ENSC2003 - Lecture 15

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ENSC2003 - Lecture 14
Power in the AC Steady-State - Slides cont.

Max Power Transfer Theorem

Consider a load connected to a voltage source with internal resistance:

• Condition: $R_L=R_{th}$
• Conclusion: $P_{max,L}=\frac{V_{th}^2}{4R_{th}}$
  i.e. when $R_L=R_{th}$, the load is delivered the maximum power possible

Impedance Matching

Consider a voltage source with internal $\overline{Z_S}$ supplying power to a load $\overline{Z_L}$:

• If $\overline{Z_L}=\overline{Z_{th}}$ condition is not met, power delivered is lower than optimal

• We can improve power transfer by inserting a matching network
  • Inserted between source and load
  • Composes of purely reactive impedance

• Here, we have inserted unknown components $X_1$ and $X_2$ to be our matching network
  • $\overline{Z_{in}}=j{X}_1+j{X}_2||\overline{Z_L}$
• We can solve for $X_1$ and $X_2$ by solving for $\overline{Z_{in}}=\overline{Z_{th}}$
  • The real and imaginary component of solution gives two eqns
  • Thus, we can solve for both values of impedance
• Then knowing impedance, we can determine if each component should be an inductor or capacitor

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ENSC2003 - Lecture 16