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  • Thread starter ashkash
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Homework Statement



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).

Homework Equations





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.

Homework Statement





Homework Equations





The Attempt at a Solution

 

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Answers and Replies

  • #2
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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:

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