Band Pass Filter: Calculate C1=C2 for 17.3 kHz

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Discussion Overview

The discussion revolves around calculating the values of capacitors C1 and C2 for a band pass filter designed to achieve a center frequency of 17.3 kHz. Participants explore the relevant equations and circuit configurations, particularly focusing on the role of resistors and the application of Kirchhoff's Current Law (KCL) in analyzing the circuit.

Discussion Character

  • Homework-related
  • Technical explanation
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • One participant presents an equation for the center frequency and calculates a capacitor value, questioning the relevance of R2 in the circuit.
  • Another participant expresses confusion about the equations involving R2 and seeks clarification on writing KCL equations for the opamp circuit.
  • Further replies discuss the mix of KCL and other principles in the equations, suggesting a method to identify unknowns and formulate equations.
  • Participants share KCL equations they derived for the circuit, with one participant indicating a potential sign error in their equations.
  • There is a discussion about the virtual ground concept in opamp circuits, with participants confirming its implications for circuit analysis.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the correctness of the equations or the impact of R2 on the circuit's function. There are multiple viewpoints regarding the application of KCL and the interpretation of circuit components.

Contextual Notes

Some participants express uncertainty about the application of KCL and the role of specific circuit elements, indicating a need for further clarification on the equations and their derivation.

sticky430
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Homework Statement



29ntq42.jpg


Given: K=17, R1=R2=6,247 Ohm

Calculate the value of C1=C2=C to set the center frequency of the filter to 17.3 kHz.

Homework Equations



w0 = 1/[C*sqr(Rth*KR2)] from lecture notes
R1=Rth

The Attempt at a Solution



w0 = 1/[C*sqr(Rth*K*R2)]
C= 1/[w0*sqr(Rth*K*R2)]
C= 1/[2*pi*17.3k*sqr(6247*17*6247)]
C= 3.57e-10 F

The equation above is from a similar circuit that doesn't have R2. I wasn't sure if it still would work. Looking at the circuit above. It seems like R2 does not impact the function of the circuit.

Any help would be appreciated.

Thanks.
 
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sticky430 said:

Homework Statement



29ntq42.jpg


Given: K=17, R1=R2=6,247 Ohm

Calculate the value of C1=C2=C to set the center frequency of the filter to 17.3 kHz.


Homework Equations



w0 = 1/[C*sqr(Rth*KR2)] from lecture notes
R1=Rth


The Attempt at a Solution



w0 = 1/[C*sqr(Rth*K*R2)]
C= 1/[w0*sqr(Rth*K*R2)]
C= 1/[2*pi*17.3k*sqr(6247*17*6247)]
C= 3.57e-10 F

The equation above is from a similar circuit that doesn't have R2. I wasn't sure if it still would work. Looking at the circuit above. It seems like R2 does not impact the function of the circuit.

Any help would be appreciated.

Thanks.

If the equations are for a circuit without an R2, then why is there an R2 in the equations? Maybe I'm being dense.

Do you understand how to write the KCL equations for an opamp circuit with feedback? That's how you can solve for the transver function of this circuit.

EDIT -- Welcome to the PF, BTW!
 
The equation uses K*R2 which is equal to R2 in the similar circuit.

No, I don't know how to write KCL equation for opamp circuit with feedback. It's been a very long time since I used it. Can you help me get started?
 
sticky430 said:
The equation uses K*R2 which is equal to R2 in the similar circuit.

No, I don't know how to write KCL equation for opamp circuit with feedback. It's been a very long time since I used it. Can you help me get started?

In this case, the equations are a mix of KCL and something else. The theme is to figure out how many unknowns you are dealing with, and to see that you can write the same number of unique equations to help you to solve for those unknowns.

So in this circuit, Vout is an unknown, and (call it) V1 is an unknown. Call the voltage at the intersection of R1 and C2 "V1". You might initially be inclined to also call the V- input to the opamp a variable, but it's not. Why not?

So write 2 equations for these two unknown voltages. The equation for V1 is just a KCL equation, but the equation for Vout is a slight variation. Still very solvable. Does that help?
 
berkeman said:
In this case, the equations are a mix of KCL and something else. The theme is to figure out how many unknowns you are dealing with, and to see that you can write the same number of unique equations to help you to solve for those unknowns.

So in this circuit, Vout is an unknown, and (call it) V1 is an unknown. Call the voltage at the intersection of R1 and C2 "V1". You might initially be inclined to also call the V- input to the opamp a variable, but it's not. Why not?

So write 2 equations for these two unknown voltages. The equation for V1 is just a KCL equation, but the equation for Vout is a slight variation. Still very solvable. Does that help?

V- does not need to be called a variable because the V+ is connected to ground thus V- is a virtual ground too. Right?

The KCL equation I got for node V1 is:
KCL1: (V1-Vin)/R1 = (Vout - V1)/(1/sC) + V1/(R2 + (1/sC)).

For Vout node i got:
KCL2: Vout/KR2 + (Vout - V1)/(1/sC) = 0

Are those equation correct? So, now I use KCL2 and solve for Vout? Then substitute it into KCL1 and solve for what?
 
sticky430 said:
V- does not need to be called a variable because the V+ is connected to ground thus V- is a virtual ground too. Right?

The KCL equation I got for node V1 is:
KCL1: (V1-Vin)/R1 = (Vout - V1)/(1/sC) + V1/(R2 + (1/sC)).

For Vout node i got:
KCL2: Vout/KR2 + (Vout - V1)/(1/sC) = 0

Are those equation correct? So, now I use KCL2 and solve for Vout? Then substitute it into KCL1 and solve for what?

Correct about V- = 0V.

You have a sign error in your first equation. Write KCL equations as the sum of all currents out of a node = 0.
 

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