FILTERS

There are numerous types of filters that have been developed over the years. The most popular types are still ready available today from multiple sources and with few exceptions are going to be custom designed and built for each application. The designer can readily narrow down the choices once the key performance requirements are known. Filters can be grouped by response and by physical implementation. Filter responses can be broken down into numerous categories and sub-categories. All filters will fall into one of the first four fundamental categories; lowpass, highpass, bandpass and band reject. Response can be broken even further by the behavior within the passband and reject band and the number of sections, where the number of sections dictates the shape of the rejection portion of the curve. Physical implementation can be grouped into such types as Tubular, lumped element (or discrete), cavity, suspended substrate and ceramic.

Filter response should be the easiest and first decision since this is generally given as part of the requirements. The pass band covers the range of frequencies that must pass through a filter with minimum rejection or loss. The cutoff point, Fc, is the edge of the passband and is generally considered the 3dB point where the loss of the filter is 3dB higher than the center of the passband. Beyond the cutoff frequency the response of the filter provides increased loss and is the beginning of the rejection band. The four basic responses are shown below for clarification.

These responses can be further subdivided into more subtle response characteristics that impact the flatness of the pass band and the rejection rate for out-of-band frequencies. Some examples are Chebychev, Butterworth, Bessel, Gaussian and elliptic plus other far less prevalent types. These names are dictated by the mathematics behind the filter transfer function and are named after famous mathematicians and scientists who were responsible for their development. A Butterworth filter response provides smooth passband response with no ripple but the rejection just beyond the cutoff point does increase as quickly as a Chebychev response. A Bessel response filter is characterized by a gentle roll off in response across the passband, a much slower increase in rejection after the cutoff point but provides constant delay across the entire passband, something that Chebychev and Butterworth filter cannot do. If not specified, a Chebychev response will generally be assumed by most filter suppliers. It provides the best compromise between low passband loss and ripple, good VSWR and highest out-of-band rejection. Figure 5, below provides a handy comparison of how insertion loss and delay are impacted by three more popular filter types.

As mentioned above, the number of sections dictates the shape of the rejection portion of the filter response. Figure 6 below shows the relative difference between 1, 2, 3, 4 and 5 section Butterworth filters.

Having the specifications for the required filter one can quickly determine the type of response needed (high pass, low pass etc), then the response function needed (Chebychev, Butterworth etc) and then the number of sections required to get the necessary rejection. But even armed with this much information the selection process isn’t over. One needs to contend with the physical implementation and often a particular response can be implemented in two or more different physical styles. Each implementation has tradeoffs but the primary ones are of applicable frequency range, size, cost and time to deliver. Some physical styles may have the cost range desired but cannot be built in the frequency range of interest. The variation in size from one style to the next can be significant and is frequency dependent. The following table provides a quick summary of the frequency range limitations of these various types:

The above information is a generalization across multiple suppliers. Each supplier may have slightly different design limitations.

A simple way to go about the selection process is to settle on the specific response style then choose the physical implementation from the above table. Once the implementation is selected, use the handy pull down menus from the VTI Microwave Configurator to select one of the listed suppliers for that style of filter. This will link you to their web site where design tools and graphs are provided to further define the precise filter requirements to meet your needs.