Introduction to Electronic Systems (电路基础)

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1 Introduction to Electronic Systems (电路基础)
信息与通信工程学院 梁 栋

2 课 程 简 介 课程信息 教学安排 所获奖项及资助 英文名称： Introduction to Electronic Systems
中文名称：电子系统(电路基础) 学 分： 3学分 网 站： 教学安排 授课对象：国际学院电信工程及管理、电子商务及法 律本科一年级学生 授课时间：春季学期前12周讲理论，后4周安排实验 教 材：Introductory Circuits for Electrical and Computer Engineering，张民改编，电子工业出版社，2009年 所获奖项及资助 2007年成为国家级双语教学示范课程 2007年获得原电信工程学院“优秀教学团队”称号

3 课 程 主 要 内 容 Chap1. Circuit Variables and Circuit Elements
Chap2. Some Circuit Simplification Techniques Chap3. Techniques of Circuit Analysis Chap4. The Operational Amplifier Chap5. The Natural and Step Response of RL and RC Circuits Chap6. Natural and Step Response of RLC Circuits Chap7. Sinusoidal Steady-State Analysis Chap8. Balanced Three-Phase Circuits

4 Chap 3 Techniques of Circuit Analysis
Part II Node Voltage Analysis Corresponding to Chap in textbook

5 Trace of Our Footstep Up to now, we have learned 4 methods to analyze resistive DC circuits KCL and KVL (In Chap 1) Source Transformation (In Chap 2) Superposition (In Chap 2) Mesh-Current Analysis (In Chap 3) Today we will introduce a new method Node Voltage Analysis

6 Outline of Node Voltage Analysis
Two Concepts Reference node Node Voltage Principle of Node Voltage Analysis 4-step method Utilization of Node Voltage Analysis Circuits with only Current Sources Circuits with Current and Voltage Sources Circuits with Dependent Sources

7 Part 1 Two concepts

8 ground or reference symbol
Reference Node (参考节点) Are these the same circuits? For convenience of analysis, we designate one node as the reference node assumed to be connected to ground. Node c in this case. or ground or reference symbol Ground represents the zero reference Since reference node is arbitrarily selected, it is not necessarily the lowest voltage in the circuit.

9 Node Voltage (节点电压) va a
The node voltage is the voltage difference between the respect node to the reference. Also refer to textbook in p60 a va For node a, the node voltage va is equal to the voltage across of R2.

10 Part 2 A simple example to introduce the principle of Node Voltage Analysis

11 4-step method for Node Voltage Analysis
Step 1. Identify essential nodes Essential node a Essential nodes Reference nodes Essential node c Reference node back

12 4-step method for Node Voltage Analysis
Step 2. Express currents as a function of node voltages for each essential node (except for the reference node) va is Step 3. Apply KCL at the essential nodes except for the reference node back

13 4-step method for Node Voltage Analysis
Step 4. Solve equations to calculate node voltages back

14 NODE a (Essential node)
About trivial nodes We can also apply KCL at trivial nodes and obtain the same results. NODE a (Essential node) a a b b NODE b (Trivial node) By substitution, the same equation is achieved After all, trivial node analysis is not necessary for consideration of minimizing equation numbers.

15 General steps of Node Voltage Analysis
STEPS TO THE SOLUTION Step 1: Identify nodes Example Step 2: Express currents as a function of node voltages Example Step 3: Apply KCL at each essential node except for reference node Example Step 4: solve the resulting n–1 simultaneous linear equations for the voltages where n is the number of essential nodes Example

16 Part 3 Utilization of Node Voltage Analysis

17 Utilization of Node Voltage Analysis
3 scenarios I: Circuits with only Current Sources II: Circuits with Current and Voltage Sources III: Circuits with Dependent Sources

18 Case1. Circuits with only Current Sources
Example V1=? V2=?

19 Circuits with only Current Sources
Step 1: Identify nodes 1 2 3 3

20 Circuits with only Current Sources
Step 2: Express currents as a function of node voltages I3 G3(V1-V2) G1V1 3 3

21 Circuits with only Current Sources
Step 3: Apply KCL at each essential node except for reference node I3 I1 G3(V1-V2) G1V1 KCL applied to each non-grounded node gives: for node 1 self conductance at node 1 （自电导） mutual conductance between nodes 1 & 2 （互电导）

22 Circuits with only Current Sources
G3(V2-V1) I2 G2V2 for node 2 self conductance at node 2 mutual conductance between nodes 2 and 1

23 Circuits with only Current Sources
Step 4 solve the resulting n –1 simultaneous linear equations for the voltages where n is the number of essential nodes (n=2) Also can be written in matrix form Note: Self conductance occupy the main diagonal Mutual conductance occupy the off-diagonal with minus sign (-) In the right side, the positive sigh used for in-current

24 The comparison between KCL&KVL and Node Voltage Analysis
基尔霍夫法 未知数包括所有元件的电流和电压 方程组由KVL、KCL和欧姆定律三类方程组成 缺点：未知数 个数和方程个 数较大 网孔电流法 未知数仅包括网孔电流 方程组仅包括KVL方程，其中各个支路的电压依据欧姆定律，用网孔电流来表示。 优点：未知数个数和方程个数大大下降 节点电压法 未知数仅包括节点电压 方程组仅包括KCL方程，其中各个支路的电流依据欧姆定律，用节点电压来表示。 优点：未知数个数和方程个数大大下降

25 Case 2. Circuit with Current and Voltage Sources
1. When the voltage source is connected directly to the ground. Note that va = vs and vb is the only unknown. We can apply KCL at node b to get:

26 A Similar Example Example 3.2 in Textbook p62 v1 v1

27 Super node Solution 2. When the voltage source is not connected to ground. Since we know the voltage between a and b, we can apply KCL to supernode ab as if it were a single node. We can apply KCL to node ab resulting in: Solving for vb.

28 Case 3. Circuit with Dependent Sources
Express the controlling current or voltage in terms of the node voltages. so, Applying KCL at node b Substituting for vc and solving for vb.

29 Node Voltages or Mesh Currents?
Planar circuits can usually be analyzed using either node voltages or mesh currents. When do we use one vs. the other method? In general whatever approach yields the smaller number of simultaneous linear equations is the best approach. Voltages sources especially dependent ones are easier with node voltages. Current sources are easier analyzed with mesh currents. Mesh currents seem to result in fewer sign errors.