5. Circuit Theorems + Conversions

• Voltage Source


  Principal source of energy in electronic applications – ideally provides a constant voltage to a load even when the load resistance varies

  
• Practical voltage source


  • Internal resistance RS
  • Open Circuit Voltage Vs
  • Rule RL > 10RS

  
• Current Source


  Provides a constant current to a load even when resistance of the load varies
• Practical Current Source


  • Ideal Current Source
  • Current Divider
  • Rs >> RL
  • for ideal Rs > 10 x RL
  • Load current when RL = 100Ω, 1kΩ, 10kΩ
• Converting a Current Source into a Voltage Source

  1. VS=ISRs

  2. Remains same

  3. VS=ISRS =(10mA)(1kΩ)=10v

  4. RS=1kΩ

  
• Superposition Theorem


  Determine currents and voltages in circuits that have multiple sources by taking one source at a time

  
• Steps for Superposition Theorem

  1. Take each voltage (or current) source at a time – replace each of the other voltage (or current) sources with either a short for a voltage source or an open circuit for a current source.

  2. Determine the particular current or voltage that is required as if there was only one source in the circuit.

  3. Take the next source in the circuit and repeat steps 1 and 2.

  4. To find the actual current or voltage, add or subtract the currents or voltages due to each individual source.

  
• Demonstration of superposition mode

  • Current in R2?
  • Alternative Way:

  
• Thévenin's Theorem


  Simplifies circuits to standard equivalent forms – simplifies the analysis of complex circuits
• Thévenin's equivalent voltage (VTH) and equivalent resistance (RTH)


  • VTH is defined as the open circuit voltage between two points in the circuit
  • RTH is the total resistance appearing between two terminals in a given circuit with all the sources replaced by their internal resistances.

  
• Thévenizing a portion of a circuit

  • View of a Circuit from a particular resistor e.g. R3

  
• Thévenizing a bridge circuit


  • VL? RL?
• Summary of Thévenin's Theorem

  1. Remove any load between the terminals between which you want to find the Thévenin equivalent circuit.

  2. Determine the voltage VTH across open terminals.

  3. Determine the resistance RTH between the two terminals with all the voltage sources shorted and the current sources open circuit.

  4. Connect VTH and RTH in series to produce the Thévenin equivalent for the original circuit.

  5. Place the load resistor (step 1) across the terminals of the Thévenin equivalent circuit.

  
• Determining VTH and RTH by measurement

  • RTh
  • RL
  • VTh
• Norton's Theorem


  Reduce complex circuits to simpler equivalent forms
• Norton's Equivalent Current (IN)


  • IN is defined as the short circuit current between two points in a circuit

  
• Determining IN


  1. Total current

  2. Current divider
• Norton's Equivalent Resistance (RN)


  • RN is the total resistance appearing between two terminals in a given circuit with all sources replaced by their internal resistances.

  
• Summary of Norton's Theorem

  1. Short the terminals between which you want to find the Norton equivalent circuit.

  2. Determine the current (IN) through the shorted terminals.

  3. Determine the resistance (RN) between two terminals (opened) with all the voltages shorted and all the current sources opened (RN = RTH).

  4. Connect IN and RN in parallel to produce the complete Norton equivalent for the original circuit.

  
• Maximum Power Transfer Theorem

  Maximum power is transferred to the load when the load resistance is equal to the source resistance of the circuit
• Ohm's Law


  • I=V/R, P=I2R
  • P=I2RL
• Converting a Voltage Source into a Current Source

  1. Terminal equivalency: For the same load resistance the same load voltage and the same load current are produced by both sources.

  2. IS = VS/RS

  3. Same for both sources