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Optimise amp selection in active analogue filters

30 Dec 2015  | Bonnie Baker

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For the Chebyshev lowpass filter, the two graphs in Figure 3 define the responses of even and odd order filters. Note the direction of the ripple signal (within the magnitude of Rp). For even order filters, the ripple rides on top of the DC gain of the filter. For odd order filters, the ripple rides underneath. In both graphs, there are also two definitions of the cut-off frequency. These definitions include passband ripple frequency (fp) and the –3 dB frequency (f–3 dB). In our example, we will use the Chebyshev –3 dB frequency.


Generating a fourth-order Chebyshev filter
The circuit for this example has the following specifications:

 • Single supply = 0V to 5V
 • Lowpass
 • fourth order
 • Chebyshev filter
 • Rp = 0.5 dB
 • Corner frequency = 5kHz
 • DC gain = 20 V/V

These specifications can generate several filters, depending on how you handle the gain in both stages. For instance, if the gain of both stages is equal to the square root of 20 or 4.472 V/V, Figure 4 shows the min OpAmp BW that occurs.


Figure 4: Passband gain in stage 1 and stage 2 are matched to 4.472 V/V to achieve 20 V/V for the entire circuit.


In figure 4, the stage 1 and stage 2 min Op Amp GBW is equal to 941.026kHz and 6.7817MHz, inclusively. Appropriate amplifiers for both stages are:

• Stage 1 → OPA170 1.2MHz, 36V, single-supply, SOT553, low-power operational amplifier

• Stage 2 → OPA192 Precision, rail-to-rail input/output, low offset voltage, low input bias current op amp with e-trim

If the gain stage 1 and stage 2 is equal to the 2 V/V and 10 V/V, inclusive, Figure 5 shows the min OpAmp BW that occurs.


Figure 5: Passband gain in stage 1 and stage 2 are 2 V/V and 10 V/V to achieve 20 V/V for the entire circuit.


In figure 5, the stage 1 and stage 2 min Op Amp GBW is equal to 420.886kHz and 15.164MHz, inclusively. Appropriate amplifiers for both stages are:

• Stage 1 → OPA170 1.2MHz, 36V, single-supply, SOT553, low-power operational amplifier

• Stage 2 → OPA350 38MHz high-speed, single-supply, rail-to-rail operational amplifier

If the gain stage1 and stage 2 is equal to the 10 V/V and 2 V/V, inclusive, figure 6 shows the min OpAmp BW that occurs.


Figure 6: Passband gain in stage 1 and stage 2 are 10 V/V and 2 V/V to achieve 20 V/V for the entire circuit.


In figure 6, the stage 1 and stage 2 min Op Amp GBW are equal to 2.104MHz and 3.032MHz, inclusively. The appropriate amplifier for both stages is:

Stage 1 → OPA2131 dual 4MHz FET-input operational amplifier

Stage 2 → OPA2131 dual 4MHz FET-input operational amplifier

It looks like we have found a happy medium in that the OPA131 services both stages.


Conclusion
When you try to optimise the selection of your amplifiers in active analogue filters, you will see success, especially if you implement a gain into a multi-stage system. We adjusted the gains of the stages and successfully saw changes in amplifier bandwidth requirements.

The task of generating an accurate lowpass filter is achievable, if you are willing to do a little research. There are many software applications that generate active analogue filters, but few will go so far as to recommend appropriate amplifiers for the finished circuit. I used the Texas Instruments' Filter Designer software to write this article.


About the author
Bonnie Baker is applications engineer for WEBENCH Design at Texas Instruments.


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