Source Transformation

A Thévenin or Norton equivalent circuit is valuable for analyzing the source and load parts of a circuit. Thévenin’s and Norton’s theorems allow you to replace a complicated array of independent sources [more…]

### Analyze Circuits with Three Independent Sources Using Superposition

Use superposition to analyze circuits that have lots of voltage and current sources. Superposition helps you to break down complex linear circuits composed of multiple independent sources into simpler [more…]

### Analyze Circuits with Two Independent Sources Using Superposition

Use superposition to analyze circuits that have lots of voltage and current sources. Superposition helps you to break down complex linear circuits composed of multiple independent sources into simpler [more…]

### Analyze Circuits with Dependent Sources

You can analyze circuits with dependent sources using node-voltage analysis, source transformation, and the Thévenin technique, among others. For analyzing circuits that have dependent sources, each technique [more…]

### Describe a JFET Transistor with a Dependent Source

Transistors are amplifiers in which a small signal controls a larger signal. One type of transistor is a junction field-effect transistor (JFET). JFET transistors provide a good picture of how transistor [more…]

### Circuit Analysis and Mesh-Current Equations

*Mesh-current analysis* (*loop-current analysis*) can help reduce the number of equations you must solve during circuit analysis. Mesh-current analysis is simply Kircholff’s voltage law adapted for circuits [more…]

### How to Work with Voltage Sources in Node-Voltage Analysis

Voltages across each device in a circuit can be described using node-voltage analysis (NVA). Node-voltage analysis reduces the number of equations you have to deal with when performing circuit analysis [more…]

### Simplify Circuit Analysis by Transforming Sources in Circuits

With transformation, you can modify a complex circuit so that in the transformed circuit, the devices are all connected in series or in parallel. By transforming circuits, you can apply shortcuts such [more…]

### Closed, Open, and Short Circuits

You need a closed path, or *closed circuit,* to get electric current to flow. If there's a break anywhere in the path, you have an *open circuit,* and the current stops flowing — and the metal atoms in the [more…]

### How to Calculate Power in an LED Circuit

The amount of energy consumed by an electronic component is known as *power* (abbreviated *P*), measured in watts (abbreviated *W*). Here is the equation for calculating power: [more…]

### Transistors and Electrical Signals

Transistors are commonly used to amplify signals. An *electrical signal* is the pattern over time of an electrical current. Often, the way an electrical signal changes its shape conveys information about [more…]