Transcript ppt
EE 1270: Introduction to Electric Circuits 0 Lecture 7: Mesh Analysis Chapter 4 Techniques of Circuit Analysis: Sections 4.5-4.7 EE 1270 Introduction to Electric Circuits Suketu Naik Node, Branch, Loop, Mesh Node (current sum) 1 Mesh (voltage sum) Branch Node: A point where two or more circuit elements join Mesh: A loop that does not enclose any other loops Branch: A circuit path that contains two nodes Loop: A path with starting node=last node; can contain many meshes EE 1270 Introduction to Electric Circuits Suketu Naik Mesh: More Examples 2 Remember that mesh current represents shared current within a mesh as you go around the loop EE 1270 Introduction to Electric Circuits Suketu Naik Mesh in an Actual Circuit 3 Can you identify meshes in the above circuit? EE 1270 Introduction to Electric Circuits Suketu Naik 4 Mesh-Current Method Find unknown currents by summing the voltages in a mesh Example 4.4: a) Find the power for each voltage source b) Find vo Step1: Draw Mesh Currents EE 1270 Introduction to Electric Circuits Suketu Naik Mesh-Current Method 40 2ia 8(ia ib ) 0 8(ib ia ) 6ib 6(ib ic ) 0 6(ic ib ) 4ic 20 0 10ia 8ib 0ic 0 8ia 20ib 6ic 0 0ia 6ib 10ic 20 EE 1270 Introduction to Electric Circuits 5 Step2: Write Mesh-Current Equations by Summing Voltages around the Meshes Passive Sign Convention Step3: Solve Simultaneous Equations in Standard Form Suketu Naik Mesh-Current Method 6 ia= 5.6 A ib= 2 A ic= -0.8 A p40V= (40 V)(-5.6 A)=224 W p20V= (20 V)(-0.8 A)=-16 W Passive Sign Convention Both vol. sources are delivering (generating) power to the circuit v0= 8(ia-ib)=8(5.6-2)=28.8 V EE 1270 Introduction to Electric Circuits Suketu Naik AP4.7 7 Find the power associated with the voltage source and the power dissipated in the 8 Ω resistor Simultaneous Equations: Solution p80 V = p8 Ω = Passive Sign Convention Positive Power means it is consumed (dissipated) Negtive Power means it is generated (delievered) EE 1270 Introduction to Electric Circuits Suketu Naik Positive and Negative Power 8 Positive Power means it is consumed by a circuit element, i.e. vol. source, cur. source, resistor, capacitor, inductor etc Negtive Power means it is generated (delievered) by a cur. source or a vol. source The positive or negative sign depends on the polarity of the voltage and direction of the current Q: Where happens to the dissipated or consumed power in a resistor? A: EE 1270 Introduction to Electric Circuits Suketu Naik AP4.8b 9 Find the power associated with the dependent source Simultaneous Equations: Passive Sign Convention Solution p-3vϕ = EE 1270 Introduction to Electric Circuits Suketu Naik Supermesh 10 Circuit with current source between two meshes Combine meshes to create supermesh and ignore the current source EE 1270 Introduction to Electric Circuits Suketu Naik AP4.12 11 Find the power dissipated in the 1 Ω resistor Simultaneous Equations: Passive Sign Convention Solution p1Ω = EE 1270 Introduction to Electric Circuits Suketu Naik Example: Transistor Circuit 12 An NPN transistor can be used as an amplifier EE 1270 Introduction to Electric Circuits Suketu Naik Example Fig. 4.27-4.28: Transistor Circuit 13 The transistor circuit can be analyzed using the supermesh Find iB, iE, and iC if Vcc=15 V, R1=100 kΩ, R2=50 kΩ, Vo=0.65 V, Rc=10 kΩ, RE=4.25 kΩ, β=300 EE 1270 Introduction to Electric Circuits Suketu Naik