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RC Filters and Bode Plots

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Recipe #32 — rc filters and bode plots

The earlier high-pass and low-pass circuits can now be viewed in a new way: not just as schematics, but as responses that change continuously with frequency.

f_C = 1 / (2πRC)

The filter does not hit a brick wall

A low-pass filter does not pass everything below f_C perfectly and suddenly erase everything above it. The change is gradual. A high-pass behaves the same way in the opposite direction.

Reading the Bode plot

The horizontal axis represents frequency on a logarithmic scale: equal distances represent equal ratios such as 10 Hz → 100 Hz → 1 kHz. The vertical axis shows gain in decibels. A first-order RC response changes at about 20 dB per decade well beyond its corner.

Example

R = 10 kΩ and C = 0.01 µF gives f_C ≈ 1.59 kHz. The same R and C values can make either a low-pass or high-pass depending on which component is in series and where the output is taken.

Try these yourself

What is special about the cutoff frequency of a simple first-order RC filter? The magnitude is about 3 dB below the passband level Every signal suddenly becomes zero The resistor becomes an inductor Frequency stops existing

The standard first-order cutoff point is approximately −3 dB relative to the passband.

What does a logarithmic frequency axis make easy to show? A very wide frequency range on one graph Only one exact frequency DC current direction only Mechanical relay motion

A log axis compresses decades of frequency into manageable equal-ratio spacing.

What is the far-from-cutoff slope of a first-order RC response? About 20 dB per decade Exactly 1 dB per century No slope 1000 V per second

One reactive pole produces an asymptotic magnitude slope of about 20 dB per decade.

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