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Math Help - RC Network

  1. #1
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    RC Network

    In a 3-terminal linear RC network, sinusoidal input, what is the maximum
    gain (out/inp) possible?
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  2. #2
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    Quote Originally Posted by bobbyk
    In a 3-terminal linear RC network, sinusoidal input, what is the maximum
    gain (out/inp) possible?
    Now my memory of circuit analysis is a bit hazy - but this is a passive
    network so at best energy must be conserved, and usualy lost, so the
    maximum gain should be 1.

    RonL
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  3. #3
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    RC network

    I want the maximum voltage gain, so power has nothing to do with it.
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  4. #4
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    Quote Originally Posted by bobbyk
    I want the maximum voltage gain, so power has nothing to do with it.
    Unity power gain is the same thing as unity voltage gain as both the
    input and output in this case are sinusoids.

    Maybe I'm just getting confused because that is the way the
    systems I work on in my real life work

    RonL
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  5. #5
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    RC Network

    As Wolfgang Pauli used to say when encountering an absurd statement, "That's not even wrong!"

    No offence, but your knowledge of electrical networks does seem to be somewhat limited.

    I love you anyway.
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  6. #6
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    Quote Originally Posted by bobbyk
    As Wolfgang Pauli used to say when encountering an absurd statement, "That's not even wrong!"

    No offence, but your knowledge of electrical networks does seem to be somewhat limited.

    I love you anyway.
    The caveat in the my last post was supposed to serve as a warning that
    I had my doubts about the last thing that I had written. If you were misled
    I must apologise, sorry.

    RonL
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  7. #7
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    In response to your original question. If you do steady state sinusoidal analysis on the RC circuit you will find that that complex gain (assuming that vout is measured across the capacitor) takes the form:

    vout = vin / (1 + RCwj)

    It can be seen that the maximum gain you can get occurs when the angular frequency w is 0 (DC) and the gain is 1.

    If you look at the voltage across the resistor the form is:

    vout = vin / (1 - j/RCw)

    This function has gain 1 when w is infinite.

    Hope that answered your question. You can never get more than a gain of 1 for any simple passive RC or RL circuit.
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  8. #8
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    I guess I didn't make myself clear! I was asking about a general 3-terminal RC network having any number of resistors and capacitors connected in any
    manner whatsoever - not about your trivial example.
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  9. #9
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    My apologies!

    In a passive network of ONLY capacitors and resistors or ONLY inductors and resistors, the gain will never be greater than unity... the maximum gain really depends on how the components are connected.

    To work out the maximum gain, you derive a function for the gain in terms of w. Get the derivative of that function and set it to zero to get the value of w resulting in the maximum gain and then substitute that value into the original function to get your gain. This gets mighty complicated to slove for even a small network but thats what "mathematica" type tools are for.
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  10. #10
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    How do you know the gain can never be greater than unity? Do you have
    a proof? If so, I'd like to see it. Please don't try to appeal to the conservation of energy as Captain Black did - it has no bearing on the problem!
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  11. #11
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    Unfortunately, I can't give you a "simple" proof of why it doesn't exceed unity. I will suggest that if you do derive the function for the gain and it's derivative (as I suggested in my last post) that you'll never get a gain greater than 1.

    The only time you can get voltage-gain in a passive network is when there are both capacitors and inductors present. That's just a known fact.
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  12. #12
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    Smile

    I'm not asking for a "simple" proof - even a complicated proof will do! You say it's a known fact. Known by whom? Can you give me references to that fact?

    Later:

    I don't need a proof, because it's NOT true! (But I'd SURE lile to see one!)

    I want to thank you for teaching me how to analyze networks. I tried your method on some various ones, until I came across one with an open-circuit voltage gain of 1.078! It had 2 resistors and 2 capacitors. Now this is only
    slightly greater than 1, but it does show that all your previous comments
    are wrong!

    Even later:

    Now I've found a 2-resistor 2-capacitor network with a maximum gain of 1.15!
    Last edited by bobbyk; July 16th 2006 at 05:04 PM. Reason: New information
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  13. #13
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    Did you see my post about the maximum gain of an RC network?
    Well, how do you respond?
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  14. #14
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    Quote Originally Posted by bobbyk
    Later:

    I don't need a proof, because it's NOT true! (But I'd SURE lile to see one!)

    I want to thank you for teaching me how to analyze networks. I tried your method on some various ones, until I came across one with an open-circuit voltage gain of 1.078! It had 2 resistors and 2 capacitors. Now this is only
    slightly greater than 1, but it does show that all your previous comments
    are wrong!

    Even later:

    Now I've found a 2-resistor 2-capacitor network with a maximum gain of 1.15!
    Can you post a diagram of the circuit?

    Thanks

    RonL
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  15. #15
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    RC network

    Sure. I'd love to, but I can't seem to.
    5spice is a beautiful program whereby you can define networks and inputs and it will solve for the various outputs.

    Well, I can't upload my 5spice files. I don't know why.
    I have 5spice files for RC networks and their frequency response
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