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How far can you trust the various free active filter design tools?

What do you really get using a supplier tool for an multiple feedback (MFB) low pass active filter? Let’s continue the quest for the best results using the example designs from Part 1.

In this online design tool accuracy quest, delivered RC values from four of the available supplier tools for a relatively simple 2^{nd} order low pass filter implemented as a MFB topology. Here, in this follow-up article, those values will be applied in simulation to compare the resulting filter shape to the ideal target extracting the fit errors for each solution. Nominal fit errors arise from both the standard value constraint on the RC’s and the finite amplifier gain bandwidth product (GBW or GBP). The output spot and integrated noise results for each of the RC solutions using the same op amp model will show slight differences due to both the resistor scaling and noise gain peaking differences.

The noise gain shapes within the MFB filter arise from both the desired filter shape and the noise gain zeroes. Solutions vary widely on their peak noise gain due to those noise gain zeroes delivered by the specific RC solutions. Those differences will be illustrated in these example designs also showing the differences in the minimum in-band loop gain (LG) for the RC solutions delivered by the different tools.

**Nominal gain response fit errors to the ideal response **

There are numerous ways to assess fit error. All of these tools deliver very close response shapes across most of the frequency span where most of the deviation will be occurring around the peaking portion of the response. As a simple measure of fit, the extracted f_{0} and Q for each implementation circuit will be compared to their ideal targets extracting a % error for each. Those two errors will be RMS’d to get a combined error metric. Since a gain of −10V/V target was used in the examples carried over from part 1, and the input resistor is forced to a standard value, all of the solutions hit the desired DC gain very closely using input and feedback resistor values one decade apart (with very slight loop gain errors).

The ADI tool (1) allows simulated data download using whichever op amp is selected for the design – the LTC6240 (2) here. To continue the noise and loop gain comparisons across the different solutions, the RC solutions will be ported to TINA (3) and use the LMP7711 (4) as a common op amp for the noise simulations across each. Since the ADI tool also targeted a slightly different filter shape (1.04dB peaking vs 1.0dB in the other tools), its response fit results will be isolated out for comparison purposes first.

ADI target response shape:

A_{v} = -10V/V (20dB)

f_{peak} = 54.34kHz

f_{-3dB} = 100kHz

Q=0.9636 (1.04dB peaking)

f_{o} = 80kHz

Using the circuit of **Figure 1** (and the RC numbering shown there), the two ADI solutions will be simulated both in the ADI tool using the LTC6240 and in TINA using the LMP7711 model (fig. 1 is the TINA setup using the LMP7711). The key requirement for valid fit comparisons is the op amps’ true single pole open loop gain bandwidth product. Testing the LMP7711 Aol response with the TINA model showed a 26MHz GBW vs its reported 17MHz GBW. The model was modified to 17MHz (increasing C2 from 20pF to 33.3pF in the macro) prior to simulations to get comparable results to the LTC6240 simulation data out of the ADI tool. The LTC6240 does not appear in the TINA library for easy Aol testing, but we will assume it matches its datasheet GBW = 18MHz.

**Figure 1** Active filter simulation showing ADI non-GBW adjusted RC values in TINA with the LMP7711

The first level of mismatch to target is the standard resistor value selection. With 5-RC values to choose, and only 3 design targets, the E24 (5% steps) C values are usually chosen first, then the exact R solutions for the 3 design targets are taken to E96 (1% steps) as a final result. Those values can be placed into the ideal (infinite GBW) equations 8-10 (in Part 1) to first assess how much error should be expected at this step. With standard C values chosen first, the exact solutions for the 3 R’s will have standard values above and below the exact results. It is possible (but not likely implemented in these current tools) to test the 8 standard value permutations above and below the exact solutions for closeness of fit and then “snap” from the exact to the least error standard values. More often, the 3 exact solutions resistors are snapped to their closest standard value separately. There will be some randomness in the fit error depending on how nearly the exact solutions initially approached standard E96 resistor values.

Next, those values can be applied to finite GBW op amp models and simulated to extract final nominal fit error before RC tolerancing is even applied. Table 1 summarizes these results for both the downloaded data from the ADI tool using the LTC6240 model, and those from TINA using the modified GBW LMP7711 model. Note that none of the finite GBW op amp simulations hit the desired 100kHz f_{-3dB} frequency within 1% using these nominal standard RC values.

**Table 1** Summary fit error results for the ADI targets and solutions

The ideal opamp values are assuming an infinite GBW where the errors are due only to the standard resistor values chosen. The GBW adjusted RC values cannot be applied to the ideal equations 8-10 (Part 1) as they will appear to be mistargeted. Using the actual op amp models show the nominal results, without adjusting the RC values for GBW, with a large 3.4% to 4.2% RMS error. This arises from choosing an aggressively low GBW device for this design. However, the ADI GBW adjusted RC values greatly improve this to only 1.2% to 1.8% nominal RMS error in f_{o} and Q. These have grown slightly, as should be expected, from the 0.41% error arising from just the E96 standard R value snaps. **Figure 2** shows these simulated results, compared to ideal, zoomed in around the peak value.

These nominal response shapes are close, but not exact, to the target. The effect of RC component tolerancing will then spread out the expected response shapes from these already nominally shifted results. The gray LMP7711 with the GBW adjusted RC values looks like the worst fit in the plot, and is the worst fit to Q, but it is the lowest RMS fit error with the best fit to f_{o} and the resulting f_{-3dB}. It is apparent that if the nominal responses are already shifted quite a bit from the target, improving that fit would go a long way to delivering a spread more centered on target when the RC tolerancing is included (note, the ADI tool also provides response spread envelope data download – beyond the scope of this discussion).

**Figure 2** Zoomed in response match around the targeted peaking of 1.04 dB at 54.34 kHz

[Continue reading on EDN US: Tool RC results]

**Related articles:**

- Testing op amp tools for their active filter design accuracy and dynamic range
- Design second- and third-order Sallen-Key filters with one op amp
- Advanced considerations for gain and Q sequencing in multistage lowpass active filters
- Designing RC active filters with standard-component values
- TI improves its active filter design tool
- Active-filter circuit and oscilloscope inspect a Class D amplifier’s output

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