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Tetraoxygen
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Homework Statement
I am supposed to find the circuit design for a first-order low-pass filter. The filter must be made of resistors and capacitors only (no inductances). Furthermore, the output voltage must be measured over a resistor or something in parallel with a resistor.
Homework Equations
Impedance for a capacitor is 1/[jwC], for a resistor is R
Voltage divider for impedances
The Attempt at a Solution
i) Attempt at following those constraints:
A resistor R1 in series with the signal source and in series with (a resistor R2 in parallel with a capacitor C). Note: I realize this is not a strictly low-pass filter.
Impedance over the series resistor
z1 = R1
Impedance over the parallel component
z2 = R2/[jwCR1 + 1]
Equivalent impedance
z = (R1 + R2)[jwCR1R2(1/[R1+R2) + 1]/[jwCR2+1]
As far as I can tell, this is actually a bandpass (or reject) filter with cutoff frequencies at
(R1 + R2)/(C R1 R2) and 1/(C R2).
ii) I realize I can make an RC low-pass filter (but then the output voltage is not measured over a resistor) and an RL low-pass filter (but then there is an inductor).
Please help. Or, if you know definitively that this is an impossible task, please tell me so. Thanks.