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Why is amplifier GBP so Confusing? Insight #12

In nearly 50 years of voltage-feedback amplifier (VFA) introductions, one of the key specifications has been the gain bandwidth product (GBP). Over time, different development groups have delivered numbers that depart from the original definition resulting from misconceptions. Reconciling the simulation model to the data sheet is never easy, but some of that will be covered as well. With a true GBP extracted, how then might you use that to set the require GBP margin for a particular low pass active filter design? Find out next month in Insight #13.

Misleading GBP data
Most designers start out with the simple idea: for a VFA with a certain GBP, using simple external resistive feedback and gain setting elements (or just a straight feedback connection for gain of +1 V/V), the resulting small-signal bandwidth (SSBW) comes from dividing the noise gain (NG) into the GBP. That’s correct if:

  1. The GBP is reported correctly.
  2. At the Loop Gain (LG) = 0 dB crossover. the phase margin is 90° as in a single-pole system.

Both assumptions are suspect. Over time, various errors have crept into the GBP reported in datasheets. One of the most common is to report the AOL = 0 dB frequency as the GBP where higher-order poles have pulled that back in frequency from the true 1-pole AOL projected crossover with 0 dB. An older OPA134 (Ref. 1) device, with a recently updated model, illustrates this effect in Figure 1. This simulated AOL gain and phase does closely match the datasheet (Fig. 9 in Ref. 1). The output meter is rotated here to report not phase shift, but phase margin directly.

test circuit for gain bandwidth produce
Figure 1. Open Loop Gain and Phase Simulation shows 9.7 MHz GBP and 7.8 MHz AOL = 0 dB Crossover.

An easy way to get the “true” GBP for most unity-gain stable devices is at the 40 dB AOL frequency and multiply that by 100. For the OPA134, that’s 9.7 MHz whereas the higher-frequency pole (note the phase shift above 1 MHz showing that) pulls the AOL = 0 dB crossover back to 7.8 MHz — close to the datasheet reported 8 MHz GBP. You need the “true” GBP for several reasons. The most basic lets you predict the closed-loop F-3dB when the gain gets so high as to produce a 90° phase margin. For instance, at a gain of -99 V/V (NG=100 V/V), the closed-loop response F-3dB is indeed 97 kHz as predicted using the “true” GBP as shown in Figure 2.

Figure 2. Noise Gain of 100 V/V Closed Loop response shows actual available GBP = 9.7 MHz.

Going to lower gains with lower phase margin actually extends the F-3dB bandwidth far beyond what even using the “true” GBP would predict. Classical treatment of Bode analysis (Ref. 2) simply divides the NG into the GBP to predict closed loop F-3dB.

Bench measurements have long refuted this with a vague “low phase margin bandwidth extension” kind of comment. Recent analysis has produced the much more useful relationship for a second-order LG systems shown in Figure 3. This curve correctly starts out at a 1X multiplier for a 90° phase margin. Moving left to lower phase margins it quickly rises to a 1.6X multiplier below the very common 65° to 60° nominal phase margin used in many designs. It then goes asymptotic to 1.57X as the phase margin moves below 35°. As this is happening, the response peaking also increases (Fig. 2 in Ref. 3) as the phase margin moves below 65.5° (Butterworth, maximally flat).

Figure 3. This second-order analysis shows SSBW extension vs. phase margin at LG=0 dB crossover.

Using the OPA134 as a unity-gain follower would have the same LG curve as the AOL curve of Fig. 1. There, the 7.8 MHz LG=0 dB crossover shows 53° phase margin. That should then produce (using Fig. 3) a 1.61×7.8 MHz = 12.6 MHz F-3dB with about 1 dB peaking in the small-signal response (Fig. 2 in Ref. 3). The actual gain of 1 simulated response in Figure 4 nearly matches this with 1.78 dB peaking and an F-3dB = 13.6 MHz.

Figure 4. Unity gain buffer simulation with the OPA134 showing 1.8dB peaking and 13.6 MHz F-3dB.

With the “true” GBP in hand, the SSBW at higher gains can be correctly estimated. The lower gain, lower phase margin conditions, never could be accurately estimated using just the “true” GBP product and the NG. But Fig. 3 helps with that using a LG simulation extracting the resulting LG=0 dB crossover frequency and the phase margin at crossover. Even with this better understanding of the open-loop-to-closed-loop response using the updated TINA model, the closed-loop response curves (Figure 5) in the OPA134 datasheet remain perplexing.

Figure 5. Closed loop response curves from the OPA134 datasheet (Fig. 10 in Ref. 1) showing very low unity gain bandwidth vs. the simulation of Fig. 4.

The gain of 100 V/V F-3dB matches what the “true” GBP predicts (and Fig. 2), but the gain of 1 SSBW seems very low and does not match anything. This reported curve may have been bandlimited running into a slew limit using too high an output test level. If we solve for the implied VOPP using the 4 MHz F-3dB and the 50 V/μsec slew rate, that yields an imputed test level of 4 VPP. There is not enough information in the datasheet to resolve this, but it is likely a much lower test level (like 100 mVPP) would have more closely matched the new model response in Fig. 4.

Many common op amp design flows required the “true” GBP for accurate design. These include transimpedance designs (Reference 3), low gain inverting compensation using decompensated VFA’s (Ref. 4), and active filter designs considered in the upcoming Insight #13. Don’t get too far into any of these designs without verifying the simulation models’ “true” GBP using the approach of Fig. 1.

References

  1. TI OPA134, “SoundPlusTM High Performance Audio Operational Amplifier” http://www.ti.com/lit/ds/symlink/opa134.pdf
  2. Burr Brown application note “Feedback Plots Define Op Amp AC Performance” Jerry Graeme, 1991, http://www.ti.com/lit/an/sboa015/sboa015.pdf
  3. Planet Analog article “Stability Issues for High Speed Amplifiers: Introductory Background and Improved Analysis, Insight #5”, Michael Steffes, Feb. 3, 2019, https://www.planetanalog.com/author.asp?section_id=3404&doc_id=565056&
  4. EDN article “Unique compensation technique tames high bandwidth voltage feedback op amps”, Michael Steffes, Feb. 27, 2019, https://www.edn.com/design/analog/4461648/Unique-compensation-technique-tames-high-bandwidth-voltage-feedback-opamps

 

 

 

 

 

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