Foundations of analog and digital electronic circuits: Part 2
➤ Gửi thông báo lỗi ⚠️ Báo cáo tài liệu vi phạmNội dung chi tiết: Foundations of analog and digital electronic circuits: Part 2
Foundations of analog and digital electronic circuits: Part 2
FIRST-ORDER TRANSIENTS IN LINEAR ELECTRICAL NETWORKS10As illustrated in Chapter 9, capacitances and inductances impact circuit behavior. The effect of Foundations of analog and digital electronic circuits: Part 2 f capacitances and inductances is so acute 111 high-speed digital cữ-cuils, for example, dial our simple digital abstractions developed in chapter 6 based on a sialic discipline become insufficient lor signals that undergo transitions. Therefore, understanding the behavior of circuits containing cap Foundations of analog and digital electronic circuits: Part 2 acitors and inductors is important. In particular, this chapter will augment our digital abstraction with the concept ol delay to include the effectsFoundations of analog and digital electronic circuits: Part 2
of capacitors and inductors.Looked at positively, beaiuse they can store energy, capacitors and inductors display rhe memory property, and offer signaFIRST-ORDER TRANSIENTS IN LINEAR ELECTRICAL NETWORKS10As illustrated in Chapter 9, capacitances and inductances impact circuit behavior. The effect of Foundations of analog and digital electronic circuits: Part 2 l of the voltages and currents in the network will have the same square wave shape. But indude 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 l Foundations of analog and digital electronic circuits: Part 2 igutv 9.1 in chapter 9. The linear analysis techniques already develc iped — n< ide equal i< ins, supcrp< isilirin, etc — arc adequate for finding appFoundations of analog and digital electronic circuits: Part 2
ropriate network equations to analyze these kinds of circuits. I lowever, the formulations turn out to be differential equations rather than algebraicFIRST-ORDER TRANSIENTS IN LINEAR ELECTRICAL NETWORKS10As illustrated in Chapter 9, capacitances and inductances impact circuit behavior. The effect of Foundations of analog and digital electronic circuits: Part 2 CHAPTER TEN FIRST ORDti TRANSIENTSThis 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 expiations, (liaptcr 12 will discuss systems containing two storage elements. Syste Foundations of analog and digital electronic circuits: Part 2 ms with two storage elements are described by second-order differential expiations.1 I ligher-order systems arc also possible, and are discussed briefFoundations of analog and digital electronic circuits: Part 2
ly in Qiapter 12.This chapter Will start by analyzing sunpie circuits containing one capacitor, one resistor, and possibly a source. We Will then analFIRST-ORDER TRANSIENTS IN LINEAR ELECTRICAL NETWORKS10As illustrated in Chapter 9, capacitances and inductances impact circuit behavior. The effect of Foundations of analog and digital electronic circuits: Part 2 RC CIRCUITSlet 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 soiuce-resistoi-capacito Foundations of analog and digital electronic circuits: Part 2 r circuit. On the basis of the Thévenin and Norton equivalence discussion in Section 3.6.1, this circuit could result Irom a Norton transformation appFoundations of analog and digital electronic circuits: Part 2
lied to a more complicatedFIGURE 10.2 Capnótcx dunging transient1. However. .1 circuit With two storage elements that can be replaced by a single equiFIRST-ORDER TRANSIENTS IN LINEAR ELECTRICAL NETWORKS10As illustrated in Chapter 9, capacitances and inductances impact circuit behavior. The effect of Foundations of analog and digital electronic circuits: Part 2 citance is tile sum of live two capacitances.10.1 Analysis of RC CircuitsCHAPTER TEN505FIGURE 10.3 A more complicated circuit that can be transformed into the simpier circtit in Figure 10.2a by using I hé.ẹnin and Norton transformations.circuit containing many sources and resistors, and one capacito Foundations of analog and digital electronic circuits: Part 2 r, as suggested in I Igurc* 103.1 x*l US assume we wish to find the capacitor voltage !/(■■ We will use* the node methFoundations of analog and digital electronic circuits: Part 2
so. As shown in figure 10.2a, we lake the bottom node as ground, w hich leaves US w ith one unknown node voltage corresponding to the lop ncxlc*. rheFIRST-ORDER TRANSIENTS IN LINEAR ELECTRICAL NETWORKS10As illustrated in Chapter 9, capacitances and inductances impact circuit behavior. The effect of Foundations of analog and digital electronic circuits: Part 2 Step 3 of the node method, we write KCL for the top node in Figure 10.2a, substituting the constituent relation for a capacitor from Equation 9.9,I'c -dvc/0 = V I C^.-10.1K illOr, rewriting,lit RC cAs promised, the problem can be formulated in one line. Ihit to find t'(:(t), we must solve a non homo Foundations of analog and digital electronic circuits: Part 2 geneous, linear first -order ordinary differential expiation with constant coefficients. This is not a difficult task, but one that must be* done systFoundations of analog and digital electronic circuits: Part 2
ematically using any mcthcxl of solving differential equations.To solve this equation, we will use the method of homogeneous and ỊKtr-ticnlar solutionFIRST-ORDER TRANSIENTS IN LINEAR ELECTRICAL NETWORKS10As illustrated in Chapter 9, capacitances and inductances impact circuit behavior. The effect of Foundations of analog and digital electronic circuits: Part 2 fundamental theorem of differential equations, lite method states that the solution to the nonhomogeneous differential 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 differential506CHA Foundations of analog and digital electronic circuits: Part 2 PTER TEN FIRST-ORDER TRANSIENTSequationFoundations of analog and digital electronic circuits: Part 2
derived from the original nonhomogeneous equation by selling the driving function, t{l) in this case, to zero. Further, let Vf-jlt) Ise any solution FIRST-ORDER TRANSIENTS IN LINEAR ELECTRICAL NETWORKS10As illustrated in Chapter 9, capacitances and inductances impact circuit behavior. The effect of Foundations of analog and digital electronic circuits: Part 2 the honiOỊỊtmeous solution andis called the particular solution. when dealingFIRST-ORDER TRANSIENTS IN LINEAR ELECTRICAL NETWORKS10As illustrated in Chapter 9, capacitances and inductances impact circuit behavior. The effect ofGọi ngay
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