Passbandrippel

Passbandrippel, commonly referred to as passband ripple, describes the variation of a filter’s magnitude response within its passband. It is a standard performance metric in both analog and digital filter design, and it is particularly emphasized in Chebyshev Type I and elliptic (Cauer) filters.

Definition and measurement

The passband is the frequency range where signals are intended to pass with minimal attenuation. In this region, the filter’s gain deviates from the ideal unity value due to design choices, component tolerances, and finite precision. Passband ripple is typically quantified as the peak-to-peak variation of the passband magnitude, expressed in decibels as Rp. If the passband amplitude varies between A_min and A_max in linear scale, Rp can be described as Rp = 20 log10(A_max/A_min). In many designs, A_min ≈ 1−δ and A_max ≈ 1+δ, with Rp related to δ by Rp = 20 log10((1+δ)/(1−δ)).

Design implications

A smaller Rp yields a flatter passband but often requires a higher filter order or a wider transition band to meet stopband specifications. Chebyshev Type I filters exhibit equiripple behavior in the passband, while Butterworth filters aim for a monotonic passband with no ripple. Elliptic filters, in contrast, show ripples in both the passband and stopband, achieving steeper transitions for a given order.

Causes and measurement practice

Passband ripple arises from the filter’s transfer function, component tolerances, quantization, and finite precision in implementation. Designers assess Rp by inspecting the magnitude response over the passband, noting the maximum deviation from the target gain.

Applications

Passband ripple is a key criterion in telecommunications, audio processing, RF front-ends, and any application requiring predictable gain within the passband while meeting specified stopband attenuation.