Lesson 17 Flashcards — Analog Filters

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1. How does a real filter differ from an ideal one?

A real filter rolls off gradually — there is no wall. Frequencies near the cutoff are partially attenuated, and sharpening the transition costs more components, size, and money.

2. Define the cutoff frequency.

The frequency at which output power falls to half the passband value. Since power goes as voltage squared, the voltage falls to \(1/\sqrt{2} = 0.707\).

3. Why is cutoff also called the −3 dB point?

Because \(10\log_{10}(0.5) = -3\ \text{dB}\). 'Cutoff', 'corner frequency', 'half-power point', and '−3 dB point' all name the same thing.

4. What kind of filter is an R-C circuit with the output across the capacitor?

Low-pass. At DC the capacitor is an open, so the output sees the full source; at high frequency it is a short and the output goes to zero.

5. What kind of filter is a C-R circuit with the output across the resistor?

High-pass. Same two components as the R-C case — the filter type depends on where you take the output.

6. Give the cutoff frequency for R-C and C-R circuits.

\(f_\text{cutoff} = 1/(2\pi RC)\). At that frequency \(|Z_C| = R\) and the two elements contribute equally.

7. Give the cutoff frequency for R-L and L-R circuits.

\(f_\text{cutoff} = R/(2\pi L)\).

8. Give the quick test for identifying a filter type by inspection.

Ask what the reactive element does at DC (capacitor → open, inductor → short), then ask whether the output survives. Survives at DC means low-pass; killed at DC means high-pass.

9. What is the gain one decade past the cutoff of a first-order filter?

\(1/\sqrt{1+10^2} = 0.0995\), i.e. −20 dB. One decade costs 20 dB — the standard first-order rolloff.

10. Your measured cutoff differs from the computed one. Is that a problem?

Not necessarily. Component tolerances (a ±10% capacitor moves the cutoff ±10%) plus probe and breadboard stray capacitance explain modest discrepancies. A disagreement you can explain is a good result. (You will see this first-hand at the Lesson 19 lab.)