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CIRCUIT ANALYSIS

CIRCUIT ANALYSIS. KIRCHHOFF’S VOLTAGE LAW. ENGR. VIKRAM KUMAR B.E (ELECTRONICS) M.E (ELECTRONICS SYSTEM ENGG:) MUET JAMSHORO. BRANCHES AND NODES Branch: Elements connected end-to-end, nothing coming off in between (in series) OR

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CIRCUIT ANALYSIS

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  1. CIRCUIT ANALYSIS KIRCHHOFF’S VOLTAGE LAW ENGR. VIKRAM KUMAR B.E (ELECTRONICS) M.E (ELECTRONICS SYSTEM ENGG:) MUET JAMSHORO

  2. BRANCHES AND NODES • Branch: Elements connected end-to-end, nothing coming off in between (in series) OR A circuit element between two nodes

  3. Node: Place where elements are joined—entire wire • OR • Any point where 2 or more circuit elements are connected together • - Wires usually have negligible resistance • - Each node has one voltage (w.r.t. ground)

  4. Loop – a collection of branches that form a closed path returning to the same node without going through any other nodes or branches twice

  5. Example • How many nodes, branches & loops? R1 + Vo - Is + - Vs R2 R3

  6. Example • Three nodes R1 + Vo - Is + - Vs R2 R3

  7. Example • 5 Branches R1 + Vo - Is + - Vs R2 R3

  8. Example • Three Loops, if starting at node A A B R1 + Vo - Is + - Vs R2 R3 C

  9. Basic Laws of Circuits Kirchhoff’s Voltage Law:  Kirchhoff’s voltage law tells us how to handle voltages in an electric circuit. Kirchhoff’s voltage law basically states that the algebraic sum of the voltages around any closed path (electric circuit) equal zero. The secret here, as in Kirchhoff’s current law, is the word algebraic.   There are three ways we can interrupt that the algebraic sum of the voltages around a closed path equal zero. This is similar to what we encountered with Kirchhoff’s current law.

  10. Kirchoff’s Voltage Law (KVL) • The algebraic sum of voltages around each loop is zero • Beginning with one node, add voltages across each branch in the loop (if you encounter a + sign first) and subtract voltages (if you encounter a – sign first) • Σ voltage drops - Σ voltage rises = 0 • Or Σ voltage drops = Σ voltage rises

  11. Path - V 2 + Path + “rise” or “step up” (negative drop) “drop” V 1 - KIRCHOFF’S VOLTAGE LAW (KVL) • The sum of the voltage drops around any closed loop is zero. We must return to the same potential (conservation of energy). Closed loop: Path beginning and ending on the same node Our trick: to sum voltage drops on elements, look at the first sign you encounter on element when tracing path

  12. Examples of three closed paths: v2 v3 +  +  2 1 +  + +  va vb vc - 3 KVL EXAMPLE b a c Path 1: Path 2: Path 3:

  13. Basic Laws of Circuits Kirchhoff’s Voltage Law: Consideration 1: Sum of the voltage drops around a circuit equal zero. We first define a drop. We assume a circuit of the following configuration. Notice that no current has been assumed for this case, at this point. _ v2 + + + v1 v4 _ _ _ + v3

  14. Basic Laws of Circuits Kirchhoff’s Voltage Law: Consideration 1. We define a voltage drop as positive if we enter the positive terminal and leave the negative terminal. v1 _ + The drop moving from left to right above is + v1. _ v1 + The drop moving from left to right above is – v1.

  15. Basic Laws of Circuits Kirchhoff’s Voltage Law: Consider the circuit of following Figure once again. If we sum the voltage drops in the clockwise direction around the circuit starting at point “a” we write: - v1 – v2 + v4 + v3 = 0  drops in CW direction starting at “a” _ v2 + + + v1 v4 _ _ • “a” _ + v3 - v3 – v4 + v2 + v1 = 0  drops in CCW direction starting at “a”

  16. Basic Laws of Circuits Kirchhoff’s Voltage Law: Consideration 2: Sum of the voltage rises around a circuit equal zero. We first define a drop. We define a voltage rise in the following diagrams: _ v1 + The voltage rise in moving from left to right above is + v1. v1 _ + The voltage rise in moving from left to right above is - v1.

  17. Basic Laws of Circuits Kirchhoff’s Voltage Law: Consider the circuit of Figure 3.7 once again. If we sum the voltage rises in the clockwise direction around the circuit starting at point “a” we write:  + v1 + v2 - v4 – v3 = 0 rises in the CW direction starting at “a” v2 _ + + + v1 v4 _ _ • “a” _ + v3  + v3 + v4 – v2 – v1 = 0 rises in the CCW direction starting at “a”

  18. Basic Laws of Circuits Kirchhoff’s Voltage Law: Consideration 3: Sum of the voltage rises around a circuit equal the sum of the voltage drops. Again consider the circuit of following Figure in which we start at point “a” and move in the CW direction. As we cross elements 1 & 2 we use voltage rise: as we cross elements 4 & 3 we use voltage drops. This gives the equation, p v1 + v2 = v4 + v3 _ v2 + 2 + + v1 v4 1 3 _ _ 4 _ + v3

  19. Basic Laws of Circuits Kirchhoff’s Voltage Law: Comments. • We note that a positive voltage drop = a negative voltage rise. • We note that a positive voltage rise = a negative voltage drop. • We do not need to dwell on the above tongue twisting statements. • There are similarities in the way we state Kirchhoff’s voltage • and Kirchhoff’s current laws: algebraic sums … • However, one would never say that the sum of the voltages • entering a junction point in a circuit equal to zero. • Likewise, one would never say that the sum of the currents • around a closed path in an electric circuit equal zero.

  20. Example • Kirchoff’s Voltage Law around 1st Loop A I1 + I1R1 - B R1 + Vo - I2 + I2R2 - Is + - Vs R2 R3 C Assign current variables and directions Use Ohm’s law to assign voltages and polarities consistent with passive devices (current enters at the + side)

  21. Example • Kirchoff’s Voltage Law around 1st Loop A I1 + I1R1 - B R1 + Vo - I2 + I2R2 - Is + - Vs R2 R3 C Starting at node A, add the 1st voltage drop: + I1R1

  22. Example • Kirchoff’s Voltage Law around 1st Loop A I1 + I1R1 - B R1 + Vo - I2 + I2R2 - Is + - Vs R2 R3 C Add the voltage drop from B to C through R2: + I1R1 + I2R2

  23. Example • Kirchoff’s Voltage Law around 1st Loop A I1 + I1R1 - B R1 + Vo - I2 + I2R2 - Is + - Vs R2 R3 C Subtract the voltage rise from C to A through Vs: + I1R1 + I2R2 – Vs = 0 Notice that the sign of each term matches the polarity encountered 1st

  24. Kirchhoff’s Voltage Law: Further details. For the circuit of Figure there are a number of closed paths. Three have been selected for discussion. - + v2 - v5 + Path 1 - - - v1 v4 v6 + + + Path 2 v3 v7 Figure Multi-path Circuit. - + + - Path 3 - + + v8 v12 v10 + - - + v11 - - v9 +

  25. Kirchhoff’s Voltage Law: Further details. For any given circuit, there are a fixed number of closed paths that can be taken in writing Kirchhoff’s voltage law and still have linearly independent equations. We discuss this more, later. Both the starting point and the direction in which we go around a closed path in a circuit to write Kirchhoff’s voltage law are arbitrary. However, one must end the path at the same point from which one started. Conventionally, in most text, the sum of the voltage drops equal to zero is normally used in applying Kirchhoff’s voltage law.

  26. Kirchhoff’s Voltage Law: Illustration from Figure “b” Using sum of the drops = 0 • - + v2 - v5 + - - - Blue path, starting at “a” - v7 + v10 – v9 + v8 = 0 v1 v4 v6 + + + v3 v7 - + + - “a” • Red path, starting at “b” +v2 – v5 – v6 – v8 + v9 – v11 – v12 + v1 = 0 - + + v8 v12 v10 + - - Yellow path, starting at “b” + v2 – v5 – v6 – v7 + v10 – v11 - v12 + v1 = 0 + v11 - - v9 +

  27. THE END

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