Analog Filter Circuits NCEES Ref Handbook p206 - Understanding R1 & R2 in Fig.2

Click For Summary

Discussion Overview

The discussion revolves around the interpretation of resistor configurations R1 and R2 in an analog filter circuit as depicted in Fig.2 of the NCEES Reference Handbook. Participants explore the implications of these configurations on circuit analysis, particularly in relation to transfer functions and the behavior of capacitors in the circuit.

Discussion Character

  • Technical explanation
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • One participant questions how R1 and R2 can be considered parallel, suggesting they should be in series due to the capacitor acting as an open circuit in the long run.
  • Another participant argues that the terms "series" and "parallel" are not relevant for circuit analysis beyond elementary cases, proposing that R1 and R2 can be treated as parallel from the perspective of the capacitor.
  • Several participants discuss the derivation of the transfer function H(s) and express confusion over the equations used in the analysis, particularly regarding the relationships between currents i1, i2, and ic.
  • There are inquiries about the validity of certain equations and whether additional terms are needed in the circuit analysis.
  • One participant suggests that using Thevenin's theorem may clarify the relationship between R1 and R2.
  • Another participant expresses skepticism about the assertion that R1 and R2 are parallel, questioning the role of the voltage source v1 in this context.
  • There is a discussion about the implications of the critical angular frequency and whether the equivalent resistance RP will always equal the capacitor's impedance.

Areas of Agreement / Disagreement

Participants exhibit disagreement regarding the classification of R1 and R2 as parallel or series, with multiple viewpoints presented. The discussion remains unresolved as participants explore different interpretations and approaches to the circuit analysis.

Contextual Notes

Participants express uncertainty about the completeness and correctness of the equations used in their analysis, indicating potential missing assumptions or dependencies on specific definitions. The discussion includes varying levels of familiarity with circuit analysis techniques, which may affect interpretations.

xconwing
Messages
20
Reaction score
0
3nSCvlR.png

NCEES Reference Handbook p.206Hi,

My question is: In Fig.2, how can R1 and R2 be parallel? If anything, it should be in series because capacitor in the long run is an open.

Thanks ahead.
 
Last edited:
Engineering news on Phys.org
Hi and welcome.
"Series" and "parallel" are just names. They are not relevant to the analysis of circuits - except for the most elementary cases. But, if you bear in mind that a voltage source (v1) has zero impedance and if you replace it with a piece of wire, then, from the point of view of the C, they are in parallel and the equivalent resistance can be calculated with that formula.
 
Consider form of the transfer function in the s-domain for that circuit. Introducing Rp gives a shorter way to write it down and calculate.
 
sophiecentaur said:
Hi and welcome.
"Series" and "parallel" are just names. They are not relevant to the analysis of circuits - except for the most elementary cases. But, if you bear in mind that a voltage source (v1) has zero impedance and if you replace it with a piece of wire, then, from the point of view of the C, they are in parallel and the equivalent resistance can be calculated with that formula.

thanks for that answers (and others too )

how did they come to the equation H(s)?
I tried to do the circuit analysis but it didn't come out the same, will put it up here when i find a decent equation editor
 
xconwing said:
how did they come to the equation H(s)?
I tried to do the circuit analysis but it didn't come out the same, will put it up here when i find a decent equation editor
Let i1 be current through R1, ic current through C, and i2 current through R2.
For sine wave voltage input it holds:

i1 = ic+ i2
v1 = i1·R1 + ic/(jωC)
0 = i2·R2 - ic/(jωC)

From this you find (express) i2.
Then, H(s)=H(jω)=v2/v1= (i2·R2)/v1.
Finally, when you introduce Rp=R1·R2/(R1+R2), you'll get the result.
 
zoki85 said:
Let i1 be current through R1, ic current through C, and i2 current through R2.
For sine wave voltage input it holds:

eq.1 i1 = ic+ i2
eq.2 v1 = i1·R1 + ic/(jωC)
eq.3 0 = i2·R2 - ic/(jωC)

From this you find (express) i2.
eq.4 Then, H(s)=H(jω)=v2/v1= (i2·R2)/v1.
eq.5 Finally, when you introduce Rp=R1·R2/(R1+R2), you'll get the result.

Is eq.2 missing: v1 = i1·R1 + ic/(jωC) + i2·R2?
Is eq.3 suppose to be: 0 = i1·R1 - i2·R2 - ic/(jωC)?
Also, how does eq.5 implement onto eq.4?
 
Nothing is missing. 2nd eq. is for the first closed loop: v1 - R1 - C and 3rd eq. is for second closed loop: C-R2.
Do you understand this?
 
zoki85 said:
Nothing is missing. 2nd eq. is for the first closed loop: v1 - R1 - C and 3rd eq. is for second closed loop: C-R2.
Do you understand this?

Okay, I understand eq.1-3, 2&3 are from KVL. i2 should express from which eq.? Why v1 become a short?
 
Last edited:
i2 to be expressed as one of the solutions to the given system of 3 linear equations (other two solutions are i1 and ic but you don't need them). What "v1 become a short"? I don't understand you
 
  • #10
xconwing said:
Okay, I understand eq.1-3, 2&3 are from KVL. i2 should express from which eq.? Why v1 become a short?
Eqn 3 comes from saying "because C and R2 are connected in parallel, then the voltage across C equals the voltage across R2."

Eqn 1 comes from saying "the voltage across C equals V1 minus the voltage lost across R1".
 
  • #11
zoki85 said:
i2 to be expressed as one of the solutions to the given system of 3 linear equations (other two solutions are i1 and ic but you don't need them). What "v1 become a short"? I don't understand you
That is how they get the RP to be R1 and R2 parallel right?

As for finding H(s), the path using system of equation is kind of tedious. My i2 came out to be pretty ugly, maybe the algebra is wrong somewhere or it just simply ugly. I try to use the voltage divider approach, where Rx is C and R2 parrallel.

vf7y5Dl.png
 
Last edited:
  • #12
H(s) tells you Vout/Vin. I'm wondering why you are needing to find I2 ?

For a complex impedance, you should be using Zx not Rx. Rx should be used only where the element is known to be a pure resistance.
 
Last edited:
  • #13
NascentOxygen said:
H(s) tells you Vout/Vin. I'm wondering why you are needing to find I2 ?

For a complex impedance, you should be using Zx not Rx. Rx should be used only where the element is known to be a pure resistance.

I was trying out the method suggested by zokia85 in post #5
 
  • #14
xconwing said:
That is how they get the RP to be R1 and R2 parallel right?

As for finding H(s), the path using system of equation is kind of tedious. My i2 came out to be pretty ugly, maybe the algebra is wrong somewhere or it just simply ugly. I try to use the voltage divider approach, where Rx is C and R2 parrallel.

vf7y5Dl.png
Oho, looks like you know how to use a voltage divider principle in complex impedance domain:)
Then, it is obvious you obtained what you wanted:

cdot%20\frac{R_{1}R_{2}}{R_{1}+R_{2}}}%3D\frac{R_{2}}{R_{1}%281+sCR_{2}%29+R_{2}}.gif


I don't know what the heck you were doing with the system of equations, but i2 turns up quickly and quite nicely in a form:

gif.latex?i_{2}%3D\frac{v_{1}}{R_{1}+R_{2}+j\omega%20\cdot%20CR_{1}R_{2}}.gif


NascentOxygen said:
H(s) tells you Vout/Vin. I'm wondering why you are needing to find I2 ?
He doesn't need to, but when someone asks questions wether R1 and R2 are in series or parallel it is more pedagogical to show approach with fundamentals of circuit analysis.
 
  • #15
Okay, so far the algebra checked off their final equation against my. Though I still don't understand how they see R1 and R2 as being parallel, the v1 is in the way. If you say, turn v1 into a short, why?
 
  • #16
xconwing said:
Okay, so far the algebra checked off their final equation against my. Though I still don't understand how they see R1 and R2 as being parallel, the v1 is in the way. If you say, turn v1 into a short, why?
Not 100% sure, but my guess is they prefer approach to the problem by the method of Thevenin's theorem
In that case the filter circuit can be replaced by equivalent Thevenin's circuit with:
gif.latex?V_{th}%3D\frac{R_{1}}{R_{1}+R_{2}}\cdot%20v_{1}.gif

gif.latex?Z_{th}%3D\frac{R_{1}R_{2}}{R_{1}+R_{2}}%3D%20R_{p}.gif

in order to find current and voltage of capacitor's impedance Xc :
gif.latex?i_{c}%3D\frac{V_{th}}{Z_{th}+X_{c}}.gif

gif.gif
 
  • #17
Ugh, I see. They want to be fancy schmancy. :rolleyes:

Okay, one last thing. That omega, the way they set it up seem like RP will ALWAYs be equal to capacitor impedance. Is that the case?
 
Last edited:
  • #18
xconwing said:
That omega, the way they set it up seem like RP will ALWAYs be equal to capacitor impedance. Is that the case?
Are you drunk?
 
  • #19
No, I'm sober, are you?
Av6Bxz1.png
 
  • #20
ωc is the critical angular frequency. ω can vary between 0 and ∞ rad/s . Just have a look at Fig.1 . And stop trolling.
 
  • #21
Nah brah, I'm extremely lazy so "trolling" is not something I do. However, I am curious about every detail of any particular concept. With your word and mine, shall we call this whole thing "curious" "trolling"

Thanks for the inquired infos
-X
 

Similar threads

Need help in understanding these circuits
  • · Replies 2 ·
Replies
2
Views
2K
Help with my math in this 2nd order audio filter circuit
  • · Replies 6 ·
Replies
6
Views
2K
How to calculate R1 and R2 in this RC circuit
  • · Replies 3 ·
Replies
3
Views
3K
Finding Thevenin Equiv for Circuit w/ R1, R2, R3, R4, R5
  • · Replies 7 ·
Replies
7
Views
4K
How to find power dissipation of a resistor in this circuit?
  • · Replies 21 ·
Replies
21
Views
8K
Optimization Problem with an RC BP filter
  • · Replies 98 ·
4
Replies
98
Views
7K
Bootstrapping Amplifiers, and Signal Bypasses
  • · Replies 4 ·
Replies
4
Views
2K
Series motors, switched to parallel
  • · Replies 15 ·
Replies
15
Views
2K
Calculating R1 and R2 for Opto-Triac Output Circuit
  • · Replies 34 ·
2
Replies
34
Views
6K
Electrical Circuits - Parallel vs. Series
  • · Replies 14 ·
Replies
14
Views
2K