Improved chaotic Colpitts oscillator for ultrahigh frequencies

Improved chaotic Colpitts oscillator for ultrahigh frequencies
. A. Tamas ˇ evic ˇ ius, S. Bumeliene and E. Lindberg
A novel version of the Colpitts oscillator is presented generating chaotic oscillations at gigahertz frequencies. In contrast to the standard oscillator the inductor is moved from the collector circuit of the transistor to the base circuit. PSpice simulations demonstrate chaos at the fundamental frequencies of 0.5, 1 and 2 GHz employing transistors with a threshold frequency of 9 GHz.
VE
VE
VC a
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Introduction: A number of simulations and experiments show that chaotic oscillations in the standard single-transistor Colpitts oscillator can be generated at the fundamental frequencies f * not higher than % 0.1 fT, where fT is the threshold frequency of the employed transistors. For example, chaos was demonstrated experimentally at f * ? 23 MHz [1] using the 2N2222A and at f * ? 26 MHz [2] using the 2N3904 transistors, both with the same fT of 300 MHz. By means of PSpice simulations chaos was predicted at f * ? 500 MHz using the AT41486 transistor with fT ? 3 GHz [1] and at f * ? 1 GHz employing the microwave BFG520 transistor with fT ? 9 GHz [2]. Experiments with the BFG520 transistors showed reliable chaotic oscillations at f * % 500 MHz; however, only weak chaos was observed at f * % 1 GHz [3]. Moreover, PSpice analysis indicated [4] that chaos at f * % 1 GHz was due to parasitic elements, for example wiring inductance and wiring loss resistance. Better results can be achieved in a more sophisticated two-stage Colpitts oscillator [5, 6]. The double-transistor oscillator promises higher fundamental frequencies [5] and provides smoother power spectra [6]. In this Letter we suggest an alternative to the double-transistor oscillator. It is an extremely simple modi?cation of the single-transistor Colpitts oscillator that enables generation of chaos up to several gigahertz.
VE
VE
VC b
VC
VE
VE
VC c
VC
Fig. 2 Phase portraits, emitter voltage VE against collector voltage VC
Standard version (left) and improved version (right) for different fundamental p frequencies f * % (2p (LC1C2=(C1 t C2)))à1. V0 ? 8 V, I0 ? 15 mA a f * ? 0.5 GHz; L ? 20 nH, C1 ? C2 ? 10 pF, R ? 30 O, Rb ? 39 O b f * ? 1 GHz; L ? 10 nH, C1 ? C2 ? 4.3 pF, R ? 36 O, Rb ? 20 O c f * ? 2 GHz; L ? 3 nH, C1 ? C2 ? 2.2 pF, R ? 36 O, Rb ? 4 O
Fig. 1 Circuit diagrams of chaotic Colpitts oscillators
a Standard version b Improved version
Circuitry: Circuit diagrams of the standard and the improved chaotic Colpitts oscillators are both shown for comparison in Fig. 1. The main difference between the usual Colpitts oscillator (Fig. 1a) and the improved version (Fig. 1b) is that the inductor L is moved from the collector circuit to the base. In addition, there is a series resistor Rb in the base circuit. The standard version has a typical common-base con?guration; however, the improved circuit cannot be attributed to any common-node con?guration.
Results and discussion: Simulations were performed using Electronics Workbench Professional simulator, based on the PSpice software. The BFG520 transistor discussed previously was employed in the circuits. Phase portraits in Fig. 2 and power spectra in Fig. 3 show that the improved version has an advantage over the standard Colpitts oscillator at gigahertz frequencies (power spectra from the standard oscillator are not presented here since they exhibit trivial discrete structure for f * ? 1 GHz and f * ? 2 GHz).
Fig. 3 Power spectra of collector signals from improved oscillator for different f *
Circuit parameters are the same as in Fig. 2. Note different frequency scales in the plots. a f * ? 0.5 GHz b f * ? 1 GHz c f * ? 2 GHz
ELECTRONICS LETTERS 9th December 2004 Vol. 40 No. 25

The basic mechanism behind the improvement of the Colpitts oscillator is that the inductor L, the resistor Rb and the capacitor CCB (zero-bias collector–base capacitance is about 0.5 pF for the BFG520 transistors) combine in an auxiliary resonance loop. This is indicated by spectral rises at faux % 1.9 GHz and faux % 3.8 GHz in Figs. 3b and c, respectively. We note that these frequencies are rather close to the 2nd harmonics of the corresponding fundamental frequencies; however, they do not coincide exactly with them, faux 6? 2f *. Moreover, variation of transistor and circuit parameters shows that faux is sensitive to the value of CCB, but not to C1 and C2. In the standard version of the Colpitts oscillator CCB grounds the collector node and acts as a parasitic element destroying chaotic oscillations [2]. Meanwhile in this new circuit L and Rb screen CCB from the ground and thus diminish its negative in?uence. Conclusion: We have demonstrated that the improved Colpitts oscillator with the BFG520 or similar type transistor can generate chaotic oscillations in the ultrahigh frequency range (300 MHz to 1 GHz), in the L (1 to 2 GHz) and the S (2 to 4 GHz) microwave bands. Acknowledgment: This work was supported in part by Lithuanian State Science and Studies Foundation under contract No. T-62=04. # IEE 2004 Electronics Letters online no: 20047019 doi: 10.1049/el:20047019 16 September 2004
. A. Tamas ˇ evic ˇ ius and S. Bumeliene (Semiconductor Physics Institute, A. Gos tauto 11, Vilnius LT-01108, Lithuania) ˇ E-mail: tamasev@p?.lt E. Lindberg (Oersted-DTU Department, Technical University of Denmark, Oersted Plads, Kgs Lyngby DK-2800, Denmark)
References
1 2 Wegener, C., and Kennedy, M.P.: ‘RF chaotic Colpitts oscillator’. Proc. 3rd Workshop NDES’95, Dublin, Ireland, July 1995, pp. 255–258 . . ˇ enys, A., Mykolaitis, G., Tamas ˇevic ˇ ius, A., Bumeliene, S., Lasiene, G., C Anagnostopoulos, A.N., and Lindberg, E.: ‘Towards microwave chaos with two-stage Colpitts oscillator’. Proc. 9th Workshop NDES 2001, Delft, The Netherlands, June 2001, pp. 97–100 . Mykolaitis, G., Tamas ˇ evic ˇ ius, A., and Bumeliene, S.: ‘Experimental demonstration of chaos from the Colpitts oscillator in the VHF and the UHF ranges’, Electron. Lett., 2004, 40, (2), pp. 91–92 . Tamas ˇ evic ˇ ius, A., Mykolaitis, G., Bumeliene, S., Baziliauskas, A., Krivickas, R., and Lindberg, E.: ‘VHF and UHF chaotic Colpitts ′ vora, Portugal, May oscillators’. Proc. 12th Workshop NDES 2001, E 2004, pp. 328–331 . ˇ enys, A., Tamas ˇ evic ˇ ius, A., Mykolaitis, G., Bumeliene, S., C Anagnostopoulos, A.N., and Lindberg, E.: ‘Two-stage chaotic Colpitts oscillator’, Electron. Lett., 2001, 37, (9), pp. 549–551 . Bumeliene, S., Tamas ˇ evic ˇ ius, A., Mykolaitis, G., Baziliauskas, A., and Lindberg, E.: ‘Hardware prototype of the two-stage chaotic Colpitts ′ vora, oscillator for the UHF range’. Proc. 12th Workshop NDES 2001, E Portugal, May 2004, pp. 99–102
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ELECTRONICS LETTERS 9th December 2004 Vol. 40 No. 25

新视野大学英语第三版第二册读写教程2课后答案和翻译

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非线性混沌电路实验报告

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2010SIMPLEST CHAOTIC CIRCUIT

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Multisim仿真—混沌电路汇编

Multisim仿真—混沌电路 1104620125

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蔡氏电路MATLAB混沌仿真

蔡氏电路的Matlab混沌 仿真研究 班级： 姓名： 学号：

摘要 本文首先介绍非线性系统中的混沌现象，并从理论分析与仿真计算两个方面细致研究了非线性电路中典型混沌电路，即蔡氏电路反映出的非线性性质。通过改变蔡氏电路中元件的参数，进而产生多种类型混沌现象。最后利用软件对蔡氏电路的非线性微分方程组进行编程仿真，实现了双涡旋和单涡旋状态下的同步，并准确地观察到混沌吸引子的行为特征。 关键词：混沌；蔡氏电路；MATLAB仿真 Abstract This paper introduce s the chaos phenomenon in nonlinear circuits. Chua’s circuit was a typical chaos circuit, thus theoretical analysis and simulation was made to research it. Many kinds of chaos phenomenon on would generate as long as one component parameter was altered in C hua’s circuit．On the platform of Matlab, mathematical model of Chua’s circuit was programmed and simulated to acquire the synchronization of dual and single cochlear volume. Meanwhile, behavioral characteristics of chaos attractor were observed. Key words：chaos phenomenon；Chua’s circuit；Simulation

混沌粒子群优化算法

混沌粒子群优化算法¨ 计算机科学2004V01．31N-o．8 高鹰h2谢胜利1 (华南理工大学电子与信息学院广州510641)1 (广州大学信息机电学院计算机科学与技术系广州510405)2 摘要粒子群优化算法是一种新的随机全局优化进化算法。本文把混沌手优思想引入到粒子群优化算法中，这种方 法利用混沌运动的随机性、遍历性和规律性等特性首先对当前粒子群体中的最优粒子进行混池寻优，然后把混沌寻优 的结果随机替换粒子群体中的一个粒子。通过这种处理使得粒子群体的进化速度加快t从而改善了粒子群优化算法摆 脱局部极值点的能力，提高了算法的收敛速度和精度。仿真结果表明混沌粒子群优化算法的收敛性能明显优于粒子群 优化算法。 关键词粒子群优化算法。混沌手优，优化 ’ChaosParticle Swarm OptimizationAlgorithm GAO Yin91”XIESheng—Lil (College of Electronic＆Information EngineeringtSouth China University of Technology，Guangzhou 510641)1 (Dept．of Computer Science and Technology．GuangzhouUniversity·Guangzhou 510405)2 Abstract Particle swarm optimization is anewstochastic global optimization evolutionaryalgorithm．In this paper， the chaotic search is embeddedinto original particle swarm optimizers．Based on the ergodicity，stochastic property and

2非线性电路混沌实验

非线性电路混沌实验 混沌是非线性系统中存在的一种普遍现象,它也是非线性系统所特有的一种复杂状态。 混沌研究最先起源于1963年洛伦兹(E.Lorenz)研究天气预报时用到的三个动力学方程,后来又从数学和实验上得到证实。无论是复杂系统,如气象系统、太阳系,还是简单系统,如钟摆、滴水龙头等,皆因存在着内在随机性而出现类似无轨、但实际是非周期有序运动,即混沌现象。由于电学量(如电压、电流)易于观察和显示,因此非线性电路逐渐成为混沌及混沌同步应用的重要途径,其中最典型的电路是美国加州大学伯克利分校的蔡少棠教授1985年提出的著名的蔡氏电路(Chua ’s Circuit)。就实验而言,可用示波器观察到电路混沌产生的全过程,并能得到双涡卷混沌吸引子。 本实验所建立的非线性电路包括有源非线性负阻、LC 振荡器和RC 移相器三部分；采用物理实验方法研究LC 振荡器产生的正弦波与经过RC 移相器移相的正弦波合成的相图(李萨如图)，观测振动周期发生的分岔及混沌现象。 【实验目的】 观测振动周期发生的分岔及混沌现象；测量非线性单元电路的电流—电压特性；了解非线性电路混沌现象的本质；学会自己制作和测量一个使用带铁磁材料介质的电感器以及测量非线性器件伏安特性的方法。 【实验原理】 1.非线性电路与非线性动力学 实验电路如图1所示，图1中只有一个非线性元件R ，它是一个有源非线性负阻器件。电感器L 和电容C 2组成一个损耗可以忽略的谐振回路；可变电阻R V 和电容器C 1串联将振荡器产生的正弦信号移相输出。本实验中所用的非线性元件R 是一个三段分段线性元件。图2所示的是该电阻的伏安特性曲线，从特性曲线显示中加在此非线性元件上电压与通过它的电流极性是相反的。由于加在此元件上的电压增加时，通过它的电流却减小，因而将此元件称为非线性负阻元件。 图1非线性电路原理图 图2非线性元件伏安特性 图1电路的非线性动力学方程为： 1121)(1 C C C C U g U U G dt dU C ?--?= L C C C i U U G dt dU C +-?=)(2112 2 (1) 2C L U dt di L -=

传递函数和信号流图

Chapter 3 Transfer Functions Block Diagrams Signal-Flow Graphs

混沌系統與訊號處理實驗室Transfer Functions -Impulse Response ()()()() y t g t d g t δτττ ∞ ?∞ =?=∫Convolution!!! Linear Time-Invariant system g (t ) δ(t ) y (t ): impulse response △T →0

混沌系統與訊號處理實驗室Transfer Function of an LTI system G (s ) ()()()()()()()() () y t g t u t Y s G s U s Y s G s U s =?∴=?∴= 　()()()()()() ()1 100111 10101 10 110 m n n n m n n m n n m m n m m m m m m n n n d u t d y d y a a y b b u t dt dt dt s a s a Y s b s b s b U s b s b s b G s s a s a ???????????+++=++?+++=++++++∴=+++ g (t )u (t )y (t ) If g (t ) can be characterized by the following ODE: ()()with all initial conditions =0G s L g t ????

混沌系統與訊號處理實驗室 ()1 10 1 10m m m m n n n b s b s b G s s a s a ????+++=+++ mn improper T.F. ()()()()()2 2 325325151 32 x x x u u s s X s s U s s G s s s ++=+?++=++?=++ Def: Characteristic Equation ()()()()1 10 1 10 1 1000 m m m m n n n n n n N s b s b s b G s D s s a s a D s s a s a ??????+++=+++=?+++=

混沌系统的电路实现与仿真分析

混沌系统的电路实现与仿真分析 1. 设计思路 混沌系统模块化设计方法的主要思路是，根据系统的无量纲状态方程，用模块化设计理念设计相应的混沌电路，其中主要的模块包括：反相器模块、积分器模块、反相加法比例运算模块和非线性函数产生模块。 2. 设计过程 第一步，对混沌系统采用Matlab 进行数值分析，观察状态变量的时序图、相图，观察系统状态变量的动态范围； 第二步，对变量进行比例压缩变换。我们通常取电源电压为±15V ，集成运放的动态范围为±13.5V ，如果系统状态变量的动态范围超过±13.5，则状态变量的动态范围超过了集成运放的线性范围，需要进行比例压缩变换，如没有超出，则不需要进行变换。 举例：变换的基本方法 ?????? ?=== w k z v k y u k x 32 1 代入原状态方程，然后重新定义u →x ，v →y ，w →z 得到的状态方程即为变量压缩后的状态方程。 第三步，作时间尺度变换。将状态方程中的t 变换为τ0t ，其中τ0为时间尺度变换因子，设τ0=1/R 0C 0，从而将时间变换因子与积分电路的积分时间常数联系起来。 第四步，作微分-积分变换。 第五步，考虑到模块电路中采用的是反相加法器，将积分方程作标准化处理。 第六步，根据标准积分方程，可得到相应的实现电路。 第七步，采用Pspice 仿真软件或Multisim 仿真软件对电路进行仿真分析。

3. 设计举例：Lorenz 系统的电路设计与仿真 Lorenz 系统的无量纲归一化状态方程为 bz xy z y xz cx y ay ax x --=--=+-= （1） 其中当a=10，b=8/3，c=28时，该系统可以展现出丰富的混沌行为。 MATLAB 仿真程序如下： function dx=lorenz(t,x) %?¨ò?oˉêy a=10; b=8/3;c=28; %?¨ò??μí32?êy %***************************************** dx=zeros(3,1); dx(1)=a*(x(2)-x(1)); dx(2)=c*x(1)-x(1).*x(3)-x(2); dx(3)=x(1).*x(2)-b*x(3); %*********************************?¨ò?×′ì?·?3ì clear; options=odeset('RelTol',1e-6,'AbsTol',[1e-6,1e-6,1e-6]); t0=[0 500]; x0=[1,0,0]; [t,x]=ode45('Lorenz',t0,x0,options); n=length(t); n1=round(n/2); figure(1); plot(t(n1:n),x(n1:n,1)); %×′ì?xμ?ê±Dòí? xlabel('t','fontsize',20,'fontname','times new roman','FontAngle','normal'); ylabel('x1','fontsize',20,'fontname','times new roman','FontAngle','normal'); figure(2); plot(x(n1:n,1),x(n1:n,3)); %x-z?àí? xlabel('x','fontsize',20,'fontname','times new roman','FontAngle','italic'); ylabel('Z','fontsize',20,'fontname','times new roman','FontAngle','italic'); figure(3); plot3(x(n1:n,1),x(n1:n,2),x(n1:n,3)); %x-y-z?àí? xlabel('x','fontsize',20,'fontname','times new roman','FontAngle','italic'); ylabel('y','fontsize',20,'fontname','times new roman','FontAngle','italic');

Memristor Based Chaotic Circuits

Memristor Based Chaotic Circuits Bharathwaj Muthuswamy Electrical Engineering and Computer Sciences University of California at Berkeley Technical Report No. UCB/EECS-2009-6 https://www.wendangku.net/doc/ab11482954.html,/Pubs/TechRpts/2009/EECS-2009-6.html January 15, 2009

Copyright 2009, by the author(s). All rights reserved. Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. To copy otherwise, to republish, to post on servers or to redistribute to lists, requires prior specific permission. Acknowledgement Many thanks to Prof. Leon O. Chua for his support and guidance.

研究生英语(一年级下)课后习题及答案2

Unit6 The culture of New York City is shaped by centuries of immigration, the city's size and variety,and its status as the cultural capital of the United States. Because of its 1) _sheer_ size and cultural influence,New York has been the 2)subject_ of many different, and often 3)_contradictory_ ,portrayals in the mass media. From the sophisticated and 4)_worldly_ metropolis seen in many Woody Allen films, to the hellish and 5)_chaotic_ urban jungle depicted in such movies as Martin Scorsese's Taxi Driver,New York has served as the unwitting backdrop for every conceivable on big city life.In the early years of film NewYork City was characterized asurbane and 6)_sophisticated_. By the city's period in the 1970s, however, films like Midnight Cowboy, The French Connection,Marathon Man, and Death Wish showed New York as full of chaos and 7)_violence_. With the city's ienaissance in the 1980s and 1990s came new portrayals on television; Friends, Seinfeld, and Sex andthe City showed life in the city to be 8)_glamorous_ and interesting. Nonetheless a disproportionate number of 9)_crime_ dramas,such as Law & Order, continue to make criminality in the city in their subject, even as New York has become the 10)__safest___ large city in the United States in the last two decades. Unit7 Risk compensation is the idea that individuals tend to adjust their behavior in response to what they perceive as changes in the level of risk.Imagine,what would happen if safety regulations were to require all cars to be made of cardboard,fitted with inefficient brakes and with a sharp spike in the center of the steering column; if all roads were paved with a substance having the same friction coefficient as ice ,and if all drivers were obliged to change every other month or,better yet,if there were no rules about which side of the road to drive on.The evidence suggests that there would be no increase,and possibly a decrease,in road accident fatalities,but there would be a Substantial decrease in the efficiency of the road transport system.It seems that the potential safety benefit of most improvements to road or vehicles is considered as a performance benefit.As a result of safety improvements it is now possible to travel farther and faster with approximately the same risk of being killed. Unit8 Intelligent Transport System(ITS) is the name given to the application of computer and communication technologies to transport problems.In a(n) rapidly changing society the emphasis on road technology improvements to assist in road management has been identified.The rapid advances in ITS technologies have enabled the collection of data or intelligence which provides relevant and timely information to road managers and users. Japan seems to have initiated the whole modern day notion of ITS with work carried out in the 1980s.The United States was also addressing the application of ITS at an early stage in the course of the Electronic Route Guidance project(ERGS) in the 1970s.The European Union picked up the theme,and referred to it as Road Transport Informatics.In the course of time the name of this technology was subjected to many changes until the USA gave it the name ITS.Intelligent Transport systems include wider application of technology to transit systems as well as private cars and highways.Benefits given by ITS to any transportation system that introduce it are:improved safety,improved traffic efficiency,reduced congestion,improved environmental quality and energy efficiency and improved economic productivity. Unit9 Northern Canada, including the Northwest Territories,is an expensive place to live. Housing is at least 60% more expensive in the north than it is in southern Canada.Food prices are also higher, by at least 20%.Since building materials and foodstuffs are imported from the south ,the higher prices are primarily due to transportation costs. Communities far away from Yellowknife have higher costs, and communities served only by aircraft have the highest food and housing costs. For example, foodstuffs shipped by air to remote communities such as Sachs Harbour on Banks Island are 80% more expensive than they are in Yellow knife. To offset these high food and housing costs, wages are higher than those in southern Canada .In addition, most people live in public or staff housing, where rents are subsidized .Government employees living in remote communities receive an isolated post allowance payment to help offset the higher cost of living. unit10 The moral imperative begins by considering the value of education which is much deeper than earning potential or building human https://www.wendangku.net/doc/ab11482954.html,cation is what it takes to lead fuller lives and to contribute to our nation and the world. Higher education in particular affords students the opportunities to explore history, debate important issues, and discover their passions and potential . Our founders understood how important education is to the idea of America as a just, equitable, and productive society. A nation of educated individuals is more likely to strengthen the institutions: in government, in business and in the schools they rely upon. Consider graduation rates. Fifteen percent of our high schools produce half of our dropouts, and these schools are disproportionately in low-income areas with mostly minority students. Nationally ,one of every two African American and Hispanic students drops out of high school. If we are a nation dedicated to equality, we cannot be satisfied with the status quo. Helping more students make it to college and succeed there is a morally urgent challenge. Unit6 The culture of New York City is shaped by centuries of immigration, the city's size and variety,and its status as the cultural capital of the United States. Because of its 1) _sheer_ size and cultural influence,New York has been the 2)subject_ of many different, and often 3)_contradictory_ ,portrayals in the mass media. From the sophisticated and 4)_worldly_ metropolis seen in many Woody Allen films, to the hellish and 5)_chaotic_ urban jungle depicted in such movies as Martin Scorsese's Taxi Driver,New York has served as the unwitting backdrop for every conceivable on big city life.In the early years of film NewYork City was characterized asurbane and 6)_sophisticated_. By the city's period in the 1970s, however, films like Midnight Cowboy, The French Connection,Marathon Man, and Death Wish showed New York as full of chaos and 7)_violence_. With the city's ienaissance in the 1980s and 1990s came new portrayals on television; Friends, Seinfeld, and Sex andthe City showed life in the city to be 8)_glamorous_ and interesting. Nonetheless a disproportionate number of 9)_crime_ dramas,such as Law & Order, continue to make criminality in the city in their subject, even as New York has become the 10)__safest___ large city in the United States in the last two decades. Unit7 Risk compensation is the idea that individuals tend to adjust their behavior in response to what they perceive as changes in the level of risk.Imagine,what would happen if safety regulations were to require all cars to be made of cardboard,fitted with inefficient brakes and with a sharp spike in the center of the steering column; if all roads were paved with a substance having the same friction coefficient as ice ,and if all drivers were obliged to change every other month or,better yet,if there were no rules about which side of the road to drive on.The evidence suggests that there would be no increase,and possibly a decrease,in road accident fatalities,but there would be a Substantial decrease in the efficiency of the road transport system.It seems that the potential safety benefit of most improvements to road or vehicles is considered as a performance benefit.As a result of safety improvements it is now possible to travel farther and faster with approximately the same risk of being killed. Unit8 Intelligent Transport System(ITS) is the name given to the application of computer and communication technologies to transport problems.In a(n) rapidly changing society the emphasis on road technology improvements to assist in road management has been identified.The rapid advances in ITS technologies have enabled the collection of data or intelligence which provides relevant and timely information to road managers and users. Japan seems to have initiated the whole modern day notion of ITS with work carried out in the 1980s.The United States was also addressing the application of ITS at an early stage in the course of the Electronic Route Guidance project(ERGS) in the 1970s.The European Union picked up the theme,and referred to it as Road Transport Informatics.In the course of time the name of this technology was subjected to many changes until the USA gave it the name ITS.Intelligent Transport systems include wider application of technology to transit systems as well as private cars and highways.Benefits given by ITS to any transportation system that introduce it are:improved safety,improved traffic efficiency,reduced congestion,improved environmental quality and energy efficiency and improved economic productivity. Unit9