Short/Open Circuit time constant method: b1

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SUMMARY

The discussion centers on the short circuit time constant method for determining the 3dB point of a high pass filter, specifically the relationship between the sum of poles and the short circuit time constant seen by individual capacitors. The formula b1 is defined as the sum of the short circuit time constants for each capacitor when all other capacitors are replaced by short circuits. The participants seek clarity on how this relationship holds true, particularly in the context of two capacitors, C1 and C2, with respective resistances R1 and R2.

PREREQUISITES
  • Understanding of high pass filter design
  • Familiarity with capacitor and resistor circuit behavior
  • Knowledge of time constant calculations in electrical circuits
  • Basic grasp of pole-zero analysis in filter design
NEXT STEPS
  • Study the derivation of the short circuit time constant method in filter design
  • Learn about pole-zero placement and its impact on filter performance
  • Explore practical examples of high pass filter calculations
  • Investigate the implications of capacitor configurations on circuit behavior
USEFUL FOR

Electrical engineering students, circuit designers, and anyone involved in filter design and analysis will benefit from this discussion.

kougou
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Homework Statement



The short circuit time constant method for determining 3dB point for high pass filter says

b1= the sum of short circuit time constant seen by each individual capacitor with the all other capacitor replaced by short circuit.

b1 is also = the sum of pole1, pole2...


I am not very convince by this statement. How should I see that
[the sum of poles] = b1 = [the sum of short circuit time constant seen by each capacitor] ?

Thank you
 
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. Homework EquationsThe equations are given in the statement. The Attempt at a SolutionI am not sure how to conceptually prove this statement. I have read some articles and it says that it is due to the fact that all other capacitor are short circuited, hence resulting in b1 = [the sum of short circuit time constant seen by each capacitor]. However, I am not sure how to interpret this conceptually. For example, if the high pass filter consists of two capacitors, C1 and C2 with resistance R1 and R2 respectively, then the sum of the poles [C1/(R1 + R2)] + [C2/(R1 + R2)] = b1 [C1/R1 + C2/R2] ? I am not sure how to explain this. Any help would be appreciated. Thank you.
 

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