SPICE OPUS在电路模拟中的应用

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"Circuit Simulation with SPICE OPUS" 是一本关于使用SPICE OPUS进行电路模拟的书籍，属于科学、工程和技术领域的建模与仿真系列。该书可能由Nicola Bellomo主编，由一系列专家顾问编辑，如M. Avellaneda（经济建模）、K.J. Bathe（固体力学）、P. Degond（半导体和传输建模）、A. Deutsch（生命科学中的复杂系统）以及W. Kliemann（随机建模）等。书中涵盖了广泛的科学计算和工程应用。 SPICE（Simulation Program with Integrated Circuit Emphasis）是一种广泛使用的电路模拟软件，尤其在电子设计自动化领域。SPICE OPUS是SPICE的一个特定实现，提供了更高级的功能和用户界面，用于模拟和分析各种电子电路。该书可能详细介绍了如何使用SPICE OPUS进行电路设计、验证和优化，包括以下知识点： 1. **电路理论基础**：书中可能会回顾电路理论的基本概念，如欧姆定律、基尔霍夫定律，以及线性和非线性元件的工作原理。 2. **SPICE语法和命令**：介绍SPICE OPUS的输入语言，包括节点电压法、元件模型参数定义、模拟控制命令等。 3. **电路模型**：讲解不同类型的电子元件模型，如电阻、电容、电感、二极管、晶体管等，以及如何在SPICE中构建这些模型。 4. **模拟与分析**：详细阐述如何设置和执行电路模拟，以及如何解析和解读模拟结果，如瞬态分析、交流分析、噪声分析等。 5. **优化和参数扫描**：介绍如何通过SPICE OPUS进行电路参数优化和敏感性分析，以便于设计最佳电路配置。 6. **高级功能**：可能包含高级特性，如蒙特卡洛模拟、统计分析、多物理场耦合等。 7. **实例研究**：提供实际电路设计案例，帮助读者将理论知识应用到实践中，理解SPICE OPUS在解决具体问题时的应用。 8. **故障诊断和调试**：讲解如何处理模拟错误和不准确结果，以及如何调试电路模型。 9. **软件接口和用户界面**：介绍SPICE OPUS的图形用户界面，包括电路图绘制、结果可视化和报告生成等功能。 10. **与其他工具的集成**：可能讨论如何将SPICE OPUS与其他电子设计自动化工具（如CAD软件）配合使用，实现完整的电路设计流程。通过深入学习这本资源，读者不仅可以掌握SPICE OPUS的使用，还能深化对电路分析和设计的理解，从而在电子工程领域提升专业技能。

Chapter 1

Introduction to Circuit Simulation

This chapter introduces the reader to the basic notions in the ﬁeld of circuit simula-

tion. It is highly recommended that you read this chapter before reading any other

part of the book simply to become familiar with the terminology used in the chapters

that follow.

We will start with an introduction to circuit operating point calculation. Then we

will continue with operating point sweeps and deﬁnitions of differential gain, resis-

tance, and conductance. Next we move on to time-domain modeling and analysis.

A large part of this chapter is dedicated to the frequency-domain analysis of

circuits with small signal excitations. We will give a brief introduction to Fourier

transformation and small signal circuit modeling followed by a short tutorial on

small signal noise modeling and analysis. At the end of the chapter, we move to the

Laplace transformation, s-domain modeling, and pole-zero analysis.

The order in which analyses are described in this chapter is somewhat different

than in subsequent chapters. We have done this because the basic principles of the

Fourier and Laplace transformations are harder to understand than circuit analysis

in the time domain. On the other hand, the implementation of the two transforms is

much more related to operating point analysis than it is to time-domain analysis.

Be aware that Y in this chapter denotes the Fourier transform of the circuit so-

lution vector. In all the remaining chapters, Y denotes the complex admittance, as

used everywhere else in the literature on circuit theory.

1.1 Signals and Linear Systems

A signal y is a map y W R ! R. The domain of the map is also referred to as

time (t). We denote a signal by y.t/.

AsystemS maps an input signal y

.t/, also referred to as excitation, to an out-

put signal y

out

.t/ D S

.t/

(response) (Fig. 1.1). Suppose we have two input

signals y

in1

.t/ and y

in2

.t/.Lety

out1

.t/ and y

out2

.t/ denote the corresponding re-

sponses of system S.Ify

in1

.t/ D y

in2

.t/ for all t<T implies y

out1

.t/ D y

out2

.t/ for

all t<T regardless of the choice of T , we say that the system is causal. Circuits are

causal systems.

T. Tuma and

A. B

urmen, Circuit Simulation with SPICE OPUS, Modeling and

Simulation in Science, Engineering and Technology, DOI 10.1007/978-0-8176-4867-1

 Birkh

auser Boston, a part of Springer Science+Business Media, LLC 2009

2 1 Introduction to Circuit Simulation

Systemy

(t) y

out

(t)

Fig. 1.1 A system maps the input signal y

.t/ (excitation) to the output signal y

out

.t/ (response)

AsystemS is linear if it satisﬁes the following two requirements:

.t/

D AS

.t/

(1.1)

in1

.t/ C y

in2

.t/

D S

in1

.t/

in2

.t/

(1.2)

Property (1.2) is also referred to as the superposition property. It means that the

response of a linear system to multiple superpositioned excitations is simply the

superposition of responses to individual excitations. This makes it possible to obtain

the response of a system by adding up the responses to individual components of

the excitation.

Linear systems possess many other useful properties. The interested reader may

refer to [47]. Despite the fact that we are discussing nonlinear circuit simulation,

much useful information can be obtained from linearized circuit models, which in

turn can be treated as linear systems.

A system is time invariant if S

.t CT/

D y

out

.t C T/for all values of T

where y

out

D S

.t/

. A linear time-invariant (LTI) system is characterized by its

impulse response h.t/. The impulse response is the response of the system to a

particular type of input signal – the Dirac impulse ı.t/. ı.t/ is zero for all values

of t, except for 0. Nothing can be said about the value of ı.0/, except that it is

inﬁnite. In fact, the Dirac impulse is deﬁned by its integral

1

ı.t/dt D 1.

The response to an arbitrary excitation can be expressed with the impulse re-

sponse in the following manner:

out

.t/ D h.t/ y

.t/ D

1

h.t /y

./d: (1.3)

The operation denoted by  is called convolution. An LTI system is causal if its

impulse response satisﬁes h.t / D 0 for all t<0. For causal LTI systems the convo-

lution simpliﬁes to

out

.t/ D h.t/ y

.t/ D

1

h.t /y

./d: (1.4)

If an LTI system is excited with a sinusoidal signal of frequency f (e.g.,

cos.2ft C '

/), it responds with a superposition of a transient signal and a

phase-shifted sinusoidal signal A

out

cos.2ftC '

The unit of the impulse response is the unit of the output signal divided by the

unit of the input signal and the unit of time. If the input is a voltage (V) and the

output is a current (A), the unit of the impulse response is

. For more on linear

systems theory see [47].

1.2 Lumped Circuits 3

1.2 Lumped Circuits

Suppose the circuits we are considering are small. By small we mean that they are

signiﬁcantly smaller than the wavelength of electromagnetic radiation that corre-

sponds to the highest frequency at which the circuit operates. Such circuits belong

to the class of lumped circuits.

If we take, for instance, an audio ampliﬁer, we can be pretty sure that the fre-

quencies of signals in such a circuit are below 100 kHz. The wavelengths that

correspond to these frequencies are greater than 3km (assuming that the speed

of light is 3  10

m=s). So any reasonably sized audio ampliﬁer can be treated

as a lumped circuit. On the other hand, for a computer with its bus operating at

800 MHz the corresponding wavelength is 37.5 cm. With typical distances of 10 cm

between the processor and the memory, such circuits cannot be classiﬁed as lumped

circuits. The design techniques that apply to lumped circuits cannot be used for

motherboards of such computers.

Lumped circuits can be described as a set of branches. Every branch is connected

to a pair of nodes (P and N). The state of a node A is described by a voltage (v

This voltage is often referred to as the node potential or node voltage. Every branch

B is associated with a branch current (i

) and a branch voltage (v

). The orientation

of the branch voltage is indicated by the C and  signs and is associated with the

branch current which ﬂows from the C sign to the  sign (see Fig. 1.2).

A large variety of different branches can be deﬁned. They differ in the way the

branch current (or voltage) is expressed using other node voltages, branch voltages,

and branch currents in the circuit. For instance, a simple linear time-independent

resistive branch can be deﬁned with the following branch equation:



D 0; (1.5)

where R is a property of the branch and as such a constant. Similarly, a linear time-

independent capacitive branch is deﬁned with the following branch equation:

C

D 0; (1.6)

where t denotes the time.

Note that time independence does not mean that the voltage and the current are

time independent. On the contrary, they depend on time in general. Time indepen-

dence means that the resistance (R) and the capacitance C are constant. Similarly,

Fig. 1.2 Abranchwithits

associated branch voltage (v

)

and branch current (i

)

+-v

4 1 Introduction to Circuit Simulation

branches for nonlinear resistors and capacitors are obtained by replacing relations

(1.5) and (1.6) with i

f

/ D 0 and i



/ D 0, where f

.x/ and f

.x/

are nonlinear functions.

An element model consists of one or more branches and zero or more internal

nodes. Take, for instance, a diode (Fig. 1.3, left). Its model comprises one linear re-

sistive branch (R

), one nonlinear resistive branch (f

/), one nonlinear capacitive

branch (f

/), and one internal node (N).

Until now we have not mentioned anything about how the connection of multiple

branches to a node is modeled mathematically. In lumped circuits nodes cannot

accumulate charge, so the sum of all branch currents ﬂowing into a node must be

equal to the sum of all branch currents ﬂowing out of the node. In other words the

sum of all incident branch currents must be zero for every node. This requirement

is also referred to as the Kirchhoff current law (KCL) and is illustrated in Fig. 1.4.

Any branch voltage can be expressed as the difference of the node voltages that

belong to the two nodes to which the branch is connected (v

v

, see Fig. 1.2).

This is just a special form of the Kirchhoff voltage law (KVL).

The KVL states that the sum of all branch voltages in any closed loop consisting

of branches must be 0. Branch voltages are taken as negative if the branch direction

does not agree with the direction of the loop (see Fig. 1.5). We can quickly see that

by deﬁning the branch voltage as the difference of two node voltages, the KVL is

satisﬁed by deﬁnition.

A circuit consists of one or more elements connected to nodes. By replacing the

elements with their respective models, we can write a set of equations that uniquely

)

+-v

Fig. 1.3 A diode (left) and its associated model (right) comprising a linear resistive branch (R

a nonlinear resistive branch (f

/), a nonlinear capacitive branch (f

/), and an internal node

(N). The C sign beside the capacitance and resistance symbols indicates the polarity of the corre-

sponding nonlinear branch

Fig. 1.4 Kirchhoff’s current

law. The sum of all incident

branch currents at a node

must be 0. For node N this

requirement can be written as

i

D 0.Branch

currents that by orientation

ﬂow into the node are taken

as negative

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