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Ebook Foundations of analog and digital electronic circuits: Part 2

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Nội dung chi tiết: Ebook Foundations of analog and digital electronic circuits: Part 2

Ebook Foundations of analog and digital electronic circuits: Part 2

FIRST-ORDER TRANSIENTS IN LINEAR ELECTRICAL NETWORKS10As illustrated ill Chapter 9, capacitances and inductances impact circuit behavior, rhe effect o

Ebook Foundations of analog and digital electronic circuits: Part 2of capacitances and inductances is so acute in high-speed digital cứ-cuils, for example, that our simple digital abstractions developed in (liapler 6

based on a sialic discipline become insufficient lor signals that undergo transitions. Therefore, understanding the behavior of circuits containing ca Ebook Foundations of analog and digital electronic circuits: Part 2

pacitors and inductors is important. In particular, this chapter will augment our digital abstraction with the concept ol delay to include the effects

Ebook Foundations of analog and digital electronic circuits: Part 2

of capacitors and inductors.Looked al positively, because they can store energy, capacitors and inductors display the memory property, and offer sign

FIRST-ORDER TRANSIENTS IN LINEAR ELECTRICAL NETWORKS10As illustrated ill Chapter 9, capacitances and inductances impact circuit behavior, rhe effect o

Ebook Foundations of analog and digital electronic circuits: Part 2ll of the voltages and currents in the network will have the same square-wave shape. But include one capacitor in the circuit and very different wavef

orms will appear — sections of exponentials, spikes, and sawtooth waves. Figure 10.1 shows an example of Such waveforms for the two-inverter system of Ebook Foundations of analog and digital electronic circuits: Part 2

I'igure 9.1 in chapter 9. rhe linear analysis techniques already developed — node equations, superposition, etc — areadecpiate for finding appropriat

Ebook Foundations of analog and digital electronic circuits: Part 2

e network equations to analyze these kinds of circuits. I lowever, the formulations turn out to be differential equations rather than algebraic expiat

FIRST-ORDER TRANSIENTS IN LINEAR ELECTRICAL NETWORKS10As illustrated ill Chapter 9, capacitances and inductances impact circuit behavior, rhe effect o

Ebook Foundations of analog and digital electronic circuits: Part 2R TEN FIRST-ORDER TRANSIENTSI llis chapter will discuss systems containing a single storage clement, namely, a single capacitor or a single inductor.

Such systems are described by simple, first-order differential equations. chapter 12 will discuss systems containing two storage dements. Systems with Ebook Foundations of analog and digital electronic circuits: Part 2

two storage elements are described by second-order differential equations.1 I lighcr-order systems are also possible, and are discussed briefly in Gi

Ebook Foundations of analog and digital electronic circuits: Part 2

apter 12.Ulis chapter Will start by analyzing Simple circuits containing one capacitor, one resistor, and possibly a source. We W ill then analyze cir

FIRST-ORDER TRANSIENTS IN LINEAR ELECTRICAL NETWORKS10As illustrated ill Chapter 9, capacitances and inductances impact circuit behavior, rhe effect o

Ebook Foundations of analog and digital electronic circuits: Part 2UITSlet US illustrate first-order systems with a lew primitive examples containing a resistor, a capacitor, and a source. We first analyze a current s

ource driving the so-called parallel RC circuit.10.1.1 PARALLEL RC CIRCUIT, STEP INPUTShown in Figure 102a IS a sunpie source-resistor-capacitor circu Ebook Foundations of analog and digital electronic circuits: Part 2

it. On the basis of the Thẽvenin and Norton equivalence discussion ut Section 3.6.1, this circuit could result from a Norton transformation applied to

Ebook Foundations of analog and digital electronic circuits: Part 2

a more compliance!FIGURE 10.2 CííỊxicitcx dunging transient.1. However. a Grant With two storage elements that can be replaced by a single equivalent

FIRST-ORDER TRANSIENTS IN LINEAR ELECTRICAL NETWORKS10As illustrated ill Chapter 9, capacitances and inductances impact circuit behavior, rhe effect o

Ebook Foundations of analog and digital electronic circuits: Part 2 is rise sum of rise two capacitances.10.1 Analysis of RC CircuitsCHAPTER TEN505♦FIGURE 10.3 A more complicated circuit that can be transformed into t

he simpỏer circuit in figure 10.2a by using I hớrenĩn and Norton transformations.circuit containing many sources and resistors, and one capacitor, as Ebook Foundations of analog and digital electronic circuits: Part 2

suggested tn figure 103. In US assume we wish Io find the capacitor voltage ư('. We will use the ncxle method described in (chapter 3 Io do so. As sho

Ebook Foundations of analog and digital electronic circuits: Part 2

wn in figure 10.2a, we take the bottom node as ground, w hich leaves us with one unknown node voltage* corresponding to the lop node, rhe voltage al t

FIRST-ORDER TRANSIENTS IN LINEAR ELECTRICAL NETWORKS10As illustrated ill Chapter 9, capacitances and inductances impact circuit behavior, rhe effect o

Ebook Foundations of analog and digital electronic circuits: Part 2ode method, we write KCL for the top node in Figure 10.2a, substituting the constituent relation for a capacitor from Equation 9.9,Or, rewriting,■(A _

l'c . ^dl'cdl'C , VC. _ Ht)dl RC c-10.1-10.2As promised, the problem can be formulated in one line, hut to find Fc(z), we must solve a nonhomogencous Ebook Foundations of analog and digital electronic circuits: Part 2

, linear first-order ordinary differential equation with constant coefficients. This is not a difficult task, but one that must be done systematically

Ebook Foundations of analog and digital electronic circuits: Part 2

using any method of solving differential equations.To solve this equation, we will use the method of homogeneous and particular solutions because thi

FIRST-ORDER TRANSIENTS IN LINEAR ELECTRICAL NETWORKS10As illustrated ill Chapter 9, capacitances and inductances impact circuit behavior, rhe effect o

Ebook Foundations of analog and digital electronic circuits: Part 2heorem of differenti.ll equations, ihe method states tli.it the solution to the nonhomogeneous differenti.ll equation can be obtained by summing toget

her the homogeneous solution and the particular solution. More specifically, let t'ctM be any solution to the homogeneous differential506CHAPTER TEN F Ebook Foundations of analog and digital electronic circuits: Part 2

IRST-ORDER TRANSIENTSequation(/re VC _ 0 dt RC-103associated with our nonhomogeneous differential equation 10.2. rhe homogeneous equation is derived f

Ebook Foundations of analog and digital electronic circuits: Part 2

rom the original nonhomogencous equation by selling the driving function, t{l) in this case, to zero, Further, let Vcyự) lx? any solution to Equation

FIRST-ORDER TRANSIENTS IN LINEAR ELECTRICAL NETWORKS10As illustrated ill Chapter 9, capacitances and inductances impact circuit behavior, rhe effect o

Ebook Foundations of analog and digital electronic circuits: Part 2nneous solution and Vaịí) is called the particular solution. when dealing with circuit responses, the homogeneous solution is also called the natural

response of the circuit because it depends only on the internal energy storage properties of the circuit and not on external inputs, lire particular s Ebook Foundations of analog and digital electronic circuits: Part 2

olution IS also called the forced response or the forced solution because it depends on the external inputs to the circuit.

FIRST-ORDER TRANSIENTS IN LINEAR ELECTRICAL NETWORKS10As illustrated ill Chapter 9, capacitances and inductances impact circuit behavior, rhe effect o

FIRST-ORDER TRANSIENTS IN LINEAR ELECTRICAL NETWORKS10As illustrated ill Chapter 9, capacitances and inductances impact circuit behavior, rhe effect o

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