Questions: Filter Selection and Practical Applications

Question 1

A digital communication system transmits pulses at 1 Mbps. The receiver filter must preserve the shape and timing of pulses to minimize intersymbol interference. Which filter approximation type is most appropriate?

• A. Chebyshev — its steep rolloff provides maximum frequency isolation between adjacent symbols
• B. Butterworth — its flat passband ensures all frequency components are passed equally
• C. Bessel — its linear phase response preserves pulse shape by delaying all frequencies equally
• D. Higher-order RC — its simplicity reduces component count and cost

Answer: (C)

Pulse integrity depends on phase linearity: all frequency components of a pulse must be delayed by the same amount (linear phase, or equivalently, constant group delay). A Bessel filter is designed specifically for this property — it sacrifices steep rolloff to maintain linear phase across the passband. Chebyshev (option A) achieves steep rolloff at the cost of passband ripple and nonlinear phase, which would smear pulse edges. Butterworth (option B) has flat passband amplitude but nonlinear phase near the cutoff. When timing integrity matters, Bessel is the correct choice.

Question 2

An engineer designing a filter for a 50 Ω RF system uses a passive LC filter specified for 50 Ω source and load impedance. If the filter is connected to a 1 kΩ source, which effect is most likely?

• A. The cutoff frequency shifts upward because higher source impedance raises the RC time constant
• B. The frequency response deviates significantly from specification because the filter was designed for a specific impedance environment
• C. Performance improves because less current is drawn from the source
• D. The filter becomes a bandpass rather than a lowpass filter due to impedance mismatch

Answer: (B)

Passive LC filter responses depend critically on the source and load impedances they are embedded in — the filter and its terminations form a coupled network. The transfer function was derived assuming 50 Ω on each side. Driving from 1 kΩ fundamentally changes the network's behavior: the passband ripple, cutoff frequency, and rolloff shape will all differ from the design specification. This is not a minor perturbation — it can cause the passband to collapse or resonate unexpectedly. Impedance matching is not optional in passive filter design.

Question 3

A filter with higher order always provides steeper rolloff than a lower-order filter of the same approximation type.

• T. True
• F. False

Answer: True

Each additional filter order adds 20 dB/decade of rolloff (for Butterworth) or equivalent attenuation increase for Chebyshev and Bessel. A first-order Butterworth rolls off at 20 dB/decade; a second-order at 40 dB/decade; an nth-order at 20n dB/decade. This is a fundamental property: more poles in the transfer function mean steeper attenuation beyond the cutoff. The tradeoff is complexity (more components), cost, and in active filters, the need for more op-amp stages, each with its own gain-bandwidth limitations.

Question 4

For audio signal processing applications below 1 MHz, active RC filters are generally inferior to passive LC filters because they require a power supply.

• T. True
• F. False

Answer: False

For signal-level applications below a few MHz, active RC filters are generally preferred over passive LC designs. Active filters can provide gain (not just attenuation), buffer impedance between stages, and achieve high-order responses without inductors — which are bulky, expensive, have parasitic resistance, and behave non-ideally at low frequencies where they must be physically large. The power supply requirement is a minor cost compared to these advantages. Passive LC filters become necessary at RF frequencies (above ~100 MHz) where op-amp bandwidth becomes a limiting constraint.

Question 5

Explain the key tradeoff between Chebyshev and Bessel filter approximations, and describe one application where each is the better choice.

Model answer: Chebyshev: achieves steeper rolloff than Butterworth/Bessel for the same filter order by allowing controlled ripple in the passband. Best when you need to meet a tight stopband attenuation specification and can tolerate amplitude variation in the passband (e.g., separating adjacent radio channels with tight spacing). Bessel: sacrifices steep rolloff for linear phase (constant group delay), which preserves pulse shapes and avoids ringing. Best in digital communication receivers or measurement systems where timing accuracy and pulse integrity matter more than frequency selectivity.

The underlying tradeoff is between frequency-domain performance (how sharply you attenuate) and time-domain performance (how faithfully you reproduce transients). Chebyshev optimizes the frequency-domain criterion at the cost of time-domain behavior. Bessel optimizes time-domain behavior at the cost of shallow rolloff. No single filter can be simultaneously optimal in both domains — the engineer must identify which criterion is binding for the application.