The General Feedback Theorem-A Final Solution for Feedback Systems
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《自动控制原理》部分中英文词汇对照表AAcceleration 加速度Angle of departure分离角Asymptotic stability渐近稳定性Automation自动化Auxiliary equation辅助方程BBacklash间隙Bandwidth带宽Block diagram方框图Bode diagram波特图CCauchy’s theorem高斯定理Characteristic equation特征方程Closed-loop control system闭环控制系统Constant常数Control system控制系统Controllability可控性Critical damping临界阻尼DDamping constant阻尼常数Damping ratio阻尼比DC control system直流控制系统Dead zone死区Delay time延迟时间Derivative control 微分控制Differential equations微分方程Digital computer compensator数字补偿器Dominant poles主导极点Dynamic equations动态方程EError coefficients误差系数Error transfer function误差传递函数FFeedback反馈Feedback compensation反馈补偿Feedback control systems反馈控制系统Feedback signal反馈信号Final-value theorem终值定理Frequency-domain analysis频域分析Frequency-domain design频域设计Friction摩擦GGain增益Generalized error coefficients广义误差系数IImpulse response脉冲响应Initial state初始状态Initial-value theorem初值定理Input vector输入向量Integral control积分控制Inverse z-transformation反Z变换JJordan block约当块Jordan canonical form约当标准形LLag-lead controller滞后-超前控制器Lag-lead network 滞后-超前网络Laplace transform拉氏变换Lead-lag controller超前-滞后控制器Linearization线性化Linear systems线性系统MMass质量Mathematical models数学模型Matrix矩阵Mechanical systems机械系统NNatural undamped frequency自然无阻尼频率Negative feedback负反馈Nichols chart尼科尔斯图Nonlinear control systems非线性控制系统Nyquist criterion柰奎斯特判据OObservability可观性Observer观测器Open-loop control system开环控制系统Output equations输出方程Output vector输出向量PParabolic input抛物线输入Partial fraction expansion部分分式展开PD controller比例微分控制器Peak time峰值时间Phase-lag controller相位滞后控制器Phase-lead controller相位超前控制器Phase margin相角裕度PID controller比例、积分微分控制器Polar plot极坐标图Poles definition极点定义Positive feedback正反馈Prefilter 前置滤波器Principle of the argument幅角原理RRamp error constant斜坡误差常数Ramp input斜坡输入Relative stability相对稳定性Resonant frequency共振频率Rise time上升时间调节时间 accommodation timeRobust system鲁棒系统Root loci根轨迹Routh tabulation(array)劳斯表SSampling frequency采样频率Sampling period采样周期Second-order system二阶系统Sensitivity灵敏度Series compensation串联补偿Settling time调节时间Signal flow graphs信号流图Similarity transformation相似变换Singularity奇点Spring弹簧Stability稳定性State diagram状态图State equations状态方程State feedback状态反馈State space状态空间State transition equation状态转移方程State transition matrix状态转移矩阵State variables状态变量State vector状态向量Steady-state error稳态误差Steady-state response稳态响应Step error constant阶跃误差常数Step input阶跃输入TTime delay时间延迟Time-domain analysis时域分析Time-domain design时域设计Time-invariant systems时不变系统Time-varying systems时变系统Type number型数Torque constant扭矩常数Transfer function转换方程Transient response暂态响应Transition matrix转移矩阵UUnit step response单位阶跃响应VVandermonde matrix范德蒙矩阵Velocity control system速度控制系统Velocity error constant速度误差常数ZZero-order hold零阶保持z-transfer function Z变换函数z-transform Z变换。
Pure mathematics1 1Algebraic expression代数表达式Index laws指数定律Indices(index的复数形式)指数Notation注释Simplify化简Power指数Base底Exponent指数Expression表达式Term项Numerator分子Expand展开Possible可能Fraction分数Bracket括号Product乘积Multiply乘Collecting like terms合并同类项Linear一次的Diagram图形Rectangle长方形Square正方形Length长度Width宽Side length边长Area面积Shade阴影Cuboid长方体Dimension维Show that证明Volume体积Given that已知Constant常数Value值Factorize因式分解Factor因子Opposite相反的Completely完全地Common factor公因式Quadratic二次的Form形式Real number实数Positive正的Negative负的Include包含Surd无理数Add加Sum和Take out提取Difference差Difference of two squares平方差Cancel取消,相互抵消Similarly同样的Rational有理的Rational number有理数Integer整数Square root平方根Evaluate求…的值Substitute代替Calculator计算器Square number平方数Irrational number无理数Decimal小数的Expansion展开式Never-ending无限的Never repeat不循环的Exact准确的Answer答案Manipulate操作Denominator分母Rationalizing denominator分母有理化Rearrange调整Prime质数Work out计算Hence然后Fully完全地State陈述Solve解决Equation方程2Quadratics二次方程式Quadratic equation二次方程Solution解Real solution实根Set设置Root根Distinct不同的Repeated root重根Case情况Straightforward简单直接的Symbol符号Plus加,正Minus减,负Factorization因式分解Shape形状Section部分Formula公式Reading off读取Coefficient系数Necessary必要的Significant figures有效数字Choose选择Suitable适当的Method方法Trapezium梯形Height高Discard丢弃Completing the square完全平方(配方)Frequently经常的Useful有用的Process过程Original最初的Determine决定Otherwise另外Function函数Mathematical数学上的Relationship关系Map映射Set集合Input输入Output输出Single单一的Notation符号Represent代表Domain定义域Range值域,范围Member成员Define定义Minimum最小的Occur发生Explain解释Consider考虑Graph图像Curve曲线Parabola抛物线Sketch画图Identify确定Key关键的Feature特征Overall整体的Cross交叉,横过Axis轴Coordinate坐标Turning point转折点(顶点)Maximum最大的Since因为Symmetrical对称的Symmetry对称性Line of symmetry对称轴Half-way位于中途的Explore探测Technology技术Plot绘制Scale刻度However但是,不管怎样Smooth平滑的Relevant相关的Intercept截距Label标记Axes(axis的复数)坐标轴Discriminant判别式Sign符号Check核实Inequality不等式Calculate计算Match匹配Prove证明Algebra代数学Diver跳水运动员Launch发射Springboard跳板Meter米Pool水池Second秒Model模型High高的Hit撞击Reach达到Non-zero非零3Equations and inequalities 方程和不等式Simultaneous联立的Linear simultaneous equations一次方程组Elimination消元法Substitution置换Quadratic simultaneous equations 二次方程组Up to直到,多达Make sure确保Correctly正确地Simplest最简的Graphically以图表形式As因为Satisfy满足Intersection相交Simultaneously同时地Intersect相交Once一次Twice两次Result结果,导致Produce产生Graph paper坐标纸Accurately准确地Verify验证Linear inequalities一次不等式Set notation集合符号Number line数轴Overlap重叠Separately单独地Illustrate图解,阐明Quadratic inequalities二次不等式Corresponding相应的Critical临界的Require要求Describe描述Interpret解释Region区域,范围Coordinate grid坐标网Dotted line虚线Solid line实线Vertex顶点Vertices(vertex的复数)顶点Within在内部,之内4Graphs and transformations 图像和转换Cubic三次的Cubic function三次函数Several几个Depend on取决于Touch接触Coordinate axes坐标轴Indicate表明,显示Reciprocal倒数的Reciprocal function反比例函数Such as例如Asymptote渐近线Approach接近Reach到达Quadrant象限Point of intersection交点Steeper更陡峭的Eventually最后,终于Reason理由,原因Appropriate恰当的Number数量Translate平移Transform改变Alter改动Subtract减Outside在外面Vertically竖直地Translation平移Vector矢量Horizontally水平地Direction方向In terms of用…来表示Slide滑动Stretch伸缩Scale factor比例系数Double两倍Halve减半,对分Inside在里面Triple三倍的Reflection反射(镜面对称) Alternatively二选一Parallel平行Lie on坐落在Pass through穿过Apply应用Unfamiliar陌生的,不熟悉的Specific特殊的Origin原点Position位置Image像Suggest提议Mark标记5Straight line graphs直线图像Gradient斜率Straight line直线Join连接Distance距离Formula公式Collinear共线的Intercept截距Define定义Either两者中的任一个Condition条件Triangle三角形General equation一般式Parallel平行Perpendicular垂直Whether是否Quadrilateral四边形Trapezium梯形Right angle直角Congruent全等的Neither两者都不Hypotenuse直角三角形斜边Line segment线段Scalene不等边的Respectively分别地Go through通过6Trigonometric ratios三角比Cosine rule余弦定理Miss缺失Version版本Exchange交换Standard标准Prove证明Opposite对边Adjacent邻边Pythagoras’theorem勾股定理Letter字母Round四舍五入Final最终的Coastguard海岸警卫队Station驻地Bearing方位Away from远离Appropriate适当的Mark标记Airport机场Due north正北Due east正东Due west正西Due south正南Sail航行Helicopter直升飞机Tee球座Flag旗Particular特定的Hole孔,洞Golf course高尔夫球场Yard码(1码=3英尺)Tee shot发球台Land着陆Largest最大的Farmer农场Field场地Fence栅栏Cargo货物Plane平面Kilometer千米Sine rule正弦定理Refer to涉及Data数据Remain剩余Located on坐落于Zookeeper动物管理员Enclosure围场Llama骆驼Diagonal对角线Surveyor检验员Measure测量Elevation高程,仰角Apart相距Assumption假设Mathematical数学的Model模型Obtuse钝角Acute锐角Isosceles等腰的Circle圆Radius半径Centre圆心Least最小的Instead代替Crane吊车Anchored固定Wreck破坏Suspend悬挂Cable缆绳Rotate旋转Level对准Proof证明Triangular plot三角图Involve涉及Trigonometry三角函数Encounter遇到Decide决定Mast桅杆In order that为了Interfere干扰Efficient有效的Hiker徒步旅行者Radar雷达Perimeter周长Tangent正切Periodic周期性的Repeat重复的Certain确定的Interval间距Period周期Undefined无意义的Knowledge知识Periodicity周期性Verify证明Variation变化Rock pool潮汐潭Midday中午During在…期间Non-exact非精准的Significant figure有效数字Windmill风车Sail帆Tower塔Deduce推导Dune沙丘Realistic现实的7Radians弧度Radian弧度So far到目前为止Probably大概,可能Degree度Revolution循环Around围绕Circle圆Subtend朝着Arc圆弧Circumference周长Convert转换Without没有Multiple倍数Arc length弧长Sector扇形Radius半径Contain包含Perimeter周长Border边界Pond池塘Consist由…组成Edge边缘Minor arc劣弧Major arc优弧Chord弦Diameter直径Template模板Brooch胸针Ferris wheel摩天轮Pod蚕茧,豆荚Estimate估计Speed速率Patio露台Lawn草坪Design设计Earring耳环Nearest最近点(精确到)Segment弓形Radii(radius的复数形式) A plot of…的一块Erect建造Along沿着Subtract减Tangent切线Ratio比例Bound关,围入Decimal place小数Midpoint中点Semicircular半圆Drawer抽屉Handle把手Difference差Badge徽章Equilateral等边的Railway铁路Track轨迹Prism三棱镜Attempt尝试Mistake错误8Differentiation微分Gradient斜率Constantly不断地Although然而Comment on对…评论Copy抄写,复制Complete完成Table表格Hypothesis假设Derivative导数Principle原理Detail细节Account解释Originate起源Formalize确定,形成Approach方式,方法Limit极限Tend to趋向Gradient function斜率函数Evaluate求…的值Fixed value定值Limiting value定值Definition定义One-at-a-time一次一个Turning point转折点(顶点)Slope斜率Disappear消失Polynomial多项式Normal切线First order derivative一阶导数Second order derivative二阶导数Rate of change变化率Respect to关于Displacement位移Acceleration加速度Local局部的9Integration积分Reverse相反的Differ不同Integrate求积分Integral积分Indefinite不确定的Indefinite integral不定积分Elongated拉长的,伸长的Arrow箭Fire射击Castle城堡Drop off下降Cliff悬崖Cyclist骑行者Pure mathematics2 1Algebraic methods代数方法Division除法Dividing polynomial多项式除法Finite有限的Whole number整数Long division长除法Quotient商Remainder余数Factor theorem因式定理Remainder theorem余数定理Logical逻辑的Structured有组织的Argument论据Statement命题Conjecture猜想Previously预先Establish建立Deduction推导Desired想要的Conclusion结论Odd number奇数Demonstration示范,演示Even number偶数Identical完全相等的Identity恒等式Parallelogram平行四边形Rhombus菱形Congruent全等的Exhaustion穷举法Consecutive连续的Square number平方数Break into拆分Is suited to适合于Disprove反驳Counter-example反例Sufficient充分的Prime number质数Divisible可整除的Either…or…二者择一的Cube number立方数Hold有效Claim宣称Opposite edge对边Hexagon六边形Regular hexagon正六边形Side length边长Reason原因2Coordinate geometry in the (x,y)plane解析几何Bisector二等分线Perpendicular bisector中垂线Averaging求平均值Endpoint端点Circumcentre外心Equidistant等距的Fixed point定点Vector向量Property性质Unique独一无二的Circumcircle外接圆3Exponentials and logarithms 指数和对数Exponential指数的Decrease减小Increase增加Smooth光滑的,平滑的Increasing function增函数Decreasing function减函数Justify证明Logarithms对数Specific特定的Button按钮Typically典型的Natural logarithms自然对数Instance实例Multiplication law乘法定律Division law除法定律Power law指数定律Recognize识别Attention注意Condition条件Complicated复杂的Whenever无论何时Convenient方便的Suppose假设Notice注意Particular特别的4The binomial expansion二项式展开Binomial二项式Pascal’s triangle杨辉三角(帕斯卡三角形)Immediately直接地Pattern图案Adjacent相邻的Investment投资Interest rate利率Annum年,岁Approximation近似值Ignore忽略Factorial notation阶乘Combination组合Superscript上标Subscript下标Probability可能性Toss投Likelihood可能性Ascending powers升幂Individual个别的Estimation估值Engineering工程学Science科学Percentage error百分误差Microchip微型集成电路片Faulty有缺点的Chip芯片Restrict限制Achieve达到School fair学校园游会Prize奖赏Digit数字Display显示5Sequences and series数列和级数Arithmetic sequence等差数列Arithmetic progression等差数列Common difference公差Arithmetic series等差级数(等差数列前n项求和)Exceed超过Inclusive包含的Stick棒子Pentagon五角形Geometric sequences等比数列Geometric progression等比数列Common ratio公比Converge收敛Alternating sequence交错数列Million百万Geometric series等比级数(等比数列前n项求和)Sum to infinity无限项求和Divergent发散的Convergent收敛的Recurring循环的Sigma notation求和符号Capital首都,大写字母Signify表示Recurrence relations递推关系Previous term前一项First term初项Generate生成,产生Periodic sequence周期数列Period周期Salary薪水Profit利润Predict预言Annual年度的Business商业Financial金融的Advisor顾问Fold折叠Thickness厚度Unrealistic不切实际的Investor投资人Account账户Thereafter以后Deposit存款,定金Wage工资Rise上升Gear齿轮Successive连续的Intermediate中间的Valuable有价值的Commission佣金Insurance保险Policy政策Prospector勘探者Drill钻孔Subsequent随后的Available可获得的Payment报酬Virus病毒Infect传染Diagnose诊断Overfish过度捕捞Chess象棋Chessboard棋盘Sponsored赞助的Polygon多边形Appointment约会,任命6Trigonometric identities and equations三角恒等式和方程Unit circle单位圆Anticlockwise逆时针Quadrant象限Equivalent相等的Equilateral triangle等边三角形Isosceles right-angled triangle等腰直角三角形Identity恒等式Reflex优角(大于180度,在第三、四象限)Principal value主值Inverse trigonometric function反三角函数Justification理由7Differentiation微分Strictly严格地Interval区间Stationary point驻点Local maximum局部最大Greatest value最大值Local minimum局部最小Least value最小值Point of inflection拐点,反曲点Immediate最接近的Vicinity邻近,附近Second derivative二次求导Rate of change改变的快慢Convex凸Concave凹Establish建立,证实Liter升Instant瞬间Tank水槽Cuboid长方体的Sheet薄片Metal金属Sphere球体Displacement位移Cylinder圆柱体Perimeter周长Semicircular半圆的Semicircle半圆Frame框架Split分离,分开Motion运动Damped阻尼Spring弹簧Bent弯的Biscuit饼干Tin罐头Close-fitting紧贴的Lid盖子Thin薄的,瘦的Wastage损耗Obtain获得Percentage百分比Store储存Capacity容量Container容器Calculus微积分学8Integration积分Definite integral定积分Indefinite integral不定积分Whereas反之,然而Upper limit上限Lower limit下限Square bracket中括号Magnitude大小Negligible可忽略的Straddle跨坐Unless除非Complicated复杂的Trapezium梯形Trapezium rule梯形法则Beneath在…下面Strip条,带Boundary边界Adjacent相邻的Improve改善Accuracy精确度Approximation近似值Underestimate低估Overestimate高估Compare比较Pure mathematics3 Common multiple公倍数Improper fraction假分数Partial fractions部分分数Degree次数Modulus function模函数Absolute value绝对值Argument辐角Set notation集合符号Piecewise-defined function分段函数Composite function复合函数Inverse function反函数Secant正割Cosecant余割Cotangent余切Interval区间Symmetry对称性Symmetrical对称的Chord弦Inverse trigonometric function反三角函数Addition formulae加法公式Compound-angle formulae复合角公式Double-angle formulae二倍角公式Round四舍五入Exponential function指数函数Natural logarithms自然对数Trend趋势Outlier极值Chain rule链式法则Product rule乘法法则Quotient rule除法法则Continuous连续的Fixed point iteration定点迭代Successive连续的Converge收敛Staircase diagram梯形图Cobweb diagram网状图Diverge发散Pure mathematics4 Contradiction反驳Assert主张Falsehood虚假Negation反论Prime number质数Split分解Separate独立的Parametric equation参数方程Variable变量Parameter参数Revolution循环Plot绘图Valid有效的As long as只要Condition条件Accurate精确的Ascending上升的Approximation近似值Implicit differentiation隐函数微分Explicitly明确的Implicit隐含的Rate of change变化率Hemisphere半球Cylindrical圆柱形的Conical圆锥形的Concave凹Convex凸Integrand被积函数Integration by substitution换元积分法Integration by part分部积分法Polynomial多项式Separating the variables分离变量General solution通解Boundary condition边界条件Directed line segment有向线段Parallelogram平行四边形Unit vector单位向量Column vector列向量Position vector位置矢量Scalene不等边的Clockwise顺时针Anticlockwise逆时针Coplanar共面的Parallelepiped平行六面体Trisect三等分Hexagon六边形Regular hexagon正六边形Direction vector方向向量Anchor固定Dot product点乘。
《国际贸易》英文名词解释International Trade(国际贸易)International trade is the international exchange of goods and services between countries. This type of trade gives rise to a world economy, in which prices, or supply and demand, affect and are affected by global events.Free Trade(自由贸易)The main idea of free trade is that supply and demand factors, operating on a global scale, will ensure that production happens efficiently. Therefore, nothing needs to protect or promote trade and growth because market forces will do so automatically.Protectionism(贸易保护主义)In contrast, protectionism holds that regulation of international trade is important to ensure that markets function properly. Advocates of this theory believe that market inefficiencies may hamper the benefits of international trade and they aim to guide the market accordingly. Production Possibilities Curve /Frontier(生产可能性曲线/边界)A Production Possibilities Frontier is a graph that shows the various combinations of output that the economy can possibly produce, given the available factors of production and the existing technology . Opportunity Cost(机会成本)Opportunity Cost means whatever must be given up to obtain some item. Supply Curve(供给曲线)A Supply Curve is a graph that shows the relationship between the price of a good and the quantity supplied.Demand Curve (需求曲线)A Demand Curve is a graph that describes the relationship between the price of a good and the quantity demanded.Excess Supply Curve(出口供给曲线)Because Excess Supply is a situation in which quantity supplied is greater than quantity demanded, Excess Supply Curve can be defined as a graph that depicts the relationship between the price and the available quantity for export of a product. Excess Supply Curve can be derived from subtracting a supply curve with a corresponding demand curve. Excess Demand Curve(进口需求曲线)Because Excess Demand is a situation in which quantity demanded is greater than quantity supplied, Excess Demand Curve can be defined as a graph that depicts the relationship between the price and the desirable quantity for import of a product. Excess Demand Curve can be derived from subtracting a demand curve with a corresponding supply curve. Consumer Surplus(消费者剩余)Consumer Surplus means a buyer’s willingness to pay minus the amount the buyer actually pays. Consumer surplus measures the benefit to buyersof participating in a market.Producer Surplus (生产者剩余)Producer Surplus is the amount a seller is paid for a good minus the seller’s cost. Producer surplus measures the benefit to sellers of participating in a market.Economies of Scale(规模经济)Economies of Scale means the property whereby the long-run average cost falls as the quantity of output increases.Diseconomies of Scale(规模不经济)Diseconomies of Scale means the property whereby the long-run average cost rises as the quantity of output increases.Constant Returns to Scale(规模报酬不变)Constant Returns to Scale means the property whereby the long-run average cost stays the same as the quantity of output changes. Indifference Curve(无差异曲线)Indifference Curve is a curve that shows consumption bundles that give the consumer the same level of satisfaction.The Gravity Model(引力模型)In its basic form, the gravity model assumes that only size and distance(经济规模和距离) are important for trade in the following way:Tij = A x Yi x Yj /Dij两国之间的贸易规模与经济规模成正比,与两国之间的距离成反比。
电气术语中英文对照表—电路的基本概念及定律电源 source电压源 voltage source电流源 current source理想电压源 ideal voltage source理想电流源 ideal current source伏安特性 volt—ampere characteristic电动势 electromotive force电压 voltage电流 current电位 potential电位差 potential difference欧姆 Ohm伏特 Volt安培 Ampere瓦特 Watt焦耳 Joule电路 circuit电路元件 circuit element电阻 resistance电阻器 resistor电感 inductance电感器 inductor电容 capacitance电容器 capacitor电路模型 circuit model参考方向 reference direction参考电位 reference potential欧姆定律 Ohm’s law基尔霍夫定律 Kirchhoff’s law基尔霍夫电压定律 Kirchhoff’s voltage law(KVL)基尔霍夫电流定律 Kirchhoff’s current law(KCL)结点 node支路 branch回路 loop网孔 mesh支路电流法 branch current analysis网孔电流法 mesh current analysis结点电位法 node voltage analysis电源变换 source transformations叠加原理 superposition theorem网络 network无源二端网络 passive two—terminal network 有源二端网络 active two—terminal network 戴维宁定理 Thevenin's theorem诺顿定理 Norton’s theorem开路(断路)open circuit短路 short circuit开路电压 open-circuit voltage短路电流 short-circuit current电气术语中英文对照表—交流电路直流电路 direct current circuit (dc)交流电路 alternating current circuit (ac)正弦交流电路 sinusoidal a—c circuit平均值 average value有效值 effective value均方根值root—mean-squire value (rms)瞬时值 instantaneous value电抗 reactance感抗 inductive reactance容抗 capacitive reactance法拉 Farad亨利 Henry阻抗 impedance复数阻抗 complex impedance相位 phase初相位 initial phase相位差 phase difference相位领先 phase lead相位落后 phase lag倒相,反相 phase inversion频率 frequency角频率 angular frequency赫兹 Hertz相量 phasor相量图 phasor diagram有功功率 active power无功功率 reactive power视在功率 apparent power功率因数 power factor功率因数补偿 power-factor compensation串联谐振 series resonance并联谐振 parallel resonance谐振频率 resonance frequency频率特性 frequency characteristic幅频特性amplitude-frequency response characteristic 相频特性 phase—frequency response characteristic截止频率 cutoff frequency品质因数 quality factor通频带 pass—band带宽 bandwidth (BW)滤波器 filter一阶滤波器 first-order filter二阶滤波器 second—order filter低通滤波器 low—pass filter高通滤波器 high—pass filter带通滤波器 band—pass filter带阻滤波器 band—stop filter转移函数 transfer function波特图 Bode diagram傅立叶级数 Fourier series电气术语中英文对照表-三相电路三相电路 three-phase circuit三相电源 three-phase source对称三相电源 symmetrical three—phase source对称三相负载 symmetrical three—phase load相电压 phase voltage相电流 phase current线电压 line voltage线电流 line current三相三线制 three—phase three—wire system三相四线制 three—phase four-wire system三相功率 three-phase power星形连接 star connection(Y—connection)三角形连接 triangular connection(— connection ,delta connection) 中线 neutral line电路的暂态过程分析编辑本段回目录暂态 transient state稳态 steady state暂态过程,暂态响应 transient response换路定理 low of switch一阶电路 first-order circuit三要素法 three-factor method时间常数 time constant积分电路 integrating circuit微分电路 differentiating circuit磁路与变压器编辑本段回目录磁场magnetic field磁通 flux磁路 magnetic circuit磁感应强度 flux density磁通势 magnetomotive force磁阻 reluctance电动机编辑本段回目录直流电动机 dc motor交流电动机 ac motor异步电动机 asynchronous motor同步电动机 synchronous motor三相异步电动机 three—phase asynchronous motor单相异步电动机 single—phase asynchronous motor旋转磁场 rotating magnetic field定子 stator转子 rotor转差率 slip起动电流 starting current起动转矩 starting torque额定电压 rated voltage额定电流 rated current额定功率 rated power机械特性 mechanical characteristic电气术语中英文对照表—继电器—接触器控制按钮 button熔断器 fuse开关 switch行程开关 travel switch继电器 relay接触器 contactor常开(动合)触点 normally open contact常闭(动断)触点 normally closed contact时间继电器 time relay热继电器 thermal overload relay中间继电器 intermediate relay可编程控制器(PLC)可编程控制器 programmable logic controller语句表 statement list梯形图 ladder diagram电气术语中英文对照表—半导体器件本征半导体intrinsic semiconductor掺杂半导体doped semiconductorP型半导体 P—type semiconductorN型半导体 N-—type semiconductor自由电子 free electron空穴 hole载流子 carriersPN结 PN junction扩散 diffusion漂移 drift二极管 diode硅二极管 silicon diode锗二极管 germanium diode阳极 anode阴极 cathode发光二极管 light-emitting diode (LED)光电二极管 photodiode稳压二极管 Zener diode晶体管(三极管) transistorPNP型晶体管 PNP transistorNPN型晶体管 NPN transistor发射极 emitter集电极 collector基极 base电流放大系数 current amplification coefficient场效应管 field—effect transistor (FET)P沟道 p—channelN沟道 n—channel结型场效应管 junction FET(JFET)金属氧化物半导体 metal—oxide semiconductor (MOS)耗尽型MOS场效应管 depletion mode MOSFET(D—MOSFET)增强型MOS场效应管 enhancement mode MOSFET(E-MOSFET)源极 source栅极 grid漏极 drain跨导 transconductance夹断电压 pinch—off voltage热敏电阻 thermistor开路 open短路 shorted基本放大器放大器 amplifier正向偏置 forward bias反向偏置 backward bias静态工作点 quiescent point (Q—point)等效电路 equivalent circuit电压放大倍数 voltage gain总的电压放大倍数 overall voltage gain饱和 saturation截止 cut—off放大区 amplifier region饱和区 saturation region截止区 cut-off region失真 distortion饱和失真 saturation distortion截止失真 cut—off distortion零点漂移 zero drift正反馈 positive feedback负反馈 negative feedback串联负反馈 series negative feedback并联负反馈 parallel negative feedback共射极放大器 common-emitter amplifier射极跟随器 emitter-follower共源极放大器 common—source amplifier共漏极放大器 common—drain amplifier多级放大器 multistage amplifier阻容耦合放大器 resistance-capacitance coupled amplifier 直接耦合放大器 direct- coupled amplifier输入电阻 input resistance输出电阻 output resistance负载电阻 load resistance动态电阻 dynamic resistance负载电流 load current旁路电容 bypass capacitor耦合电容 coupled capacitor直流通路 direct current path交流通路 alternating current path直流分量 direct current component交流分量 alternating current component变阻器(电位器)rheostat电阻(器)resistor电阻(值)resistance电容(器)capacitor电容(量)capacitance电感(器,线圈)inductor电感(量),感应系数inductance正弦电压 sinusoidal voltage集成运算放大器及应用差动放大器 differential amplifier运算放大器 operational amplifier(op—amp)失调电压 offset voltage失调电流 offset current共模信号 common-mode signal差模信号 different—mode signal共模抑制比 common—mode rejection ratio (CMRR)积分电路 integrator(circuit)微分电路 differentiator(circuit)有源滤波器 active filter低通滤波器 low—pass filter高通滤波器 high-pass filter带通滤波器 band-pass filter带阻滤波器 band—stop filter波特沃斯滤波器 Butterworth filter切比雪夫滤波器 Chebyshev filter贝塞尔滤波器 Bessel filter截止频率 cut—off frequency上限截止频率 upper cut—off frequency下限截止频率 lower cut—off frequency中心频率 center frequency带宽 Bandwidth开环增益 open—loop gain闭环增益 closed-loop gain共模增益 common—mode gain输入阻抗 input impedance电压跟随器 voltage—follower电压源 voltage source电流源 current source单位增益带宽unity-gain bandwidth频率响应 frequency response频响特性(曲线)response characteristic波特图 the Bode plot稳定性stability补偿 compensation比较器 comparator迟滞比较器 hysteresis comparator阶跃输入电压step input voltage仪表放大器 instrumentation amplifier隔离放大器 isolation amplifier对数放大器 log amplifier反对数放大器antilog amplifier反馈通道 feedback path反向漏电流 reverse leakage current相位phase相移 phase shift锁相环 phase—locked loop(PLL)锁相环相位监测器 PLL phase detector和频 sum frequency差频 difference frequency波形发生电路振荡器 oscillatorRC振荡器 RC oscillatorLC振荡器 LC oscillator正弦波振荡器 sinusoidal oscillator三角波发生器 triangular wave generator方波发生器square wave generator幅度 magnitude电平level饱和输出电平(电压) saturated output level电气术语中英文对照表—功率放大器功率放大器 power amplifier交越失真 cross-over distortion甲类功率放大器 class A power amplifier乙类推挽功率放大器class B push-pull power amplifierOTL功率放大器 output transformerless power amplifierOCL功率放大器 output capacitorless power amplifier电气术语中英文对照表—直流稳压电源半波整流 full-wave rectifier全波整流 half—wave rectifier电感滤波器 inductor filter电容滤波器 capacitor filter串联型稳压电源 series (voltage) regulator开关型稳压电源 switching (voltage) regulator集成稳压器 IC (voltage) regulator电气术语中英文对照表-晶闸管及可控整流电路晶闸管 thyristor单结晶体管 unijunction transistor(UJT)可控整流 controlled rectifier可控硅 silicon-controlled rectifier峰点 peak point谷点 valley point控制角 controlling angle导通角 turn—on angle电气术语中英文对照表-门电路与逻辑代数二进制 binary二进制数 binary number十进制 decimal十六进制 hexadecimal二—十进制 binary coded decimal (BCD)门电路 gate三态门tri-state gate与门 AND gate或门 OR gate非门 NOT gate与非门 NAND gate或非门 NOR gate异或门 exclusive—OR gate反相器 inverter布尔代数 Boolean algebra真值表 truth table卡诺图 the Karnaugh map逻辑函数 logic function逻辑表达式 logic expression电气术语中英文对照表-组合逻辑电路组合逻辑电路 combination logic circuit译码器 decoder编码器 coder比较器 comparator半加器 half—adder全加器 full-adder七段显示器 seven-segment display电气术语中英文对照表—时序逻辑电路时序逻辑电路 sequential logic circuitR-S 触发器 R—S flip—flopD触发器 D flip—flopJ—K触发器 J—K flip—flop主从型触发器 master—slave flip—flop置位 set复位 reset直接置位端direct—set terminal直接复位端direct-reset terminal寄存器 register移位寄存器 shift register双向移位寄存器bidirectional shift register计数器 counter同步计数器 synchronous counter异步计数器asynchronous counter加法计数器 adding counter减法计数器 subtracting counter定时器 timer清除(清0)clear载入 load时钟脉冲 clock pulse触发脉冲 trigger pulse上升沿 positive edge下降沿 negative edge时序图 timing diagram波形图 waveform电气术语中英文对照表-脉冲波形的产生与整形稳态触发器 monostable flip—flop双稳态触发器 bistable flip—flop无稳态振荡器 astable oscillator晶体 crystal555定时器 555 timer电气术语中英文对照表-模拟信号与数字信号的相互转换模拟信号 analog signal数字信号 digital signalAD转换器analog —digital converter (ADC)DA转换器 digital—analog converter (DAC)电气术语中英文对照表—半导体存储器只读存储器 read—only memory(ROM)随机存取存储器 random-access memory(RAM)可编程ROM programmable ROM(PROM)。
电路的基本概念及定律电源source [sɔ:s]电压源voltage source电流源current source理想电压源ideal voltage source理想电流源ideal current source伏安特性volt-ampere characteristic电动势electromotive force电压voltage['vəultidʒ]电流current['kʌrənt]电位potential[pəu'tenʃəl]电位差potential difference欧姆Ohm伏特Volt安培Ampere瓦特Watt焦耳Joule电路circuit电路元件circuit element电阻resistance电阻器resistor电感inductance电感器inductor电容capacitance电容器capacitor电路模型circuit model参考方向reference direction 参考电位reference potential欧姆定律Ohm’s law基尔霍夫定律Kirchhoff’s law基尔霍夫电压定律Kirchhoff’svoltage law(KVL)基尔霍夫电流定律Kirchhoff’scurrent law(KCL)结点node支路branch回路loop网孔mesh支路电流法branch current analysis网孔电流法mesh current analysis 结点电位法node voltage analysis 电源变换source transformations叠加原理superposition theorem网络network无源二端网络passive two-terminal network有源二端网络active two-terminal network戴维宁定理Thevenin’s theorem诺顿定理Norton’s theorem开路(断路)open circuit短路short circuit开路电压open-circuit voltage短路电流short-circuit current交流电路直流电路direct current circuit (dc)交流电路alternating current circuit (ac)正弦交流电路sinusoidal a-c circuit平均值average value有效值effective value均方根值root-mean-squire value (rms)瞬时值instantaneous value电抗reactance感抗inductive reactance容抗capacitive reactance法拉Farad亨利Henry阻抗impedance复数阻抗complex impedance相位phase初相位initial phase相位差phase difference相位领先phase lead相位落后phase lag倒相,反相phase inversion频率frequency角频率angular frequency 赫兹Hertz相量phasor相量图phasor diagram有功功率active power无功功率reactive power视在功率apparent power功率因数power factor功率因数补偿power-factor compensation串联谐振series resonance并联谐振parallel resonance谐振频率resonance frequency频率特性frequency characteristic 幅频特性amplitude-frequencyresponsecharacteristic相频特性phase-frequencyresponsecharacteristic截止频率cutoff frequency品质因数quality factor通频带pass-band带宽bandwidth (BW)滤波器filter一阶滤波器first-order filter二阶滤波器second-order filter低通滤波器low-pass filter高通滤波器high-pass filter带通滤波器band-pass filter带阻滤波器band-stop filter转移函数transfer function波特图Bode diagram傅立叶级数Fourier series三相电路三相电路three-phase circuit三相电源three-phase source对称三相电源symmetricalthree-phasesource对称三相负载symmetrical three-phase load相电压phase voltage相电流phase current线电压line voltage线电流line current三相三线制three-phase three-wire system三相四线制three-phase four-wire system三相功率three-phase power星形连接star connection(Y-connection)三角形连接triangularconnection( -connection ,deltaconnection)中线neutral line 电路的暂态过程分析暂态transient state稳态steady state暂态过程,暂态响应transient response换路定理low of switch一阶电路first-order circuit三要素法three-factor method时间常数time constant积分电路integrating circuit微分电路differentiating circuit磁路与变压器磁场magnetic field磁通flux磁路magnetic circuit磁感应强度flux density磁通势magnetomotive force磁阻reluctance电动机直流电动机dc motor交流电动机ac motor异步电动机asynchronous motor同步电动机synchronous motor三相异步电动机three-phaseasynchronousmotor单相异步电动机single-phaseasynchronousmotor旋转磁场rotating magnetic field 定子stator转子rotor转差率slip起动电流starting current起动转矩starting torque额定电压rated voltage额定电流rated current额定功率rated power机械特性mechanical characteristic继电器-接触器控制按钮button熔断器fuse开关switch行程开关travel switch继电器relay接触器contactor常开(动合)触点normally open contact常闭(动断)触点normally closed contact时间继电器time relay热继电器thermal overload relay中间继电器intermediate relay可编程控制器(PLC)可编程控制器programmable logic controller语句表statement list梯形图ladder diagram半导体器件本征半导体intrinsic semiconductor掺杂半导体doped semiconductor P型半导体P-type semiconductor N型半导体N--type semiconductor自由电子free electron空穴hole载流子carriersPN结PN junction扩散diffusion漂移drift二极管diode硅二极管silicon diode锗二极管germanium diode阳极anode阴极cathode发光二极管light-emitting diode (LED)光电二极管photodiode稳压二极管Zener diode晶体管(三极管)transistor PNP型晶体管PNP transistor NPN型晶体管NPN transistor发射极emitter集电极collector基极base电流放大系数current amplification coefficient场效应管field-effect transistor (FET)P沟道p-channelN沟道n-channel结型场效应管junction FET (JFET)金属氧化物半导体metal-oxide semiconductor (MOS)耗尽型MOS场效应管depletion mode MOSFET(D-MOSFET)增强型MOS场效应管enhancement mode MOSFET (E-MOSFET)源极source栅极grid漏极drain跨导transconductance夹断电压pinch-off voltage热敏电阻thermistor开路open短路shorted基本放大器放大器amplifier正向偏置forward bias 反向偏置backward bias静态工作点quiescent point (Q-point)等效电路equivalent circuit电压放大倍数voltage gain总的电压放大倍数overall voltage gain饱和saturation截止cut-off放大区amplifier region饱和区saturation region截止区cut-off region失真distortion饱和失真saturation distortion截止失真cut-off distortion零点漂移zero drift正反馈positive feedback负反馈negative feedback串联负反馈series negative feedback并联负反馈parallel negative feedback共射极放大器common-emitter amplifier射极跟随器emitter-follower共源极放大器common-source amplifier共漏极放大器common-drain amplifier多级放大器multistage amplifier 阻容耦合放大器resistance-capacitance coupled amplifier直接耦合放大器direct- coupled amplifier输入电阻input resistance输出电阻output resistance负载电阻load resistance动态电阻dynamic resistance负载电流load current旁路电容bypass capacitor耦合电容coupled capacitor直流通路direct current path交流通路alternating current path 直流分量direct current component交流分量alternating current component变阻器(电位器)rheostat电阻(器)resistor电阻(值)resistance电容(器)capacitor电容(量)capacitance电感(器,线圈)inductor电感(量),感应系数inductance 正弦电压sinusoidal voltage集成运算放大器及应用差动放大器differential amplifier 运算放大器operational amplifier(op-amp)失调电压offset voltage失调电流offset current共模信号common-mode signal差模信号different-mode signal共模抑制比common-mode rejection ratio (CMRR)积分电路integrator(circuit)微分电路differentiator(circuit)有源滤波器active filter低通滤波器low-pass filter高通滤波器high-pass filter带通滤波器band-pass filter带阻滤波器band-stop filter波特沃斯滤波器Butterworth filter切比雪夫滤波器Chebyshev filter 贝塞尔滤波器Bessel filter截止频率cut-off frequency上限截止频率upper cut-off frequency下限截止频率lower cut-off frequency中心频率center frequency带宽Bandwidth开环增益open-loop gain闭环增益closed-loop gain共模增益common-mode gain输入阻抗input impedance电压跟随器voltage-follower电压源voltage source电流源current source单位增益带宽unity-gain bandwidth频率响应frequency response频响特性(曲线)response characteristic波特图the Bode plot稳定性stability补偿compensation比较器comparator迟滞比较器hysteresis comparator 阶跃输入电压step input voltage仪表放大器instrumentation amplifier隔离放大器isolation amplifier对数放大器log amplifier反对数放大器antilog amplifier反馈通道feedback path反向漏电流reverse leakage current相位phase相移phase shift锁相环phase-locked loop(PLL)锁相环相位监测器PLL phase detector和频sum frequency 差频difference frequency波形发生电路振荡器oscillatorRC振荡器 RC oscillatorLC振荡器 LC oscillator正弦波振荡器sinusoidal oscillator三角波发生器triangular wave generator方波发生器square wave generator 幅度magnitude电平level饱和输出电平(电压)saturated output level功率放大器功率放大器power amplifier交越失真cross-over distortion甲类功率放大器class A power amplifier乙类推挽功率放大器class B push-pull power amplifierOTL功率放大器output transformerless power amplifier OCL功率放大器output capacitorless power amplifier直流稳压电源半波整流full-wave rectifier全波整流half-wave rectifier电感滤波器inductor filter电容滤波器capacitor filter串联型稳压电源series (voltage) regulator开关型稳压电源switching (voltage) regulator集成稳压器IC (voltage) regulator 晶闸管及可控整流电路晶闸管thyristor单结晶体管unijunction transistor (UJT)可控整流controlled rectifier可控硅silicon-controlled rectifier 峰点peak point谷点valley point控制角controlling angle导通角turn-on angle门电路与逻辑代数二进制binary二进制数binary number十进制decimal十六进制hexadecimal二-十进制binary coded decimal (BCD)门电路gate三态门tri-state gate与门AND gate或门OR gate非门NOT gate与非门NAND gate 或非门NOR gate异或门exclusive-OR gate反相器inverter布尔代数Boolean algebra真值表truth table卡诺图the Karnaugh map逻辑函数logic function逻辑表达式logic expression组合逻辑电路组合逻辑电路combination logic circuit译码器decoder编码器coder比较器comparator半加器half-adder全加器full-adder七段显示器seven-segment display时序逻辑电路时序逻辑电路sequential logic circuitR-S 触发器R-S flip-flopD触发器 D flip-flopJ-K触发器J-K flip-flop主从型触发器 master-slave flip-flop置位set复位reset直接置位端direct-set terminal直接复位端direct-reset terminal寄存器register移位寄存器shift register双向移位寄存器bidirectional shift register计数器counter同步计数器synchronous counter 异步计数器asynchronous counter 加法计数器adding counter减法计数器subtracting counter 定时器timer清除(清0)clear载入load时钟脉冲clock pulse触发脉冲trigger pulse上升沿positive edge下降沿negative edge时序图timing diagram波形图waveform脉冲波形的产生与整形单稳态触发器monostable flip-flop双稳态触发器bistable flip-flop无稳态振荡器astable oscillator晶体crystal555定时器555 timer模拟信号与数字信号的相互转换模拟信号analog signal数字信号digital signal AD转换器analog -digital converter (ADC)DA转换器digital-analog converter (DAC)半导体存储器只读存储器read-only memory (ROM)随机存取存储器random-access memory(RAM)可编程ROM programmable ROM (PROM)。
高中必修数学知识点总结及公式大全1.二次函数的标准形式为y=ax^2+bx+c。
The standard form of a quadratic function is y=ax^2+bx+c.2.一次函数的标准形式为y=kx+b。
The standard form of a linear function is y=kx+b.3.三角函数sin、cos、tan分别表示正弦、余弦、正切。
The trigonometric functions sin, cos, tan represent sine, cosine, tangent respectively.4.三角函数的周期性是它们的重要特征之一。
The periodicity of trigonometric functions is one oftheir important characteristics.5.平行四边形的面积公式为S=底×高。
The formula for the area of a parallelogram isS=base×height.6.直角三角形的勾股定理为a^2 + b^2 = c^2。
The Pythagorean theorem for a right-angled triangle isa^2 + b^2 = c^2.7.两点间距离公式为d=sqrt[(x2-x1)^2 + (y2-y1)^2]。
The distance formula between two points is d=sqrt[(x2-x1)^2 + (y2-y1)^2].8.二次方程的解法包括用公式法和配方法。
The methods for solving quadratic equations include using the formula and completing the square.9.函数奇偶性的判定方法是f(-x) = f(x)或f(-x) = -f(x)。
教师资格认定考试初级中学英语模拟题45一、单项选择题在每小题列出的四个备选项中选择一个最佳答案。
1. While the others were trying hard to come up with (江南博哥)a possible solution to the tough problem, I ______ a brilliant idea.A.struck onB.counted onC.occurred toD.appealed to正确答案:A[考点] 考查动词短语辨析。
[解析] 句意:当其他人努力提出这个棘手问题的可能解决办法的时候,我突然想到一个绝妙的主意。
strike on意为“突然想到”;count on意为“指望,依靠”;occur to意为“想到,想起”,一般不用人作主语;appeal to意为“呼吁”。
故本题选A。
2. In meaningful practice, the focus is on the production, comprehension or exchange of ______.A.structuresB.sentencesC.formD.meaning正确答案:D[考点] 考查口语教学。
[解析] 意义练习是在机械性练习的基础上,学生独立运用语言材料进行真实意义的听、说、读、写的活动。
这种练习不再是模仿和重复孤立的句子或词和词组,而是运用词、词组和句型组织和表示真实意义的对话、阅读课文回答问题、写作小短文等,强调的是意义的表达。
故本题选D。
3. Of the people who work here, ______ are French and ______ English.A.half; halfB.the half; the halfC.a half; a halfD.a half; the half正确答案:A[考点] 考查数词。
[解析] 句意:在这儿工作的人一半是法国人,一半是英国人。
2020-2021《国际贸易学》(双语)期末课程考试试卷A本试卷适用于。
试卷所需时间120分钟。
一、单项选择题:(共25小题,每小题1分,共25分)1. Which of the following says that any dollar of gain or loss will be equally valued, regardless of who experiences it?A.Consumer surplusB.Producer surplusC.ArbitrageD.One-dollar, one-vote metric2. Consider a typical two-country model. In the exporting country, consumers will be ______ and producers will be______ with the opening of international trade. A. Happy; happy B. Unhappy; happy C. Unhappy; unhappy D. Happy; unhappy3. The author of the Wealth of Nations was:A. David RicardoB. Paul SamuelsonC. Adam SmithD. Karl Marx4. The theory of comparative advantage was first presented by: A. Adam Smith B. Karl MarxC. David RicardoD. Eli Heckscher5. The theory that predicts that trade occurs because of differences in the availability of factor inputs across countries and the differences in the proportions in which the factor inputs are used in producing different products is called:A. The Stolper-Samuelson theoryB. The Heckscher-Ohlin theoryC. Comparative advantageD. Absolute advantage6. The Stolper-Samuelson theorem would predict that trade between the United States, a capital-abundant country, and Mexico, a labor-abundant country, should lead to:A. Higher wages in both countriesB. Lower wages in both countriesC. Higher wages in MexicoD. Lower wages in Mexico7. If the domestic country is labor abundant, which of the following groups will gain in the short-run, but lose in the long-run? A. Domestic landowners in the farming sectorB. Domestic landowners in the cloth-making sectorC. Foreign landowners in the farming sectorD. Foreign workers in the cloth-making sector 8. Immiserizing growth effect can occur when:A. A large country experiences a growth in the production of its export-oriented goods.B. There is a decline in the research and development investments in a large country.C. The terms of trade of a small country decline.D. The import-competing goods are overproduced in a large country.9. Which of the following is the value of the difference between exports and imports for a product? tradeB.Intra-industry tradeC.Product differentiationD.Returns to scale 10. China is a net importer of:A. Shoes and other footwearB. Scientific equipmentC. ToysD. Clothing and accessories11. The clustering of some industries, such as banking and finance in New York City and high-technology computer production in Silicon Valley, can be explained by: A. External scale economies. B. Monopolistic competition. C. Intra-industry trade. D. The demand for variety. 12. If a small country imposes a tariff on imported motorcycles, the world price of motorcycles will _____ and the domestic price of motorcycles will _____. A. Rise; rise B. Fall; riseC. Stay constant; riseD. Stay constant; fall13. If a country with monopsony (买方垄断) power imposes a tariff on imported farm equipment, the world price of farm equipment will: A. Fall B. Rise院系: 专业班级: 姓名: 学号:装 订 线C. Be unaffectedD. Become equal to the domestic price of farm equipment. 14. A nontariff barrier operates by: A. Limiting the quantity of imports.B. Increasing the cost of getting imports to market.C. Creating uncertainty about the conditions under which imports will be permitted.D. All of the above.15. One of the reasons that protectionists and government officials may favor using a quota instead of a tariff is:A. Quotas generate more revenue for the government than do tariffs.B. A quota ensures that the quantity of imports is strictly limited.C. Quotas create less market distortions than do tariffs.D. Quotas give less power to politicians than do tariffs.16. Which of the following subsidies is prohibited under WTO rules? A. Subsidies to research and development.B. Subsidies to assist disadvantaged regions within the exporting country.C. Subsidies that are used to assist firms in meeting environmental regulations.D. Subsidies that are used to encourage firms to export more.17. Which of the following allows member countries to import from other member countries freely, but imposes trade barriers against imports from outside countries? A. A trade embargo B. A trade bloc C. The most favored nation principle D. Trade creation 18. Which of the following features does a customs union have? I. Free trade among the members. II. Common external tariffs.III. Free movement of factors of production. IV. Harmonization of all economic policies.A. IB. I and IIC. I, II, and IIID. I, II, III, and IV19. Which of the following is a free-trade area that includes the United States, Mexico, and Canada?A. NAFTAB. MERCOSURC. EUD. ASEAN 20. When a large country imposes an import quota:A. World prices rise.B. World prices fall.C. Domestic prices fall.D. Domestic production falls.21. Which of the following countries provides government supports to its farmers? A. The United States B. JapanC. The European UnionD. All of the above22. Which of the following states that any trade concession given to any foreign country must be given to all other countries having the same status? A.A trade embargo B.A trade bloc C.The most favored nation principle D.Trade creation23. China’s policies towards FDI _____ inv estments that bring in advanced technology, _____investments that use old technologies and_____ investments in traditional Chinese crafts.A. Encourage; encourage; prohibitB. Discourage; encourage; encourageC. Encourage; discourage; prohibitD. Discourage; discourage; encourage24. ______ is the movement of people from one country to another country in which they plan to reside for some noticeable period of time.A. Domestic tradeB. International tradeC. Internal migrationD. International migration25. Which of the following has overseen the global rules of government policy toward international trade since 1995?A. World Trade OrganizationB. General Agreement on Tariffs and TradeC. International Monetary FundD. World Bank二、判断题(共10小题,每小题1分,共10分)1. The value of foreign trade is the total amount of a nation’s foreign trade, i.e. the total amount of import and export (of goods) within a certain period. Then the value of international trade is the total value of foreign trade of all countries throughout the world.2. While international trade will benefit both the importing and exporting country in a two-country world, the gains from trade in the exporting country will usually be greater than the gains from trade in the importing country.3. Free trade is a zero-sum activity. That is, one county always gains and the other always loses from free trade.: 专业班级: 姓名: 学号:装 订 线4. Mercantilists believe that when one country benefited from international trade it was at the expense of another country or countries.5. In the two-country, two-good model, both countries can gain from trade as long as their relative advantages and disadvantages in producing different goods are different.6. Factor-price equalization theory predicts that the price of labor and land within a country will equalize.7. In the short-run after trade opens, wages and land rents can be expected to rise in the expanding sector.8. It is possible for a large country to be better off, worse off, or no better off/no worse off as a result of a tariff being imposed.9. The use of a trade restriction by one country can cause other countries to retaliate, and may lead to a trade war in which all countries use high import barriers.10. Antidumping duties increase economic well-being in the United States by protecting import-competing firms.三、计算分析题(共2小题,每小题10分,共20分)(1) For each product for Japan, calculate the IIT share.(2) Japan is an importer of large civilian aircraft. What economic theory or concept best explain s this aspect of Japan’s trade?2. Suppose that $80 of imported wool (input) goes into the domestic production of a suit(final commodity). Suppose also that the free trade price of the suit is $100, but thenation imposes a 10% nominal tariff on each imported suit. The price of suits to domestic consumers would be $110.(a) Suppose that no tariff is imposed on the imported wool. (b) Suppose that the tariff rate on the imported wool is 10%. (c) Suppose that the tariff rate on the imported wool is 12%. (d) Suppose that the tariff rate on the imported wool is 20%. (1) Calculate the ERP for the domestic suits industry. (2) Interpret the meaning of this calculated ERP.四、简答题(共4小题,每小题8分,共32分)1. “According to Ricardo’s analysis, a country exports any good whose production requires fewer labor hours per unit than the labor hours per unit needed to produce the good in the foreign country. That is, the country exports any good in which its labor productivity is higher than the labor productivity for this good in the foreign country.” Do you agree or disagree? Why?2. A free-trade equilibrium exists in which the United States exports machinery and imports clothing from the rest of the world. The goods are produced with two factors: capital and labor. The trade pattern is the one predicted by the H-O theory. An increase now occurs in the U.S. endowment of capital, its abundant factor.a. What is the effect on the shape and position of the U.S. production-possibility curve?b. What is the effect on the actual production quantities in the United States if the product price ratio is unchanged? Explain.3. What are the two official definitions of dumping? Under the Anti-Dumping Agreement, under what circumstances, WTO Members can impose anti-dumping measures?4. How are trade creation and trade diversion defined, and what roles do they play in the world gains and losses from a trade bloc?五、论述题(共1小题,共13分)1. A country currently prohibits any FDI into the country. Its government is considering liberalizing this policy. You have been hired as a consultant to a group of foreign firms that wants to see the policy loosed. They ask you to prepare a report on the major arguments for why the country should liberalize the policy. What will your report say?专业班级: 姓名: 学号:装 订 线2020-2021《国际贸易学》(双语)期末课程考试试卷A 答案二、判断题:(共10小题,每小题1分,共10分)三、计算分析题(共2小题,每小题10分,共20分)1. (1) Here is the calculation for perfumes: M X IIT --=||1=016.0|2422|1=--(2) The theory based on substantial scale economies, for the world, two firms produce large civilian aircraft. Boeing produces most of its aircraft in the U.S., and Airbus in Europe. It would be very difficult for a Japanese firm to achieve sufficient scale if it tried to enter into aircraft production. With no local production, Japan imports large civilian aircraft. (3分)2. (1) According to the formula ERP=[(t-a i t i )/(1-a i )]×100%, or ERP=[(V’-V)/V]×100%, we can get the following answers:(a) If t i =0%, we have ERP=50%(2分);(b) If t i =10%, we have ERP=10% (2分);(c) If t i =12%, we have ERP=2%(2分);(d) If t i =20%, we have ERP=-30%(2分)(2) ①If t>t i , ERP>t; ②If t=t i , ERP=t; ③If t<t i , ERP<t ; ④If t i becomes extremely high, then ERP will become negative. (2分)四、简答题(共4小题,每小题8分,共32分)1. Disagree. This statement describes absolute advantage. It would imply that a country that has a higher labor productivity in all goods would export all goods and import nothing.(2分)Ricardo instead showed that mutually beneficial trade is based on comparative advantage —trading according to maximum relative advantage.(3分)The country will export those goods whose relative labor productivity (relative to the other country and relative to other goods) is high, and import those other goods whose relative labor productivity is low.(3分)2. a. The entire U.S. production-possibilities curve shifts out, with the outward shift relatively larger for t he good that is intensive in capital. If the U.S. trade pattern follows the Heckscher-Ohlin theory, then this good is machinery. Growth is biased toward machinery production. (4分)b. According to the Rybczynski theory, the quantity produced of machinery increases and the quantity produced of clothing decreases if the product price ratio is unchanged. The extra capital is employed in producing more machinery, and the machinery industry must also employ some extra labor to use with the extra capital. The extra labor is drawn from the clothing industry, so clothing production declines. (4分)3. One definition of dumping is selling an export at a price lower than the price charged to domestic buyers of the product within the exporting country. This definition emphasizes international price discrimination.(2分)The second definition is selling an export at a price that is lower than the full average cost of the product plus a reasonable profit margin.(2分)(1) Dumping is occurring;(1分) (2) The domestic industry producing the like product is suffering material injury or threat of material injury.(2分) (3) There is a causal link between the two.(1分)4. (1) Trade creation is the increase in total imports resulting from the formation of a trade bloc. Trade creation occurs because importing from the partner country lowers the price in the importing country, so that some high-cost domestic production is replaced by lower-priced imports from the partner, and because the lower price increased the total quantity demanded in the importing country. (2分)Trade diversion is the replacement of imports from lower-cost suppliers outside the trade bloc with higher-cost imports from the partner. It occurs because the outside suppliers remain hindered by tariffs, while there is no tariff on imports from the partner. (2分)(2) Trade creation creates a gain for the importing country and the world. Trade diversion creates a loss for the importing country and the world.(2分)The importing country and the world gain from the trade bloc if trade creation gains exceed trade diversion losses. (2分)五、论述题(共1小题,共13分)1. Key points that should be included in the report.(1) FDI brings new technologies into the country.(1分)(2) FDI brings new managerial practices into the country.(1分)(3) FDI brings marketing capabilities into the country. These can be used to better meet the needs of the local market. They may be particularly important in expanding the country’s exports by improving the international marketing of products produced by the multinational firms that begin production in the country.(3分)(4) FDI brings financial capital into the country, and expands the country’s ability to invest in domestic production capabilities.(2分)(5) The local affiliates of the multinationals raise labor skills by training local workers.(1分)(6) Technological spillover benefits accrue to the country as it hosts FDI, because some of themultinationals’ technology, managerial practices, and marketing capabilities spread to local firms as they learn about and imitate the multinational’s intangible assets. Taken together, these first six items serve to increas e the country’s supply-side capabilities for producing (and selling) goods and services.(3分)(7) In addition, the country’s government can gain tax revenues by taxing the profits of the local affiliates established by the foreign multinationals.(2分)。
摘要混沌是一种特殊复杂的非线性动力学行为,也是自然界普遍存在的现象。
由于它对初值的极端敏感性及高度随机性,自六十年代发现以来,一直受到研究者的极大关注。
而从九十年代初提出混沌同步以来,由于它在保密通讯、信息科学以及生命科学中广泛的应用背景,使得它成为当前混沌研究中的一大热点。
本文首先介绍了混沌及混沌同步的一些基本知识及定义,并介绍了混沌同步的一些方法:驱动-响应同步方法、耦合同步方法、自适应同步方法、输出反馈同步方法及噪音同步等一些方法。
文章在第四章介绍了小增益定理的相关知识。
小增益定理是非线性理论中一个非常重要并且比较难的定理,但它在判定一个系统是否是输入状态稳定时很有作用。
本文基于小增益定理提出了一种新的混沌同步控制方法,将同步误差系统分成两个子系统,在适当的状态反馈控制下分别判定它们是输入状态稳定的,然后求出满足小增益定理时控制参数的取值范围,则在控制参数取值范围内,同步误差系统是原点渐近稳定的,混沌系统从而达到同步。
文章最后介绍了小增益定理在混沌同步中的应用。
通过三个具体的例子,Liu系统的混沌同步、耦合发电机系统的混沌同步以及Liu系统与统一混沌系统地混沌同步,说明了小增益定理理论上的可行性,随后的数值仿真亦验证了这种方法的可行性。
关键词:混沌;混沌同步控制;小增益定理;Liu系统;统一混沌系统;耦合发电机系统AbstractAs a complex nonlinear dynamical behavior, chaos is a general phenomenon in nature. Because of its extreme sensitivity to initial conditions, and its high randomness generated by deterministic equations, the birth of chaos has been a source of great excitement in scientific and engineering communities. At the beginning of 1990’s, chaos synchronization was presented. Since then, due to its great applications in secure communication, information science and biotic science, chaos synchronization has become a hot spot of research.In this dissertation, firstly, the conceptions of chaos and chaos synchronization are reviewed and some methods on chaos synchronization such as, drive-response synchronization、coupling synchronization、adaptive synchronization、out-put feedback synchronization are recalled.Secondly, the small gain theorem is introduced in chapter 4. This theorem is an important but difficult theorem in nonlinear systems and it is very useful in judging input-to-state stability. Based on this theorem, a new method is proposed for chaos synchronization. By this method we divide error dynamical system into two subsystems and use a suitable linear state feedback controller to make the two subsystems be input-to-state stable, hence we can get the range of the controller’s parameter by the small gain theorem, and thus the error dynamical system becomes globally asymptotically stable. Therefore the chaotic system can be synchronized.Finally, we discuss the applications of this method in chaos synchronization. Three examples and a numerical simulation are shown to verify the feasibility of this method.Keywords : Chaos; Chaos synchronization; The small gain theorem; Liu system;Unified chaotic system; Dynamical system of coupled dynamosII1 引言1.1 混沌理论的历史与发展非线性科学是人们研究非线性现象的基础科学,它是自本世纪六十年代以来,在各门以非线性为特征的分支学科的基础上逐步发展起来的综合性学科。
The General Feedback Theorem:A Final Solution for Feedback Systems ■R. David Middlebrookre you an analog or mixed-signal design engineer or a reli-ability engineer? Are you a manager, a design-reviewcommittee member, or a systems integration engineer?Did you “fall off a cliff” when in your first job you discov-ered that the analysis methods you learned in college simply don’t work?There is help available. Design-oriented analysis [(D-OA) don’t forget the hyphen!] is a paradigm based on the recogni-tion that design is the reverse of analysis, because the answer to the analysis is the starting point for design.Conventional loop or node analysis leads to a result in the form of a “high entropy expression,” which is a ratio of sums of products of the circuit elements. The more loops or nodes, the greater the number of factors in each product. By common experience, we know that we will sink into algebraic paraly-sis beyond two or three loops or nodes. Such an analysis result is useless for design.In contrast, analysis results need to be derived in the form of “low entropy expressions,” in which elements, such as impedances, are arranged in ratios and series-parallel combi-nations and not multiplied out into sums of products. This is the most important principle of D-OA, whose objective is to enable a designer to work backwards from an analytic result and change element values in an informed manner in order to make the answer come out closer to the desired result (the specification). D-OA is the only kind of analysis worth doing, since any other is a waste of time.There are many methods of D-OA, some of them little more than shortcuts or tricks, but here the spotlight is on a new approach to analysis and design of feedback systems, based on the general feedback theorem (GFT).A typical analysis procedure followed by designers, and integration and reliability engineers, is to throw the whole cir-cuit into a simulator and see what it does, possibly including attempts to measure the loop gain as well as external proper-ties. The design phase may consist of little more than tweak-ing and sensitivity simulations.A much more efficient approach is to begin with a simple circuit in terms of device models absent capacitances and other parasitic effects and then to add these sequentially. Even if you do little or no symbolic analysis, successive sim-ulations tell you in what ways which elements affect the result, so that when you finally substitute your library process and device models, you have a much better handle on where their effects originate.This procedure of “D-OA by simulator” is significantly enhanced when the simulator incorporates the GFT, because the results for a feedback system are exact and not impaired by the approximations and assumptions inherent in the con-ventional single-loop model. Moreover, it may no longer be necessary to attempt hardware measurements of loop gain, which in itself is a considerable saving of time and effort. What Is the Conventional Approach?The well-established method of analyzing a feedback sys-tem begins with the familiar block diagram of Figure 1, from which the feedback ratio K and the loop gain T=AK are calculated. The designer’s job is to set K and the for-ward gain A so that the final closed-loop gain H meets a specification, usually with the help of circuit-simulator soft-ware. Several iterations, often aided by hardware measure-ments of the loop gain, may be needed before the closed-loop gain meets the specification.R. David Middlebrook (rdm@) is Professor Emeritus of Electrical Engineering at California Institute of Technology inPasadena, California.AUnfortunately, this approach can give incorrect results,stemming from the fact that the conventional block diagram of Figure 1is an incomplete representation of the actual hard-ware system. Your immediate reaction to this allegation may be: “If I’ve noticed any discrepancies between the predicted and the actual results, they’ve been small enough to neglect,or I’ve just ignored them anyway.”Wouldn’t it be better to be able to get the exact analysis results quickly and easily so that you could accurately predict the actual system performance? This desirable situation is now realized through use of the GFT.Let’s start by reviewing in more detail the conventional approach based on Figure 1, for which the closed-loop gain H (the “answer”) is given byH =A 1+AK =A1+T.(1)A “better” form isH =1K AK1+AK =H ∞T 1+T =H ∞11+1T=H ∞D ,(2)whereH ∞≡1K≡ideal closed-loop gain (3)T ≡AK ≡loop gain .(4)It is convenient to define a discrepancy factor D as a unique function of TD ≡T 1+T ≡11+1T≡discrepancy factor ,(5)so that the closed-loop gain H can be expressed concisely asH =H ∞D .(6)Form (2) is “better” because H ∞represents the specifica-tion and is the only known quantity at the outset. So,K =1/H ∞is designed to meet the specification, and the onlyhard part is designing the loop gain T so that the actual closed-loop gain H meets the specification within the required tolerances. That is, the discrepancy factor D must be close enough to one over the specified bandwidth.One of the principles of D-OA is embodied in (2) and (6),namely “Get the quantities you want in the answer into the statement of the problem as early as possible.” In this case,H ∞is the desired gain, and D is the discrepancy between H ∞and the actual answer you’re going to get. Equally important,A is banished from the answer, because it contributes only via T , and its own value is of no interest.It is clear from (5) that D is a unique function of T , which has several useful consequences. First, when T is large, D ≈1,which leads to the desired result that H ≈H ∞. Second, when T is small, D ≈T and is small also, leading to a significant dis-crepancy between H ∞and T .Third, where the magnitude of T falls to one, the crossover frequency, marks the end of the frequency range over which T performs its useful function. How T crosses over determines the degree of peaking exhibited by D dur-ing its transition between one when T is large to T when T is small. According to (5), peaking in D is related to the phase margin of T , and translates by (6) directly to the closed-loop response H .Thus, (5) and (6) expose the well-known unique relation-ship between loop gain phase margin and both the frequency and time domain responses of the closed-loop gain.What’s Wrong with the Conventional Approach?The model of Figure 1is incomplete because it does not account for bidirectional signal transmission in the boxes. In fact, the boxes are drawn as arrowheads on purpose to emphasize that reverse transmission is excluded. If both boxes have reverse transmission, there is also a nonzero reverse-loop gain, and it is convenient to lump together all the properties omitted from this block diagram under the label nonidealities.Consequently, all analysis based on this model also ignores the nonidealities.In most textbooks and handbooks you can find whole sections that postulate a model in which each box of Figure 1is replaced by a two-port model, thus retaining the bidirectionality of a real circuit. However, there are several disadvantages to this approach:1)Four different sets of two-port models are required to represent the four possible feedback configurations:shunt-shunt, series-shunt, etc., and in three of the four,the model itself is still inaccurate because common-mode gain is ignored.2)E ven though the nonidealities are incorporated in the model, how do you account for their effects upon the loop gain and the closed-loop response?3)Because the circuit elements are buried inside the two-port parameters, which are themselves buried in expres-sions for the loop gain and closed-loop gain, the results are high entropy expressions and are essentially useless for design.Figure 1.The familiar single-loop block diagram of a feedback sys-tem. The arrowhead shapes imply that the signal goes only one way.The Dissection Theorem Is a Completely General Property of a Linear System ModelThe GFT sweeps away all the a priori assumptions and approximations inherent in the previously described conven-tional approach and produces low entropy results directly in terms of the circuit elements. This is accomplished because the GFT does not start from a block diagram model but is developed from a very basic property of a linear system, the dissection theorem.The dissection theorem says that any “first level” transfer function (TF) H of a linear system can be dissected into a com-bination of three “second level” TFs TF 1, TF 2, and TF 3according toH =TF 11+1TF 31+1TF 2.(7)These TF symbols are intentionally anonymous so that differ-ent physical significances can be assigned later.The second-level TFs are calculated in terms of an injected test signal u z , as shown in Figure 2. The injected test signal sets up u x going “forward” towards the output u o , and u y going “backward” towards the input u i , such that u x +u y =u z , in which u x , u y , u z may be all voltages or all currents, and u i and u o can independently be a voltage or a current.The second level TFs are defined byTF 1≡u o u i u y =0TF 2≡u y u x u i =0TF 3≡u y u xu o =0,(8)and the first-level TF H is simply the output divided by the input (the “gain”) in the absence of the test signal:H ≡u o u i u z =0.(9)In (8), TF 2is the ratio of the signal going backward to the signal going forward from the test signal injection point,under the condition that the original input signal is zero. This is a “single injection” (si) calculation, the familiar method by which any TF is calculated.TF 1is the ratio of the output to the input when u y is nulled,a condition that is established by adjustment of the test signal u z so that its contribution to u y is exactly equal and opposite that from u i . This is a less familiar “null double injection” (ndi)calculation. Note that, while H and TF 1are both ratios of out-put to input, their values are different because, even if theinput u i is the same, the u o for TF 1contains a component due to u z that is absent in the u o for H .An ndi calculation is made after an ndi condition has been established and is always easier and simpler than an si calculation. This is not an accident: any element in the sys-tem that supports a null signal might as well not be there and does not appear in the calculation or in the result.Also, you don’t have to know what the relation between the two injected signals is; all you have to know is the equivalent information that the null exists. To emphasize this, consider the way to make the null self-adjusting shown in Figure 3: the imaginary infinite gain amplifier automatically nulls u y , and to calculate TF 1from (8), you simply use the fact that u y is nulled, and you don’t have to know what u z is. The method of Figure 3can be imple-mented in a circuit simulator, since the “nulling amplifier”bandwidth is infinite, even if its gain is not.The TF 3in (8) is also an ndi calculation, and no further explanation is necessary. The (different) ndi condition can be established by connecting the nulling amplifier input to u o instead of to u y .If you’re not familiar with the dissection theorem, you can easily verify (7) by setting up a set of equations that represent the properties of a linear system containing two independent sources u i and u z :u x =A u o +B u z (10)u y =C u i +D u z (11)u z =u x +u y .(12)You can evaluate the TFs of (8) and (9) in terms of the A ,B ,C ,D coefficients. For example, to find TF 1, set u y =0in (11) and solve for the ratio u z /u i =−C /D that nulls u y . In (10), u x =u z by virtue of u y =0 in (12). Thus,u o =(1−B )u z /A . Finally, substitute u z /u i =−C /D to get TF 1=(B −1)C /AD . Likewise, find TF 2and TF 3, and insert all three TFs into (7) to confirm that the result for H is the same as that obtained directly from (10)–(12) by setting u z =0, which makes u x =−u y and H =−C /A .What Is the Dissection Theorem Good for?The dissection theorem is completely general, the only con-straint being that it applies to linear systems. As with most theorems, the important thing is what is it good for, and how do you use it?Figure 2.General model of a linear system with input u iand output u o and an injected test signal u z .Figure 3.How to set up an ndi condition: u y is automatically nulled.At first sight, you might think that replacing one calcula-tion by three is a step in the wrong direction. On the contrary, since (7) is itself a low entropy expression, the influences of TF2and TF3in modifying TF1are exposed, which is helpful design-oriented information. Moreover, since two of the three second-level definitions of (8) are ndi calculations, the dissec-tion theorem replaces a single complicated calculation by three potentially simpler calculations, thus implementing another of the principles of D-OA: “divide and conquer.”Nevertheless, these are minimum benefits, and much greater benefits accrue if the second-level TFs have useful physical interpretations. Thus, the second level TFs (8) them-selves contain the useful design-oriented information, and you may never need to actually substitute them into (7). For example, if TF2, TF3 1, H≈TF1.How do we determine the physical interpretations of (8)? In the above discussion based on Figure 2, nothing was said about where in the system model the test signal is injected. Different test-signal injection points define different sets of coefficients A,B,C,D and, hence, different sets of second level TFs. However, when a mutually consistent set is substi-tuted into (7), the same H results:H=TF1a1+1TF3a1+1TF2a=TF1b1+1TF3b1+1TF2b= (13)Therefore, the key decision in applying the dissection theo-rem is choosing a test signal injection point so that at least one of the second level TFs has the physical interpretation you want it to have.The Dissection Theorem Can Morphinto the Extra Element TheoremFor example, if the injection point is chosen so that u y goes into (voltage across, or current into) a single impedance Z, (7) becomesH=H|Z=∞1+Z n Z1+Z d Z,(14)in which Z d, Z n are respectively the driving-point imped-ance and the null driving-point impedance seen by Z, and H|Z=∞is the value of H when Z is infinite. In this form, the dissection theorem becomes the extra element theorem (EET), of which a useful special case is when Z is the only capacitance in an otherwise resistive circuit. Then, H|Z=∞is the first level TF (the “gain”) when the capacitance C is absent (zero), and the pole and zero are exposed directly as 1/CR d and 1/CR n.The E E T will not be further discussed here, because the spotlight is on another example of the choice of injec-tion point.The Dissection Theorem Can Morphinto the GFTIt is easy to see that the block diagram of Figure 4represents (7) and is immediately recognizable as an augmented version of the conventional feedback block diagram of Figure 1, which represents (2). So, where does the test signal have to be injected so that TF1has the physical interpretation of H∞?The answer is obvious: since H∞is H when the error sig-nal vanishes (infinite loop gain), and TF1is H when u y is nulled, then u z must be injected at the error summing point so that u y represents the error signal.At the same time, this makes TF2have the physical inter-pretation of the loop gain T, since the test signal injection point is inside the loop.Finally TF3, which does not have a corresponding appear-ance in Figure 1, is a new TF that can be designated T n, since by (8) it is defined as a loop gain with u o nulled.Following the above procedure, (7) becomesFigure 4.This augmented block diagram with anonymous TFs represents the dissection theorem (7).Figure 5.When the test signal is injected inside the loop at the error-summing point, the dissection theorem of (7) becomes the GFT (15). Figure 6.This block diagram for the GFT is a morphed version of Figure 4, in which T n(or H0) represents the main effects of the nonidealities.H=H∞1+1Tn1+1T,(15)and, in this form, the dissection theorem becomes the GFT. For the second-level TFs to have the desired physical inter-pretations TF1=H∞, TF2=T, TF3=T n, the test signal u z must be inside the loop and at the error summing point, as illustrated in Figure 5. Then, (8) becomesH∞≡u ou iu y=0T≡u yu xu i=0T n≡u yu xu o=0.(16)With H∞, T, and T n calculated from (16), the result (15) is rep-resented by the “augmented” block diagram of Figure 6.Because, superficially, Figure 6differs from Figure 1only in the presence of an additional block that contains the nonideal-ities, it is important to emphasize the fundamental difference between the conventional approach and that based on the GFT.In the conventional approach, the block diagram of Figure 1is the starting point, in which reverse transmission in both boxes is ignored, and the result (2) is developed from Figure 1.In the GFT approach, Figure 5is the starting point, and the result (15) is developed from (16) directly from the com-plete circuit without any assumptions or approximations.Since (15) is represented by Figure 6, the block diagram of Figure 6is part of the result. The boxes in Figure 6are unidirection-al and do not necessarily correspond to any separately identifi-able parts of the circuit. The values of these boxes, expressed in terms of the second level TFs H∞, T, and T n, automatical-ly incorporate any nonidealities that may be present in the actual circuit.Although the augmented block diagram exhibits a “loop,”it represents any linear system even if there is not a physical-ly discernible loop. An example is a Darlington follower, for which the GFT affords a means of investigating the well-known potential instability.It is apparent that the null loop gain T n contains the first-order effects of nonidealities, although there may also be sec-ond-order effects upon the loop gain T. Thus, the T in (2) may not be the same as the correct T in (15).Since it was convenient in (5) to introduce the discrepancy factor D as a unique function of T, it is likewise useful to intro-duce the null discrepancy factor D n as a unique function of T n, according toD n≡1+T nT n≡1+1T n≡null discrepancy factor(17) so that the final result for the first level TF T can be writtenH=H∞DD n.(18)Figure 7.A simple feedback amplifier model with the error voltage and the error current identified.The importance of this result is that the familiar tenet must be modified: the closed-loop frequency domain and time domain responses are no longer uniquely determined by the loop gain T and its phase margin.Instead, these responses are modified by a noninfinite value of the null loop gain T n via a nonunity value of the null discrepancy factor D n.Calculation of the second level TFs H∞, T, and T n can be done symbolically, or numerically by use of a circuit simula-tor. The Intusoft ICAP/4 simulator incorporates GFT tem-plates that apply a voltage or current test signal, set up the appropriate si and ndi conditions, and perform the required calculations. As a user, all you have to do is choose the prop-er test-signal injection point, which is inside the loop at the error-summing point.However, before proceeding to a circuit example, it is nec-essary to make an extension of the dissection theorem.The GFT for Two Injected Test SignalsIs the “Final Solution”From Figure 2, the Dissection Theorem was developed in terms of a single injected test signal u z, but a general version can be developed in terms of any number of test signals injected at different points. The EET interpretation in terms of N test signals becomes the NE E T, and, although this is “NEET,” it won’t be discussed further here.For the GFT interpretation, the most useful version employs two injected test signals, a voltage e z and a current j z,both injected at the error-summing point. This is because, to make H∞equal to 1/K, the ideal closed-loop gain, both the error voltage v y and the error current i y have to be nulled simultaneously.For dual voltage and current injected test signals at the error-summing point, the GFT of (7) remains exactly the same, except that the definitions of the TFs are extend-ed. In particular,H∞≡u ou iv y,i y=0,(19)which says that H∞is established by the double-null triple-injection (dnti) condition that e z and j z are mutually adjusted with respect to u i so that v y and i y are both nulled. The defin-itions of T and T n are each extended to a combination of volt-age and current loop gains established by ndi conditions for T and by dnti conditions for T n. These definitions are not dis-played here because the circuit examples will be treated by use of the Intusoft ICAP/4 GFT templates, in which all the calculations needed for dual test signal injection are included and are, therefore, transparent to the user.Are dnti calculations even easier than ndi calculations? Absolutely: the more signals are nulled, the more circuit ele-ments do not appear in the answer. This constitutes another round of the “divide and conquer” approach: you make a greater number of less complicated calculations.Figure 8.The crucial step: choose the test signal injection point inside the loop so that v y is the error voltage and i y is the error current.How to Use a Circuit Simulator Incorporating GFT TemplatesIn any case, if you’re going to use a circuit simulator rather than doing symbolic analysis, all you need to do is choose an injection point inside the loop at the error-summing point, plus select the appropriate GFT template according to whether single or dual test signal injection is required to null simultaneously the voltage and cur-rent error signals. The template does simu-lation runs to calculate the second-level TFs H∞, T, and T n in (15) and does post-simulation calculations to produce the dis-crepancy factors D and D n in (18).A Simple FeedbackAmplifier ExampleA series-shunt feedback amplifier circuit model is shown in Figure 7. The forward path is a simplified model of a typical inte-grated circuit (IC) in which voltage gain isachieved in the first two stages, which may be differential, and current gain is achieved in the final Darlington follower stage. In this first example, the frequency response is deter-mined by the sole capacitance C c. Each active device is repre-sented by a simple bipolar junction transistor (BJT) T-model, which has the advantage of also representing a field-effect transistor (FE T) by setting the drain current equal to the source current, as is done in this example.Figure 9.An Intusoft ICAP/4 GFT template provides the injected test signals e z and j z, and performs the simulations and postprocess-ing required to obtain H∞, T, and T n, and hence H, for the GFT of (15).Figure 10.The expectations are borne out: H∞is flat at 20 dB, and T has a singlepole. The null loop gain T n is not infinite because of nonzero reverse transmissionthrough the feedback path (a feedforward path).To apply the GFT, the crucial first step is to choose the test signal injection point that makes H∞, T, and T n have the desired interpretations of ideal closed-loop gain, loop gain, and null loop gain.The error voltage is the voltage between the input and the fed back voltage at the feedback divider tap point, labeled v y in Figure 7. The error current is the current drawn from the feedback divider tap point, labeled i y in Figure 7. The test sig-nals e z and j z are to be injected inside the loopso that v x and i x are the driving signals for theforward path, as shown in Figure 8. Thus, thetest signal configuration meets the two condi-tions that injection occurs at the error-sum-ming point, and is inside the loop, implement-ing the general model of Figure 5.To invoke the GFT template, the appropri-ate dual-injection icon is selected and connect-ed to provide the test signals e z and j z, as inFigure 9. The icon also provides the systeminput signal e i and observes the output signalv o, because it has to adjust the test signals rel-ative to the input to establish various nulls,one of which is the output signal.Another principle of D-OA is “figure out as much as you can about the answer before youplunge into the analysis.”In this case, we expect H∞to be 1/K, the rec-iprocal of the feedback ratio that was initiallychosen to meet the system specification, because the injection configuration was specifically set up to achieve this. Here, 1/K=(R1+R2)/R1=10⇒20 dB, flat at all frequencies.We expect T to be large at low frequencies and to have a sin-gle pole determined by C c. Consequently, D will be flat at essentially 0 dB at low frequencies, with a pole at the crossover frequency of T, beyond which D will be the same as T.We expect T n to be noninfinite and, consequently, D n to be not 0 dB, because there is nonzero reverse transmission throughFigure 11.T and T n replaced by their corresponding discrepancy factorsD=T/(1+T)and D n=(1+T n)/T n. The normal closed-loop gainH=H∞DD n differs from H∞not only because of D, but also because of D n, although this effect is small.the feedback path. That is, if the forward path through the active devices dies, the input signal e i can still reach the output v o by going through the feedback path in the “wrong” direction. The principal benefit of the GFT is to permit calculation of this effect, which is not accounted for in the conventional model, in order to determine whether or not it is significant.The GFT results for the three second-level TFs for the model of Figure 9are shown in Figure 10, and the expectations are indeed borne out. The results are repeated in Figure 11with the loop gains replaced by their corresponding discrepancy factors, both of which are essentially 0 dB atlow frequencies. Also shown is thefinal result for the first level TF H, theclosed-loop gain, which from (18) isthe direct superposition of the H∞, D,and D n graphs.This final result shows that thebandwidth of H is determined bythe T crossover frequency, as in theconventional approach, and thatreverse transmission (“wrongway”) through the feedback pathdoes not have any significant effectuntil the much higher null loopgain crossover frequency.A More Realistic FeedbackAmplifier ModelThe more interesting model ofFigure 12includes two addedcapacitances for each active device.This is a much more realistic model,and, of course, library device mod-els can be substituted. What are ourexpectations for the results in com-parison with those for Figure 9?Since all the extra elements arecapacitances, we expect the low-fre-quency properties to remain the same,but the dominant pole, and, hence, theloop gain crossover frequency wouldbe lowered. Therefore, to enable amore meaningful comparison betweenthe two circuits, C c in Figure 12hasbeen reduced sufficiently to preservethe same loop gain crossover frequen-cy. Nevertheless, the extra capacitancescreate more poles and zeros, so thehigh-frequency loop gain is expectedto be more complicated.The major consequence of thepresence of the extra capacitances isthat there is now a second feedfor-ward path (through a string of capac-itances), in addition to that throughthe feedback path in the “wrong”direction, through which the input signal can reach the output. Also, there is now nonzero reverse transmission through the forward path, which in turn creates a nonzero reverse loop gain. It is not necessary to separate these nonidealities, because they are all automatically account-ed for in the calculation of the loop gain (usually little effect) and in the null loop gain (the major effect).The quantitative results of the GFT template simulations for Figure 12shown in Figures 13 and 14bear out the expectations. The null loop gain crossover frequency is drastically lowered, and even though the magnitude of the null discrepancy factor。