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RC Band-Stop Filter Circuit Voltage out calculation

Discussion in 'Electronics Homework Help' started by Sam2002tii, Mar 16, 2014.

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  1. Sam2002tii

    Sam2002tii

    4
    0
    Mar 16, 2014
    see attached pdf schematic

    Trying to calculate V out at notch frequency of 795.77Hz

    How do I combine the values of XC and R to find the total Zt of the circuit? Once I have the total Zt how do I find the voltage out across the Load resistor at notch frequency?

    I understand using phasor addition to combine the values of XC and R, but I'm not really sure how to do this with this series-parallel band stop filter circuit.

    Thanks, Sam
     

    Attached Files:

  2. Harald Kapp

    Harald Kapp Moderator Moderator

    11,283
    2,583
    Nov 17, 2011
    Hello to the forum.

    First we have to ensure a common understandin g of the circuit and the question.

    Where is Vout? It's the first step in finding an answer because the voltages across different elements in the circuit will behave differently with frequency. So knowing which voltage is Vout is essential.

    You surely can't mean the total Z of the full circuit , because as this question implies
    one of the resistors is the load. It very probably is R4, but you have to be specific.

    Assuming, from the above, that Rload=R4 and Vout = V(R4), redraw the diagram slightly by moving R4 out to the right and re-label it Rload. Also mark Vout across Rload. You will now have a circuit with
    - an input voltage to the left
    - a frequency dependent impedance Z=f(R1, R2, R3, C1, C2, C3, frq), where frq=frequency and
    - an output voltage Vout across a load resistor to the right

    You now use Kirchhoff's laws, Thevenin theorem and what else you know about circuit theory to find the impedance Z=f(R1, R2, R3, C1, C2, C3, frq). I recommend you do this the hard way manually on a sheet of paper, although if you're lazy Google will give you the answers with a few mouse clicks.

    The impedance Z and the load Rload form a frequency dependent voltage divider. By applying the rules for a voltage divider to this setup you arrive at an equation for Vout=f(frq). Insert the values for all Rs, Cs and the notch frequency and you have the solution.
    By the way: it is not uncommon to express the result in decibles. You know how to compute them from teh voltage, don't you?
     
  3. Laplace

    Laplace

    1,252
    184
    Apr 4, 2010
    What you have there is an RC Twin-T Notch Filter, as shown in the attached image. In theory, at the notch frequency the level of attenuation provided by the twin-T notch filter is infinite. It operates by phase shifting the signals in the different legs and adding them at the output. At the notch frequency, the signals passing through each leg are 180 degrees out of phase and cancel out, providing a complete null of the signal. However in practice close tolerance components are required to achieve a good null.

    Since your circuit diagram shows 5% resistor tolerance, are you expected to calculate the actual notch attenuation at maximum tolerance deviation for an unbalanced condition? If that is the case then I would recommend starting with the node equations (3 of them) to find the transfer function (Vout/Vin) and calculate the performance for the unbalanced phase from that.
     

    Attached Files:

  4. Sam2002tii

    Sam2002tii

    4
    0
    Mar 16, 2014
    Thanks for your help.

    Yes R4 is the load resistor.

    I redrew the picture like you recommend, but I still can't figure out the right values. I'm struggling with the proper way to combine the Xc and R values in series parallel.

    Is R3 in parallel with C3? Can you simply combine these two values as if they were parallel? Same with C1 and R2. Can you combine those values in parallel and then combine them with the two main circuit branches in parallel?

    Also what do you mean about a google search? Are there circuit calculators that would give me my answer? I'm more concerned about how to do this than just getting the correct answer, If I could find the correct answer, I would be able to check my work.

    Thanks again.
     
  5. Sam2002tii

    Sam2002tii

    4
    0
    Mar 16, 2014
    @Laplace

    Thanks for the input


    The 5% doesn't matter. All I need to find is the voltage out at R4 (the load resistor) based on the notch frequency of 795.77 Hz

    I'm struggling with figuring out how to find/add up the voltage drops to find the output voltage at R4. I understand that this is basically a voltage divider based on frequency, but I don't understand how to combine the Xc values and R values to break down the voltages across each component
     
  6. Harald Kapp

    Harald Kapp Moderator Moderator

    11,283
    2,583
    Nov 17, 2011
    Read this. It explains (in an admittedly short way) how the filter can be computed.
     
  7. Laplace

    Laplace

    1,252
    184
    Apr 4, 2010
    There are websites that provide analysis services, such as http://sim.okawa-denshi.jp/en/TwinTCRtool.php but this problem includes a load resistor which complicates the calculation. I don't believe this is a voltage divider problem as it seems to need a full nodal analysis. Have included an attachment beginning with the node equations necessary for this analysis, and have shown the Bode plot for a 0.0002 radian bandwidth around the filter notch to illustrate just how narrow the notch is at the center. I don't believe the graph showing a maximum attenuation of 330dB is really all that accurate since the answer is so dependent on exact component values, an numerical round-off errors in the calculator prevent obtaining a mathematically pure result. Nevertheless, it shows the filter behavior you need to overcome in order to get the correct answer.
     

    Attached Files:

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