Ebook Foundations of analog and digital electronic circuit: Part 2
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Ebook Foundations of analog and digital electronic circuit: 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 circuit: 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 circuit: Part 2pacitors and inductors is important. In particular, this chapter will augment our digital abstraction with the concept ol delay to include the effectsEbook Foundations of analog and digital electronic circuit: Part 2
of capacitors and inductors.Looked al positively, because they can store energy, capacitors and inductors display the memory property, and offer signFIRST-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 circuit: 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 waveforms 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 circuit: Part 2 I'igure 9.1 in chapter 9. rhe linear analysis techniques already developed — node equations, superposition, etc — areadecpiate for finding appropriatEbook Foundations of analog and digital electronic circuit: Part 2
e network equations to analyze these kinds of circuits. I lowever, the formulations turn out to be differential equations rather than algebraic expiatFIRST-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 circuit: 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 circuit: 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 GiEbook Foundations of analog and digital electronic circuit: 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 cirFIRST-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 circuit: 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 source 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 circuit: Part 2it. On the basis of the Thẽvenin and Norton equivalence discussion ut Section 3.6.1, this circuit could result from a Norton transformation applied toEbook Foundations of analog and digital electronic circuit: 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 equivalentFIRST-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 circuit: 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 the 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 circuit: Part 2suggested 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 shoEbook Foundations of analog and digital electronic circuit: 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 tFIRST-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 circuit: 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 circuit: Part 2, linear first-order ordinary differential equation with constant coefficients. This is not a difficult task, but one that must be done systematicallyEbook Foundations of analog and digital electronic circuit: Part 2
using any method of solving differential equations.To solve this equation, we will use the method of homogeneous and particular solutions because thiFIRST-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 circuit: Part 2heorem of differenti.ll equations, ihe method states tli.it the solution to the nonhomogeneous differenti.ll equation can be obtained by summing together 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 circuit: Part 2IRST-ORDER TRANSIENTSequation(/re VC _ 0 dt RC-103associated with our nonhomogeneous differential equation 10.2. rhe homogeneous equation is derived fEbook Foundations of analog and digital electronic circuit: 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 circuit: 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 circuit: Part 2olution 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 oFIRST-ORDER TRANSIENTS IN LINEAR ELECTRICAL NETWORKS10As illustrated ill Chapter 9, capacitances and inductances impact circuit behavior, rhe effect oGọi ngay
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