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### Why do low and high-pass filters differ so much when they have the same components?

The simplest low- and high-pass filters both have a capacitor and a resistor in series in a four-terminal network. However in the low-pass case, the output voltage is across the capacitor, and in the high-pass case, the output voltage is across the resistor. Here's a qualitative description of what's going on in each filter case:

• In the low-pass case, you measure voltage across the capacitor, and current comes through the resistor. For low frequencies (slow signals compared to the charging time), the capacitor gets charged up or discharged, reaching the input voltage, or a significant fraction of the input voltage, across it within an oscillation cycle; so the output follows the input signal. For high frequencies, in contrast, the capacitor never gets a chance to fully charge and develop the full input voltage across it: just as it gets started charging, the voltage sign and current direction wiggle back the other way and discharge it. So you never see the input voltage across the capacitor at high frequency.

• In the high-pass filter case, you measure voltage across the resistor, and current has to come through the capacitor. You get more voltage drop for more current going through the capacitor and on through the resistor. If frequency is high (rapidly thrashing voltage on the capacitor), the capacitor transmits current easily (always in the early charging or discharging part of its cycle) and current flows through the resistor. So the output voltage can be a large fraction of the input voltage at high frequency. In contrast, at low frequency, the signal is slow, and the capacitor will discharge or charge up on the timescale of an oscillation cycle. Charged or discharged capacitors don't pass current (capacitors ``block DC currents'') so there won't be much current through the resistor and not much voltage drop across it. So not much signal gets through to the output in the low frequency case.

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Kate Scholberg 2017-02-13