From: "Terry Walker"

To: "Joe Sousa"

Subject: positive feedback in the VT opamps such as K2-W

Date: Wed, 14 Dec 2011 22:53:15 -0800

Hi Joe,

Greetings again from California!  I received a copy of the Radiotron Designer’s Manual by Langford-Smith (the big ‘red book’) last week (I already had one, but this one was from an old friend I occasionally see), and was looking through it at random when I came across the information in the six pages which are attached.  This was in a section written by Langford-Smith on feedback, both negative and positive.  I got interested in what positive feedback was covered, and was surprised to find the schematics shown in Figs 7.15A and 7.15C.

Since the use of positive feedback is a signature and important feature of the GAP/R opamps, the striking similarity of these figures to the second stage and output CF he commonly used, as in the K2-W, is important.   I don’t know if you have covered this in your web site before, but the question naturally occurs of whether GAP may have come across this or a prior reference and used the information when he designed his amplifers, or if this information was published after the K2-W et al were designed.  I am not sufficiently familiar with the development time line.  The first publication date on the 4th edition is 1952, whereas 3d edition, which does not mention positive feedback, is variously listed as 1940 or 1945.  The promotional photo on opamp history shows the K2-UX as 1946 andthe K2-W series as 1947, so this predates the 4th edition.  I wonder if this particular design idea can be traced more exactly to determine if GAP independently invented it, or if there was some common usage and publication of it which both he and Langford-Smith would have been familar.  Langford-Smith seems to treat it as common knowledge.

 I just now went and looked in the Rad Lab series vol 18 on Vacuum Tube Amplifiers, and found that pages 473 – 479 cover the use of positive feedback in a low frequency amplifier to reduce its input voltage error and essentially increase its gain to infinity.  In particular see Figs 11-57 and 11-59 through 11-61.  The second stage of Fig 11-60 is particularly significant.  This work was apparently done during wartime, and should have been known to GAP by the time he designed his amplifiers.  The original volume has a publication date of 1948, so timing is murky.  If you need scans of these pages I can send them.

 Anyway this looked like more that a simple coincidence.  Do you have more information?

 Best regards,


Subject:  Re: positive feedback in the VT opamps such as K2-W

From: Joe Sousa 

Date:Thu, Dec 15, 2011 11:19 pm

To:" Terry Walker"

Hi Terry:

I don't know if George Philbrick used Positive Feedback before he started his business, while he worked for the Foxboro company.

In the 1950 time frame, I would expect that George was aware of positive feedback as shown in the rbsect5.pdf attachment that you sent, and which I reattached for our friends in the cc list, should they have an answer. I think that by the 1940's, Bode and Nyquist had already formalized a lot of feedback theory that Black got started in the 1920's and this probably was distilled the Rad Lab book you refer. The question of invention would more likely have to do with how he applied PFB and to what end. For example, capacitive PFB was quite popular in the 1920's to effect Miller capacitance neutralization in triodes.

In the case of the basic two stage plus follower opamp topology of the K2-W, K2-X class, the PFB was applied around the last two stages. This means that the PFB could only hope to reduce the average AVOL error, but not the mostly second order non-linearity of the output stage. See some measurements at

One reason why linearity was not improved with PFB in the K2-W and K2-XA topology is that the PFB was not around an early stage, as shown in your attachments rbsect5.pdf and rbsect11.pfb so that the non-linearity of the output stage would be divided down by the increased early stage gain.

But PFB was still very useful in Integrator applications of the K2-W because it reduced the parabolic errors that finite linear AVOL causes when an opamp integrator integrates a step. In the case of a full scale integration, even the relatively small second order linearity error may cancel out at least partially, as this residual summing junction non-linear error swings positive or negative as the output swings to full scale. The bulk of the work of Analog computers was integration and differentiation.

PFB remains a mainstay of modern monolithic opamps, and can often be applied with improvements well beyond the 20dB boost that was realized in the K2-W, due to monolithic device matching. One of the reasons why PFB remains popular and practical is that it can be usually implemented without adding new poles to the main signal path, as was the case with Philbrick's tube opamps.

Infinite AVOL can only be reached with PFB if the linearity is already perfect for the stage around which PFB is applied. This is true in the limit of small signal conditions and perfect matching, but not so under large signal.

I remain curious about the origin of Philbrick's particular implementation of PFB, by counter-intuitively lifting the cathode (gm=1mS) of the Miller stage off the ground with a degenerative 10k resistor, just so that PFB could be intuitively harvested from the cathode follower current gain with a 220k resistor. And no new poles, nor tubes! See



From:Daniel Sheingold

Date:Fri, Dec 16, 2011 10:15 pm

To:Joe Sousa

Hi Joe (et al):

The first time I'm aware of GAP using PFB in main amplifier design was in either the K2-W or possibly the K2-UX. The predecessor of the K2 series, used in the first-generation K3-Series "black boxes" was the board-wired "Beta" (2-12AX7) amplifier. My recollection is that the cathode of U2A was tied firmly to ground.

The "alpha" amplifier was the single-tube back-end inverter-follower. It was used as the gain-of-1 inverting op amp in those K3s that provided the opposite polarity output to make both the + and - outputs available. Come to think of it, I believe he might have used PFB to goose up the open-loop gain of that stage. But it wasn't until the later designs that he included PFB in the two-tube amplifier--when the beta amplifiers were liberated from the K3s to become a separate product.

The first-generation K3s were designed before my time by George and people who had been separated in a severe cutback. I was the first hire fresh after those happenings (November '49). I was one of four active employees: George, his brother Fred (administration), a technician (Lawrence McIntosh), and myself. Two people I later met who had been in the first generation of GAP/R employees were Milt Rubin and Jim Reswick. I believe Milt was later with either AFCRL or Lincoln Lab, Jim was with the ME Dept. at MIT.

The design was clever (in conserving tubes) but marginal for computing and in terms of drift! We didn't have really good amplifier design until Bruce Seddon came aboard. He made the USA (Universal Stabilized Amplifier) manufacturable in its final version, the USA-3. The biggest customer for that was HP's Dymec Division--it was the key component of their DVM, which was all solid state, except for an outhouse on the back, which held the USA-3 and its power supply. Imagine their pain--there simply weren't any good transistor amplifiers at the time (mid-to-late '50s).


From:"Terry Walker"

Date:Sat, Dec 17, 2011 11:02 am

To:"Joe Sousa"

Hi Joe,

 I got Dan’s response – thanks for sending the email on to him.  It is nice to hear history from a first person involvement.

 Just for completeness, I am sending you a scan of the pages 472-479 from the MIT vol 18 I referred to previously.  On further perusal, I find that this chapter is involved with detailed mathematical analysis of feedback systems, and introduces positive FB as one case to examine.  Here you can see the graphing of the effect of positive FB in Figure 11-57a, and the amplifer in Fig 11-60 which I felt has such a striking resemblence to the K2-W.  Except for the first stage being (optionally) another positive FB stage instead of a differential stage, the circuit is essentially the same.

Anyway, this was the basis for the comments I sent to you previously.

Merry Christmas,


From:Joe Sousa

Date:Sat, Dec 17, 2011 2:19 pm

To: "Janis and Terry Walker"

Cc:Daniel Sheingold

Hi Terry:

Thank you very much for the additional references. This is very good material for the Philbrick Archive. I plan to post a distillation of this email chain in the Archive, including Dan's first observer remarks.

This Rad Lab V18 book  was published in 1948, which is roughly coincidental with the K2-UX development. This could explain why George did not try to patent his version of PFB in the K2 series.

There is a free version of the Rad Lab V18 book on the web at

The rest of the Rad Lab series is at

I reattached your scans for the benefit of our friends in the cc line.

When first looking at the PFB example you point out in pages 478-479 I wondered how did PFB improve linearity? The answer is that it is the PFB around the first stage that causes the linearity improvement, not the PFB around the second stage as is done in the K2-W.

You are quite correct that the K2-W topology is equivalent to the example in the book, except that the K2-W could have benefited from PFB around the first stage, if the non-inverting input were given up. The other benefit of the first stage PFB is that it also serves to equalize the first stage plate voltages, thus nominally cancelling the intrinsic -1.5V offset that is present at the inverting input of the K2-W.

When the K2-W is combined with the K2-P chopper amplifier, the non-inverting leg is sacrificed but the combination offers DC Avol in excess of a Million and infinitesimal (100uV=1ppm/FS) offset. I wonder how smooth the frequency response is for this combination. With a GBW product around 200kHz, the open loop dominant pole should be around 10Hz, while the K2-P has a "single lag of at least 22sec." If a smoother response were desired, the PFB around the first stage would have boosted the gain from 15kV/V to perhaps 150kV/V while reducing the input offset. If the application were an early integrator based Digital Voltmeter, the smoother response might have provided a straighter integration with quicker settling at the start and end of integration.

On a related topic, Dan mentioned recently that one method to reset tube integrators was with neon bulbs that were excited by RF. This was quite the revelation for me, considering my long standing hobby interest in all glow tubes. I confirmed Dan's assertion by taking a NE2 bulb near one of my decorative plasma globes, while measuring the NE2 resistance with a conventional analog Ohmmeter. I got resistance values between 10k and 100k. The Ohmmeter draws it's test current from a 1.5V cell. When I rotated the NE2 to make one cathode glow more than the other, I measured up to 0.5V with a 100k load and a 20uA short circuit current. A NE2 with a third terminal wrapped around the glass makes a very special triode with external field plate control. Maybe this will finally get me to continue in the English side of the RadioMuseum forum, the  German language Teslator thread by Dietmar Rudolph. A modern small plasma globe can serve as a Teslator by removing the bulb.




From:"Terry Walker"

Date:Sat, Dec 17, 2011 11:43 pm

To:"Joe Sousa"

Hi Joe,

I leave it to you to try modifying a K2-W circuit to add the PFB in the first stage as in vol 18, and see if the benefits you predict are realized.  I like the idea, as I never have liked the built-in offset of the original design.  On using the K2-P, if the Avol goes up to 1 million and GBW = 200 KHz, the primary pole would have to be at 0.8 sec or longer.  Please recheck your math.   I have always felt that the specification of ‘at least 22 sec time constant’ actually was done for two reasons: 1) to reduce 60 Hz at the K2-P output, and 2) to make sure that the loop was stable for any gain even if the primary amplifier turned out to have a much higher gain. 

The use of a neon as a hi-z switch is an interesting idea.  I have heard of them being used in charge pump applications which required very low drift between pump pulses (this eliminates diodes and their leakage).  It was in Electronics in the 70’s, with a MOSFET on the opamp input for low input current.

Thanks for the references on where to get the Rad Lab series for free.  You should put that on your site as an important reference for all things tube.  I originally paid $250 for it on CD many years ago, and recently have been able to collect about 2/3 of the series (all the books of interest to me) from local sources since there have been a lot of older EEs dying off here in the Palo Alto area in the last 10 years, so they turn up in the local used book store and the library book sale.

The most fantastic volume in the series is the one on servomechanisms.  Those engineers did amazing things in WW2 to compute functions needs for various fire control systems, and made some very unusual mechanical computing mechanisms.


From:Daniel Sheingold 

Date:Sun, Dec 18, 2011 10:11 pm

To:Joe Sousa, "Terry Walker"

Thanks, Terry. Very interesting. The K2-W, K2-UX, and their predecessor that was integrated (before my time) into the wiring of the K3-C Adder and K3-J Integrator building blocks, all used 12AX7s (with higher gain)  instead of 6SL7s. I wonder when the 12AX7 became generally available?

Also, the K3-C used a pot connected: Vin, summing point, Vout, with a front dial calibrated nonlinearly (and "pseudologarithmically") from 0 to 100, with 1.0 in the center. It was driven by a cascode input buffer, and there was a small amount of positive overall feedback to beef up the "accuracy" at high gains. I've forgotten how this was accomplished.


From:Joe Sousa 

Date:Tue, Dec 20, 2011 11:25 pm

To:Daniel Sheingold , "Terry Walker"

Dan, the 12AX7 is listed at  with a registration date of 25.Sep.1947.

See the K3-C data sheet and schematic at: 

It shows the PFB you refer to. It's purpose is not obvious, except as a means to get toward infinite gain in the Max setting of the main control knob, without going to zero input resistance at the second stage input. Perhaps the dial accuracy at higher gains also improves, as you suggest.


p.s.: It is truly amazing how you remember this arcane detail!

From:"Terry Walker"

Date: Wed, Dec 21, 2011 12:11 am

To: "Joe Sousa"

Hi Joe,

 The use of PFB in the K3-C has the big advantage of reducting the maximum gain required of the variable gain stage from 100 to about 36, thereby making the system performance a factor of 3 less sensitive to variations in the open loop gain of opamp2.  This relaxed performance errors against line voltage variations and the resultant variation of tube characteristics with heater voltage (or temperature).  It basically uses opamp1 to make up the difference in a controlled way governed by the PFB resistor network.

 However, the PFB network has as one of its most important resistors the pot setting the Vos of opamp1, so the actual accuracy of the front panel pot scale was dependent on the Vos of the opamp1 (and its Vos pot resistance).  This may have led to the input tube of opamp1 having to be selected (or tested for critical matching at its operating point) in order to get the overall calibrations of the variable scale to be accurate at the high gain settings.  This problem could have been solved by providing an additional pot in any of several ways (which affect the voltage feedback of the 680K resistor) that would permit adjusting the PFB ratio without significant effect on the Vos adjustment for opamp1.

 It was a good design tweak, and one wonders how it was discovered.

 Aside from the use of PFB, I have used the effective gain control circuit of the opamp2 stage with monolithic ICs several times when I wanted a system gain to be easily variable over a range of say 0.1 to 10, with 1.0 at the center, by using a 10K pot with 1.11K resistors at each end.   It is extremely convenient.

 Thanks for the additional information.  I had not noticed the PFB in the K3-C before.