Short/Open Circuit time constant method: b1

In summary, the short circuit time constant method for determining the 3dB point of a high pass filter states that b1 is equal to the sum of the short circuit time constant seen by each individual capacitor with all other capacitors replaced by a short circuit. This can also be represented as the sum of the poles of the filter. While some may question the validity of this statement, it can be proven by considering the fact that with all other capacitors short circuited, the resulting b1 will be equal to the sum of the time constants of each individual capacitor. This can be further demonstrated with a simple example of a high pass filter consisting of two capacitors and resistors.
  • #1
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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  • #2
. 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.
 

Related to Short/Open Circuit time constant method: b1

1. What is the Short/Open Circuit Time Constant Method?

The Short/Open Circuit Time Constant Method, also known as the b1 method, is a technique used to determine the time constant of a circuit. This method involves measuring the voltage across a circuit when it is short-circuited and when it is open-circuited, and then using those values to calculate the time constant.

2. How is the time constant calculated using this method?

The time constant is calculated by taking the difference between the voltage measured when the circuit is open and the voltage measured when the circuit is shorted, and then dividing that difference by the voltage when the circuit is open. This value is then multiplied by the resistance of the circuit.

3. What is the purpose of using the Short/Open Circuit Time Constant Method?

This method is often used in circuit analysis and design to determine the time constant of a circuit, which is a measure of how quickly a circuit can respond to changes in voltage or current. It can also be used to analyze the behavior of an electronic circuit and to determine the stability of a system.

4. Are there any limitations to using this method?

One limitation of the Short/Open Circuit Time Constant Method is that it assumes the circuit has a single, dominant time constant. This may not always be the case, and in more complex circuits, other methods may be needed to accurately determine the time constant.

5. Can this method be used for all types of circuits?

The Short/Open Circuit Time Constant Method can be used for most types of circuits, including RC, RL, and RLC circuits. However, it may not be suitable for circuits with nonlinear elements or circuits with multiple time constants. In these cases, other methods may need to be used to determine the time constant.

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