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### How to Describe the Frequency Response of Filter Circuits

Filter circuits (such as low-pass filters, high-pass filters, band-pass filters, and band-reject filters) shape the frequency content of signals by allowing only certain frequencies to pass through. You [more…]

### Show Frequency Response of a Circuit with Bode Plots

To study a range of frequencies, you use Bode plots. Bode plots help you visualize how poles and zeros affect the frequency response of a circuit. You can express the frequency response gain [more…]

### Making Low-Pass and High-Pass Filters with RC Circuits

With simple RC circuits, you can build first-order RC low-pass (LPF) and high-pass filters (HPF). These simple circuits can give you a foundational understanding of how filters work so you can build more-complex [more…]

### Create Band-Pass and Band-Reject Filters with RLC Series Circuits

There are many applications for an RLC circuit, including band-pass filters, band-reject filters, and low-/high-pass filters. You can use series and parallel RLC circuits to create band-pass and band-reject [more…]

### Create Band-Pass and Band-Reject Filters with RLC Parallel Circuits

There are many applications for an RLC circuit, including band-pass filters, band-reject filters, and low-/high-pass filters. You can use series and parallel RLC circuits to create band-pass and band-reject [more…]

### Laplace Transforms and *s*-Domain Circuit Analysis

Laplace transform methods can be employed to study circuits in the *s*-domain. Laplace techniques convert circuits with voltage and current signals that change with time to the [more…]

### Describe Second-Order Circuits with Second-Order Differential Equations

If you can use a second-order differential equation to describe the circuit you’re looking at, then you’re dealing with a second-order circuit. Circuits that include an inductor, capacitor, and resistor [more…]

*s*-Domain Analysis: Understanding Poles and Zeros of F(s)

Laplace transforms can be used to predict a circuit's behavior. The Laplace transform takes a time-domain function *f(t)*, and transforms it into the function [more…]

### Analyze a First-Order RC Circuit Using Laplace Methods

Using the Laplace transform as part of your circuit analysis provides you with a prediction of circuit response. Analyze the poles of the Laplace transform to get a general idea of output behavior. Real [more…]

### Analyze an RLC Circuit Using Laplace Methods

Using the Laplace transform as part of your circuit analysis provides you with a prediction of circuit response. Analyze the poles of the Laplace transform to get a general idea of output behavior. Real [more…]

### Analyze a First-Order RL Circuit Using Laplace Methods

Using the Laplace transform as part of your circuit analysis provides you with a prediction of circuit response. Analyze the poles of the Laplace transform to get a general idea of output behavior. Real [more…]

### Generalize Impedance to Expand Ohm’s Law to Capacitors and Inductors

Use the concept of impedance to gernalize Ohm’s law in phasor form so you can apply and extend the law to capacitors and inductors. After describing impedance, you use phasor diagrams to show the phase [more…]

### How to Use Phasors for Circuit Analysis

A *phaso*r is a complex number in polar form that you can apply to circuit analysis. When you plot the amplitude and phase shift of a sinusoid in a complex plane, you form a phase vector, or phasor. [more…]

### Analyze an RLC Second-Order Parallel Circuit Using Duality

Second-order RLC circuits have a resistor, inductor, and capacitor connected serially or in parallel. To analyze a second-order parallel circuit, you follow the same process for analyzing an RLC series [more…]

### Analyze a Series RC Circuit Using a Differential Equation

A first-order RC series circuit has one resistor (or network of resistors) and one capacitor connected in series. First-order RC circuits can be analyzed using first-order differential equations. By analyzing [more…]

### Find the Zero-Input and Zero-State Responses of a Series RC Circuit

To find the total response of an RC series circuit, you need to find the zero-input response and the zero-state response and then add them together. A first-order RC series circuit has one resistor [more…]

### Find the Total Response of a Series RC Circuit

After finding the zero-input response and the zero-state response of an RC series circuit, you can easily find the total response of the circuit. Remember that a first-order RC series circuit has one resistor [more…]

### Analyze a Parallel RL Circuit Using a Differential Equation

A first-order RL parallel circuit has one resistor (or network of resistors) and a single inductor. First-order circuits can be analyzed using first-order differential equations. By analyzing a first-order [more…]

### Find the Zero-State Response of a Parallel RL Circuit

A first-order RL parallel circuit has one resistor (or network of resistors) and a single inductor. First-order circuits can be analyzed using first-order differential equations. By analyzing a first-order [more…]

### Find the Total Response of a Parallel RL Circuit

After finding the zero-input response and the zero-state response of an RL parallel circuit, you can easily find the total response of the circuit. Remember that a first-order RL parallel circuit has one [more…]

### How to Solve Differential Equations Using Op Amps

The op amp circuit can solve mathematical equations fast, including calculus problems such as differential equations. To solve a differential equation by finding [more…]

### How to Prepare an Op Amp Circuit to Do Complex Mathematics

By adding a capacitor to an operational-amplifier (op amp) circuit, you can use the op amp circuit to do more-complex mathematical operations, like integration and differentiation. Practically speaking [more…]

### Describe Circuit Inductors and Compute Their Magnetic Energy Storage

In circuits, inductors resist instantaneous changes in current and store magnetic energy. Inductors are electromagnetic devices that find heavy use in radiofrequency [more…]

### Calculate the Total Capacitance for Parallel and Series Capacitors

Capacitors store energy for later use. The capacitance is the ratio between the amount of charge stored in the capacitor and the applied voltage. Capacitance is measured in [more…]

### Find the Power and Energy of a Capacitor

Capacitors store energy for later use. The instantaneous power of a capacitor is the product of its instantaneous voltage and instantaneous current. To find the instantaneous power of the capacitor, you [more…]