ENSC2003 - Lecture 6

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ENSC2003 - Lecture 5
Ideal and Practical Sources - Slides

Practical Voltage Sources

• Review: An ideal voltage source produces fixed voltage across its terminals, irrespective of current driven → see ideal voltage sources

  • An ideal voltage source would have an internal $R_{out}$ of $0\text{ohm}$

• A practical voltage source includes an ideal voltage source $V_S$ in series with an internal resistor $R$

  

• Part of the power generated by the voltage source is consumed by the internal resistor → reduction in the voltage generated by source

  

• $V_A$ at output terminals is lower than voltage generated by source $V_S$:
  $V_A=V_S-V_R$

A small value of internal resistance $R$ and a large value of the load resistance $R_A$ are good for power transfer to load:
$V_A=\frac{R_A}{R_A+R}{V}_S$

Practical Current Sources

• Review: An ideal current source produces a fixed current, irrespective of voltage across its terminals → see ideal current sources

  • An ideal current source has infinite internal resistance ($R_{out}=\infty$)

• A practical current source includes an ideal current source $I_S$ in parallel with an internal resistor $R$

  

• Part of the power generated by ideal current source $I_S$ is consumed by the internal resistor $R$

• $I_A$ at output terminals is lower than current generated by source $I_S$:
  $I_A=I_S-I_R$

A large value of internal resistance $R$ and small value of the load resistance $R_A$ are good for power transfer to load:
$I_A=\frac{R}{R_A+R}{I}_S$

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Superposition - Slides

Superposition

• This technique applies only when your circuit system is linear
• Given $f(u)$ is an output of a system with input $u$, the system is said to be linear if:
  • $f(\alpha u)=\alpha f(u)$ -> homogeneity
  • $f(u+v)=f(u)+f(v)$ -> additivity

Capacitors and inductors are considered linear elements

• The only non-linear elements in this unit are dials and optional amplifiers
• A circuit is linear if it contains only linear elements

Steps for superposition analysis:

1. Keep only one independent source active, turn off other sources
   • Replace off voltage sources -> short circuits
   • Replace off current sources -> open circuits
2. Repeat step 1 for each independent source
3. Determine the contribution of each source on the given resistor and then sum to get the total

Read walkthrough in slides

• Lets use this circuit as an example:

  

• We need to find the value of $V_x$

  

• Example of replacing independent sources:

  

  • Here, we can now use NTD to solve for $V_{x1}$
    • In other cases, you can use whichever analysis technique is most efficient (e.g. VD, CD, NTD, Mesh)
  • Repeat for each independent source

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Source Transformation - Slides

Source Transformation

• Consider same network “A” is attached to two separate sources
  • Both sources have same source resistance $R_S$
• How can we get both sources to produce the same current and voltage into network A?

If the equation $V_S=R{i}_s$ is met → both sources are identical

• Knowing this, we can transform a voltage/current source into its alternate form in our circuit:

  

• This is useful because we can switch a resistor from being in series and parallel in order for us to combine resistors → see slides

Source transformation is key for simplifying circuits

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ENSC2003 - Lecture 7