Testing op amp tools for their active filter design accuracy and dynamic range
The major op amp suppliers continue to improve and update their online design tools. Here, three of the major tools will be applied to the same relatively simple 2nd order multiple feedback (MFB) example design. The tools will be navigated as best they can to the same response targets and the RC values scaled to the same range. While a lot of focus goes into sensitivities and response spreads due to component tolerances, every design first moves off the nominal target at the standard value selection step. Those tools that support actual op amp implementations, will also depart from nominal due to the typical gain bandwidth product (GBP or GBW) for the op amp selected in implementation. This review will assess three final design accuracy metrics in two parts. This first part will set up the response targets and navigate to the solutions, while the second part will compare these metrics:
- With standard RC values forced onto the design and a minimum GBP op amp selected, how nearly does the typical value response match the desired target response shape?
- The MFB design flows can reduce the noise gain peaking. Some tools do this better than others and an SNR analysis for each output will illustrate those differences.
- Since the tools deliver slightly different noise gain profiles over frequency, the minimum loop gain in the passband will vary. All other things being equal, higher loop gain will give lower distortion. A comparison of noise gains over frequency subtracted from the op amp Aol will give the different loop gains for the designs where the minimum values will be compared.
Author background and disclaimers
The author has participated in the development and introduction of over 80 high speed amplifier products spanning five suppliers and 32 years. Having delivered literally hundreds of active filter designs to designers worldwide, and leading the online op amp tools development for Intersil, the internal nuances of common op amp based designs has been a perpetual area of interest and incremental improvement.
The design tools considered here are regularly changed and improved. This two-part investigation will be making a best good faith effort to exercise the public tools available in Nov. 2017. Not only is the intent to show some fine scale differences in the results, but to show methodologies to assess the merits of a particular design. Enroute, some tool navigation notes will be necessary. The author has made every effort to understand and exercise the tools in the best way possible. The aim is to arrive at a set of RC values from each of the tools to get very similar final results. Then to apply those RC values to a set of simulations using the same op amp model where the only differences in performance can be attributed to the RC values delivered.
Target active filter response
A single 2nd order low pass filter stage will be selected for design. The MFB (or Rauch) topology will be selected as representative of many current active filter designs using fully differential amplifiers (FDAs). The MFB requires a voltage feedback amplifier (VFA) where precision VFA-based FDAs have been one of the most active new product areas in recent years. FDAs are not well supported by the current tools, but the design results illustrated here using VFA op amps can be applied to FDA designs as well (1). System designs applying the most recent FDAs often include an MFB filter implementation. Those design requirements span a wide range of gains (0.1V/V to 200V/V) where a few examples can be found in (2) sections 9.1.4 and 9.2.1. While attenuating MFB designs using FDAs are common in practice, it does not appear that the current tools support gain magnitudes <1 for the MFB.
The aim here is to target a moderately difficult active filter stage with slight peaking and assess fine scale differences in the results delivered by the different tools. As will be shown in Part 2, the MFB has a noise gain shape that includes peaking due to both the desired filter peaking and noise gain zeroes that vary in the results delivered by the different tools. Here, a modest 1dB peaking target in the response shape will allow the separate noise gain zero peaking to be easily seen. Most op amp-based filter literature seems to assume a gain of 1V/V design for simplicity. Here a more challenging gain of 10V/V (20dB) design will be targeted with an F−3dB at 100kHz. The targeted small signal filter frequency response will be:
- DC gain of −10V/V (20dB)
- Small signal response peaking of 1dB
- Small signal response −3dB frequency at 100kHz.
This discussion will focus on the small signal gain response and how well the tools hit that target vs. an ideal response. Nominal deviations in the f0 and Q < 0.5% should be expected due to standard value RC selections. The requisite equations to describe all this follow.
Ideal 2nd order low pass equation:
- A is the DC gain
- ω0 is the characteristic or natural frequency (ωn). Will mainly use frequency (f0 = ω0/2π) in Hz.
- Q is the degree of complexness for the target poles, Q>0.707 will start to show peaking.
From this, all the important relationships can be delivered.
Peaking in dB (this is the expected maximum peaking above the DC gain)
This can be solved for Q given a target or simulated maximum peaking. Converting the dB peaking to a linear peaking over the DC gain (called α here), and solving for Q gives Equation 3:
A 1dB peaking target is a linear gain increase of 1.122. Placing that into Equation 3 gives a target Q of 0.957. From the simulated response shapes delivered by the different tools, Equation 3 will be used to extract the actual Q in the nominal (standard value but exact RC values) designs.
The frequency at which the peak gain should occur is given by Equation 4:
The frequency at which the small signal response will be down −3dB is given by Equation 5. Using the required Q to hit a 1dB peak, Equation 5 can be used to target a characteristic frequency, f0. For the 100kHz F−3dB target with a Q=0.957, the fo solves to 80.26kHz. Going back to Equation 4 with this gives an expected fpeak = 54.08kHz.
Using the simulated peaking to extract the Q by Equation 3, Equations 4 and 5 can then be used with the actual Q to get two estimates of the simulated fo where those will be averaged to assess closeness of fit in the results delivered by the different tools.
A final key equation to use with one of the tools is the frequency at which the peaked response passes back through the DC gain, called the passband or cutoff frequency, fcutoff in a Chebyshev design flow. Solving Equation 6 for the required fcutoff to get a 100kHz f−3dB using a Q=0.957 gives fcutoff = 76.47kHz.
Summarizing these nominal targets:
- DC gain = -10V/V (20dB) (the MFB is inverting gain, but only magnitudes used in design)
- Peaking = 1dB (linear peaking of 1.122) implies a Q = 0.957.
- f−3dB = 100kHz
- f0 = 80.26kHz
- fpeak = 54.08kHz
- fcuttoff = 76.49kHz