基于电路课程的横拓展与纵延伸衔接的教学模式研究

1、1前言电路课程是高等院校电子信息类学科专业和英他相关专业的一门重要的基础平台课。该 课程的设置历史久远，意义重大，许多理论内容已相当成熟。但由于电子信息类学科及行业 的迅猛发展，木课程仍需进行必要的革新。虽然多年来，国内高校电路课程的建设取得许多 重要成果，教学水平不断提升1-2,然而事实证明，对该课程的进一-步发展和改革的方向还 不明确。河南大学物理学院的物理学、通信工程和电子信息科学与技术等专业均开设本课程，而 木课程的知识内容繁多，理论性、结构性比佼强，定理多，为后续课程的学习提供必要的理 论慕础知识，前后知识点联系紧密。因此，学生在理解知识点时易出现理解不透彻、分析不 到位、解题不顺利

2、等诸多窘态。本文以电子信息学科专业为例，讨论运用横拓展和纵延伸立 体衔接教学模式，在教学电路课程一阶全响应这一节内容时的丿施教方法和过程。2电路课程横拓展和纵延伸教学模式介绍电路应用内容的横拓展电路课程除了经典理论的讲解，在一阶电路全响应的教学过程 中应适当引入横向知识的介绍，尤其一阶电路中的动态元件电容c和电感l,存在充放电的 物理过程。如汽车的一些“泊车辅助装置”一一倒车雷达装备中，在通过超声波感应情况下，当汽 布尾部离后面障碍物达到1.2 m吋，可釆用一阶rc充放电，再通过电压比较器来实施报警 效应效果。其中还涉及时间常数丫的大小來决定报警声音的急促性。再有在实际测试设备和实验仪器屮，常

3、用方波作为测试信号，如何能将迟滞比较器的高 低电平连续输出，且占空比等于0.5?这时可以利用一阶rc电路的全响应來完成，通过电 容c的充电、放电交替进行来实现；如果知道了全响应的三耍素，即可得出宽窄不一的矩形 波。基础知识的纵向延伸电路课程木身是一门源于物理的学科，其屮所含的定理和结论以 严格的数学作为依据，利用物理和数学工具来描述和解决工程化的问题。因此，在电路课程 学习z前，会涉及大屋的先修课程，如高等数学、大学物理、线性代数、图论、信号系统 等知识。-些学生对这些先修课程掌握得不理想，必然会影响本课程的学习。在对河南大学 物理与电子学院10多年的教学研究中发现，上述先修知识要求是学牛在学

4、习中觉得怵i难的 首要原因。这要求教师在先修课程的相关内容上进行基础知识和方法的引入。此外，在讲授 未接触过的知识z前，可以考虑从实际应用的例了出发，引导学生对电路基木原理的思考和 简单分析。如一阶rc电路三要素中的f（8）值，在开关断开或闭合后的无穷时刻，判别 电容c最终电压uc（8）。因此，要使学生提高对于教材屮知识点的理解和把握能力，使拓展法有的放矢，达到预 期的效果，首先要找准重难点的突破口和切入点3；其次，对知识点内容的选择和讲解要 实现真正意义上的拓展，作为学生思维活动的一种扩展，着眼于训练学生的思考能力，不搞 “一言堂”教学模式；另外还可通过教学引导和习题训练应用相结合，最终达到

5、能活跃学生 思维、增强解决问题能力的目的。3电路课程横抓展和纵延伸衔接的教学模式运用挖掘知识点内涵，充分理解知识点运用条件在理论教学课堂中，对所耍讲授的知识点 m正确引导和强调，让学生深刻理解其潜在的含义和m用条件。如对一阶电路全响应的描述:“当一个非零初始状态（动态元件的初始储能不为零）的一阶受到外施激励时，电路的响应 称为全响应。”通过对一阶电路全响应的描述来分析重难点后，对学生分析如下问题。1）动态元件的初始储能，在此为电压或电流到底多人？是需要求解还是一眼可看出來？2）在此描述的外施激励是线性的独立源，还是线性的受控源？3）求解动态元件上的电流电压响应时，该元件以外的端口在哪里？4）如

6、何将电路简化为仅含一个动态元件、一个独立电源和一个等效电阻的三个元件组 成的电路？（适当引导学生回忆第四章的戴维南等效定理来解决该问题。）5）対rc 阶电路t=rxc,对rl 一阶电路t二l/r,时间常数t如何求解?6）外施独立电源的个数给定了吗？如何化为一个独立电源？围绕这些问题开展教学，既可以让学生积极思考，又可以很好地进行纵向和横向知识的 展开，做到目标明确；同时可以将相关知识山点及线、山线到血，达到融会贯通的目标。一阶电路全响应的横拓展和纵延伸在肓流电源激励下，由于一阶全响应电路在分析时 需要求解三个要素：初始值f（0+）、t 时刻的稳态值f （-）、时间常数丫，后代入公式 f （t）

7、 =f （°°） +f （0+） -f（8）e?ct/ t求解响应。而这三个要素的求法，尤其要熟练地能 将动态元件以外的一端口化为戴维南等效才可以，求出等效电阻req和开路电压uoco而对 -阶全响应电路知识点的分析，本文采川横拓展和纵延伸的立体衔接教学模式來说明一端口 线性等效，如图1框图所示。从图1框图可知，对一阶电路全响应的知识内容，釆用横向拓展方法和纵向延伸的教学 策略和模式，能正确地让学牛领会如何去分析全响应电路，能清晰了解在求解三要素时要求 具备的基础知识。4知识点横拓展和纵延仲的施教在上述基础上，仍以一阶电路全响应为例，対知识点如何进行横拓展和纵延伸的施教加

8、以说明。横拓展的施教法由上对知一阶电路全响应求解，关键在于如何求解动态元件以外端口的戴维南等效。围绕开路电压和戴维南等效电阻的计算，可同时进行知识点的横拓 展。英中的开路电压可以采用电路课程中的基尔霍夫电压定理（kvl、kcl）、网孔电流、回 路电流、结点电压、电压叠加定理等方法来分析计算。假设一阶动态元件电容c以外是一个 包含受控源的含源一端口，其等效电阻的计算有两种常用方法：去除独立电源后的端口外加 电压/电流比值法、开路电压与短路电流比值法。如包含受控源的含源一端口戴维南等效电 阻问题，可采用如图2所示方法来计算。对于含有独立源的一端口等效电卩fl req求解，图2 (a)保留了独立电源

9、us。在独立电 源us作用下,分别求出端口开路电压uoc和短路后的短路电流isc, req=uoc/isco图2 (b) 去除独立源us后，在参考方向尽呆不变的情况下，在端口处人为加上一个电压源u后，求 出产生的端口电流i,建立u与i的线性关系，可得req=u/l从图2可看出，在课堂讲授过程中，要着重引导和培养学半対于知识点的横拓展思维4, 进一步找出其屮的区别和联系，只有充分理解电路定理的使川条件，才能在面对问题时胸有 成竹，进而正确解决电路问题。纵延伸的施教法纵延伸施教主要将该知识点的前后和关内容大致贯穿起来5-6,以期 达到温故而知新的功效。比如一阶电路全响应关键求出动态元件以外端口的戴

10、维南等效，对 于没有独立电源的一端口电路，常分为仅市线性电阻构成和仅由线性电阻、受控源构成的一 端口。对于仅含线性电阻构成的一端口，总可以采用串联、并联或星形三角形变换等方法來 求解等效req。对于仅含线性电阻和受控源构成的一端口，当一端口内受控源的控制支路在 该一端口电路内时，由于无独立源存在，该支路的电压u和电流i均为零，则受控源得不到 激励，一端口的开路电压uoc=0o iii电路齐性定理得知，此一端口外加一个独立电压源后, 端口电压与端口电流成线性关系，町求出等效电阻req。因此，其对应的戴维南定理也蜕变 为一等效电阻。再如一阶全响应电路涉及受控源如何处理，控制量支路是哪个，如何分析可

11、采用前面章 节的kcl、kvl等定律的相关内容來解决。无论一阶电路哪种响应，时间常数t的求解也很 关键，这也涉及一阶动态电路的基础内容。另外，在一阶电路全响应分析过程中，发现它是 一阶零输入响应和一阶零状态响应共同作用的结果，如图3所示(以一阶rc电路为例)， 也是稳态分量和瞬时分量共同作用的结果。(a) 一阶全响应电路可分解为图3 (b)的一阶零状态电路和图3 (c)的一阶零输入响 应电路两部分的组合。利用前面知识可以求出电容c在时间匸0时，开关合上后的电压uc (t)表达，在此不予详述。解决好一阶电路全响应问题，可以正确分析和解决实际电路屮 c的充放电过程和最终仪器仪表的显示结果。通过纵延

12、伸的施教，让学牛能将前后知识很好地贯穿融合起來。如此实施的横拓展知识 点回顾和纵延伸知识点贯穿的教学模式，能使学牛正确理解电路内容，并灵活运用。5结语通过对一阶电路全响应的横拓展和纵延伸教学模式的施教论述和演示，诠释了在一些电 路知识点的讲授过程中，注意采用横拓展和纵延伸衔接的教学模式进行内容讲解，使学生能 够在潜移默化屮将已学过的知识复习巩固多次，并进一步加深了学生知识连贯性，更好地锻 炼了学生利用已学的电路知识来分析新知识点引发的新问题，同时采用一些分析方法来高效 地解决新问题。教师在讲授时，学生也无形地掌握了知识点的横拓展和纵延伸的重要性，从 而活跃了电子信息类专业学牛的思维，扩大了学牛

13、的知识血，提高了学生对问题求解时的应 变能力7-8o因此，在电路课程教学屮，教师应当努力创造条件，采川各种新的教*模式和 教学手段来增强课堂教学效果，提高学生的综合分析能力和索养，为今后生活和工作获取新 知识、新能力奠定良好的基础。1 in troducti oncircuit course is a professional electronic information disciplines in colleges and universities, and other related professio nal less on an important foun datio n plat

14、form set up the long history, the course is of great significanee, many theories content has been quite mature but due to the rapid developme nt of electronic in formation discipli ne and industry, this course still n eed to make the necessary innovation. although over the years, the domestic many i

15、mportant achieveme nts have bee n made of circuit course in colleges and universities, improve teachi ng level 1-2, however it has been proved that the directi on of further developme nt and reform of the course is not clear.henan university physics institute of physics, communication engineering an

16、d electronic in formatio n scie nee and tech no logy and other professio nal to ope n this course, and the kno wledge co nt ent of the course is various, str on ger theory, structural, theorem, provide necessary theory foundation for the follow-up courses learning knowledge, knowledge before and aft

17、er close ties as a result, students in understand!ng knowledge easily understand thoroughly, in sufficient analysis, problem solving is not smooth, and many other embarrassme nt. electr onic in format! on professi onal discipli nes, for example, discussed with the model of tra nsverse and ion gitudi

18、 nal exte nsion of the three-dime nsional teachi ng cohesi on, first-order circuit course in teachi ng the whole resp onse whe n the content of the sectio n of teachi ng method and processtwo tran sverse and ion gitudi nal exte nsion circuit course teachi ng mode is in troducedapplication content of

19、 transverse expansion circuit courses in addition to the interpretation of classical theory, in the full resp onse of first-order circuit in the teachi ng process should be proper introductio n of horiz on tai kno wledge in troductio n, especially dyn amic comp orient in a first-order circuit capaci

20、ta nee c and in du eta nee l, there is the physical process of chargi ng and dischargi ng.as some ''car parking assist device1' - reversing radar equipment, through the ultrasonic sensor case, when the car tail from behind obstacles up to 1.2 m, can use a first order rc charge and discha

21、rge, and then to implement alarm effects by voltage comparator. which also involves time constant to determine the size of the tau shortness of alarm sound.again in the actual test equipme nt and experime ntal apparatus, square wave is comm only used as a test signal, how can continuous output, high

22、 and low level of hysteresit comparator and duty ratio equal to 0.5? at this time can make use of the response of the first-order rc circuit, by charging and discharging capacitanee c to implement alternate; if you know a full response of the three elements, can draw or width of the rectangular wave

23、basic knowledge of the iongitudinal extension of circuit course itself is a is the result of physical science, which con tains the theorem and con clusi on with strict mathematics as the basis, using the physical and mathematical tools to describe and solve engineer!ng problems. before the circuit c

24、ourse, therefore, involve a lot of courses, such as advaneed mathematics, university physics, linear algebra, knowledge of graph theory, signals and systems, etc. some of the students to master these courses are not ideal, will inevitably affect the learning of this course. in the hena n un iversity

25、 institute of physics and electr onic found in more tha n 10 years of teachi ng research, the ap knowledge requirement is the leading cause of students find difficult in learning. this requires teachers to a prior course of releva nt content on the in troducti on of the basic kno wledge and method i

26、n additi on，before teachi ng did not come into contact with kno wledge, can consider from the example of practical application, guide students to think and simple analysis of the basic principle of circuit. consistent order rc circuit (up) f value of the three elements, an infinite moment after the

27、switch is open or closed, discriminant capacitance c final voltage uc (up).therefore, to make students improve for un d erst a nding and grasp of kno wledge in the teaching material, to make targeted development law, achieve the desired effect, the first thing to find difficulty breach and the break

28、through point of the quarter-final? 'he asked 3. second, the choice of knowledge content and explain to realize in the true sense, as an extension of students1 thinking activities, focus on training students' ability to think, don't make a centralized hteachi ng mode; also can be used th

29、rough the guida nee of teachi ng and exercise trai ning, combi ning can eve ntually achieve active stude nts' thin king and en hance their ability to solve the problem 3 circuit course teachi ng model of tra nsverse and longitudi nal extensi on of cohesi onmining knowledge connotation, fully und

30、erstand knowledge using conditions in theoretical teachi ng in the classroom, to correctly guide and to teach kno wledge points should be emphasized, let the stude nts un d erst a nd the meaning of its potential and applicatio n conditions. such as the description of the complete response of first-o

31、rder circuit: "when a nonzero initial state (dynamic components of the initial energy storage is not zero) of the first order are motivated by the applied, the response of the circuit is called full response.n through the description of the complete response of first-order circuit analysis afte

32、r the difficult point, analysis the problems of students.1) the dynamic components of the initial energy storage, in this for voltage or current exactly how much? it is need to solve or eye can see out?2) in this descripti on applied to stimulate is lin ear in depe ndent source, or a lin ear con tro

33、lled source?3) to solve the current voltage response on the dynamic components, the components outside the port in where?4) how to simplify the circuit for only contains a dynamic element an independent power supply and an equivale nt resista nee of the three comp on ents of the circuit? (properly g

34、uide stude nts to recall the fourth chapter theve nin equivale nt theorem to solve the problem.)5) tau = r * c for rc first-order circuits, the rl first-order circuit tau = l/r, time constant of tau how to solve?6) applied the number of independent power given? how do i into a separate power supply?

35、 around these problems in the teachi ng, can let the student positive thinking, and is a goodway to long itudinal and horiz on tai kno wledge, do specific goals; at the same time can be related knowledge from point and line, from line to plan巳 achieve mastery goals.the first order circuit transverse

36、 and iongitudinal extension of the response under de excitation, the first-order full response in circuit analysis needs to solve three key elements: initial value f (0 +), the steady-state value of t up time f (up), the time constant of tau, offspring into the formula of f (t) = f (up) + f (0 +) -

37、f (up) e? ct/tau solving the response. the three elements of religion, especially could skillfully dynamic components outside the port into the thevenin equivale nt to, and the equivale nt resista nee the req and ope n circuit voltage uoc and the analysis of the first-order circuit response all know

38、ledge, and based on the transverse and ion gitudi nal extensi on of cohesive teachi ng mode with stereo port lin ear equivale nt projector, as shown in figure 1 block diagram.from figure 1 block diagram, the knowledge content of complete response of first-order circuit, the vertical and horiz on tai

39、 developme nt method and the teachi ng strategy and mode, can make students understand how to correctly analyze whole response circuit, can clear understanding on the basis of solving three elements required knowledge4 teachi ng kno wledge of transverse and longitudinal extensi onon the basis of the

40、 above, still all first-order circuit response, for example, transverse and iongitudinal extension of knowledge how to teach the teaching method of developing cross by a on the full response to solve the first-order circuit, the key lies in how to solve the dyn amic comp orients outside the theve ni

41、n equivale nt of the port. around the ope n circuit voltage and theveni n equivale nt resista nee calculati on, can make kno wledge of tra nsverse expansi on at the same time the open circuit voltage of which can use kirchhoff's voltage of circuit course theorem (kvl and kcl), mesh loop current,

42、 node voltage, voltage and current superposition theorem and other methods to analysis and calculation. assumes that the first order dyn amic comp onents outside the capacita nee c is a source of con trolled source port, there are two types of commonly used method to calculate the equivalent resista

43、nce: after removal of independent power supply port and voltage/current ratio method, open circuit voltage and short circuit curre nt ratio method such as containing con trolled source containing the source of a port problem, theveni n equivale nt resista nee method can be used as show n in figure 2

44、.for a port that contain independent source equivalent resistance the req, figure 2 (a) retain the in dependent power supply to us. in the role of in depe ndent power supply us, respectively calculate uoc port open circuit voltage and short circuit after the short circuit current isc, the req =uoc/i

45、sc. figure 2 (b) remove the in depe ndent source after the us, on the basis of the ref ere nee directi on as far as possible, at the port for plus a voltage source, after u find out the port curre nt i, established linear relationship between u and i, can get the req = u/l.as you can see in figure 2

46、, in the process of classroom teachi ng, to guide and cultivate the stude nts emphatically for horiz on tai expa nd thought 4 kno wledge, further find out the d iff ere nee and conn ecti on, only fully understa nd the conditions of use of circuit theorem, to have answers, and in the face of the prob

47、lems and properly solve the problem of circuitthe vertical exte nsion of teachi ng method lon gitudi nal extensio n teachi ng mainly to the knowledge of releva nt content before and after roughly forme 5-6, in order to reach the effect of consider. such as first-order circuit response all key the th

48、evenin equivalent of dynamic components outside the port, a port for no independent power supply circuit, often divided into only consists of li near resistor and composed of lin ear resistor, con trolled source only one port. for only contains linear resistor consisting of a port, the total can be

49、used in series, parallel, or star triangle transform method to solve the equivalent the req. for only contains linear resista nee and con trolled source of one port, when a port within a port con trol branch in the con trolled source circuits in side, because there is no in depe ndent source, the cu

50、rre nt i and bra nch voltage u are zero, is not con trolled source excitatio n, a port ope n circuit voltage uoc = 0. by circuit homogeneity theorem, the port plus an independent voltage source, a linear relati on ship with ports voltage and curre nt, equivale nt resista nee can be calculated the re

51、q. therefore, its corresp onding theve nin theorem also cha nge to an equivalent resista nee.order again, like a full response involving how to deal with the controlled source circuits, control branch is which, how to analysis can be used in the previous chapter of kcl and kvl law to solve related c

52、ontent. whatever response of first-order circuit time constant is also key of solving the tau, this also involves the basis of the first order dynamic circuit. in addition, in the first order circuit full resp onse analysis in the process, found that it is a first order zero in put response and outc

53、ome of combined action of first-order zero state response, as shown in figure 3 (a first order rc circuit, for example), is also the result of combined action of the steady state and transient component.(a) first-order circuit can be decomposed into full response figure 3 (b) the first order of zero

54、 state circuit and figure 3 (c) the first-order zero in put response of the circuit the combination of the two parts the previous knowledge can be used to calculate capacitanee c at time t = 0, switch close after voltage uc (t), not be detailed here solution of the first-order circuit response problem completely, correctly an a lyze and solve practical circuit c of charge and discharge