Tricky Circuit

A resistor–capacitor high-pass filter

Let fast changes through

RC means Resistor Capacitor: a resistor and capacitor form a high-pass filter that reduces slow changes and passes faster ones. Gain is output sine-wave amplitude divided by input amplitude; hertz (Hz) counts cycles per second. A nanofarad (nF) is one billionth of a farad, and a millisecond (ms) is one thousandth of a second.

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EXPERIMENT BENCH

Change the circuit settings, predict the readings, then check a challenge. These are learning models, with the assumptions explained in each lesson.

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Why it works

Ideal unloaded steady sine-wave model, with output across the resistor. Gain is an amplitude ratio, not a power ratio; startup and constant-voltage transients are omitted.

R is resistance, C capacitance, f signal frequency and fc cutoff frequency. fc = 1/(2πRC); gain = f/√(f² + fc²); time constant τ = RC. At cutoff, gain is about 70.7%, not zero.

Difficulty

  1. Build · Build it

    Power on at 10 kΩ, 100 nF and 100 Hz. Read gain about 53.2%.

    Need a hint?

    R = 10 kΩ; C = 100 nF; f = 100 Hz → 53.2%

  2. Explore · Change one thing

    At 10 Hz, adjust R and C for gain at most 10%.

    Need a hint?

    R = 10 kΩ; C = 100 nF; f = 10 Hz → 6.27%

  3. Solve it · Solve the challenge

    At 1000 Hz, achieve gain at least 98% and cutoff between 150 and 170 Hz.

    Need a hint?

    R = 10 kΩ; C = 100 nF; f = 1000 Hz → 98.76%

Extra reading and circuit recipes

Let fast changes through

A useful pattern

The low-pass has a series resistor and a capacitor to 0 V. Exchanging their positions, with output still across the lower component, gives this high-pass: series capacitor, resistor to 0 V.

Beyond the model

Increasing R or C lowers cutoff. With the same input frequency, this high-pass filter then passes a larger amplitude.

A useful trap to avoid

A series capacitor does not pass every changing signal equally; slow changes can still be strongly reduced.

R doubles while C and input frequency stay fixed. High-pass gain…

  1. increases
  2. decreases
  3. becomes exactly 100%
Read more

Cutoff halves. The same signal now lies farther above cutoff, so its amplitude is reduced less.

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