1. How to Teach the Analysis of Electrical Circuits at Technical Universities Dalibor Biolek University of Defence Brno and Brno University of Technology Czech Republic

2. Prerequisities of teaching the analysis Heuristic versus algorithmic methods The very first things for the very beginners The truly basic circuits Networks theorems,.. Special techniques for OpAmp analysis Special techniques for OTA analysis Solving more complicated circuits on PC Conclusions Lecture Outline Cultivating the "Engineering touch" inside student's mind

3. Basics of EE “The very first things for the very beginners" Network theorems Prerequisities of teaching the analysis Understanding the analyzed circuit Understanding before analysis Understanding during analysis Understanding after analysis

4. Heuristic methods of analysis Heuristic versus algorithmic methods Teacher: You need only the K.L. I and II and  's law plus basic circuit theorems. Analyze the circuit as you want. No method is prescribed! Student: I am confused. It is really more complicated than if you prescribe me a concrete method. Teacher: That's life. Nobody will give you directions how to solve concrete problems..

5. Algorithmic methods of analysis Heuristic versus algorithmic methods Teacher: Here you have an algorithm. It enables the analysis of various circuits via unified way. Student: Great! Now I can correctly solve circuits which I never understood! Teacher: You study them not as your tool but as a tool of SPICE-like programs.

6. Summary Before you teach the analysis: proper practicing of "very first things for very beginners" + truly basic circuits (voltage and current dividers) + network theorems First heuristic methods, then algorithmic First linear resistive circuits, then the other Utilize the knowledge about the circuit for its proper analysis, and the analysis for better understanding of circuit behavior

7. The very first things for the very beginners What is the NODE What is serial and parallel connection Do you really understand the Ohm's Law? Orientation of voltages and currents Understanding the Kirchhoff's Laws Cultivating the “Engineering Touch" inside student's mind, i.e. knowledge that electrical circuit operates in such a way that its behavior at any time instance cannot be in contradiction with three simple laws of EE. Two phases of cultivating the “Engineering Touch": 1] Really deep understanding of  's Law and Kirchhoff's Laws plus basic network theorems and methods. 2] Solving many examples, how to use the knowledge from item 1 for the solution of concrete circuit by creative, "detective" procedures.

8. The very first things for the very beginners What is the NODE

9. The very first things for the very beginners What is serial and parallel connection

10. The very first things for the very beginners Do you really understand the Ohm's Law? 1V 1k  I=1V/1k 

11. The very first things for the very beginners Orientation of voltages and currents V I V I VV I I

12. The very first things for the very beginners Understanding the Kirchhoff's Laws I x =? 342  A 10.29mA 0 0 I x = 10.29mA-342  A=9.948mA K.L. I

13. The very first things for the very beginners Understanding the Kirchhoff's Laws K.L. II 5V 3V V x =? 5V 3V V x =8V 5V 3V  0V  5V  -3V 5-(-3)=8V Method of potentials

14. The truly basic circuits Voltage divider Current divider Loaded dividers

15. Network theorems,... The superposition theorem The substitution theorem Thévenin and Norton theorems Equivalence of R-circuits Equivalence of V and I sources Wye-delta transfiguration Extra element theorem

16. OpAmp Analysis OpAmp as 5-outlet device + supply sources DC I/O behavior + important parameters Golden rules + when they are true Theory of the DWARF Prerequisities of the analysis

17. Vd 1V OpAmp Analysis Theory of the DWARF I must set V d = 0  -1V  0V 

18. OpAmp Analysis The Golden Rules The OpAmp input currents are zero When OpAmp operates in linear regime then Vd=0 else such circuit I cannot analyze so far

19. OpAmp Analysis Methods of analysis based on The Golden Rules Check the negative feedback in the circuit. If yes, then: Mark V d =0 and I input =0 directly to the circuit schematics Solve the rest of the circuit as you want…..with the utilization of K.L’s, Ohm’s L., plus creative approach..

20. OpAmp Analysis Methods of analysis based on The Golden Rules “Single-Stroke” solution Indirect solution All the circuits containing OpAmps can be from one of two groups: Sequential computing of voltages and currents of individual circuit components without side-computing, utilizing only K’s L’s +  ’s L. Sequential computing of voltages and currents cannot be executed without side-computing. Method of Potentials Wye-Delta Transfiguration Method of the Key Quantity = = Method of One Attempt and One Mistake the Extra Element Theorem

21. OpAmp Analysis “Single-Stroke” solution Negative feedback 0A 0V 0A 1] 1V 2] 1V 3] 1V 4] 1mA 5] 6] 1V 7] 2V 8] 1V 9] 1mA 10] 11] 2mA 12] 2V 13] 4V 14]

22. OpAmp Analysis Indirect solution Negative feedback 0A 0V 0A 1] 0.5V 2] 0.5V 3]3] ?

23. OpAmp Analysis Indirect solution - Method of the Key Quantity (1 Attempt+1Mistake) 0A 0V 0A 0.5V 0.5V 0.1mA 1.1V 0.11mA 1V1V 0.21mA 0.21V 0.21mA 2.1V 0.31V 0.1V 0.5V  0.31V 0.5V=(50/31)*0.31V 3.41V multiplication

24. 0A 0V 0A 0.5V 0.5V 0.1mA 1.1V 0.11mA 1V1V 0.21mA 0.21V 0.21mA 2.1V 0.31V 0.1V 3.41V OpAmp Analysis Indirect solution - Method of the Key Quantity (1 Attempt+1Mistake) 0.1613mA 1.774V 0.1774mA 1.613V 0.3387mA 0.3387V 0.3387mA 3.387V 0.5V 0.1613V 5.5V *50/31 0.5V

25. OpAmp Analysis Indirect solution - Extra Element Theorem (EET) Z i o S S K  o S i S d Z o S 0  i S 2 n Z n I n U i S 0 0  S 3 d n k d n Z Z Z Z K Z Z Z Z KK       1 1 1 1 0 or i ko k S S K,  i o S S K 0, 0  i S i S 0,o S ko S, 1 driving point impedance double injection null

26. OpAmp Analysis Indirect solution - Extra Element Theorem (EET) d n k d n Z Z Z Z K Z Z Z Z KK       1 1 1 1 0 8V

27. OpAmp Analysis Indirect solution - Extra Element Theorem (EET) d n k d n Z Z Z Z K Z Z Z Z KK       1 1 1 1 0 Z = 1k 8V K 0 = -1 K k = 0 Z n = 0 Z d = ? 1mA 1V  0V 1V 1mA 2mA 2V 3V Z d = 3k   -2V 8*(-0.25) K = -1/(1+3/1)=-0.25

28. 3V3V OpAmp Analysis Indirect solution - Extra Element Theorem (EET) d n k d n Z Z Z Z K Z Z Z Z KK       1 1 1 1 0 Z=1k K 0  0A 0V 0A 3V 3V K k =1 Z d  Z n =? 0V0V 3V 1V 2V 1mA Z n =3k  4V 3*4/3 K=1(1+1k/3k)=4/3

29. OpAmp Analysis Indirect solution - Extra Element Theorem (EET) KoKo KkKk 0 ∞

30. OTA Analysis OTA as 5 (or more) -outlet device + supply sources DC I/O behavior + important parameters Golden rules + when they are true Prerequisites of the analysis

31. OTA Analysis The Golden Rules The OTA input currents are zero When OTA operates in linear regime then I out =g m V in else such circuit I cannot analyze so far

32. OTA Analysis Methods of analysis based on The Golden Rules “Single-Stroke” solution Indirect solution Sequential computing of voltages and currents of individual circuit components without side-computing, utilizing only K’s L’s +  ’s L. Sequential computing of voltages and currents cannot be executed without side-computing. Method of Potentials Wye-Delta Transfiguration Method of the Key Quantity = = Method of One Attempt and One Mistake the Extra Element Theorem

33. OTA Analysis Indirect solution - Method of the Key Quantity (1 Attempt+1Mistake) 0.6mA 1V 0A 1mA 1V -1V 1V 0.2mA 2V 1mA 1.2mA 0.6mA *(-0.6/1.2) 0.5mA 1V 0.5V

34. Solving circuits on PC The recommended series of steps Symbolic analysis via SNAP PSpice on the level of input files PSpice on the level of CAPTURE (briefly) PSpice via Micro-Cap v.9 or higher

35. Conclusions From heuristic to algorithmic methods From resistive to RCL, passive to active, linear to nonlinear circuits From DC to other types of analyses Solving the contradiction: student needs the analysis for understanding the circuit and he needs to understand the circuit prior its analysis  well sophisticated system of education based on heuristic approach Break the established system of teaching the analysis via OrCad PSpice