第3章 Multisim7高级分析方法
确定扫描起始值、终止值及增量步长
确定扫描起始值、终止值及增量步长 确定扫描起始值、终止值及增量步长
列出扫描时的参数值，数字间可用空格、逗点或分号隔开
More Options
DC Operating Point （直流工作点） Transient Analysis （瞬态分析） AC Frequency Analysis （交流频率分析）
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1.构造电路 极型晶体管放大电路的交流小信号等效电路，分析 该电路的输入阻抗、输出阻抗及其电路的转移函数。
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2.启动传输函数分析工具 选择Simulate / Analysis / Transfer function
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2.启动传输函数分析工具 传输函数分析对话框选项说明
项 目 Input source （输入电源） Voltage（电压） Output node（输出节点） Output reference （输出参考点） Current（电流） 默认值 电路中的电源 选中 电路中的节点 接地 未选 要分析的电压节点 电压的参考点 输出电流的变量 注 释 选择电压源或电流源
Points to sweep （选择扫描方式）
Decade （十倍刻度扫描） Liner （线性刻度值） Octave （八倍刻度扫描） Liste （取列表值扫描） 选中
确定扫描起始值、终止值及增量步长 确定扫描起始值、终止值及增量步长
列出扫描时的参数值，数字间可用空格、逗点或 分号隔开 未选 选中 未选 选中该项，进行直流工作点的参数扫描分析 选中该项，进行瞬态参数扫描分析，可以修改瞬 态分析时的参数设置 选中该项，进行交流频率参数扫描分析，可以修 11 改交流频率分析时的参数设置
温度扫描分析就是研究温度变化对电路性能的影响， 如果未设定温度扫描，Multisim7将在固定温度27℃下对 电路进行仿真分析。该分析相当于在不同的工作温度下 多次仿真电路性能。但如果要了解不同温度下电路性能 的变化，应采用Multisim7 提供的温度扫描分析工具。 Multisim7中的温度扫描分析不是对所有元件都有效，仅 限于考虑一些半导体器件和一些虚拟电阻。
Gain Analysis （增益分析）
Analysis type （分析类型） Impedance Analysis （互阻抗分析） Input impedance （输入阻抗） Output impedance （输出阻抗） Input（＋） （输入（＋）） Nodes （节点） Input（－） （输入（－））
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1.构造电路
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2.启动蒙特卡罗分析工具 选择Simulate / Analysis / Monte Carlo
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蒙特卡罗分析Tolerance页
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蒙特卡罗分析选项Model tolerance list页说明
选项框 Current list of tolerances Parameter Type Parameter Device Type Name Parameter 项 目 列出目前的元件模型容差 注 释
性。由于可选择电流或电压，所以分析的结果可以是
电压增益、电流增益、跨导及转移阻抗等。
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1.构造电路
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2.启动零极点分析工具 选择Simulate / Analysis / Pole-Zero
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零极点分析对话框选项说明
选项框 项 目 默认值 选中 未选 未选 未选 注 释 输出电压 / 输入电压 输出电压 / 输入电流 从输入端看进去时的电压 / 电流 从输出端看进去时的电压 / 电流 正的输入端节点
删除已选择的容差。
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蒙特卡罗分析Analysis Parameters页
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蒙特卡罗分析Analysis Parameters页说明
选项框 项 目 默认值 Transient analysi 1 注 释 选择分析类型，Transient analysi（瞬态分 析）、AC analysis（交流分析）、DC operating（直流分析）。 误差分析执行次数，必须大于等于2。。 选择要观察的输出节点。 选择比较函数。
More Option （选择分析类型）
DC Operating Point （直流工作点） Transient Analysis （瞬态分析） AC Frequency Analysis （交流频率分析）
3.查看分析结果
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3.3温度扫描分析 （Temperature Sweep Analysis）
AC Sensitivity （交流灵敏度）
分析结果产生一个分图
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3.检查分析结果 直流灵敏度 分析结果
交流灵敏度 分析结果
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3.2参数扫描分析 （Parameter Sweep Analysis）
参数扫描分析是在用户指定每个参数变化值的情况 下，对电路的特性进行分析。在参数扫描分析中，变化
的参数可以从温度参数扩展为独立电压源、独立电流源、
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2.启动温度扫描分析工具
温度扫描分析对话框选项说明
选项框
Sweep Parameters Points to sweep （选择扫描方 式）
项 目
Temperature
默认值
起始温度
注 释
Decade （十倍刻度扫描） Liner （线性刻度值） Octave （八倍刻度扫描） Liste （取列表值扫描） 选中
选择所要设定的元件模型参数或器件参数。 选择所要设定参数的器件种类，包括电路图中使用的BJT、Capacior、 Diode、Resistor、Vsource等。 选择所要设定的元件序号。 选择所要设定的参数。 当前该参数的设定值（不可更改）。 Parameter所选参数的说明（不可更改）。 选择元器件参数容差的分布类型，包括Guassian（高斯分布）和Uniform （均匀分布）。 选择容差随机数出现方式，其中选择Lot表示对各种元件参数都有相同 的随机产生的容差率，较适用于集成电路；选择Unique表示每一个 元件参数随机产生的容差率各不相同，较适用于离散元件电路。 选择容差的形式，Absolute（绝对值）和Percent（百分比）。 根据所选的容差形式设置容差值。 编辑已选择的容差。
Voltage（电压）
Output reference
Current（电流） Output scaleing （灵敏度输出格 式） Output source Absolute Relative DC Sensitivity （直流灵敏度）
电路中的节点
电路中的电源
Analysis Type （分析类型）
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3.检查分析结果
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3.6蒙特卡罗分析 （Monte Carlo Analysis）
蒙特卡罗分析是一种统计分析方法，它是在给定电 路元器件参数容差的统计分布规律的情况下，用一组伪 随机数求得元器件参数的随机抽样序列，对这些随机抽 样的电路进行直流、交流和瞬态分析，并通过多次分析 结果估算出电路性能的统计分布规律，如电路性能的中 心值和方差、电路合格率及成本等。
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1.构造电路 恒流源式差动放大器，由于Multisim7中的实际电阻没
有设计温度特性，所以这里全部采用具有温度特性的虚拟电
阻代替，讨论当温度改变时，引起元件参数的变化对电路性 能的影响。
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2.启动温度扫描分析工具
选择Simulate / Analysis / Temperature Sweep
Analysis performed （分析）
Pole Analysis （极点分析） Zero Analysis （零点分析）
3.检查分析结果
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3.5传输函数分析 (Transfer Function Analysis)
传输函数分析可以计算电路的交流小信号传输函数、 计算输入电阻和输出电阻等。对于任何非线性元件， Multisim7都将根据直流工作点先进行线性化，然后进行 小信号分析，可以指定电路中的任何一点为输出变量， 选择电路中某处所定义的独立源为输入源，从而分析这 两点的传输函数。
• 3.5传输函数分析(Transfer Function Analysis) • 3.6蒙特卡罗分析（Monte Carlo Analysis） • 3.7最坏情况分析（Worst case Analysis） • 3.8批处理分析（ Batched Analysis） • 3.9噪声指数分析（ noise Figure Analysis ） • 3.10用户自定义分析（ User defined Analysis ）
第3章 Multisim 7的高级分析方法
1
主要内容
• 3.1灵敏度分析（Sensitivity Analysis)
• 3.2参数扫描分析（Parameter Sweep Analysis）
• 3.3温度扫描分析（Temperature Sweep Analysis）
• 3.4零极点分析(Pole Zero Analysis)
未选 选中 未选
选中该项，进行直流工作点的参数扫描分析 选中该项，进行瞬态参数扫描分析，可以修改瞬态分析时 的参数设置 选中该项，进行交流频率参数扫描分析，可以修改交流频 率分析时的参数设置 16
3.检查分析结果
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3.4零极点分析(Pole Zero Analysis)
零极点分析是确定电路的小信号交流传输函数的 零点和极点。利用Multisim7提供的零极点分析工具， 分析电路或复杂网络系统的零极点，这可以取代枯燥 繁琐的手工计算，以便清楚地了解电路或系统的稳定
Device Parameter （元件参数） Model Parameter （元件模型参数）
默认值
BJT （晶体管） BJT （晶体管）
注 释
multisim电路分析方法
在Variables in Circuit栏中列出的是电路中可 用于分析的节点和变量。点击 Variables in circuit 窗口中的下箭头按钮，可以给出变量类型选择表。 在变量类型选择表中： 点击Voltage and current选择电压和电流变量。
点击Voltage选择电压变量。 点击 Current选择电流变量。 点击Device／Model Parameters 选择元件／ 模型参数变量。 点击All variables选择电路中的全部变量。
其中Output variables、 Miscellaneous Options 和Summary 3个选项与直流工作点分析的设置 一样，下面仅介绍Analysis Parameters选项， Analysis Parameters对话框如图1.6.8所示。
图1.6.8 Analysis Parameters对话框
图 1.6.5 Miscellaneous Options对话框
如果选择Use this custom analysis，可以用 来选择用户所设定的分析选项。可供选取设定的 项目已出现在下面的栏中，其中大部分项目应该 采用默认值，如果想要改变其中某一个分析选项 参数，则在选取该项后，再选中下面的Use this option选项。选中Use this option选项将在其右边
2. Parameters区 在Parameters区可以对时间间隔和步长等参数 进行设置。
Start time窗口：设置开始分析的时间。 End time窗口：设置结束分析的时间。
点击Maximum time step settings，可以设 置分析的最大时间步长。其中：
（1）设置单位时间内的采样点数 点击Minimum number of time points，可以 设置单位时间内的采样点数。
Multisim7课程设计仿真
用户可以通过元件库面板选择需要的元件，并将其拖拽到电路图 编辑区。
调整元件属性
双击元件，可以在属性对话框中修改元件的参数和属性。
电路图的绘制
01
02
03
电路图编辑区
用于绘制电路图的区域， 用户可以在此区域内自由 绘制电路图。
连线工具
提供了多种连线工具，包 括直线、曲线等，方便用 户绘制电路图中的连线。
技巧3
05 利用 Multisim 的自动化功能
。
建议
06 利用软件的自动化布局和布线
功能，提高设计效率。
Multisim 7 的未来发展与展望
发展方向1
增加更多先进的仿真功能。
01
02
展望
随着电子技术的不断发展，Multisim 7 有望 增加更多高级的仿真功能，以满足更复杂的 设计需求。
发展方向2
1 2
模拟仪器
Multisim 7提供了多种模拟仪器，如示波器、信 号发生器、功率表等，可用于测量和调试电路的 各种参数。
数字仪器
数字仪器包括逻辑分析仪、逻辑转换仪等，可用 于分析数字电路的逻辑关系和转换。
3
仪器设置与调整
用户可以根据需要设置仪器的参数，如输入信号 的幅度、频率等，以满足不同的仿真需求。
问题2
仿真结果不准确。
仿真速度过慢。
问题3
解决方法
优化电路设计，减少元件数量和复杂度，或尝试升级计 算机硬件。
提高仿真效率的技巧和建议
技巧1
合理使用虚拟仪器。
01
建议
02 在仿真过程中，根据需要选择
合适的虚拟仪器，避免不必要 的复杂度。技巧2Fra bibliotek优化电路设计。
Multisim7的高级分析方法
选中该项，进行交流频率参数扫描分析，可以修 改交流频率分析时的参数设置
3.查看分析结果
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3.3温度扫描分析 （Temperature Sweep Analysis）
温度扫描分析就是研究温度变化对电路性能的影响，如果未设定温度扫 描，Multisim7将在固定温度27℃下对电路进行仿真分析。该分析相当于在不 同的工作温度下多次仿真电路性能。但如果要了解不同温度下电路性能的变 化，应采用Multisim7 提供的温度扫描分析工具。Multisim7中的温度扫描分 析不是对所有元件都有效，仅限于考虑一些半导体器件和一些虚拟电阻。
主要内容
• 3.1灵敏度分析（Sensitivity Analysis) • 3.2参数扫描分析（Parameter Sweep Analysis） • 3.3温度扫描分析（Temperature Sweep Analysis） • 3.4零极点分析(Pole Zero Analysis) • 3.5传输函数分析(Transfer Function Analysis) • 3.6蒙特卡罗分析（Monte Carlo Analysis） • 3.7最坏情况分析（Worst case Analysis） • 3.8批处理分析（ Batched Analysis） • 3.9噪声指数分析（ noise Figure Analysis ） • 3.10用户自定义分析（ User defined Analysis ） 1
列出扫描时的参数值，数字间可用空格、逗点或 分号隔开
More Option （选择分析类型）
DC Operating Point （直流工作点）
Transient Analysis （瞬态分析）
基于Multisim 7的仿真分析
基于Multisim 7的仿真分析摘要：电子技术是电子类专业的一门主干课程，该课程既有较抽象的理论分析又有较具体的实践应用。
EDA对于这类课程的学习可以做出很大的帮助，而课程学习质量的优劣直接影响到该专业后续课程的学习以及我的电路理论分析和实践动手能力。
电子技术理论的学习应与实验同步进行，以加深感性认识，用仿真软件验证理论分析是可行有效的方法。
关键词：Multisim 7 EDA 仿真分析射频电路Simulation and Analysis Based on Multisim 7Zeng ShengAbstract:Electronic technology is the electronic profession a main course, the course is both more abstract and theoretical analysis there are more specific practical application.EDA for such courses of study can make a great help, the course of study directly affect the quality of follow-up to the professional courses of study and my analysis of circuit theory and practical ability.E-learning technology theory and experiment should be carried out simultaneously to enhance perceptual knowledge, the theoretical analysis with simulation software is feasible and effective method.Key words：Multisim 7 EDA Simulation RF Circuits第一章绪论 (3)第二章 Multisim 7常用的虚拟仪器及常用的基本分析方法 (4)第三章仿真电路的处理及基于Multisim 7的VHDL仿真知识 (5)第四章基于Multisim 7的射频电路的仿真分析 (6)4.1 引言 (6)4.2 射频电路的基本知识 (7)4.3 RF特性分析 (8)4.4 匹配网络分析 (14)第五章总结分析 (18)第六章致谢 (19)参考文献： (20)第一章绪论电子技术是电子类专业的一门主干课程，该课程既有较抽象的理论分析又有较具体的实践应用。
Multisim7的基本功能与操作
•项项目9 Multisim7基本功能与操作
5、仪器仪表齐全，精度高。 Multisim提供了数字万用表、示波器、逻辑分析仪、波 特图仪、函数信号发生器和瓦特表等18种虚拟仪器。仪表外观、 面板布置、按键功能和操作方法等与实际仪表基本相同，可以 毫无风险地进行使用。
6、强大的分析功能。 Multisim还提供了直流工作点分析、交流分析、直流扫 描分析和傅里叶分析等多种分析功能，为电路实验带来了极大 的便利。
图9-4 图形注释工具栏
•项项目9 Multisim7基本功能与操作
6、元件工具栏 如图9-5所示。元件工具栏通常在基本界面的左边。也可以 用鼠标将工具栏拖至界面的上方，呈水平状。从左至右依次是: 电源库(Source)、基本元件库(Basic)、二极管库(Diode)、晶 体管库(Transistor)、模拟元件库(Analog)、TTL元件库(TTL)、 CMOS元件库(CMOS)、数字元件库(Miscellaneous Digital)、混 合元件库(Mixed)、指示元件库(1ndicator)、其他元件库 (Miscellaneous)、射频元件库(RF)、机电类元件库 (Electromechanical)、放置分层模块、放置总线、登录 WWW．Electronics 和www．网站等。
图9-2 标准工具栏
•项项目9 isim7基本功能与操作
4、仿真开关
如图9-3所示。主要用于仿真控制。
图9.3 仿真开关
•项项目9 Multisim7基本功能与操作
5、图形注释工具栏
如图9-4所示。该工具栏主要用于在基本界面中放置各种 图形，从左至右依次是：文本、直线、折线、矩形、椭圆、圆 弧、多边形和图片。
•项项目9 Multisim7基本功能与操作
Multisim7电路设计及仿真应用
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Multisim 7电路设计及仿真应用电路设计及仿真应用Multisim 7 概述完整的电路系统设计、仿真工具；设计功能：Schematic & HDL仿真功能：SPICE VHDL/Verilog RF CoCo-simulation虚拟仪表及分析功能以及3 虚拟仪表及分析功能以及3D效果。
Multisim 7 特色所见即所得的设计环境；互动式的仿真界面；动态显示元件（如LED，动态显示元件（如LED，七段显示器等）；具有3 具有3D效果的仿真电路；虚拟仪表(包括Agilent仿真仪表）；虚拟仪表(包括Agilent仿真仪表）；分析功能与图形显示窗口。
操作环境环境参数设定Options/Preferences… ptions/P绘制电路取用元件：从元器件库中取用所需元件；摆放元件：调整元件的位置与方向；线路连接：连接元件的引脚。
元件工具栏电源按钮件按钮元本基二极管按钮钮按管体晶拟元件模元器件按元器件按钮钮元（件按钮COMS 系列）系列）器（字数他其数混合元器件按钮模指示器件按钮杂射项库元元器器件按按钮钮件频电机置元器件按钮钮按件器元设放置总线按钮钮源按资育教网站按钮按钮74取用元件放置元件——电源元件元素Multisim 7的元件均具有下列元素: 7的元件均具有下列元素:Symbol –元件符号（for Schematic）Schematic）Model –元件模型（for Simulation）Simulation）Footprint –元件外型（for Layout）Layout）Electronic Parameter–电子元件参数Parameter–User Defined Info. –使用者自定资讯Pin model—管脚模型model—General—General—元件描述取用元件取用元件-元件属性对话框在元件上双击鼠标左键开启属性对话框Label：Label：修改元件序号、标识；Display：Display：设置元件标识是否显示；Value：Value：设定元件参数值；Fault：Fault：设定元件故障。
Multisim7快速入门第3章
第3章Multisim7的元件库在所有电路仿真软件中，都需要一个仿真元件库以存放和管理仿真元件，仿真元件库中元件多少、模型的精确度将对仿真结果有着较大的影响。
本章将主要介绍Multisim7中元件库及元件的使用、元件库管理及如何在Multisim7中创建新元件等内容。
3.1元件库的管理Multisim7的元件存储在三种不同的数据库中，执行“Tools”/“Database Management”命令即可看到数据库管理信息。
主要包括Multisim Master库、Corporate Library库（仅在专业版中存在）、User库，这三种数据库功能分别说明如下：●Multisim Master库：存放Multisim7提供的所有元件，不能被修改和编辑。
●Corporate Library库：存放被企业或个人修改、创建和选择的元件，能对选择了该库的企业或个人使用和编辑。
主要是方便企业的设计团队共享经常使用的一些特定的元件。
●User库：存放被个人修改、创建和导入的元件，仅能由使用者个人使用和编辑。
该库在刚使用Multisim7时是空的，可以通过导入或由用户自己编辑和创建（详见3.3节）。
如图3-1所示的Multisim Master库和User库中都包含如下13个元件库分类：信号及电源库（Sources）、基本元件库（Basic）、二极管库（Diodes）、晶体管库（Transistors）、模拟元件库（Analog）、TTL元件库（TTL）、CMOS元件库（CMOS）、其它数字元件库（Misc Digital）、混合元件库（Mixed）、显示元件库（Indicators）、其它元件库（Misc）、射频元件库（RF）、机电类元件库（Electro-mechanical），该分类和元件工具栏中的元件库图标相对应。
在Multisim Master库下面的每个分类元件库中，还包括多个元件箱（又称为Family），各种仿真元件放在这些元件箱中以供调用。
用Multisim7分析时序逻辑电路
Multisim7分析时序逻辑电路摘要：计算机技术的飞速发展，电路可以通过计算机辅助分析和仿真技术来完成设计。
Multisim7软件就是一个专门用于电子线路仿真与设计的 EDA 工具软件。
它具有很强的逻辑仿真功能，将给定的时序逻辑电路图输入计算机后得到时序图，操作简单快捷。
论文中介绍了Multisim7软件以及时序逻辑电路的特点和分析过程，并用例题加以说明。
关键词：Multisim7，时序逻辑电路，逻辑分析仪，信号发生器随着计算机科学与技术突飞猛进的发展，用数字电路进行信号处理的优势也更加突出。
为了充分发挥和利用数字电路在处理上的强大功能，我们可以先将模拟信号按比例转化成数字信号，然后送到数字电路（可以是专用的数字信号处理电路，也可以是通用的计算机）进行处理，最后处理结果根据需要转化为相应的模拟信号输出。
自20世纪70年代开始，这种用数字模拟信号的所谓“数字化”浪潮已经席卷了电子技术几乎所有，所有的应用领域。
Multisim7把整个学习和实验过程都搬到了虚拟实验室中进行，能够使实验电路，仪器以及实验结果等一起直观地展现在学生面前，另外对电路参数调整也极其方便。
本文就采用Multisim7对时序逻辑电路进行分析。
一、Multisim7软件的介绍Multisim7是由加拿大IIT(Interaction Image Technologies)公司推出的大型设计工具软件。
Multisim7 仿真软件的前身是EWB, 又称电子工作台（Electronics Work bench），它是由加拿大IIT 公司20 世纪80 年代推出的电子电路设计和仿真软件，一经推出就受到好评，尤其在教育领域取得了巨大的成功。
EWB 软件具有界面直观，操作方便等优点，创建电路、选用元件和测试仪器均可以直接通过元件库和仪器库选取。
EWB系列软件经过了多个版本的演变，在2003年IIT 公司推出了Multisim7版本，较之以前的版本功能更加齐全，应用也更加广泛。
Multisim 7电路设计仿真教程
In J.G. Webster (ed.), Wiley Encyclopedia of Electrical and Electronics Engineering,Wiley & Sons, vol. 18, pp. 396-405, 1999Relaxation Oscillators and NetworksDeLiang WangDepartment of Computer and Information Science and Center for Cognitive ScienceThe Ohio State UniversityColumbus, OH 43210-1277Relaxation oscillations comprise a large class of nonlinear dynamical systems, and arise naturally from many physical systems such as mechanics, biology, chemistry, and engineering. Such periodic phenomena are characterized by intervals of time during which little happens, interleaved with intervals of time during which considerable changes take place. In other words, relaxation oscillations exhibit more than one time scale. The dynamics of a relaxation oscillator is illustrated by the mechanical system of a seesaw in Figure 1. At one side of the seesaw is there a water container which is empty at the beginning; in this situation the other side of the seesaw touches the ground. As the weight of water dripping from a tap into the container exceeds that of the other side, the seesaw flips and the container side touches the ground. At this moment, the container empties itself, and the seesaw returns quictly to its original position and the process repeats.Figure 1. An example of a relaxation oscillator: a seesaw with a water container at one end (adapted from(4)).Relaxation oscillations were first observed by van der Pol (1) in 1926 when studying properties of a triode circuit. Such a circuit exhibits self-sustained oscillations. van der Pol discovered that for a certain range of the system parameters the oscillation is almost sinusoidal, but for a different range the oscillation exhibits abrupt changes. In the latter case, the period of the oscillation is proportional to the relaxation time (time constant) of the system, hence the term relaxation oscillation. van der Pol (2) later gave the following defining properties of relaxation oscillations:1. The period of oscillations is determined by some form of relaxation time.2. They represent a periodic autonomous repetition of a typical aperiodic phenomenon.3. Drastically different from sinusoidal or harmonic oscillations, relaxation oscillatorsexhibit discontinuous jumps.4. A nonlinear system with implicit threshold values, characteristic of the all-or-none law.A variety of biological phenomena can be characterized as relaxation oscillations, ranging from heartbeat, neuronal activity, to population cycles; the English physiologist A.V. Hill (3) even stated that relaxation oscillations are the type of oscillations that governs all periodic phenomena in physiology.Givenrelaxation oscillations. TheimportantRELAXATION OSCILLATORSoscillators.arewith electrical circuits.van der Pol oscillator˙˙x+x=c(1−x2)˙x Figure 2. Phase portrait and trajectory of a van der Pol oscillator. A Phase portrait. The x nullcline is the cubic curve, and the y nullcline is the y axis. Arrows indicate phase flows. B limit cycle orbit. The limit cycle is labeled as pqrs, and the arrowheadswhere c > 0 is a parameter. This second-order differential equation can be transformed to a two variable first-order differential equation,˙x=c(y−f(x))(2a)˙y=−x/c(2b)Here f(x) = -x + x3/3. The x nullcline, ˙x = 0, is a cubic curve, while the y nullcline, ˙y = 0, is the y axis. As shown in Fig. 2A, the two nullclines intersect along the middle branch of the cubic, and the resulting fixed point is unstable as indicated by the flow field in the phase plane of Fig. 2A. This equation yields a periodic solution.As c » 1, Eq. (2) yields two time scales: a slow time scale for the y variable and a fast time scale for the x variable. As a result, Eq. (2) becomes the van der Pol oscillator that produces a relaxation oscillation. The limit cycle for the van der Pol oscillator is given in Fig. 2B, and it is composed of four pieces, two slow ones indicated by pq and rs, and two fast ones indicated by qr and sp. In other words, motion along the two branches of the cubic is slow compared to fast alternations, or jumps, between the two branches. Fig. 2C shows x activity of the oscillator with respect to time, where two time scales are clearly indicated by relatively slow changes in x activity interleaving with fast changes.FitzHugh-Nagumo oscillatorBy simplifying the classical Hodgkin-Huxley equations (7) for modeling nerve membranes and action potential generation, FitzHugh (8) and Nagumo et al. (5) gave the following two-variable equation, widely known as the FitzHugh-Nagumo model,˙x=c(y−f(x)+I)(3a)˙y=−(x+by−a)/c(3b) where f(x) is as defined in Eq. (2), I is the injected current, and a, b, and c are system parameters satisfying the conditions: 1 > b > 0, c2 > b, and 1 > a > 1 – 2b/3. In neurophysiological terms, x corresponds to the neuronal membrane potential, and y plays the aggregate role of three variables in the Hodgkin-Huxley equations. Given that the x nullcline is a cubic and the y nullcline is linear, the FitzHugh-Nagumo equation is mathematically similar to the van der Pol equation. Typical relaxation oscillation with two time scales occurs when c » 1. Because of the three parameters and the external input I, the FitzHugh-Nagumo oscillator has additional flexibility. Depending on parameter values, the oscillator can exhibit a stable steady state or a stable periodic orbit. With a perturbation by external stimulation, the steady state can become unstable and be replaced by an oscillation; the steady state is thus referred to as the excitable state.Morris-Lecar oscillatorIn modeling voltage oscillations in barnacle muscle fibers, Morris and Lecar (9) proposed the following equation,˙x=−g Ca m∞(x)(x−1)−g K y(x−x K)−g L(x−x L)+I(4a)˙y=−ε(y∞(x)−y)/τy(x)(4b) wherem ∞(x )=[1+tanh((x −x 1)/x 2)]/2y ∞(x )=[1+tanh((x −x 3)/x 4)]/2τy (x )=1/cosh[(x −x 3)/(2x 4)]and x 1, x 2, x 3, x 4, g Ca , g K , g L , x K , and x L are parameters. Ca stands for calcium, K for potassium, L for leak, and I is the injected current. The parameter ε controls relative time scales of x and y . Like Eq. (4), the Morris-Lecar oscillator is closely related to the Hodgkin-Huxley equations, and it is used as a two-variable description of neuronal membrane properties or the envelope of an oscillating burst (10). The x variable corresponds to the membrane potential, and y corresponds to the state of activation of ionic channels.The x nullcline of Eq. (4) resembles a cubic and the y nullcline is a sigmoid curve. When ε isTerman-Wang oscillatorconsiderations, the following equation,˙x=f (x )−y +I ˙y=ε(g (x )−y )where f(x) = 3x – x 3 + 2, g(x) = α/β)), and I represents oscillator. Thus x nullcline is a sigmoid, where αparameters. When εrelaxation oscillator. When I βperiodic solution alternates between and active (high x behavior. As shown in Fig. respectively. If I spends in these two phases. A largervan der Pol and FitzHugh-Nagumo equations. In neuronal terms, the x variable in Eq. (5) corresponds to the membrane potential, and y the state for channel activation or inactivation.NETWORKS OF RELAXATION OSCILLATORSIn late eighties, neural oscillations about 40 Hz were discovered to in the visual cortex (12-13). The experimental findings can be summarized as the following: (1) neural oscillations are triggered by appropriate sensory stimulation, and thus the oscillations are stimulus-dependent; (2) long-range synchrony with zero phase-lag occurs if the stimuli appear to form a coherent object; (3) no synchronization occurs if the stimuli appear to be unrelated. These intriguing observations are consistent with the temporal correlation theory (14), which states that in perceiving a coherent object the brain links various feature detecting neurons via temporal correlation among the firing activities of these neurons.Since the discovery of coherent oscillations in the visual cortex and other brain areas, neural oscillations and synchronization of oscillator networks have been extensively studied. Most of these models are based on sinusoidal or harmonic oscillators and rely on all-to-all connectivity to reach synchronization across the network. In fact, according to the Mermin and Wagner theorem (15) in statistical physics, no synchrony exists in one- or two-dimensional locally coupled isotropic Heisenberg oscillators, which are similar to harmonic oscillators. However, all-to-all connectivity(16)modulationrelaxationand in this case the effect of the excitatory coupling is to raise the cubic of the other oscillator by a fixed amount.Let us explain the mechanism of fast threshold modulation using the Terman-Wang oscillator as an example. The two oscillators are denoted by o1 = (x1, y1) and o2 = (x2, y2), which are initially in the silent phase and close to each other with o1 leading the way as illustrated in Fig. 4. Figure 4 shows the solution of the oscillator system in the singular limit ε→ 0. The singular solution consists of several pieces. The first piece is when both oscillators move along LB of the uncoupled cubic, denoted as C. This piece lasts until o1 reaches the left knee of C, LK, at t = t1. The second piece begins when o1 jumps up to RB, and the excitatory coupling from o1 to o2 raises the cubic for o2 from C to C E as shown in the figure. Let LK E and RK E denote the left and right knees of C E. If |y1 - y2| is relatively small, then o2 lies below LK E and jumps up. Since these interactions take place in fast time, the oscillators are effectively synchronized in jumping up. As a result the cubic for o1 is raised to C E as well. The third piece is when both oscillators lie on RB and evolve in slow time. Note that the ordering in which the two oscillators track along RB is reversed and now o2 leads the way. The third piece lasts until o2 reaches RK E at t = t2. The fourth piece starts when o2 jumps down to LB. With o2 jumping down, the cubic for o1 is lowered to C. At this time, if o1 lies above RK, as shown in Fig. 4, o1 jumps down as well and both oscillators are now in the silent phase. Once both oscillators are on LB, the above analysis repeats.Based on the fast threshold modulation mechanism, Somers and Kopell further proved a theorem that the synchronous solution in the oscillator pair has a domain of attraction in which the approach to synchrony has a geometric (or exponential) rate (16). The Somers-Kopell theorem is based on comparing the evolution rates of the slow variable right before and after a jump, which are determined by the vertical distances of an oscillator to the y nullcline (see Fig. 4).A network of locally coupled oscillatorsIn the same paper Somers and Kopell suspected that their analysis extends to a network of relaxation oscillators, and performed numerical simulations with one-dimensional rings to support their suggestion. In a subsequent study, by extending Somers and Kopell analysis, Terman and Wang proved a theorem that for an arbitrary network of locally coupled relaxation oscillators there is a domain of attraction in which the entire network synchronizes at an exponential rate (11).In their analysis, Terman and Wang employed the time metric to describe the distance between oscillators. When oscillators evolve either in the silent phase or the active phase, their distances in y in the Euclidean metric change; however, their distances in the time metric remain constant. On the other hand, when oscillators jump at the same time (in slow time), their y distances remain unchanged while their time distances change. Terman and Wang also introduced the condition that the sigmoid for the y nullcline (again consider the Terman-Wang oscillator) is very close to a step function (11), which is the case when β in Eq. (5) is chosen to be very small. This condition implies that in the situation with multiple cubics the rate of evolution of a slow variable does not depend on which cubic it tracks along.LEGION networks: Selective gatingA natural and special form of the temporal correlation theory is oscillatory correlation (19), whereby each object is represented by synchronization of the oscillator group corresponding to the object and different objects in a scene are represented by different oscillator groups which are desynchronized from each other. There are two fundamental aspects in the oscillatory correlationtheory: synchronization and desynchronization. Extending their results on synchronizing locally coupled relaxation oscillators, Terman and Wang used a global inhibitory mechanism to achieve desynchronization (11). The resulting network is called LEGION, to stand for Locally Excitatory Globally Inhibitory Oscillator Networks (19).The original description of LEGION is based on Terman-Wang oscillators, and basic mechanisms extend to other relaxation oscillator models. Each oscillator i is defined as˙xi = f (x i )−y i +I i +S i +ρ(6a)˙yi =ε(g (x i )−y i )(6b)Here f(x) and g(x) are as given in Eq. (5). The parameter ρ denotes the amplitude of Gaussiannoise; to reduce the chance of self-generating oscillations the mean of noise is set to -ρ. In addition to test robustness, noise plays the role of assisting desynchronization. The term S i denotes the overall input from other oscillators in the network:S i = ∑k ∈N (i )W ik H (x k – θx ) – W z H (z – θz )(7)where W ik is the dynamic connection weight from k to i , and N(i) is the set of the adjacent oscillators that connect to i . In a two-dimensional (2-D) LEGION network, N(i) in the simplest case contains four immediate neighbors except on boundaries where no wrap-around is used,thus forming a 2-D grid. This architecture is shown in Fig. 5. H stands for the Heaviside function, defined as H (v ) = 1 if v ≥ 0 and H (v ) = 0 if v < 0. θx is a threshold above which an oscillator can affect its neighbors. W z is the weight of inhibition from the global inhibitor z , whose activity is defined as˙z= φ (σ∞ – z ) (8)where φ is a parameter. The quantity σ∞ = 1 if x i ≥ θz for at least one oscillator i , and σ∞ = 0otherwise. Hence θz (see also Eq. (7))represents a threshold.The dynamic weights W ik 's are formed on the basis of permanent weights T ik 's according to the mechanism of dynamic normalization (20-21), which ensures that each oscillator has equal overall weights of dynamic connections, W T , from its neighborhood. According to reference (11), weight normalization is not a necessary condition for LEGION to work, but it improves the quality of synchronization. Moreover, based on external input W ik can be determined at the start of simulation.To illustrate how desynchronization between blocks of oscillators is achieved in a LEGION network, let us consider an example with two oscillators that are coupled only through the global< y2thefirst one lasts until o1both oscillators are on LB, zpiece starts when o1crosses θz, σ∞on the fast time scale. When zcubic corresponding to both o1from C to C Zis when o1P Zthat o2→P Z, and o2o1 is on RB, which lasts until o1knee of C Z at t = t2o1 jumps down to LB. When o10 in fast time. When zcorresponding to both o1 and oimmediately. Otherwise both o1terminates when o21 and o2 are never in the active phase simultaneously. In general, LEGION exhibits a mechanism of selective gating, whereby an oscillator, say o i, jumping to its active phase quickly activates the global inhibitor, which selectively prevents the oscillators representing different blocks from jumping up, without affecting o i's ability in recruiting the oscillators of the same block because of local excitation. With the selective gating mechanism, Terman and Wang proved the following theorem. For a LEGION network there is a domain of parameters and initial conditions in which the network achieves both synchronization within blocks of oscillators and desynchronization between different blocks in no greater than N cycles of oscillations, where N is the number of patterns in an input scene. In other words, both synchronization and desynchronization are achieved rapidly.The following simulation illustrates the process of synchronization and desynchronization in LEGION (19). Four patterns - two O's, one H, and one I, forming the word OHIO - are simultaneously presented to a 20x20 LEGION network as shown in Figure 7A. Each pattern is a connected region, but no two patterns are connected to each other. The oscillators under stimulation become oscillatory, while those without stimulation remain excitable. The parameter ρis set to represent 10% noise compared to the external input. The phases of all the oscillators on the grid are randomly initialized. Fig. 7B-7F shows the instantaneous activity (snapshot) of the network at various stages of dynamic evolution. Fig. 7B shows a snapshot of the network at thebeginning of the simulation, displaying the random initial conditions. Fig. 7C shows a snapshotshortly afterwards. One can clearly see the effect of synchronization and desynchronization: all the oscillators corresponding to the left O are entrained and have large activity; at the same time, the oscillators stimulated by the other three patterns have very small activity. Thus the left O is segmented from the rest of the input. Figure 7D-F shows subsequent snapshots of the network, where different patterns reach the active phase and segment from the rest. This successive "popout" of the objects continues in an approximately periodic fashion as long as the input stays on. To provide a complete picture of dynamic evolution, Fig. 7G shows the temporal evolution of every oscillator. Synchronization within each object and desynchronization between them are clearly shown in just three oscillation periods, which is consistent with the theorem proven in (11).GLeft OPattern HPattern IRight OInhibitorTimeFigure 7.A A scene composed of four patterns which were presented (mapped) to a 20x20 LEGION network. B A snapshot of the activities of the oscillator grid at the beginning of dynamic evolution. The diameter of each black circle represents the x activity of the corresponding oscillator. C A snapshot taken shortly after the beginning. D Another snapshot taken shortly after C. E Another snapshot taken shortly after D. F Another snapshot taken shortly after E. G The upper four traces show the combined temporal activities of the oscillator blocks representing the four patterns, respectively, and the bottom trace shows the temporal activity of the global inhibitor. The ordinate indicates the normalized x activity of an oscillator. Since the oscillators receiving no external input are excitable during the entire simulation process, they are excluded from the display. The activity of the oscillators stimulated by each object is combined into a single trace in the figure. The differential equations were solved using a fourth-order Runge-Kutta method. (from (19))Time delay networksTime delays in signal transmission are inevitable in both the brain and physical systems. In local cortical circuits, for instance, the speed of nerve conduction is less than 1mm/ms such that connected neurons 1 mm apart have a time delay of more than 4% of the period of oscillation assuming 40 Hz oscillations. Since small delays may completely alter the dynamics of differential equations, it is an important to understand how time delays change the behavior, particularly synchronization, of relaxation oscillator networks.Recently, Campbell and Wang (22) studied locally coupled relaxation oscillators with time delays. They revealed the phenomenon of loose synchrony in such networks. Loose synchrony indemonstrates loosely synchronous behavior in a chain of 50 oscillators with a time delay that is 3%of the oscillation period between adjacent oscillators. The phase relations between the oscillators in the chain become stabilized by the third cycle.Two other results regarding relaxation oscillator networks with time delays are worth mentioning.First, Campbell and Wang (22) identified a range of initial conditions in which the maximum time delays between any two oscillators in a locally coupled network can be contained. Second, they found that in LEGION networks with time delay coupling between oscillators, desynchronous solutions for different oscillator blocks are maintained. Thus, the introduction of time delays does not appear to impact the behavior of LEGION in terms of synchrony and desynchrony.APPLICATIONS TO SCENE ANALYSISA natural scene generally contains multiple objects, each of which can be viewed as a group of similar sensory features. A major motivation behind studies on oscillatory correlation is scene analysis, or the segmentation of a scene into a set of coherent objects. Scene segmentation, or perceptual organization, plays a critical role in the understanding of natural scenes. Although humans perform it with apparent ease, the general problem of scene segmentation remains unsolved in sensory and perceptual information processing.Oscillatory correlation provides an elegant and unique way to represent results of segmentation. As illustrated in Fig. 7, segmentation is performed in time ; after segmentation, each segment pops out at a distinct time from the network and different segments alternate in time. On the basis of new insights into synchronization and desynchronization properties in relaxation oscillator networks,several recent studies have directly addressed the scene segmentation problem.Image segmentationWang and Terman (21) have studied LEGION for segmenting real images. In order to perform effective segmentation, LEGION needs to be extended to handle images with noisy regions.Without such extension, LEGION would treat each region, no matter how small it is, as a separate segment, and result in many fragments. A large number of fragments degrade segmentation results, and a more serious problem is that it is difficult for LEGION to produce more than severalpatterns (11). This number depends on the ratio of the times that a single oscillator spends in the silent and active phases; see, for example, Figs.3 and 7. This limit is called the segmentation capacity of LEGION (21). Noisy fragments therefore compete with major image regions for becoming segments, and the major segments may not be extracted as athat a major block must contain at least one oscillator, denoted as a leader, which lies in the center area of a large homogeneous image region. Such an oscillator receives large lateral excitation from its neighborhood, and thus its lateral potential is charged high. A noisy fragment does not contain such an oscillator.More specifically, a new variable p i, denoting the lateral potential for each oscillator i is introduced into the definition of the oscillator (cf. (6)). p i→ 1 if i frequently receives a high weighted sum from its neighborhood, signifying that i is a leader, and the value of p i determines whether or not the oscillator i is a leader. After an initial time period, the only oscillators which can jump up without lateral excitation from other oscillators are the leaders. When a leader jumps up, it spreads its activity to other oscillators within its own block, so they can also jump up. Oscillators not in this block are prevented from jumping up because of the global inhibitor. Without a leader, the oscillators corresponding to noisy fragments cannot jump up beyond the initial period. The collection of all noisy regions is called the background, which is generally discontiguous.Wang and Terman have achieved a number of rigorous results concerning the extended version of LEGION (21). The main analytical result states that the oscillators with low lateral potentials will become excitable after a beginning period, and the asymptotic behavior of each oscillator belonging to a major region is precisely the same as the network obtained by simply removing all noisy regions. Given the Terman-Wang theorem on original LEGION, this implies that after a number of cycles a block of oscillators corresponding to a major region synchronizes, while any two blocks corresponding to different major regions desynchronize. Also, the number of periods required for segmentation is no greater than the number of major regions plus one.For gray-level images, each oscillator corresponds to a pixel. In a simple scheme for setting up lateral connections, two neighboring oscillators are connected with a weight proportional to corresponding pixel similarity. To illustrate typical segmentation results, Fig. 9A displays a gray-level aerial image to be segmented. To speed up simulation with large number of oscillators needed for processing real images, Wang and Terman also abstracted an algorithm that follows LEGION dynamics (21). Fig. 9B shows the result of segmentation by the algorithm. The entire image is segmented into 23 regions, each of which corresponds to a different intensity level in the figure, which indicates the phases of oscillators. In the simulation, different segments rapidly popped out from the image, as similarly shown in Fig. 7. As can be seen from Fig. 9B, most of the major regions were segmented, including the central lake, major parkways, and various fields. The black scattered regions in the figure represent the background that remains inactive. Due to the use of lateral potentials, all these tiny regions stay in the background.Auditory segregationA listener in a real auditory environment is generally exposed to acoustic energy from different sources. In order to understand the auditory environment, the listener must first disentangle the acoustic wave reaching the ears. This process is referred to as auditory scene analysis, or auditory segregation. According to Bregman (23), auditory scene analysis takes place in two stages. In the first stage, the acoustic mixture reaching the ears is decomposed into a collection of sensory elements. Secondly, elements that are likely to have arisen from the same source are grouped to form a stream that is a perceptual representation of an auditory event.Auditory segregation was first studied from the oscillatory correlation perspective by von der Malsburg and Schneider (14). They constructed a fully connected oscillator network with an ad hoc oscillator model, each representing a specific auditory feature. Additionally, there is a global inhibitory oscillator introduced to segregate oscillator groups. With a mechanism of rapidoscillators. As indicated in the figure, the array quickly segregates to two synchronized groups, within each of which the active phases of the oscillators overlap significantly. Each synchronized group corresponds to a set of correlogram channels that define the formant of a vowel; see Figs. 10B and 10C.Brown and Wang have performed systematic simulations on a vowel set used in psychophysical studies, and confirmed that the results produced by their oscillator array qualitatively match the performance of human listeners; in particular vowel identification performance increases with increasing difference in F0. As illustrated in Fig. 10, a concept emerging from their study is the use of relaxation oscillators as "gates" on their corresponding auditory channels. Specifically, the activity in a channel contributes to the percept of a sound source only when the corresponding oscillator is in its active phase.CONCLUDING REMARKSRelaxation oscillations are characterized by more than one time scale, and exhibit qualitatively different behavior than sinusoidal or harmonic oscillations. Such distinction is particularly prominent in synchronization and desynchronization in networks of relaxation oscillators. These unique properties in relaxation oscillators have led to new and promising applications to neural computation, especially scene analysis. It should be noted that networks of relaxation oscillations often lead to very complex behaviors other than synchronous and antiphase solutions. Even with identical oscillators and nearest neighbor coupling, traveling waves and other complex spatiotemporal patterns can occur (26).Relaxation oscillations with a singular parameter lend themselves to analysis by singular perturbation theory (27). Singular perturbation theory in turn yields a geometric approach to analyzing relaxation oscillation systems, as illustrated in Figs. 4 and 6. Also based on singular solutions, Linsay and Wang (28) recently proposed a fast method to numerically integrate relaxation oscillator networks. Their technique, called the singular limit method, is derived in the singular limit ε→ 0. A numerical algorithm is given for LEGION network, and it produces remarkable speedup compared to commonly used integration methods such as the Runge-Kutta method. The singular limit method makes it possible to simulate large-scale networks of relaxation oscillators.Computation using relaxation oscillator networks is inherently parallel, where each single oscillator behaves fully in parallel with all the other oscillators. This feature is particularly attractive in the context that an image generally consists of many pixels (e.g. 512x512), and current computer technology can support massive parallel computations. The network architecture such as the one shown in Fig. 5 performs computations based on only connections and oscillatory dynamics. The organizational simplicity plus continuous-time dynamics renders oscillator networks particularly feasible for VLSI chip implementation. With its computational properties plus biological plausibility, oscillatory correlation promises to offer a general computational framework. Acknowledgments. I thank X. Liu and M. Wu for their help in figure preparation. The preparation for this article was supported in part by an NSF grant (IRI-9423312) and an ONR Young Investigator Award (N00014-96-1-0676).BIBIOGRAPHY1. B. van der Pol, On 'relaxation oscillations'. Phil. Mag., 2: 978-992, 1926.2. B. van der Pol, Biological rhythms considered as relaxation oscillations. Acta Med. Scand. Suppl., 108: 76-87, 1940.3. A.V. Hill, Wave transmission as the basis of nerve activity. Cold Spring Harbour Symp. Quant. Biol., 1:146-151, 1933.。
Multisim7教程及应用
第一章电子电路的设计 (1)1.1模拟电子电路的设计方法 (1)1.2模拟电子电路的安装 (6)1.3模拟电子电路的调试 (8)1.4电子电路的故障分析与处理 (12)第二章MULTISIM 7.0 介绍 (14)一、简述 (14)二、M ULTISIM的组成及特点 (14)三、M ULTISIM的基本功能介绍 (15)四、M ULTISIM的常用操作 (34)五、M ULTISIM的分析功能 (42)第三章基础实验 (44)实验一有源滤波器 (44)实验二电压／频率转换电路 (47)实验三集成定时器应用 (49)实验四三相电相序检测与指示 (56)实验五水位控制及报警电路 (58)实验六音频放大器 (60)实验七交流电源过压、欠压保护电路 (62)实验八简易数字电压表的设计 (64)实验九数控音量高效功率放大器 (67)实验十省电防骚扰门铃 (70)实验十一数显电子秤的设计 (72)实验十二心率测试电路 (74)实验十三可调双限温度报警电路 (76)实验十四电冰箱开门报警电路 (80)实验十五LED水位计及报警电路 (85)实验十六交通灯控制电路的设计 (88)实验十七智力竞赛抢答器 (93)实验十八简易数显频率计的设计 (99)第四章设计实验 (102)实验一酒精传感器制作的检测报警器 (102)实验二热释电人体红外传感器制作的高速公路车辆计数器 (104)实验三光电指套式传感器制作的光电数字式脉搏计 (106)实验四温度传感器——电子温度计 (111)实验五气敏传感器—禁止吸烟警告器电路 (112)实验六力敏传感器—电子称重计电路 (113)实验七力敏传感器——便携式电子血压计 (114)实验八超声波倒车防撞报警电路 (117)实验九体温监测报警器 (118)第四章综合实验 (120)实验一可编程函数发生器 (120)实验二电话线路防盗器 (122)实验三简易声控电路 (124)实验四物品遗留提醒报警器 (125)实验五简易玩具电子琴 (127)实验六多功能音乐门铃 (128)第一章 电子电路的设计电子电路设计是综合运用电子技术理论知识的过程，必须从实际出发，通过调查研究、查阅有关资料、方案比较及确定，以及设计计算选取元器件等环节，设计出一个符合实际需要、性能和经济指标良好的电路。