Cutoff and the First-Order High-Pass
Highs pass, lows are blocked
Sweep the frequency from low to high. At first it is almost blocked, then it passes more and more. Find the cutoff frequency ω_c where the output rises to 1/√2 of the input, that is −3 dB.
This time the output is across the resistor
A low-pass took its output across the capacitor. A high-pass looks across the resistor of the same series RC. At low frequency the capacitor’s impedance 1/ωC is huge, so it takes almost all the voltage and the resistor gets almost none — low frequencies are blocked. As the frequency rises the capacitor’s share shrinks and the resistor receives the voltage, so high frequencies pass.
The cutoff frequency ω_c = 1/RC
Just as in the low-pass, the boundary is the frequency where the resistor’s and capacitor’s impedances are equal. That is ω_c = 1/RC, and the output drops to 1/√2 ≈ 0.707 of the input — −3 dB. Only the phase has the opposite sign: in a high-pass the output leads the input by 45 degrees, approaching +90 degrees as you go below cutoff.
Below cutoff it rises at a fixed slope
Above the cutoff the gain is flat at nearly one. Below it, each tenfold drop in frequency cuts the gain by −20 dB. On log axes the flat line above cutoff and the −20 dB/decade falling line below (a +20 dB/decade rise as you sweep up) meet at a corner, the cutoff. A high-pass is used to block the DC component and pass only the changing part of a signal — as a differentiator or a coupling capacitor.
Back to the first screen
As you raised the frequency, the pass-through gain began near zero, bent upward near the cutoff, and at exactly ω_c = 1/RC the output became 0.707 of the input, −3 dB. Above that it leveled off toward one. The same parts as a low-pass, with the single difference of taking the output across the resistor, flipped which frequencies pass clean over.