電子電路基礎(chǔ)課件CH2

1、Ch2 Basic Analysis Methods to Circuits 2.1 Equivalent Circuits2.2 The Superposition Principle 2.3 Thevenins and Nortons theorems Readings: Gao-Ch2; Hayt-Ch3, 4Circuits and Analog ElectronicsCh2 Basic Analysis Methods to Circuits 2.1 Equivalent CircuitsKey Words: Equivalent Circuits Network Equivalen

2、t Resistance, Equivalent Independent Sources 2.1 Equivalent CircuitsCh2 Basic Analysis Methods to CircuitsEquivalent Circuits NetworkTwo-terminal Circuits NetworkbN1Ia+-VN2Iab+-Vabcd651552.1 Equivalent CircuitsCh2 Basic Analysis Methods to CircuitsHow do we find I1 and I2?R1R2V+-I1I2II1 + I2 = IEqui

3、valent Resistance2.1 Equivalent CircuitsCh2 Basic Analysis Methods to CircuitsEquivalent Resistancei(t)+-v(t)i(t)+-v(t)ReqReq is equivalent to the resistor network on the left in the sense that they have the same i-v characteristics.2.1 Equivalent CircuitsCh2 Basic Analysis Methods to CircuitsEquiva

4、lent ResistanceSeries and parallel ResistanceMethod 1Method 2IVRRabo=abVIsource-freesourceVocMethod 3ISCsource(source-free)2.1 Equivalent CircuitsCh2 Basic Analysis Methods to CircuitsEquivalent ResistanceP2.1Method 1 Method 2VR1R2R3abIVSR1R2R3ab+-How do we find Rab?ISC=VS/R3 Method 32.1 Equivalent

5、CircuitsCh2 Basic Analysis Methods to CircuitsSource TransformationIdeally:An ideal current source has the voltage necessary to provide its rated currentAn ideal voltage source supplies the current necessary to provide its rated voltagePractice: A real voltage source cannot supply arbitrarily large

6、amounts of currentA real current source cannot have an arbitrarily large terminal voltage2.1 Equivalent CircuitsCh2 Basic Analysis Methods to CircuitsSource TransformationVs+-RsIsRsNote: Consistency between the current source ref. direction and the voltage Source ref. terminals. 2.1 Equivalent Circu

7、itsCh2 Basic Analysis Methods to CircuitsHow do we find I1 and I2?Equivalent SourceIs2VR1R2+-I1I2Is1I1 + I2 = Is1 - Is2Ieq2.1 Equivalent CircuitsCh2 Basic Analysis Methods to CircuitsEquivalent SourceSeries Voltage Source+-VS1VS2VSn+-VSparallel Current SourceIS1IS2ISnISIRS=RS1/ RS2/ RSn Ch2 Basic An

8、alysis Methods to Circuits 2.2 The Superposition Principle Key Words: Linearity SuperpositionCh2 Basic Analysis Methods to CircuitsLinearity2.2 The Superposition Principle Linearity is a mathematical property of circuits that makes very powerful analysis techniques possible.Linearity leads to many u

9、seful properties of circuits:Superposition: the effect of each source can be considered separately.Equivalent circuits: Any linear network can be represented by an equivalent source and resistance (Thevenins and Nortons theorems)Ch2 Basic Analysis Methods to CircuitsLinearity2.2 The Superposition Pr

10、inciple The relationship between current and voltage for a linear elements satisfies two properties:HomogeneityAdditivity *Real circuit elements are not linear, but can be approximated as linearCh2 Basic Analysis Methods to CircuitsLinearity2.2 The Superposition Principle Homogeneity:Let v(t) be the

11、 voltage across an element with current i(t) flowing through it.In an element satisfying homogeneity, if the current is increased by a factor of K, the voltage increases by a factor of K.AdditivityLet v1(t) be the voltage across an element with current i1(t) flowing through it, and let v2(t) be the

12、voltage across an element with current i2 (t) flowing through itIn an element satisfying additivity, if the current is the sum of i1 (t) and i2 (t), then the voltage is the sum of v1 (t) and v2 (t). Example: Resistor: V = R IIf current is KI, then voltage is R KI = KVIf current is I1 + I2, then volt

13、age is R(I1 + I2) = RI1 + RI2 = V1 + V2Ch2 Basic Analysis Methods to CircuitsSuperposition is a direct consequence of linearityIt states that “in any linear circuit containing multiple independent sources, the current or voltage at any point in the circuit may be calculated as the algebraic sum of t

14、he individual contributions of each source acting alone.”Superposition2.2 The Superposition Principle I2ICh2 Basic Analysis Methods to CircuitsSuperposition2.2 The Superposition Principle How to Apply Superposition?To find the contribution due to an individual independent source, zero out the other

15、independent sources in the circuit.Voltage source short circuit.Current source open circuit.Solve the resulting circuit using your favorite techniques.Loop analysisCh2 Basic Analysis Methods to CircuitsSuperposition2.2 The Superposition Principle P2.72kW1kW2kW12V+-I02mA4mACh2 Basic Analysis Methods

16、to CircuitsSuperposition2.2 The Superposition Principle P2.72kW1kW2kWIo2mAI0 = -4/3 mACh2 Basic Analysis Methods to CircuitsSuperposition2.2 The Superposition Principle P2.72kW1kW2kWI04mAI0 = 0Ch2 Basic Analysis Methods to CircuitsSuperposition2.2 The Superposition Principle P2.72kW1kW2kW12V+-I0I0 =

17、 -4 mACh2 Basic Analysis Methods to CircuitsSuperposition2.2 The Superposition Principle P2.7I0 = I0 +I0+ I0 = -16/3 mA 2kW1kW2kW12V+-I02mA4mAI0 = I0 +I0+ I0 = -16/3 mA 2kW1kW2kW12V+-I02mA4mACh2 Basic Analysis Methods to CircuitsSuperposition2.2 The Superposition Principle P2.8VR4=?Ch2 Basic Analysi

18、s Methods to CircuitsSuperposition2.2 The Superposition Principle P2.9（D/A）Decode circuit。 00000011060001101117001021000800113100190100410101001015_VoR/8+R/4R/2REEEE23222120Ch2 Basic Analysis Methods to Circuits 2.3 Thevenins and Nortons theorems Key Words: Thevenins theorems Nortons theoremsCh2 Bas

19、ic Analysis Methods to CircuitsThevenins theorem2.3 Thevenins and Nortons theorems Any circuit with sources (dependent and/or independent) and resistors can be replaced by an equivalent circuit containing a single voltage source and a single resistorThevenins theorem implies that we can replace arbi

20、trarily complicated networks with simple networks for purposes of analysisCh2 Basic Analysis Methods to CircuitsThevenins theorem2.3 Thevenins and Nortons theorems Circuit with independent sourcesRThVoc+-Thevenin equivalent circuitIndependent SourcesCh2 Basic Analysis Methods to CircuitsThevenins th

21、eorem2.3 Thevenins and Nortons theorems No Independent SourcesCircuit without independent sourcesRThThevenin equivalent circuitCh2 Basic Analysis Methods to CircuitsThevenins theorem2.3 Useful Circuit Analysis Techniques No Independent SourcesOutline of proofIf Circuit A is unchanged then the curren

22、t should be the sameUse source superpositionAll independent sources set to zero in AHow do we interpret this result?This is the Thevenin equivalentcircuit for the circuit in Part AFor ANY circuit in Part BThe voltage source is called the THEVENIN EQUIVALENT SOURCEThe resistance is called the THEVENI

23、N EQUIVALENT RESISTANCEPart a must behave likeThis circuitThevenin approachCh2 Basic Analysis Methods to CircuitsThevenins theorem2.3 Thevenins and Nortons theorems independent sourcesRThVoc(VTH)+-Circuit without independent sourcesRTHFor ANY circuit in Part Bivoresistance of network seen from porto

24、pen circuit voltageat terminal pairCh2 Basic Analysis Methods to CircuitsThevenins theorem2.3 Thevenins and Nortons theorems Circuits with independent sourcesCompute the open circuit voltage, this is VocCompute the Thevenin resistance (set the sources to zero short circuit the voltage sources, open

25、circuit the current sources), and find the equivalent resistance, this is RThCircuits with independent and dependent sources:Compute the open circuit voltageCompute the short circuit currentThe ratio of the two is RThCircuits with dependent sources onlyVoc is simply 0RTh is found by applying an inde

26、pendent voltage source (V volts) to the terminals and finding voltage/current ratioCh2 Basic Analysis Methods to Circuits2.3 Thevenins and Nortons theorems Valid partitions keep the dependent sources and their controlling variable in the same partition. Thevenins theoremCh2 Basic Analysis Methods to

27、 Circuits2.3 Thevenins and Nortons theorems Thevenins theoremP2.10 Iac=? Independent. SourcesDependent. SourcesWith Independent sourcesWithout Independent sourcesWith dependent sourcesCompute the open circuit voltage VocCompute the short circuit current IscThe ratio of the two is RTh, i.e. RTh= Voc/

28、 IscVoc is simply 0.RTh is found by applying an independent voltage source (V volts) to the terminals and finding voltage/current ratio.Without dependent sourcesCompute the open circuit voltage, VocCompute the Thevenin resistance by setting the sources to zero Short circuit the voltage sources,Open

29、circuit the current sourcesFind the equivalent resistance, RThA circuit only containing resistorsVoc is simply 0Find the equivalent resistance, RThCh2 Basic Analysis Methods to Circuits2.3 Thevenins and Nortons theorems Thevenins theoremP2.11Ch2 Basic Analysis Methods to Circuits2.3 Thevenins and No

30、rtons theorems Maximum power transferFor every choice of RL we have a different power.How do we find the maximum value?Consider PL as a function of RL and find the maximum of such function3The maximum power transfer theoremThe load that maximizes the power transfer for a circuit is equal to the Thev

31、enin equivalent resistance of the circuit.The value of the maximum power that can be transferred is Ch2 Basic Analysis Methods to Circuits2.3 Thevenins and Nortons theorems Nortons theoremVery similar to Thevenins theoremIt simply states that any circuit with sources (dependent and/or independent) a

32、nd resistors can be replaced by an equivalent circuit containing a single current source and a single resistorCh2 Basic Analysis Methods to Circuits2.3 Thevenins and Nortons theorems Nortons theoremNorton ApproachNortonCh2 Basic Analysis Methods to Circuits2.3 Thevenins and Nortons theorems Nortons theoremNorton Equivalent: Independent SourcesCircuit with one or more indep