Which statement best describes a first-order filter and how it differs from a second-order filter?

• A. It contains one energy storage element and has a single pole.
• B. It contains two energy storage elements and can exhibit resonance.
• C. It uses a dual-branch network with complex poles.
• D. It cannot be described by a pole-zero model.

Answer: (A)

A first-order filter is defined by having a single energy storage element in the signal path, such as one capacitor in an RC network or one inductor in an RL network. That lone reactive element forces the transfer function to have one pole, yielding a simple first-order differential equation and a single time constant. Because there’s only one pole, the response is monotonic and there’s no possibility of oscillation or resonant peaking. The cutoff frequency is tied directly to the location of that single pole, and the magnitude falls off at a predictable 20 dB per decade beyond the cutoff.

In contrast, a second-order filter uses two energy storage elements, which creates two poles in the transfer function. If those poles are complex conjugates, the system can exhibit resonance or a peaking response depending on the damping (the Q factor). This is why second-order filters can show oscillatory behavior and sharper or ringing responses, unlike the single-pole, non-resonant behavior of first-order filters.

So the statement that best describes a first-order filter—and how it differs from a second-order one—is that it contains one energy storage element and has a single pole. This single pole is what prevents resonance and keeps the response simple, whereas two storage elements in a second-order filter allow more complex, potentially resonant dynamics.