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Circuit Help

  1. Feb 25, 2007 #1
    1. The problem statement, all variables and given/known data

    Determine the rms value of the voltage that is measured as a function of frequency at f = 3.22MHz. e(t) = 50sqrt(2)cos(wt). A 100MHz oscilliscope is being used to measure the voltage across nodes AA' as seen in the figure. The input impedence of the oscilliscope is a 1Mohm resistor in parallel with a 13pF capacitor. Also, calculate the rms voltage value that would be measured with an ideal oscilliscope (one with an infinite input imedence).

    2. Relevant equations



    3. The attempt at a solution

    I do not know where to start with this problem. I need to calculate the rms voltage measured with an ideal oscilliscope and an oscilliscope with the specified characteristics above. I have attached the circuit image. Any help would be appreciated. thanks.
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     

    Attached Files:

  2. jcsd
  3. Feb 25, 2007 #2
    1. infinite input impedance:
    With ideal scope the schematic will be the same as given. Voltage at the output can be calculated as follows:

    Using voltage divider rule (simplify schematic to voltage source with series resistance at 5k and complex impedance):

    [tex]V_{out} = e(t)\cdot\frac{Z_{p}}{Z_{p}+R_{s}}[/tex]
    where
    [tex]Z_{p}[/tex] denotes the parallel impedance (total)
    [tex]R_{s}[/tex] denotes series resistance at 5k

    2. Finite input impedance
    Same procedure, same equation. Non-ideal scope will represent additional parallel load at the output.

    [tex]V_{out} = e(t)\cdot\frac{Z_{p}||Z_{scope}}{Z_{p}+R_{s}}[/tex]
    where
    [tex]Z_{p}[/tex] denotes the parallel impedance (excluding scope load)
    [tex]R_{s}[/tex] denotes series resistance at 5k
    [tex]Z_{scope}[/tex] denotes scope impedance
    || means parallel combination


    Remark: Since scope is a 100Mhz (sampling speed?) no aliasing or folding will occur, but some phase lag will.
    P.S Remember that impedance is a function of frequency!
     
    Last edited: Feb 25, 2007
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