Filter Workshop

Passive Filter Design


Figure 1. Design Screen for Ladder Netwoks

Summary:

Filter Workshop is a suite of passive filter-design utility programs designed to operate in the Windows* environment. It is useful in the design of passive crossover networks and other passive filter networks. It is intended for both engineering and educational use. As such, it attempts to provide enough background on the subject so that users can develop some insight for themselves. The program can assist in the design of Passive Attenuators, Passive Ladder Networks (High-Pass and Low-Pass Filters), Passive Shelving Networks, Passive Band-Reject Networks, Inductors (Roll Your Own Inductor) and Loudspeaker Impedance Correction Networks. Help screens are available throughout the program, providing step-by-step instructions along with useful information and design tips.



Figure 2. Schematic and Equations for Third-Order Ladder Network

Detailed Description:

Filter Workshop relies on an intuitive Windows* user interface to simplify the process of designing filters. Because direct access is provided to filter design parameters (coefficients, pole angles and the like) it is possible to design very complex filters, such as those having multiple-slopes, with a minimum of components.

Passive Attenuator Networks

This part of the program allows the user to engineer or reverse-engineer passive attenuators. It is comprised of two screens, a design screen and a "Formulas" screen, the latter showing a schematic diagram and the pertinent equations.

The design process is simple. We begin by selecting one of the options under "Solve For:", in this case "R1". Next we enter the load resistance (or nominal impedance) and the desired amount of attenuation in dB in the "Theoretical" column. As soon as there are entries in both of these fields, the required value for resistor R1 is calculated and displayed. Often, the calculated value for R1 will not be a standard value for a resistor or a value which we do not have on hand. The "Actual" column allows us to enter "real-world" values and determine whether the resulting attenuation is acceptable. The Copy button allows us to copy the values from the "Theoretical" column to the "Actual" column.

Passive Ladder Networks

This part of the program facilitates the design of first through fifth order high-pass or low-pass filters. It is set up in such a way that one screen handles all of the options in a logical manner, showing only those items that are pertinent. Various filter types (Bessel, Butterworth, Chebychev, Gaussian and Linkwitz-Riley) are handled. Filter Workshop is perhaps unique in that all of the filter coefficients for each type of filter are shown. For Butterworth and Linkwitz-Riley filters, the pole angles are also shown. Custom ladder-network-based filters can be designed by simply entering new coefficient values or pole angles. A complete set of "Formulas" screens shows schematic diagrams, transfer functions and component value calculations.

There are only a few steps required to design most filters. The filter type, the pass band and filter order are selected first. As selections are made, pertinent items appear on the screen. Once the pass band and filter order have been determined, one can view the schematic by clicking on the Formulas button. Next we add a value for the load resistance (or nominal load impedance) in the "Actual" column and the desired crossover frequency in the "Theoretical" column. As soon as enough information has been entered, the component values are calculated. The Copy button can be used to place the calculated values into the "Actual" column where they can be edited if necessary. Pressing the Graph button calculates the filter response based on the values in the "Actual" column and opens the Graph screen.


Figure 3. Graph of Theoretical Filter Response

The Graph Screen

Whenever a filter network has been designed, its magnitude and phase response (based on the values in the "Actual" column) can be graphed. This process is initiated whenever the Graph button is pressed. The controls located at the top of the Graph screen adjust the display resolution and initiate the Drawing process.

Passive Shelving Networks

It is sometimes useful to incorporate some form of equalization into passive crossover networks. Two types of equalization networks, Shelving and Band-Reject, can be designed using Filter Workshop.

Shelving Networks can be used to compensate for the high-frequency roll- off of horn-driver combinations and at the same time correct for the mismatch in sensitivity between woofers and high-frequency drivers. An impedance correction option matches the impedance of the shelving- network/load combination to a preceding crossover filter at the crossover frequency. This minimizes any interaction between the two networks.

Entering the values for Rload, the desired attenuation (dBatten) and the shelving frequency (F1) results in the calculation of the required component values. To determine the required impedance correction resistor, the crossover frequency must be entered. Pressing the Formulas button shows the schematic diagram, transfer functions, etc.

Passive Band-Reject Networks

If there is a peak in a loudspeaker's response, and it is not at or near the crossover frequency, it can often be compensated for by inserting a band-reject network in front of the crossover network. As long as the center frequency of the filter is at a reasonable distance from the crossover frequency there will be minimal interaction between the two networks.

Entering the values for Rload, the desired attenuation (dBatten), the center frequency (F0) and the Q results in the calculation of the required component values. There are two special options in the "Actual" column which allow the user to enter series resistance values for both of the reactive components in the filter. This can be quite useful since these real-world properties can have a strong influence on the response of the filter. This is especially true when higher Q filters are desired.

Inductor Design (Roll Your Own Inductor)

It is a relatively simple process to wind inductors, and since this can result in a substantial cost savings, a utility is provided to determine the approximate number of turns required for a given inductor value. The user must enter the wire diameter, coil dimensions, and desired inductance. The program then calculates number of turns required, the approximate outer diameter of the coil and the number of feet of wire that will be used. The outer diameter and number of feet of wire are useful in determining if the inductor can be built practically.

Loudspeaker Impedance Correction Networks

The graph of a typical woofer impedance curve generally has one or more resonance peaks in the low-frequency region, depending on box design, and a monotonically rising impedance at higher frequency (due to the inductance of the voice coil and other factors). If a particular crossover design requires that the crossover frequency fall within the rising portion at the right-hand side of the graph, an impedance correction network will be necessary. Otherwise, there is likely to be a peak in the frequency response at the crossover frequency.

Once the values for Zmin (the minimum value of impedance between the resonance peaks and the rising portion) and F2Zmin (the frequency at which Z = 2*Zmin) the value of C for the impedance correction network is calculated.

Conclusion

Filter Workshop attempts to provide an environment in which filter networks ranging from basic to fairly complex can be designed with a minimum of effort, while at the same time, providing enough background on the subject where the user can begin to make educated decisions.

*Windows is a registered trademark of Microsoft Corporation



This page Copyright (C) 1998 by Frank Ostrander. All Rights Reserved.