Bode plot of RC transfer Function

Discussion in 'Homework Help' started by Mitchy190, Apr 25, 2012.

  1. Mitchy190

    Thread Starter Member

    Apr 23, 2012
    33
    0
    Hey all, Below is a transfer function I have derived from the circuit shown:

    circuit.png

    Transfer function.png

    transfer function.jpg

    I was wondering if you could tell me if the bode plot, also attached, I created is correct and accurate for this circuit, as i am having some doubts its correct.

    Thank you!
     
  2. blah2222

    Well-Known Member

    May 3, 2010
    552
    33
    Everything looks fine except A should have R2 in the numerator not R:

    A = \frac{R_{2}}{R + R{2}}

    This makes sense because at w = 0 (DC) the capacitor is essentially an open-circuit and the circuit is just a voltage divider. Try calculating the frequency response again to confirm this for yourself.

    Hope that helped.
     
    Mitchy190 likes this.
  3. WBahn

    Moderator

    Mar 31, 2012
    17,715
    4,788
    Look at your Bode plot with the following questions in mind:

    1) What do you expect the gain to look like a DC (w=0)?
    2) What does the capacitor look like at very, very high frequencies?
    3) What should the voltage at the output then look like at very, very high frequencies?
    4) Your plot shows things going asymptotic to something at or somewhat above 20dB, which would be a voltage gain of a factor of 10 across a resistive load, which means you are managing to dump about 100x the power in this resistor compared to if it were hooked up directely across the source. Does that make sense?
    5) Examine your equation in the limit that w becomes arbitrarily large. What does it reduce to?
    6) Does the answer to #5 jive with the answer to #3?

    In figuring out the problem with answer #6, you should be led toward finding the error that blah2222 pointed out.
     
    Mitchy190 likes this.
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