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Transient Analysis of First Order RC and RL circuits

Transient Analysis of First Order RC and RL circuits The circuit shown on Figure 1 with the switch open is characterized by a particular operating condition Since the switch is open no current flows in the circuit (i=0) and vR=0 The voltage across the capacitor vc is not known and must be defined It could be that vc=0 or that

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EE 42/100 Lecture 18: RLC Circuits ELECTRONICS

The RLC circuit circuit is one of the most important and fundamental circuits As we shall see it has natural resonant frequencies • The physics describes not only physical RLC circuits but also approximates mechanical resonance (mass-spring pendulum) molecular resonance microwave cavities transmission lines buildings bridges

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Chapter 7 Response of First-order RL and RC Circuits

Procedures to get natural response of RL RC circuits 1 Find the equivalent circuit 2 Find the initial conditions: initial current I 0 through the equivalent inductor or initial voltage V 0 across the equivalent capacitor 3 Find the time constant of the circuit by the values of the equivalent R L C: 4 Directly write down the

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RL Circuits Prelab

Read over your lab manual about RL circuits 1 An RL circuit has a voltage source a resistor an inductor and a switch all in a circuit When the switch is open there is no current flowing in the circuit because the circuit is open Recall from previous labs (Ampere’s Law and Helmholtz Coils) that a magnetic field will be generated around a

What is RC in a circuit?
Note that the product RC has the unit of time. (Ohm)(Farad) → seconds RC is called the time constant of the circuit and it is often assigned the variable τ = RC . circuit for t>0. In fact, since the circuit is not driven by any source the behavior is also called the natural response of the circuit.
What is RL circuit?
Figure 14.5. 1 a shows an RL circuit consisting of a resistor, an inductor, a constant source of emf, and switches S 1 and S 2. When S 1 is closed, the circuit is equivalent to a single-loop circuit consisting of a resistor and an inductor connected across a source of emf (Figure 14.5. 1 b ).
What is RLC resonant circuit?
RLC circuits are ubiquitous. This tablet PC uses a pen that has an RLC resonant circuit in the pen. Using near field magnetic coupling, the screen is able to detect the presence of the pen, even without touching. It can use the distance information to estimate the “thickness” of lines that I draw.

RLC Circuits

The RLC circuit circuit is one of the most important and fundamental circuits. As we shall see, it has natural resonant frequencies. • The physics describes not only physical RLC circuits, but also approximates mechanical resonance (mass-spring, pendulum), molecular resonance, microwave cavities, transmission lines, buildings, bridges,

Series RLC Circuit

As we shall demonstrate, the presence of each energy storage element increases the order of the differential equations by one. So for an inductor and a capacitor, we have a second order equation. Using KVL, we can write the governing 2nd order differential equation for a series RLC circuit. Note that the solution depends on the initial charge on th

Parallel RLC Circuit

A Parallel RLC circuit is the dual of the series. In other words, the role of voltage/current and inductance/capacitance are swapped but the equation is the same. inst.eecs.berkeley.edu

Mechanical Analog: Mass-Spring-Damper System

Recall that using Newton’s law and Hook’s law, we arrive at a second order differential equation for a mass-spring system. A damper is used to model the friction of the system. inst.eecs.berkeley.edu

Fluid Flow Analog

We can construct an analog to the RLC circuit by modeling the capacitors and inductors using water tanks and turbines. As you might expect, the water flow would slosh back and forth. When the tank discharges, the water is pushed into the second tank due to the inertia of the turbine (and the water itself). Then eventually the right hand side tank

Step Response: Steady-State Solution

The steady-state solution is easy to find. If d/dt = 0, then the equation reduces to a simple DC equation. • For small L, we know the output exponentially climbs toward the solution. As the inductance is increases, we find the rate of the step response changes. We also eventually observe overshoot and ringing. inst.eecs.berkeley.edu

Second Order Equations: Homogeneous Solution

For any second order homogeneous system, the solution is an exponential function. The amplitude and the argument of the exponential must be selected to satisfy the differential equations. We shall see that the arguments can become complex, which represents oscillatory behavior. inst.eecs.berkeley.edu

Canonical Characteristic Equation

Since we will meet this same equation over and over, we solve it once and carefully categorize the solution. To do this we put the equation into a standard canonical form. The entire system is described by three constants: R, L, and C. The general equation is parameterized by two constants: ω and Q. 0 We shall show that ω represents the natural fre

I - Step Response

The system is described by two decaying time constants. There is so much loss in the system that we do not observe any kind of oscillation. For example, as the capacitor discharges, it losses too much energy to the resistor. We can almost ignore the inductance • In some applications, this is desired. The only problem is that the rate can be too sl

II - Step Response

This has the desirable characteristic that the circuit step response settles to a DC state the fastest without overshooting. In other words, the transient response is the fastest and never overshoots. • You can imagine situations where this is exactly what you want – say your cruise control in your automobile inst.eecs.berkeley.edu

III - Step Response

As evident in the plot, the quality factor plays an important role in the step response. The higher the Q, the faster the circuit reaches the desired output, but the longer it takes it to settle due to “ringing”. • Think about the shock absorbers in your car Or imagine transmitting a signal from one part of your circuit to another. The L and C wou

Series RLC Circuits Resonant Frequency Inductive Reactance & Capacitive Reactance

Transient Analysis: First order R C and R L Circuits

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