Dimensioning of Active 3-Pole Single Stage Low-Pass Filters

- This is hardly anywhere else to be found, but here it is -

Active 3-pole single stage filters need only one op-amp instead of two. But they are difficult to dimension because mathematics is by far not that straight-forward as for the usual double-stage ones. It took me a couple of days or even weeks to understand that and to prepare this utility written in Javascript. Here you can quickly dimension active 3-pole single stage Sallen-Key low-pass filters. The explicit intention of this page is to prevent semiconductor companies from selling millions of op-amps!

Restrictions: In contrast to my Active Low-Pass Filter Design and Dimensioning this utility is limited to filters with a stage gain of 1 (with one exception, see below), Chebychev filters are available in few standard ripple values only and the Sallen-Key topologie is available only.

Filter orders > 3: It is possible to dimension here the "entrance stages", i. e. stages 1 and 2 of filters with up to 9 poles (or 5 stages respectively). The remaining stages may be dimensioned using Active Low-Pass Filter Design and Dimensioning.

Method of evaluation: The evaluation of the component values is based on a set of several hundred of pre-evaluated resistors and capacitors values normalized to unity frequency. They are scaled at run-time to the desired frequency and to the users impedance requrements. All capacitor values in the table are selected from the E6-series and so that they are as close as possible to each other. If C2 and C4 differ from each other, C2 was chosen to be the smaller one so that the input impedance is kept higher. (Note: C2 and C4 may always be permuted, but different resistor value sets, not shown here, result in these cases.)

Filters with 3 equal capacitors: Often it is desirable to use 3 equal capacitors. For gains = 1 this is not possible, but for gains = 2 it is. You may enter your desired capacitor value and get three resulting resistur values.

• Note 1: This utility is available for 3rd order filters only!
• Note 2: You can reduce the gain of 2 to a gain of one by replacing R1 by an input divider of two resistors 4 x R1 each.

If you like to learn to know a mathematical way to evaluate the component values have a look at John-Paul Bedinger's "3-Pole Sallen-Key Butterworth Active Lowpass Filter: Design Sheet".

How to use: Enter the desired filter parameters and find the resulting component values below. Increase or decrease "Resistor Scaling" if the resultant resistor values shall be higher or lower. Adopt either the primary or the alternative resistor value set. Both result in the same frequency response. The advantage of the primary resistor value set is its higher input impedance and all 3 resistor values are closer to each other.

Disclaimer: This utility is based on a table of several hundred of more or less manually modified and edited values. Though I successfully tested some filters with random parameters and I believe all other values to be correct, this whole process is rather prone to error, and it would take several days for an appropriate test. Therefore I recommend to do simulations prior to trust the results evaluated here. No responsibility for any kind of errors or bugs is taken from anybody.

This page has been tested with MSIE 6 and Netscape 6.2.

Back to Active Filter Design and Dimensioning (overview).

To abbreviate atto, femto, pico, nano, micro, milli, kilo, mega, giga and tera use a, f, p, n, u, m, k, M, G and T

Desired Filter Parameters

Filter Characteristics

Filter
Order
Cutoff
Frequency

Impedance
Scaling
Capacitor C
for G = 2
 Bessel (almost no Overshoot) Butterworth (no Ripple) Chebychev 0.5 dB Ripple Chebychev 1.0 dB Ripple Chebychev 2.0 dB Ripple Chebychev 3.0 dB Ripple

 Hz

F

Goto Equal
Capacitor
Results Table

 RX and  CX Capacitor Values Primary Resistor Value Set Alternative Resistor Value Set C2 C4 C6 R1a R3a R5a R1b R3b R5b

Look at Active Low-Pass Filter Design and Dimensioning in order to dimension the remaining stages of filters with orders > 3.

Results for Filters with 3 Equal Capacitors

 C and RX   (3rd order only, Gain = 2) C R1 R3 R5

Enter the desired value for C in the Filter Parameter Table above

 Last update: November, 30th, 2005 Questions? Suggestions? Email Me! Uwe Beis