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ECE 3710 E: Circuits and Electronics

ECE 3710 E: Circuits and Electronics. Jeff Dugger. Lecture 4: 08/31/00. +. I. Vs. -. V. Vs. Voltage Sources. Provide potential to generate current. Ideal Voltage Source. Current determined by Circuit. Provides Voltage Independent of Current. I. Is. Is. V. Current Sources.

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ECE 3710 E: Circuits and Electronics

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  1. ECE 3710 E: Circuits and Electronics Jeff Dugger Lecture 4: 08/31/00

  2. + I Vs - V Vs Voltage Sources Provide potential to generate current Ideal Voltage Source Current determined by Circuit Provides Voltage Independent of Current

  3. I Is Is V Current Sources Ideal Current Source Provides Current Independent of Voltage Voltage is determined by the Circuit

  4. 1 1 + R R V I = - Units: Ohms ( ) = Volts / Amp (V/A) Ohm’s Law and Resistance I V = I R I R V OR V

  5. 1 + R - Ohm’s Law and Conductance I V = I R G I V = G OR V V I = G Units: Siemens ( S ) = Amps / Volt (A/V)

  6. Apply KVL: -Vs + V1 + V2 + V3 = 0 V1 Vs = V1 + V2 + V3 Apply Ohm’s Law: I V2 Vs = R1 I + R2 I + R3 I = (R1 + R2 + R3) I Define Equivalent Resistance: Req = R1 + R2 + R3 V3 Vs = Req I Series Resistance R1 Vs R2 R3

  7. Apply Ohm’s Law: V2 = R2 I Use Equivalent Resistance to find I: Substitute: I = Vs R2 1 V2 = Vs R1 + R2 R1 + R2 Voltage Divider V1 R1 Vs I V2 R2

  8. Apply KCL: Is = I1 + I2 + I3 Apply Ohm’s Law: Is = G1 V + G2 V + G3 V G1 = = (G1 + G2 + G3 ) V G2 = I1 I2 I3 V G3 = Define Equivalent Conductance: 1 1 1 Geq = G1 + G2 + G3 R2 R3 R1 Is = Geq V Parallel Resistance R1 R2 R3 Is

  9. 1 1 1 1 R3 R2 R1 Geq 1 Req = = 1 / R1 + 1 / R2 + 1 / R3 Parallel Resistance Apply KCL: Is = I1 + I2 + I3 G1 = G2 = R1 R2 R3 I1 I2 I3 Is V G3 = Or, Define Equivalent Resistance: V = Req Is

  10. Apply Ohm’s Law: I2 = G2 V Use Equivalent Conductance to find V: V = Is Substitute: G2 1 I2 = Is G1 + G2 G1 + G2 Current Divider R1 R2 I1 I2 Is V

  11. V = Is R1 1 I2 = Is R1 + R2 G1 + G2 Current Divider Apply Ohm’s Law: I2 = G2 V Use Equivalent Conductance to find V: R1 R2 I1 I2 Is V Substitute: Or, in terms or Resistance:

  12. Series-Parallel Circuit V1 R1 I1 Vs V3 R2 I2 R3 I3

  13. Series-Parallel Circuit I1 Vs V3 R2 I2 R3 I3 R1 V1

  14. Circuit Analysis Example R4 R2 R5 I V Vs I2 R3 R1

  15. Circuit Analysis Example R4 R5 I V Vs I2 R3 Ra Series Combination: Ra = R1 + R2

  16. Circuit Analysis Example Rb I V Vs I2 R3 Ra Parallel Combination: Rb = R4 || R5

  17. Circuit Analysis Example Rb I Vs Ra R3 V I2

  18. Gb 1 Is V = Vs + Ga + Gb Ga + Gb Circuit Analysis Example Rb KCL at this node I Vs Ra R3 V Is Is = Ga V + Gb(V - Vs) = (Ga + Gb) V - Gb Vs

  19. Ra Ra + Rb V = Vs + Ra || Rb Is Circuit Analysis Example Rb KCL at this node I Vs Ra R3 V Is Is = Ga V + Gb(V - Vs) = (Ga + Gb) V - Gb Vs

  20. R = I Any voltage No current V R = 0 I Any current No voltage V Open and Short Circuits “Open Circuit” R very large “Short Circuit” R very small

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