In this utility great importance is attached to the possibility of automatical selection of capacitors out of the E6- or E12-series. Because dimensioning has to start with a resistor value that can be used throughout all stages, all capacitor values become odd, which is quite impractical. Here you enter the approximate resistor values you wish and the utility now proposes different resistor values, so that the capacitor values will become standard values.
New: Dimensioning of Active 3-Pole Single Stage Low Pass Filters - quite unique!
High-pass filters are easier to dimension, as you start with a single capacitor value that can be used for all capacitors throughout all stages. The resistor-values anyway become odd.
The most common filter topologies are Sallen-Key and Multiple Feedback filters. The major differences are:
||Any gain is dependent on the resistor precision|
|Less components for gain = 1||Less components for gain > 1 or < 1|
|Op-amp input capacitance must possibly be taken into account||Op-amp input capacitance has almost no effect|
|Resistive load for sources even in high-pass filters||Capacitive loads can become very high for sources in high-pass filters|
In an active filter design for each stage you may select any topology of filter.
The stage order may be arbitrarily mixed. The stage order shown on the design pages is better suitable for high signal levels, a reversed stage order is better for low-noise purposes.
CA and CB Selection in Low-Pass Filters
Sallen-Key filter: In the table on the low-pass filter design pages CA and CB are calculated first for the desired RX (= RA = RB) values. In the "CX selection and resulting RX" columns the closest E6 or E12 series values for CX are selected and the corresponding values for RA and RB are calculated. You may manually enter different CA and CB, but CB must always be a minimum multiple of CA (you will get a warning if this requrement is not met). It is recommended to keep CB / CA as close as possible to this minimum mulitple so that RA and RB will be as close as possible, too. In this case the individual values of RA and RB are far less important than the correct sum of both. This might make it easier to find final values for the resistors.
Multpile Feedback filter: Basically the same, but "RB" must be replaced by "RC" and "RA" must be replaced by "RA parallel to RB".
CX Selection in High-Pass Filters
In high-pass filters you select a capacitor value CX that can be used for all capacitors in all stages. The resistor-values will be calculated correspondingly.
Part Value Tolerances
Deviations from nominal values of the passive components of course have influence on the frequency response of the filter. These deviations may be caused by component tolerances or due to the fact, that under normal circumstances the ideal values are not available. As a rough estimation it is possible to say: The lower the stage order is, the lower the influence of deviations on the frequency response is. Higher stage orders have a higher quality factor Q and deviations of R and C impinge on the resulting frequency response roughly proportional to the Q-factor.
If you want to find out more about the effects of varying values, generate the netlist of your choice and simulate it using the Monte-Carlo option.
As they are not ideal, op-amps falsify the ideal frequency response, too. The most important influence is caused by the finite gain-bandwidth product of the op-amps. In the tables above you find the GBW that is actually used in low-pass filters the corresponding stage. In high-pass filters it is the GBW used at the cutoff-frequency.
The GBW of the op-amp shall be much higher than the GBW in the tables above. It is a good approximation to say: If the op-amp GBW is 100 x Q times higher than the GBW of the corresponding stage, the amplitude error will be approx. 1 / 100 = 1%. If you want to know it more exactly, have a look in the TI-article already mentioned above.
Example 1: For an 8-pole Chebychev 3 db 100 Hz filter the highest Q is 23 and GBW is 2.4 kHz. 100 x Q x GBW = 5.5 MHz. The simulation with TL071 shows a gain error of close to 1%.
Example 2: For an 3-pole Butterworth 20 kHz filter the highest Q is 1 and GBW is 40 kHz. 100 x Q x GBW = 4 MHz. The simulation with TL071 again shows a gain error of close to 1%.
In the table below you find some op-amps and their most important characteristics:
|NE5532||10||5||Dual, low noise, high GBW, not too expensive, nice for audio, bipolar|
|LT1115||40||0,9||Ultra low noise, high GBW, very expensive, bipolar|
|AD797||110||0.9||Ultra low noise, very high GBW, very expensive, bipolar|
Do not use LM324 or LM358 for audio circuits as their unbiased output stages create lots of cross-over distortions when the output current changes direction.
Netlist Generator for Simulation
Unfortunately a simulation of the filter is not possible on this website. Instead, you may get a netlist output for the configured filter in order to simulate it on your PC. When you start to generate a netlist you may:
- For low-pass filters use component values for the desired
RX or for the selection for capacitors out of the E-series
- Generate the netlist either for the Sallen-Key or the Multiple Feedback topology
- Get time-domain (step-response) analysis and/or frequency-domain (frequency response) analysis
- Initiate Monte-Carlo settings with multiple plots, where all passive elements are randomly inaccurate as you request
- Get a netlist with ideal amplifiers or with real op-amps or with two filters of both types of amplifiers, supplied by one source
You may edit the netlists if you desire other options not provided here.
In order to simulate the netlist, execute following steps:
- Click into the netlist
- Press Ctrl-A and Ctrl-C (or Ctrl-Insert) to to select and copy the whole netlist to clipboard
- Open an ASCII text-file i. e. with the Editor or click into a previously opened one
- Press Ctrl-A and Ctrl-V (or Shift-Insert) to replace previous text by the whole netlist from clipboard
- Save the text-file (for obvious reasons into the directory and with the file-extension your simulator expects, i. e. MyFilter.NET)
- Start your simulator and select "Run Simulation from File".
Experiments have been made using SIMetrix Intro. This evaluation version allows to simulate the filter(s) above for up to 4 stages (less with more complex op-amps or more with ideal amplifiers). Plot control is provided in the netlists for SIMetrix Intro. The Windows path for the netlist file is likely to be C:\Program Files\SIMetrix4Intro\Work\mynetlist.net.