Tips for Choosing Online Engineering Calculators & Design Tools - Analogue Filters

Author : Mark Patrick, Mouser Electronics

22 August 2023

Figure 1: Transfer function of a first-order low-pass filter
Figure 1: Transfer function of a first-order low-pass filter

This next Mouser blog post on modern design tools looks at analogue filters. It introduces the basic analogue filter concept before looking at some of the tools available that can help engineers to attain better optimised designs.

Introduction to analogue filters
Filters are fundamental building blocks of signal processing systems. They are possibly most familiar to people as the high and low-pass filters that form the treble and bass tone controls on an audio amplifier. Radios use filters to select a specific radio station and reject others.

The common filter types are:
• High-pass: Allows higher frequencies through and blocks lower frequencies.
• Low-pass: Does the reverse; allowing low frequencies through while blocking high frequencies. 
• Band-pass: Only passes frequencies within a certain range.
• Band-stop or notch: Cuts out a range of frequencies.

Filter parameters 
An ideal filter would allow only the desired frequencies through and completely block all the others. Real filters can only approximate this behaviour, as described in Figure 1.

Figure 2: Butterworth vs Chebyshev transfer responses
Figure 2: Butterworth vs Chebyshev transfer responses

The transfer function of a filter is the ratio of the output to the input as a function of frequency. This is defined by the following parameters:

• Pass-band: The range of frequencies that can pass through the filter unchanged.
• Cut-off frequency: The point where the output starts decreasing, typically where the output drops by 3dB.
• Slope or roll-off: The rate at which the output drops for frequencies outside the pass-band; this is also described as the “order” of the filter.
• Stop-band: The frequency range where the output is reduced.
• For a band-pass filter, the bandwidth is the difference between the upper and lower cut-off frequencies.

Simple filters can be implemented using just passive components - with combinations of resistors (R), inductors (L) and capacitors (C) being employed. Inclusion of an active component, such as an operational amplifier, will enable more flexibility in the design. 

Figure 3: Effect of Q on the transfer function of a low-pass filter
Figure 3: Effect of Q on the transfer function of a low-pass filter

A simple first order filter can be created with just an RC circuit. More complex filter designs can get closer to the ideal response, often by using an LC circuit. However, there are always trade-offs between different parameters of the filter. 

For example, a Butterworth filter is designed to have a frequency response that is as flat as possible in the pass-band. Conversely, a Chebyshev filter design has steeper roll-off, but more ripple in the pass-band or stop-band. 

In many applications, designers need to avoid inductors. They are far from being 'ideal' components, usually having a large resistance in addition to the inductance - which makes designing with them more complicated. They can also be bulky, and that rules them out for many applications. An active design using an op-amp can eliminate the need for inductors.

Figure 4: Filter Wizard screenshot (Source: Analog Devices)
Figure 4: Filter Wizard screenshot (Source: Analog Devices)

Another important aspect of the filter is the ‘quality’ parameter - Q. A larger Q value means that the transfer function is closer to the ideal response. If Q is >0.707, there will be a peak in the transfer function. If the Q is <0.707, the filter will have a gentler slope and the roll-off will begin sooner. This is shown in Figure 3.

Very large values of Q can result in the filter oscillating or ringing when there is a sharp change in the input.

Figure 5: Screenshot of Filter Wizard (Source: Texas Instruments)
Figure 5: Screenshot of Filter Wizard (Source: Texas Instruments)

Designing a filter
The transfer function can be defined in terms of the R, C and L values. The impedance of the components and the frequency are complex numbers. The transfer function can also be defined in terms of the cut-off frequency and Q. This means solving complex polynomials in order to calculate the transfer function. If the phase response of the filter is also important, this will entail further complex calculations. The following online tools can carry out such calculations for users though. 

Analog Devices’ Filter Wizard allows engineers to interactively:
• Select filter type (low-pass, high-pass, or band-pass).
• Set the basic filter parameters: Cut-off frequency, stop-band, and so on.
• Select filter response, such Chebyshev, Bessel, Butterworth, etc.
• Evaluate the effects of op-amp characteristics, like gain-bandwidth and noise.
• Plot the filter response, including phase, considering non-ideal components.
• Save the design in various formats, including models for a SPICE circuit simulator. 
Texas Instruments’ filter design tool supports the following design steps:
• Choose a filter type (low-pass, high-pass, band-pass, or band-stop).
• Select a filter design by optimising characteristics, such as pass-band ripple, stop-band attenuation, cost, pulse response, and settling time.
• Select one or more filter responses and compare plots of frequency, phase, etc.
• Modify the op-amp and other components in the design and simulate the result.
• Finally, the design can be exported in various formats, including SPICE models.

Other tools and calculators to aid filter design
There are more specialised design tools available online. A couple of examples are listed below.
The RF Tools website includes a tool for designing LC filters for radio-frequency circuits.
Okawa Electric Design has several online calculators for designing passive and active filters using various combinations of R, C and L. 

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