gaussmarkov: diy fx

High Pass Filter

If the capacitor and resistor in the low pass filter change places, then the circuit becomes a high pass filter. Indeed the output of this high pass filter is just the output of the low pass filter subtracted from the input. So the frequencies that were attenuated most by one filter are the frequencies attenuated least by the other filter.   You could use this LTSpice setup to check this:

One way to think about this is to use the rule that

a series of capacitors and resistors has the same electronic properties no matter what order the components are connected.

This phenomenon is described for the simpler case of series of resistors here. It is also true for any series of resistors and capacitors: viewed as a single multi-part component, a series of resistors and capacitors behaves the same no matter how the individual parts are ordered.

This rule can be inferred from the way resistors and capacitors conduct AC current and the basic laws of circuit analysis:

• the current is the same on both leads of a resistor or a capacitor,
• Kirchoff’s current law,
  which implies that the same current will pass through all of the resistors and capacitors in a series, and
• Kirchoff’s voltage law,
  which makes no distinction about order: the sum of the voltage differences across components must equal the voltage drop
  across the series. No matter what order you add a list of numbers, you always get the same sum.

Now we apply these two conditions to a resistor and a capacitor in series. Given that the AC is the same through every component of the series, the voltage potential across the resistor is the same whether it sits at the beginning or the end of the series (using Ohm’s law). This is also true for the capacitor because its voltage potential must be the difference between the supply potential and the resistor’s potential (using Kirchoff’s voltage law).

Therefore, the difference between the high and low pass filters is whether the output is the voltage potential across the resistor or across the capacitor. For the low pass filter, it is across the capacitor. For the high pass filter, it is the resistor.

Because the voltage across the capacitor is attenuating high frequencies more than low, the resistor is making up for this by simultaneously allowing the high frequencies to have a greater amplitude than the low. If the output voltage is the voltage across the resistor, we see that low frequencies are attenuated more than high frequencies. That is, we have a high pass filter.