Measuring RMS Voltage of e(t) at f = 3.22MHz

[ashkash]

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.

 

[antoker]

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):

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

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

$$V_{out} = e(t)\cdot\frac{Z_{p}||Z_{scope}}{Z_{p}+R_{s}}$$
where
$$Z_{p}$$ denotes the parallel impedance (excluding scope load)
$$R_{s}$$ denotes series resistance at 5k
$$Z_{scope}$$ denotes scope impedance
|| means parallel combinationRemark: 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!