Filter Design  
  • Custom filter design
  • HP, LP, BP and Band Reject
  • Delay equalizer
  • Weighting networks
  • S-domain and Z-domain
  Expertise and Facilities

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 sub-system 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 cut-off 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 gain-bandwidth product and Q (damping). A general approximation requires that the Q and centre frequency product be only a small fraction of the gain-bandwidth product in order to maintain the desired transfer function. Similarly, rules apply to filter output amplitude, bandwidth and op amp slew-rate.

Filter Types

Basic filter types include High-Pass, Low-Pass, Band-Pass, Band-Reject and All-Pass (delay equaliser).

High-Pass filters attenuate all low frequency components below the cut-off 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.

Low-Pass filters attenuate all signal components higher than the frequency cut-off. The filter will pass all signals from dc (0 Hz) up to the lowpass cut-off point. This filter type is useful in improving signal to noise ratio by also reducing system intrinsic noise.

Band-Pass filters can be designed for broad-band or narrow-band applications and are essentially the combination of a High-Pass and Low-Pass filter pair. Whilst this concept works for broad-band applications, it cannot be applied to the Narrow-Band case which requires a separate approach.

The Band-Reject filter, sometimes called a Notch Filter is the inverse of the Narrow-Band 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.

All-Pass Filters do nothing to the frequency response of the signal, however, they exert considerable influence over the phase or time-delay of the signal. This type of filter is particularly useful in dealing with group-delay 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 time-delays 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 multi-channel 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 pass-band and reasonably steep rate of attenuation (steeper than Bessel). Step response is quite well controlled, but be prepared for a non-linear 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 non-linear, 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 cut-off 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 cut-off 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 low-pass frequency characteristics, while the zeros correspond to the roots of the numerator and correspond to the high-pass 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.

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