Roll-off

This article is about roll-off in electrical network analysis. For the dumpster, see roll-off (dumpster).

Roll-off is a term commonly used in electrical network analysis, most especially in connection with filter circuits, to describe the steepness of a network's transmission function with frequency in the transition between a passband and a stopband. The function of frequency most usually being considered is the insertion loss of the network, but could in principle be any function of frequency related to the network. It is usual to measure roll-off as a function of logarithmic frequency, consequently, the units of roll-off are either decibels per decade (dB/decade) or decibels per octave (dB/8ve). Decade being a x10 increase in frequency and octave being a x2 increase in frequency. Note that roll-off can occur with decreasing frequency as well as increasing frequency. This depends on the bandform of the filter being considered: for instance a low-pass filter will roll-off with increasing frequency, but a high-pass filter or the lower stopband of a band-pass filter will roll-off with decreasing frequency.

First order roll-off

A simple first order network such as a RC circuit will have a roll-off of 20dB/decade. This is approximately equal (to within normal engineering required accuracy) to 6dB/8ve and is the more usual description given for this roll-off. This can be shown to be so by considering the voltage transfer function, A, of the RC network:

$A={\frac {V_{o}}{V_{i}}}={\frac {1}{1+i\omega RC}}$

Frequency scaling this to RC=1 and forming the power ratio gives,

$|A|^{2}={\frac {1}{1+\omega ^{2}}}$

In decibels this becomes,

References

• J. William Helton, Orlando Merino, Classical control using H [infinity] methods: an introduction to design, pages 23-25, Society for Industrial and Applied Mathematics 1998 ISBN 0898714249.
• Todd C. Handy, Event-related potentials: a methods handbook, pages 89-92, 107-109, MIT Press 2004 ISBN 0262083337.
• Fay S. Tyner, John Russell Knott, W. Brem Mayer, Fundamentals of EEG Technology: Basic concepts and methods, pages 101-102, Lippincott Williams & Wilkins 1983 ISBN 089004385X.