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Feedback, feedforward & Error Correction

Recently I ran into the issue of input Common Mode (CM) distortion in opamps. Especially in non-inverting series feedback configurations, both inputs of an opamp can show appreciable signal swing even when the input signal difference is very small, in linear operation. The large input swing in bipolar opamps causes relatively large non-linear input current swings, and in FET opamps it causes large voltage swings and thus non-linear input currents due to non-linear input capacitances. So, in both device types, common mode input causes non-linear input currents, and when you have appreciable source impedance, there's your CM input distortion!

The root cause of it is that CM signals change the voltages across the input devices with respect to the power supplies which modulates the input currents in the BJT opamp and the input capacitance voltage in the FET input opamp. So if we could somehow arrange that the power supplies move in unison with the CM input voltage, the effect would largely disappear!

Doulglas Self treats this extensively in Small Signal Audio Design, 2nd Ed, chapter 4, and calls it Rail Bootstrapping. Several implementation examples are shown, which confirm that supply bootstarpping largely eliminates the effect. An early  Engineering Report from Eiichi Funasaka and Hikaru Kondu (JAES Vol 30, nr 5, March 1982) calls it, more flowery, Feed Forward Floating Power Supply. They show example implementations similar to Self which also show large benefits in reduced IM distortion and, interestingly, increased slew rate.

Most of us know Henrik Bode's 1945 book on feedback systems. But in 1940 Bode published a monpograph Relations between Attenuation and Phase in Feedback Amplifier Design which was included in the Bell Systems Technical Journal in that year. Although this field was relatively new, he very precisely delineates what can and what cannot be done with feedback, and how to do. The insight that you need an open loop bandwidth that is as much larger than the closed loop bandwidth by the amount of feedback used is something you see rarely mentioned these days, yet is a very useful insight for a designer.

Michael Kiwanuka made me aware of a very early paper on Active-Error Feedback and Its Application to a Specific Driver Circuit by J. R. MacDonald of the IREE, from 1954! Intriguing reading for sure. I always wonder what these guys could have achieved if they had had access to our present-day active devices!

Sometimes you discover real gems. While searching for a specific paper at the University Library, Linear Audio author Marcel van de Gevel unearthed a 1938 (!) article by L. I. Farren in The Wireless Engineer about aspects of feedback amplifiers. It also contains the earliest definition I have seen of Current Feedback and Voltage Feedback.

Feedback was what we would call a hot topic in those days and lead to several letters to the Editor, among others by M. G. Scroggie (who later would write many interesting articles in Wireless World under the nome de plume Cathode Ray). Other comments were by Marinesco from Bucharest, Romania and Frommer from Budapest, Hungary. Sometimes you get the impression that Europe was more united then than it is now.

Small-Signal Distortion in Feedback Amplifiers for Audio, James Boyk and Gerald J Sussman, April 2003

Combining positive and negative feedback - John M. Miller, Electronics, March 1950. First commercial successful design using a combination of positive and negative feedback to lower distortion that I know of. Tubes, of course.

Feedback Amplifier Analysis Tools by TI's Ron Mancini. Clear expose on amp stability issues and how to avoid them.

Generalized op-amp model simplifies analysis of complex feedback schemes - Jerald Graeme, Burr-Brown Corporation. EDN, April 1993

Feedback models reduce opamp circuits to voltage dividers - Gerald Graeme, EDN June 1991

Feedback Plots define opamp AC performance - Jerald Graeme, Burr-Brown app bulletin SBOA015

Negative feedback and non-linearity - Exploring the fallacy that nfb reduces all harmonics equally - Cathode Ray, Wireless World Oct 1978. (Cathode Ray was a nom de plume of M. G. Scroggie).

Un ingénieux dispositif réducteurde distortion pour amplificateurs de puissances, Revue du Son, No 242, Juin 1973. This is an early realization that in my opinion is identical in concept to Hawksford's error correction scheme. In French, but it refers to an article in Wireless World.

A new distortion mechanism in class B amplifiers - Edward M. Cherry, AES Engineering Report, May 1981

A very old paper on Transient response, ringing and the role of feedback, from a Mr. Roddam from 1952! The oldest I have ever seen related to audio amplifiers. Courtesy of Leo Sahlsten from Finland.

Several vintage documents on thermal distortion in power stages, resulting from signal-related die temperature changes. Also called 'memory distortion': 'La distorsion thermique' Part I, Part II, by Héphaïstos (from L'Audiophile, 1984), and 'Amplifier transient crossover distortion resulting from temperature change of output power transistors', AES preprint 1896 (October 1982)

Edward Cherry's Nested Differential Feedback Concept and the NDFL Amp from ETI (1983).

A great article by Bruno Putzeys from Linear Audio Vol 1 - The F-word, or, why there is no such thing as too much feedback. No nonsense, factual, and technical, but also giving some historical perspectives to the often-heard notion that 'feedback sucks the life out of music'.


The continuing story about what is voltage feedback and what is current feedback.

It used to be so clear until someone started to call a specific type of opamp 'CFA' or 'CFB opamp'. As far as I know, the original patent was for a wideband amplifier topology. Then the marketing department got their hands on it and christened it 'CFA' One misunderstanding is that when you feed a signal back to a emittor that there is appreciable current flowing into or out of that emitter, and therefor it should be called 'current feedback'. Of course, with working feedback there is NO appreciable current - the emittor does present a low impedance, but 'the other side' of that impedance is the input voltage and with feedback the difference between input and feedback voltage is ideally zero. And zero voltage across whatever impedance is zero current. In practise, there is always an error current, which in typical cases is a fraction of a uA.

The traditional terms for the various feedback topologies have been very clearly defined, and I found a very clear explanation by, of course, W, Marchal Leach.

But it doesn't end there. The term CFA didn't just appear overnight. There's a nice trail in the famous Analog Dialog journal of the 80-ies and 90-ies. The first mention of a opamp with a low impedance inverting input is from Analog Dialog 21-1 from beginning of 1987. The correct technical term is used: transimpedance amp (current in - voltage out). The article explains in engineering terms the different behaviour of the inverting input node in the two topologies.

Then in Analog Dialog 23-3 the editor answers a reader letter about 'Current feedback and Transimpedance'. He starts with an example of an FET in a source follower configuration being a current feeedback amplifier. Then finally the naming breaks out in the open in Analog Dialog 24-1 of early 1990.