ADM
specialises in the design of precision frequency weighting
networks and manufactures a number of products in this area
as production items.
In addition,
ADM has resources to undertake custom filter network design
for clients wanting to carry out prototype design evaluation,
limited production runs or to develop filter solutions for
signal processing.
ADM has
the expertise to contribute at all levels of the design and
manufacturing process with an emphasis on signal conditioning
and measurement in noise and vibration applications.
Tutorial
on Filter Application
The performance
achieved by any signal processing system is determined by
the design of the signal conditioning subsystem adjacent
to the signal sensor or transducer. This applies equally to
both analog and digital systems and relates to the application
of frequency shaping and gain in the early stage of the signal
chain.
Signal
Conditioning
Signal
conditioning has considerable influence on performance factors
such as resolution and dynamic range. More specifically, filtering
is used to remove unwanted signals from a measurement process
allowing more amplification to be applied to the desired signal
components. A further advantage of filter application is bandwidth
reduction that results in improved signal to noise ratio by
reducing both external and intrinsic noise sources.
Filter
Response
The
concept of signal filtering is quite simple though the selection
and design of an optimum filter may be complex. A number of
standard filter responses exist, the most common being Butterworth,
Bessel and Chebyshev, these may be implemented in a number
of electronic circuit topologies. Choosing the most appropriate
filter response relates to the desired flatness in the passband,
attenuation and damping in the transition band, and linearity
of phase characteristic in the stopband.
Filter
Order
The
order or number of sections of the filter determines the steepness
of cutoff and attenuation in the stopband. The complexity
of filter design increases proportional to filter order, particularly
the selection and tolerance of passive component values to
achieve the selected response in analog filter design.
Passive
and Active Filters
The
simplest design is a Passive filter, which has no active elements
such as transistors or op amps, just resistors, capacitors
or inductors. This type of filter offers simplicity, low noise
and does not require power supplies. The down side is that
there is no control over input and output impedance and signal
loading can dramatically change performance.
Active
filters offer a more flexible approach with the advantage
of adjustable gain with high input impedance and low output
impedance. Higher order filters can more easily be designed
without the need for expensive and bulky inductors. The application
of low noise amplifiers and careful design techniques will
minimise the generation of noise. Critical filter applications
require an understanding of the relationship between centre
frequency, op amp gainbandwidth product and Q (damping).
A general approximation requires that the Q and centre frequency
product be only a small fraction of the gainbandwidth product
in order to maintain the desired transfer function. Similarly,
rules apply to filter output amplitude, bandwidth and op amp
slewrate.
Filter
Types
Basic
filter types include HighPass, LowPass, BandPass, BandReject
and AllPass (delay equaliser).
HighPass
filters attenuate all low frequency components below the cutoff
frequency and remove the dc component (0 Hz) from the signal.
This is useful in removing the dc offset that may be causing
an overload condition to occur.
LowPass
filters attenuate all signal components higher than the frequency
cutoff. The filter will pass all signals from dc (0 Hz) up
to the lowpass cutoff point. This filter type is useful in
improving signal to noise ratio by also reducing system intrinsic
noise.
BandPass
filters can be designed for broadband or narrowband applications
and are essentially the combination of a HighPass and LowPass
filter pair. Whilst this concept works for broadband applications,
it cannot be applied to the NarrowBand case which requires
a separate approach.
The
BandReject filter, sometimes called a Notch Filter is the
inverse of the NarrowBand case above. This filter offers
high attenuation over a narrow range of frequencies. A typical
application would be the rejection of a single troublesome
frequency component such as 50 Hz mains interference.
AllPass
Filters do nothing to the frequency response of the signal,
however, they exert considerable influence over the phase
or timedelay of the signal. This type of filter is particularly
useful in dealing with groupdelay problems or shaping the
phase response of a transfer function. Adaptive Delay Equalisers
are central to signal processing techniques that make mobile
phone communication intelligible.
Filter
Application
Filter
application always results in changes to the system transfer
function (frequency domain) and the transient response (time
domain). These changes may be quite subtle and not immediately
apparent but may lead to misleading results in some measurements.
For example, a vibration impact response measured with a filter
present will not be a replica of the input impact signal.
The filter will impose different timedelays to different
frequency components and the final algebraic summation of
signal terms will produce an impact that looks quite different
from the original. In addition, damping may contribute to
'ringing' caused by the presence of transient components which
may disrupt analysis and distort results. Phase matching between
filters is essential in some multichannel applications, especially
involving operations such as transfer functions or sound intensity
measurements.
Selecting
the required filter response requires some understanding of
the common filter approximations and their characteristics.
The Butterworth filter offers a maximally flat magnitude response
in the passband and reasonably steep rate of attenuation
(steeper than Bessel). Step response is quite well controlled,
but be prepared for a nonlinear phase response.
Chebyshev
filters offer steeper attenuation near the cutoff frequency
but at the expense of ripple in the passband and ringing in
the step response. The phase response is considerably nonlinear,
much worse than Butterworth.
Bessel
filters offer the best controlled step response and a linear
phase characteristic, but have a slower rate of attenuation
beyond the cutoff frequency making it necessary to employ
a higher order design for useful application.
Poles
and Zeros
Each
of these filter responses are designed from a characteristic
polynomial. These polynomials are readily available in filter
literature for most common filter types and for a range of
orders. In addition, an infinite number of other filter responses
exist in between these standard responses. The solution of
the characteristic polynomial at a particular order with a
unique set of coefficients, produces a set of quadratic factors
or roots. These roots determine the pole/zero placement.
The
pole/zero position on the real/imaginary axis (complex frequency
plane) determine the cutoff frequency of the network and
the network response. Poles correspond to the roots of the
denominator of the network transfer function and relate to
the lowpass frequency characteristics, while the zeros correspond
to the roots of the numerator and correspond to the highpass
frequency characteristics.
As
roots become progressively more complex, the damping value
will decrease, greater ringing will appear in the step response
and stability will decrease.
Filter
Synthesis
The
final filter design is a matter of extracting the polynomial
coefficients from the equation that provides the optimum pole/zero
placement and using these coefficients to synthesise the component
values for the desired filter topology.
This
filter tutorial is not intended as an in depth discussion
but instead forms a brief outline of basic filter principles
and provides some awareness of points to be understood and
considered in the design and selection of electronic filters.
