## Entering Data for a Bandpass Butterworth Filter

### Introduction

 In the stylized graph above, the ideal bandpass response is shown in blue. This displays infinite attenuation at all frequencies except the pass band which has no attenuation. The graph in red shows what the Butterworth filter can accomplish. In the filter that can be accomplished with lumped inductors and capacitors, the pass bandwidth is a bandwidth with up to three decibels of attenuation. At some larger bandwith, specify the stop bandwidth and a desired attenuation, n, in decibels. Make the slope of the graph between the 3 dB and the n dB points steeper by making the difference between the pass and stop bandwidths smaller. Choose these bandwidths wisely to design a filter that performs well in the current application.

### Example One

 Consider a range of frequencies passing through the filter, say 7000 kHz to 7300 kHz with an arithmetic mean is 7150 kHz. Determine that at 6750 kHz and 7550 kHz, the attenuation has to be 25 dB. In summary: the center frequency is 7150 kHz, the pass bandwidth is 300 kHz, the stop bandwidth is 1300 kHz, and the attenuation is 25 dB. Make the input and output termination resistances 50 Ohms. Type 7150 kHz in the top box, labeled "Center Frequency (Hz)" in a number of different fashions, using only the allowed characters 0-9, E (upper case is automatic), and . (a decimal point.) All of the following are legal: 7150000, 7.15E6, 7150E3. This is not allowed: 7150 kHz. Following the same formatting, enter 300 kHz in the second box labeled "Pass Bandwidth (Hz)." And then in the third box enter 1300 kHz, that's the box labeled "Stop Bandwidth (Hz)" Enter 25 in the fourth box, labeled "Attenuation (dB)," In the sixth box, labeled "In/Out Resistance (Ohms)," enter the resistance in ohms of the source and load which is 50. Click the "Computer Calculation" button in the green "Order" box. The computer will calculate the order and display it in the fifth box labeled "Order." Make an evaluation of the order number. It is possible that 8 (this example) was more than the number of capacitors and coils (eight of each; for band pass filters, each order requires two reactances) desired. Examine the criterion a second time. Perhaps less attenuation or a wider stop bandwidth is possible without suffering too much additional interference. For the moment, assume an order of 8 is acceptable. Click either the button labeled "Tee - Series" for a series resonant input filter, or "Pi - Shunt" for a parallel resonant input filter. See the "Help - Geometry" for more information. After that button is clicked, the calculations are made. Depending on how the configuration is set up, the results may be shown immediately. Alternatively, use the "File - Retrieve" menu item to launch the text editor to see the results, or simply compute other filters. At a later time, launch a text editor to see the files open the Butterworth filter folder and double click the files to view the data after exiting the Butterworth Calculator.

### Example Two

 Consider a fifth order band pass filter with a center frequency at 21.2 MHz, a pass bandwidth of 500 kHz with input and output termination resistances of 50 Ohms. Past experience guides this decision. Type 21.2 MHz in the top box, labeled "Center Frequency (Hz)" in a number of different fashions, using only the allowed characters 0-9, E (upper case is automatic), and . (a decimal point.) All of the following are legal: 21200000, 21.2E6, 9500E3. "21200 kHz" is not legal. Type a "5" in the fifth box in the panel labeled "Order." In the sixth box, labeled "In/Out Resistance (Ohms)," enter the termination resistances in ohms: 50. At this time, the Butterworth calculator can only handle equal input and output termination resistances.In the green "Order" panel, click the "Manual Entry" button. The center frequency, the pass bandwidth, and the order are now locked in. Then click either the button labeled "Tee - Series" for a series resonant input filter, or "Pi - Shunt" for a parallel resonant input filter. See the "Help - Geometry" for more information. See Example One for how to view the computed data or retrieve the saved data files.

### A Few Words

 Enter the center frequency as the arithmetic mean (average) of the two endpoints of the pass band. The computer will then calculate the frequencies which are the endpoints and then find the geometric mean for purposes of calculating the series resonant and parallel resonant branches of the filters. If the filter has a center frequency less than about 50 kHz to 75 kHz, consider an active filter. The low cost of top quality operational amplifiers and the associated resistors and capacitors make the active filter an attractive option. This is emphasized by the fact that inductors for these frequencies inductors tend to be bulky and expensive. If the filter has a center frequency above about 500 MHz, consider other techniques entirely. The small electrical size of the lumped elements make stray capacitances and inductances an important part of the physical layout possibly detuning the entire circuit. The largest center frequency allowed by the Butterworth Calculator is 1E10 Hz.