(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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.

2. Relevant equations

Impedance for a capacitor is 1/[jwC], for a resistor is R

Voltage divider for impedances

3. The attempt at a solution

i) Attempt at following those constraints:

A resistor R_{1}in series with the signal source and in series with (a resistor R_{2}in parallel with a capacitor C). Note: I realize this is not a strictly low-pass filter.

Impedance over the series resistor

z_{1}= R_{1}

Impedance over the parallel component

z_{2}= R_{2}/[jwCR_{1}+ 1]

Equivalent impedance

z = (R_{1}+ R_{2})[jwCR_{1}R_{2}(1/[R_{1}+R_{2}) + 1]/[jwCR_{2}+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.

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# Low-pass filter with no inductance, and voltage output over a resistor

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