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Lecture 5 Source Transformation Thevenin Equivalent Circuit Norton Equivalent Circuit.

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Presentation on theme: "Lecture 5 Source Transformation Thevenin Equivalent Circuit Norton Equivalent Circuit."— Presentation transcript:

1 Lecture 5 Source Transformation Thevenin Equivalent Circuit Norton Equivalent Circuit

2 Circuit Techinques Ohm’s Law P=VI KCL, KVL Voltage/current divider Series/parallel resistance Mesh/Nodal Analysis Source Transformation Thevenin/Norton Equivalent Circuit Superposition Principle Maximum Power Transfer

3 Source Transformation Show that i S =v S /R for any R L

4 Thevenin Equivalent Circuit

5 Determine the Thevenin Voltage (V Th ) If R L =∞ (load across a-b is removed), then V ab =V TH – R TH does not play a role!

6 3 Bit Digital to Analog Converter 741 Op-Amp Chapter 5

7 Sample DAC Waveform Digital Input DAC Output

8 Applications Most modern audio signals are stored in digital form (e.g. MP3 and CDs) and in order to be heard through speakers they must be converted into an analog signal

9 Thevenin Equivalent Circuit

10 Determine V TH

11 Methods of Finding R TH R TH =V TH /i SC – If R L =0, the short circuit current from a to b (i.e. i ab ) should equal to i sc =V Th /R TH. – So R TH =V Th /i sc If the network contains only independent sources: – Deactivate a voltage source by replacing it with a short – Deactivate a current source by replacing it with an open If the network contains dependent sources – Apply a test source

12 Calculate the Thevenin Resistance R TH

13 If the network contains only independent sources R TH ?

14 R TH

15 Methods of Finding R TH R TH =V TH /i SC – If R L =0, the short circuit current from a to b (i.e. i ab ) should equal to i sc =V Th /R TH. – So R TH =V Th /i sc If the network contains only independent sources: – Deactivate a voltage source by replacing it with a short – Deactivate a current source by replacing it with an open If the network contains dependent sources – Apply a test source

16 Degenerated Common Emitter Amplifier (from last lecture)

17 What if we drive the base with a small signal? Vin, m=1 mV Vout, m=46 mV

18 Mesh Analysis (Last Lecture) n e =2 essential nodes b e =3 essential branches 3-(2-1)=2 equations

19 Mesh Analysis (Last Lecture) 12 Clockwise around loop 1: +V in -i 1 r π -(i 1 +i 2 )R E =0 Counter-clockwise around loop 2: i 2 =g m i 1 r π V out =-i 2 R C Loop 1: clockwise Loop 2: counter-clockwise

20 Mesh Analysis (Details)

21 Determine R TH when a Dependent Source is Present ITIT

22 Methods of Finding R TH R TH =V TH /i SC – If R L =0, the short circuit current from a to b (i.e. i ab ) should equal to i sc =V Th /R TH. – So R TH =V Th /i sc If the network contains only independent sources: – Deactivate a voltage source by replacing it with a short – Deactivate a current source by replacing it with an open If the network contains dependent sources – Apply a test source

23 Another Way to Find R TH i sc

24 R TH Calculation i SC =10V/100 KOhms=0.1 mA V TH =10V/2=5V R TH =V TH /i SC =5V/0.1 mA=50 KOhms

25 Norton Equivalent Circuit A Norton Equivalent circuit consists of – Short-Circuit Current – Norton Equivalent Resistance, which is equal to Thevenin Equivalent Resistance

26 Getting A Norton Equivalent Circuit from Thevenin Equivalent Circuit Norton Equivalent Circuit Thevenin Equivalent Circuit V TH R TH I N =V TH /R TH

27 Derivation of Norton Equivalent Circuit V TH R TH I N =V TH /R TH

28 Extra Credit Assignment Derive

29 More about the Extra Credit Assignment

30 Extra Slides on Thevenin

31 Determine v ab Show that V TH = v ab

32 Determine i SC and R TH

33 Example 4.10 Determine the Thevenin Equivalent Voltage

34 Example Determine the short circuit current 2.Determine R TH

35 Slides on Source Transformation

36 R TH

37 Application Determine whether the 6V source is absorbing or delivering the power.

38 Step-by-step simplification

39 Redundant Resistor (1) Prove that the left circuit and the right circuit are equivalent for any load resistor.

40 Redundant Resistor (2) Prove that the left circuit and the right circuit are equivalent for any load resistor.

41 Example 4.9

42 Simplified Circuit


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