Example Consider two lossless transmission lines with different real characteristic impedances Zo1 = R₁ and Z02= R₂ as shown in Fig. 2.11. We wish to place a capacitor in parallel with the second line to change L Z01= R1 and Figure 2.11: Lumped element matching example. the real part of the overall impedance, and then put an inductor in series to cancel the imaginary part of the impedance. The result should be such that the impedance seen by the first line equals the real value R₁, and therefore the reflected wave on the first line is eliminated. It is straightforward to show that this requires: R₁ = jwL+. We multiply both sides by 1+ jwCR2, and force the real and imaginary parts of the equation to hold separately. The result is: = R₁ R₂ L 1-w²LC = с R₂ 1+jwCR₂ R₁ (R₂ - R₁) W R₁ R2 We can see from the second of these that this circuit can work only if R₁ < R₂ (in the other case, we have to change the positions of the inductor and capacitor). Solving the first equation for L and substituting into the second to find C, we obtain: C = Z02=R₂ 1 R₂ - R₁ R₁ S (2.20)

Example Consider two lossless transmission lines with different real characteristic impedances Zo1 = R₁ and Z02= R₂ as shown in Fig. 2.11. We wish to place a capacitor in parallel with the second line to change L Z01= R1 and Figure 2.11: Lumped element matching example. the real part of the overall impedance, and then put an inductor in series to cancel the imaginary part of the impedance. The result should be such that the impedance seen by the first line equals the real value R₁, and therefore the reflected wave on the first line is eliminated. It is straightforward to show that this requires: R₁ = jwL+. We multiply both sides by 1+ jwCR2, and force the real and imaginary parts of the equation to hold separately. The result is: = R₁ R₂ L 1-w²LC = с R₂ 1+jwCR₂ R₁ (R₂ - R₁) W R₁ R2 We can see from the second of these that this circuit can work only if R₁ < R₂ (in the other case, we have to change the positions of the inductor and capacitor). Solving the first equation for L and substituting into the second to find C, we obtain: C = Z02=R₂ 1 R₂ - R₁ R₁ S (2.20)

Power System Analysis and Design (MindTap Course List)

6th Edition

ISBN:9781305632134

Author:J. Duncan Glover, Thomas Overbye, Mulukutla S. Sarma

Publisher:J. Duncan Glover, Thomas Overbye, Mulukutla S. Sarma

Chapter2: Fundamentals

Section: Chapter Questions

Problem 2.18P: Let a series RLC network be connected to a source voltage V, drawing a current I. (a) In terms of...

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