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Range of bias voltages for power tubes in fixed bias?

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  • #16
    The way I see it (my wife always says I should ignore my own point of view because I'm not normal) is that players don't know, or want to know that much about amps. They want to think they do. But they don't want to put in the effort to actually know. So they are subjuct to the most visible information that is easily and quickly absorbed. This seems to tax the limits of their ability to familiarize themselves with their gear. So...

    A button to press that activates a meter or led panel that has an indication of "optimum" and an adjustment control right next to it would seem ideal. The voltage range of the bias control would need to be based on the Vp and tube type (to avoid any obscene mis-adjustments). I think even an amp made to work with, say, EL34's or 6L6's could be set up with an an acceptible non catastrophic range.

    JM2C
    "Take two placebos, works twice as well." Enzo

    "Now get off my lawn with your silicooties and boom-chucka speakers and computers masquerading as amplifiers" Justin Thomas

    "If you're not interested in opinions and the experience of others, why even start a thread?
    You can't just expect consent." Helmholtz

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    • #17
      Originally posted by Chuck H View Post
      The voltage range of the bias control would need to be based on the Vp and tube type (to avoid any obscene mis-adjustments). I think even an amp made to work with, say, EL34's or 6L6's could be set up with an an acceptible non catastrophic range.
      Oddly enough, it has been.

      The Workhorse amps had a switch to set either a "typical" or "hot" setting for each of EL34 and 6L6. From there the "red light/green light" adjuster let you set them in about 10 seconds.
      Amazing!! Who would ever have guessed that someone who villified the evil rich people would begin happily accepting their millions in speaking fees!

      Oh, wait! That sounds familiar, somehow.

      Comment


      • #18
        Some brands of EL34 and 6L6 bias up identically, but even different brands of 6L6 can be wildly different. So you ideally want to base "typical" settings around your preferred brand(s).

        One pot per tube sounds like a hassle if "easily adjustable" is your target, anyone can buy reasonably matched tubes at no extra cost, what should be a 30 second job becomes a 3-5minute job as each tube see-saws with adjustment...unless you use 2 independent supplies, one for each tube.

        Comment


        • #19
          Good information; thank you. I'd like to sponge up anything I can about the issue.
          Amazing!! Who would ever have guessed that someone who villified the evil rich people would begin happily accepting their millions in speaking fees!

          Oh, wait! That sounds familiar, somehow.

          Comment


          • #20
            Originally posted by MWJB View Post
            ...unless you use 2 independent supplies, one for each tube.
            Or 6 independent supplies, one for each tube.
            "Stand back, I'm holding a calculator." - chinrest

            "I happen to have an original 1955 Stratocaster! The neck and body have been replaced with top quality Warmoth parts, I upgraded the hardware and put in custom, hand wound pickups. It's fabulous. There's nothing like that vintage tone or owning an original." - Chuck H

            Comment


            • #21
              Originally posted by MWJB View Post
              ... what should be a 30 second job becomes a 3-5minute job as each tube see-saws with adjustment...unless you use 2 independent supplies, one for each tube.
              I've been pondering this. Can you explain a bit to me?

              Do you mean a separately adjustable bias voltage per tube, perhaps derived from the same raw DC supply for bias, or an isolated bias supply for each tube, or what else that I may be missing?

              Are you thinking the bias supplies will interact?

              Still gathering data.
              Amazing!! Who would ever have guessed that someone who villified the evil rich people would begin happily accepting their millions in speaking fees!

              Oh, wait! That sounds familiar, somehow.

              Comment


              • #22
                I've seen bias settings interact in a minor way as the B+ changes with current draw as you adjust tube idle currents BUT if the actual bias supply is changing with individual bias settings than you have a problem.
                That problem may be that there is a fault or it may be that it is an inappropriate circuit which was intended for a single bias adjustment and has just been duplicated by someone with limited knowledge. There is no reason why this should happen with a properly designed bias circuit.
                "High Impedance" bias supplies derived from a capacitive or resistive divider off the HV winding are more prone to these sorts of problems.
                Cheers,
                Ian

                Comment


                • #23
                  I was about to make exactly that point -- if you design the bias supply so that it's voltage divider's Z is adequately low then it's not hard to make the later replicated sections fully independent of one another. You just have to make sure that the aggregate impedance of the replicated sections is adequately higher than the supply impedance.

                  If you've got multiple tube pairs in your output section then making this work also requires that you de-bus the entire drive circuit. I've mentioned doing this in the load line drudgery thread.
                  "Stand back, I'm holding a calculator." - chinrest

                  "I happen to have an original 1955 Stratocaster! The neck and body have been replaced with top quality Warmoth parts, I upgraded the hardware and put in custom, hand wound pickups. It's fabulous. There's nothing like that vintage tone or owning an original." - Chuck H

                  Comment


                  • #24
                    Originally posted by R.G. View Post
                    I've been pondering this. Can you explain a bit to me?

                    Do you mean a separately adjustable bias voltage per tube, perhaps derived from the same raw DC supply for bias, or an isolated bias supply for each tube, or what else that I may be missing?

                    Are you thinking the bias supplies will interact?

                    Still gathering data.
                    Every amp I have had "hands on" with a pot per tube/side of the primary has see-sawed when setting idle current, bring one tube (side of the primary up) up & the other drops. Perhaps it's not hard to correct/design out, but it seems rarely done. Like I said earlier, WRT to buying matched pairs/quads (say +/-15%) unless the amp is designed for guys who are rescuing unmatched pulls from old gear, or cherry picking NOS cast offs, I generally think that individual tube bias adjustment on a 2/4 output tube P-P amp, is a fix for a problem that doesn't really exist...or if it exists, goes largely unnoticed.

                    So, if I were to do it (I really wouldn't bother), given that I'd need 2 trim pots/dividers, I'd go for an extra diode (& cap if required), a drop resistor and take one supply from a 50-55VAC winding, the other from the B+ secondary via drop resistor feeding 50-55VAC.

                    Simple, "user friendly biasing" to me ideally means cathode biasing...and ensuring preamp & power tubes use different sockets (noval vs octal) so that folks aren't stuffing 12AX7 in EL84 sockets or vice versa! :-) Guys who are hip to biasing & tube subs (which require rebiasing) are usually already ordering new matched tubes & will take it up with the vendor if they don't get them. If you're looking at an amp that will take differing types of tube (14W, 25W, 40W...though as mentioned before careful choices in brand will make this easier...but maybe somewhat defeat the purpose of adjustability?) & need a big swing in bias voltage then you are inevitably building in a "self destruct" pot for the reckless...again here, getting creative with no's of tubes used & finding a good average for cathode bias is probably better for experimenters? If you are designing in flexibility then it strikes me that you are compromising on power (which is fine), so why not save on the circuitry & extra controls & spend on more/bigger tubes?

                    Comment


                    • #25
                      Originally posted by Gingertube View Post
                      There is no reason why this should happen with a properly designed bias circuit.
                      "High Impedance" bias supplies derived from a capacitive or resistive divider off the HV winding are more prone to these sorts of problems.
                      That's my intuition, but I'm proceeding very cautiously here. What I have in mind is a bias voltage per tube where the loading on the bias supply is substantially constant. I've messed with this a bit, thought about it, and simmed it. The current from the raw bias supply varies less than about 2% from min to max bias settings over half a dozen outputs.

                      One is always at the risk of a high-impedance raw bias supply sagging under loading or with B+. Is this sag with loaded B+ a good or a bad thing? I'd love opinions and explanations.

                      Originally posted by bobp
                      I was about to make exactly that point -- if you design the bias supply so that it's voltage divider's Z is adequately low then it's not hard to make the later replicated sections fully independent of one another. You just have to make sure that the aggregate impedance of the replicated sections is adequately higher than the supply impedance.
                      I did a bit of a shift to make the bias adjustment not change the loading on the bias supply. The idea is that if you ever get an adequate bias voltage, tinkering the adjustment doesn't change the bias supply loading (much, anyway) so the bias supply itself is unaffected, except indirectly by the sag of the entire PT output caused by the primary wire resistance. Secondary wire resistance doesn't get into it, as the bias secondary (if there is one) is lightly loaded and doesn't experience the sag of the HV secondary.

                      However, bias supplies derived from the HV secondary by capacitive impedance, etc. will still sag. They will sag less with this setup than with others, but still some.

                      Keep those cards and letters coming folks. And bless you for sharing!
                      Amazing!! Who would ever have guessed that someone who villified the evil rich people would begin happily accepting their millions in speaking fees!

                      Oh, wait! That sounds familiar, somehow.

                      Comment


                      • #26
                        If the bias supply is tied to the B+ supply and is too saggy, there's always the option to regulate it. I'm sure that you've already considered the pros/cons of doing this.

                        The whole idea of de-bussing the drive on an amp to provide individually adjustable bias supply may seem more like an electronics design exercise than a practical application, especially in those cases where you can find matched tubes. The problem that I've encountered with a 6-tube circuit is that even when you buy a "matched" sextet, the sextet doesn't stay matched very long. The burn in process often leads to de-matching of the tubes, and resultant decreases in the amp's performance. Then you're left dealing with a 6-tube matched set that isn't matched any more. What to do? Buy a new matched sextet and recycle the tubes that are no longer matched into 1-tube, 2-tube or 4-tube amps?

                        When it comes to operating an amp that has 6 output tubes driven with a bussed arrangement, I think of the analogy where I release a herd of 6 cats from the house, expecting them to march through the yard in two ranks, three abreast -- it's just not going to happen.

                        Given that 6-tube sets aren't likely to stay matched, and that there's higher expense involved in trying to buy a replacement "matched" sextet that may or not stay matched, I'm inclined to think that you'd have better luck herding cats than trying to maintain a matched sextet. To me it sounds like the 6-tube problem is one that merits the added design effort required to de-bus the output stage and design a 6-way non-interactive bias supply. Not a big deal with 2 tubes, not a big deal with 4 tubes either, but for some reason 6-tube amps always seem to give me headaches. The fact that the designs out there tend to bus-up the drive circuits definitely doesn't help the problem. I think the 6-tube amp is a case where bussed-up drive circuits are just bad engineering that's driven more by bean counting than performance or ease of maintenance.
                        "Stand back, I'm holding a calculator." - chinrest

                        "I happen to have an original 1955 Stratocaster! The neck and body have been replaced with top quality Warmoth parts, I upgraded the hardware and put in custom, hand wound pickups. It's fabulous. There's nothing like that vintage tone or owning an original." - Chuck H

                        Comment


                        • #27
                          Again, I really appreciate the commentary. It spurs some thinking, which is like taking castor oil (if you're old enough to remember this as an option): at first you feel terrible, but after a while you're better than before.

                          Originally posted by MWJB View Post
                          Every amp I have had "hands on" with a pot per tube/side of the primary has see-sawed when setting idle current, bring one tube (side of the primary up) up & the other drops. Perhaps it's not hard to correct/design out, but it seems rarely done.
                          There was a small amount of this in the Workhorse amps, but it was not so bad that biasing was a problem. You might find that bringing a tube up to green, then the other, that the first would drop out, but this was trivially easy to fix. A couple of back-and-forth cycles was all it took, and since the indicator was a green light, there was no mental processing needed, and it was really fast. True, the match in bias current was not perfect, but as you note, that's not needed. The match in bias current actually reached was about +/-3%, once I dug through the error budget in the overall measure/set/indicate process in detail.

                          Like I said earlier, WRT to buying matched pairs/quads (say +/-15%) unless the amp is designed for guys who are rescuing unmatched pulls from old gear, or cherry picking NOS cast offs,
                          And again, thank you. I have never had the field experience to know how close "matched" was. I suspect it varies with how many matched sets the vendor has to choose from and how close making payroll and rent is this month.

                          I do know that initially matched pairs in these amps, set to the nominal tolerances, drifted out of the initial bias "matching" in about 1 hour of playing time, and again at about 10 hours. Maybe they settle down more after that until wear out sends them out out of the stability well again. In any case, they drift.

                          I use the engineering maxim that whatever can't be controlled must be made irrelevant. Whatever can't be controlled OR made irrelevant must be easy to adjust or fix.

                          I generally think that individual tube bias adjustment on a 2/4 output tube P-P amp, is a fix for a problem that doesn't really exist...or if it exists, goes largely unnoticed.
                          I'd agree with "unnoticed" wholeheartedly.

                          So, if I were to do it (I really wouldn't bother), given that I'd need 2 trim pots/dividers, I'd go for an extra diode (& cap if required), a drop resistor and take one supply from a 50-55VAC winding, the other from the B+ secondary via drop resistor feeding 50-55VAC.
                          OK. This is to offer two different sources of raw bias voltage? What would you think of regulating the raw voltage with a zener to wash out the variation? This is really what I was incenting people to talk about in one of my posts: how important or deleterious is the bias sagging with the B+ on peaks? Is that good, bad, or indifferent?

                          Simple, "user friendly biasing" to me ideally means cathode biasing...and ensuring preamp & power tubes use different sockets (noval vs octal) so that folks aren't stuffing 12AX7 in EL84 sockets or vice versa! :-)
                          I'd put it another way: "user friendly biasing" would mean "the user doesn't have to think about it". Cathode biasing is one way, but it suffers from the history that makes not all amps that way already. We're stuck with many amps that are already not cathode biased. Second choice would be to make the amp mystically bias itself. I've done that, but it's not simple, and not un-intrusive for a number of reasons.

                          Guys who are hip to biasing & tube subs (which require rebiasing) are usually already ordering new matched tubes & will take it up with the vendor if they don't get them.
                          I
                          I'd expect the same guys to have the insight to view tube drift as an issue. Matched pairs don't stay matched all that long, at least for the admittedly limited sample I have.

                          If you're looking at an amp that will take differing types of tube (14W, 25W, 40W...though as mentioned before careful choices in brand will make this easier...but maybe somewhat defeat the purpose of adjustability?) & need a big swing in bias voltage then you are inevitably building in a "self destruct" pot for the reckless...again here, getting creative with no's of tubes used & finding a good average for cathode bias is probably better for experimenters? If you are designing in flexibility then it strikes me that you are compromising on power (which is fine), so why not save on the circuitry & extra controls & spend on more/bigger tubes?
                          Good questions, and I will ponder them in some detail.
                          Amazing!! Who would ever have guessed that someone who villified the evil rich people would begin happily accepting their millions in speaking fees!

                          Oh, wait! That sounds familiar, somehow.

                          Comment


                          • #28
                            Originally posted by R.G. View Post
                            I've been pondering this. Can you explain a bit to me?

                            Do you mean a separately adjustable bias voltage per tube, perhaps derived from the same raw DC supply for bias, or an isolated bias supply for each tube, or what else that I may be missing?

                            Are you thinking the bias supplies will interact?

                            Still gathering data.
                            This is my work on the topic, a quad bias circuit with a range pot to swing the whole bank up/down: http://music-electronics-forum.com/t16704/#post135894
                            I haven't fiddled the knobs in a long while on this setup, so I don't recall how bad it interacts, but it does because the pots are wired as variable resistors, so the total load is not constant. I have been thinking a buffered "range" pot would be the answer to this, but haven't done anything to work on it. I also designed this when I was first starting out, so the way I constrained the range of the "range" pot is kludgy, but it works.

                            http://music-electronics-forum.com/a...-quad-bias.png

                            It on my MOSFET post PI follower proto board.


                            -Mike

                            Comment


                            • #29
                              RG wrote: "I do know that initially matched pairs in these amps, set to the nominal tolerances, drifted out of the initial bias "matching" in about 1 hour of playing time, and again at about 10 hours. Maybe they settle down more after that until wear out sends them out out of the stability well again. In any case, they drift."

                              Interesting, what happens when everything cools back down? I'm pretty used to idle current being set...amp taken away used for 6 months to a year, or more...next time I see it, idle current hasn't moved when cold/on power up and tens of minutes, even hours on idle/light use. I have seen idle current appear to drift when measured with probes, but I wonder whether this is due to bias sense resistors in the probes getting hot & drifting, as the same tubes in another amp stay rock solid, measured by other means. I have no doubt that tubes drift significantly over very long periods/hard use...but I also wonder if there is a typical assumption when we see old amps with mismatched tubes, that they "must have" been reasonably matched at some point...?

                              MWJB wrote "So, if I were to do it (I really wouldn't bother), given that I'd need 2 trim pots/dividers, I'd go for an extra diode (& cap if required), a drop resistor and take one supply from a 50-55VAC winding, the other from the B+ secondary via drop resistor feeding 50-55VAC."

                              RG replied "OK. This is to offer two different sources of raw bias voltage? What would you think of regulating the raw voltage with a zener to wash out the variation? This is really what I was incenting people to talk about in one of my posts: how important or deleterious is the bias sagging with the B+ on peaks? Is that good, bad, or indifferent?"

                              Yes, to offer 2 different sources, reduce see-sawing, set each tube independently, matched...mismatched...whatever. I have heard reports that negative bias voltage can rise under load, seems counter intuative to me (I'm not discounting it) & would wonder if a non-sagging bias supply would run colder under load as the bias VAC supply would not track the B+ sag (if your negative voltage is say 11% of plate voltage, then it's 11% at 400v or 500v)? I have no idea as to the answers though.

                              I think setting fixed bias can be critical (for reasons of repeatability as much as anything, rather than saying you must hit "#% dissipation" or "38mA precisely") and if you are going to check/set/monitor then you want a repeatable number, for that amp/system, reflective of current. There's often a tipping point where it matters - e.g. Blues Jrs, Peavey C30s & Pro Jr's run around 350vdc on the plates here, bias to 70% and they sound noticably terrible, you need late 20's mA wise, 30mA if at all possible...I deal with a lot of harp players and some run 6-15mA per tube in big fixed bias amps, if it drops below 5mA the amps won't hold a constant note, rises above 15mA you get a lot more feedback, these things are tangible & easily noticed by the player. Setting easy/safe/ball-park/rule of thumb works in a lot of cases, but just as you get the guys who must have a perfect match at 70% idle, you get odd cases where deviating from this can be make or break from a user perspective.

                              The other week a guy dropped by for check over on a prospective purchase, I was giving it a general appraisal & suggested we look at the bias, "Oh yeah, what are we looking for? 35mA, a good match?" he asked...well the guy's opening statement, previously, was that this was the best amp he had ever heard (why he wanted to buy it in the first place), when we discovered the amp was cool & mismatched from one tube to the other by a factor of x3 he suggested that this "needed fixing"...but hang on, when he heard it & played it like this, it was the best amp he had ever heard?

                              Given that the effect of biasing at idle seems somewhat arbitrary, when we consider what goes on dynamically, it does amaze me that it works so well & is entirely repeatable.

                              Sorry, i'm rambling now..

                              Comment


                              • #30
                                Originally posted by MWJB View Post
                                RG wrote: "I do know that initially matched pairs in these amps, set to the nominal tolerances, drifted out of the initial bias "matching" in about 1 hour of playing time, and again at about 10 hours. Maybe they settle down more after that until wear out sends them out out of the stability well again. In any case, they drift."

                                Interesting, what happens when everything cools back down? I'm pretty used to idle current being set...amp taken away used for 6 months to a year, or more...next time I see it, idle current hasn't moved when cold/on power up and tens of minutes, even hours on idle/light use. I have seen idle current appear to drift when measured with probes, but I wonder whether this is due to bias sense resistors in the probes getting hot & drifting, as the same tubes in another amp stay rock solid, measured by other means. I have no doubt that tubes drift significantly over very long periods/hard use...but I also wonder if there is a typical assumption when we see old amps with mismatched tubes, that they "must have" been reasonably matched at some point...?
                                A lot of my experience is with brand new tubes of new manufacture, less with old manufacture of various amount of use, so take that into consideration too.

                                The emission of electrons from a heated cathode depends on the temperature and chemical composition of the surface. It varies over time as the surface gets heated and cooled, bombarded by residual gas ions, and gradually poisoned by various processes. This is why most of the drug store tube testers were emission testers. They applied a nominal heater voltage then checked for how much plate current flowed when the tube was considered to be a diode. Over time, emission dropped. Even CRTs did this. The "picture tube rejuvenators" were devices to boost the heater voltage to get higher temps and more emission, posponing the day when the picture tube needed replaced. Some of them applied a real over temp to shake up the cathode surface and move un-poisoned oxides to the surface.

                                So there is at least one well-known way that emission changes, and it's directly related to tube current. I've never seen the scholarly works on exactly HOW tubes age, but they must exist. If they're like most engineering materials and processes, they have an S- or Z-curve. Change happens fast at first, stabilizes to a small change over most of the lifetime, and then rises as wearout sets in. That process could well account for the big drifts I saw in new tubes as well as the stability of biasing in well used amps.

                                At one time, tubes were manufactured in such large quantity that the manufacturing processes were tweaked in and produced very, very consistent products. Tubes produced in the same run on the same line by the same people were highly, highly consistent because every possible inconsistency and variation had been ruthlessly hunted down to maximize the yield of good parts. Today, we deal with remnants from different runs, and with what amounts to a cottage shop manufacturing process in out of the way corners of the technical world. I suspect that this may account for the larger variation, as well as the fact that amp makers used to get such consistent tubes that biasing in general was done with soldered-in, fixed resistors.

                                To me, that seems to make sense of tubes that drift a lot at first, then less later. The heat/cool cycle does cause drift, but its a drift from dead cold towards the fully warmed-up value that the tube's heater and cathode conditions have drifted it to. I would expect a single tube to warm up to nearly the same current each time after first being drifted-in over some tens to hundreds of hours. So an amp coming back months later at essentially the same current doesn't surprise me.

                                Yes, to offer 2 different sources, reduce see-sawing, set each tube independently, matched...mismatched...whatever. I have heard reports that negative bias voltage can rise under load, seems counter intuative to me (I'm not discounting it) & would wonder if a non-sagging bias supply would run colder under load as the bias VAC supply would not track the B+ sag (if your negative voltage is say 11% of plate voltage, then it's 11% at 400v or 500v)? I have no idea as to the answers though.
                                Interesting. I'd like to find out more about that. With only the information at hand, I'd expect the bias supply to sag (that is, get less negative) by less than half the ratio that the B+ sags (that is, get less positive) because of the workings of the transformer, rectifiers and filters under load. If you can point me to any info on that, I'd be grateful.

                                I think setting fixed bias can be critical (for reasons of repeatability as much as anything, rather than saying you must hit "#% dissipation" or "38mA precisely") and if you are going to check/set/monitor then you want a repeatable number, for that amp/system, reflective of current.
                                I agree. Hitting the same point every time with different tubes or the same tubes over their life is the critical thing. The gain of a tube depends on the physical arrangement of the metal structures inside it. The emission of the tube depends on the chemical composition of the surfaces and the temperature. Bias sets an operating condition. Gain for a given tube just is. Repeatability over tubes of the bias condition of the circuit's operation is a big deal in making the right sound.
                                There's often a tipping point where it matters - e.g. Blues Jrs, Peavey C30s & Pro Jr's run around 350vdc on the plates here, bias to 70% and they sound noticably terrible, you need late 20's mA wise, 30mA if at all possible...I deal with a lot of harp players and some run 6-15mA per tube in big fixed bias amps, if it drops below 5mA the amps won't hold a constant note, rises above 15mA you get a lot more feedback, these things are tangible & easily noticed by the player.
                                From a technical perspective, that makes sense. Getting up out of cold-bias crossover distortion is very noticeable. And gain
                                at an operating point can rise a bit as current changes. That's how most of the bias tremolos work. Yeah - operating point matters.

                                Setting easy/safe/ball-park/rule of thumb works in a lot of cases, but just as you get the guys who must have a perfect match at 70% idle, you get odd cases where deviating from this can be make or break from a user perspective.
                                The other week a guy dropped by for check over on a prospective purchase, I was giving it a general appraisal & suggested we look at the bias, "Oh yeah, what are we looking for? 35mA, a good match?" he asked...well the guy's opening statement, previously, was that this was the best amp he had ever heard (why he wanted to buy it in the first place), when we discovered the amp was cool & mismatched from one tube to the other by a factor of x3 he suggested that this "needed fixing"...but hang on, when he heard it & played it like this, it was the best amp he had ever heard?
                                Makes sense to me. In the late 90s I wrote some stuff on tube matching, the best information I had at that point. I speculated that MIS-matching tubes might well sound good in certain conditions. One tube of a pair operating at a different point in its gain curve than the other will amplify one side of the signal more than the other, and clipping will be at different signal amplitudes. That makes for non-symmetrical amplification of the signal, and the human ear *likes* this in modest amounts. Makes sense to me.

                                Given that the effect of biasing at idle seems somewhat arbitrary, when we consider what goes on dynamically, it does amaze me that it works so well & is entirely repeatable.
                                It is a bit amazing, isn't it?

                                Again, thanks for the insight. This is helping me put stuff into perspective as I go.
                                Amazing!! Who would ever have guessed that someone who villified the evil rich people would begin happily accepting their millions in speaking fees!

                                Oh, wait! That sounds familiar, somehow.

                                Comment

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