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Fender Cathodyne Phase Inverters

Discussion in 'Amp Tech Center' started by Bendyha, Aug 3, 2017.

  1. Bendyha

    Bendyha Friend of Leo's Silver Supporter

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    I've put this together, collecting up all sorts of things relating to the Cathodyne, mostly to answer the questions that I myself had, and to organize it in a way that it all made sense to me. Some of it I have posted before in my Super Champ thread,http://www.tdpri.com/threads/super-champ-1983-optimizing.473956/, but here it has been edited, clarified, corrected and expanded. I thought I'd share it, thinking it might of interest, or even help to some forum readers, although I'm sure a lot of it is basic "old hat" to many TDPRI bottle-head aficionados.

    I will present only a simplified examination of "HOW IT WORKS" and concentrate more on "HOW TO MAKE IT WORK" . Many text-books seem to cover the first very well, if perhaps somewhat technically, but not go into the second so deeply. The main concern of many Hi-fi related texts, is the mathematical analysis of the cathodyne's attributes, and how to calculate these figures. Although this can be interesting, the results are nearly all of little practical use to the hands-on builder of guitar amplifiers.

    As far as the technical assessment of the cathodyne goes, suffice it to say that the input impedance is so high as to be of little-to-no concern. Output impedance in the designs we are using is suitably low and well balanced. Distortion levels are minimal when not over-driven, and as will be discussed later, easily made controllable when they are.

    Also, as a lot of the text book coverage is from a Hi-fi perspective, with less relevance to guitar amp enthusiasts, they therefore tend to shy away from the 12AX7 in favour of better suited higher current, higher fidelity tubes.

    The post has grown longer than intended, but I hope my carrying-on isn't too long winded, I just didn't want to leave anything important out. Due to post size limits, I have split it into several parts.

    Please let me know if you spot any mistakes, and add your ideas and experiences with the cathodyne, especially if they differ from my postulations.
     
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  2. Bendyha

    Bendyha Friend of Leo's Silver Supporter

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    The Cathodyne Inverter Circuit, in particular Fender, its history, set-up, and some possible modifications.
    Background.


    This signal-wave cycle inverter is the most simple of the tube circuits used to drive a pair of push-pull output tubes, utilizing a single triode stage. It goes by various names; split load inverter, SLPI, concertina phase splitter, P-K splitter, cathode-loaded inverter, Kangaroo phase inverter, or cathodyne PI. It has been around since the mid 1930's, only undergoing slight changes to match the tube being used and the chosen biasing and coupling method applied.

    As Fender tended to use it, we have an example of the most common version of the cathodyne, self biasing with AC coupling. The advantages of this circuit are it's economy, simplicity and the fact that it does its job very well - if set-up correctly.

    Although most likely aware of the cathodyne phase inverter, Leo Fender opted to use the paraphase inverter in the first push-pull amps that he built in 1946, the Woodie Professional. He continued to use it with slight variations until in 1953 the floating (self biasing) paraphase became his first choice for the 5D series of amps, then in 1955, the 5E series nearly all changed to cathodyne PI's, with the exception of the Tremolux 5E9A. Most of these then changed over to the now standard Long-Tailed-Pair in the 1957/8 model 5F range, or the 1960/1 5G range, but not all.


    In the "Radiotron Designer's Handbook" - Langford-Smith. - 3rd.edition - 1941, besides the transformer phase splitters, there is only the cathodyne, paraphase and floating paraphase tube circuit inverters mentioned. Although differential amplifier circuits were developing through the second half of the 1930's, resulting in a form of long-tail pair, O.Schmitts cathode-coupled phase inverter, his 1937 London paper was expanded and printed in America in 1941, but had to wait until a concise mention in the 1953 4th. edition of the RDH.

    The July 1948 "Radio Craft" magazine had a good general coverage of phase inverter circuits, by J.W Straede , including the cathode-coupled long-tailed amplifier, not requiring a negative supply like the original Schmitt inverter. In the March 1953 copy of "Radio Electronics" magazine, G.F.Cooper gave a detailed description on designing a long tailed pair, as did N.Crowhurst in "Audio Craft" May 1956, together they published the 1956 "High Fidelity Circuit Design" In 1957, Fender developed his own version of the LTP, adding a presence control into the feedback loop, and with it, changed and defined the sound of Rock & Roll, and all that was to follow.


    Looking at the consecutive schematics for the Twin we see the use of all four inverters mentioned.

    1952 - 5C8 - Paraphase

    1954 - 5D8 - Floating Paraphase

    1955 - 5E8 - Cathodyne

    1957 - 5F8 - Long Tailed Pair

    But the cathodyne did not disappear from Fender's list of possible itinerant alternatives. After evolving into a push-pull amp in 1961, it was in the Princeton series that the cathodyne found it's long term home, helping to define the character of this amp for the following twenty years. Here are the pre-1985 Fender amps using the cathodyne, showing the year they where introduced, and the subsequent year that they where superseded.

    All these amps used the same Phase inverter circuitry, but with slightly different voltages & a different pair of output tubes. The negative feedback loop encompassing the cathodyne was also constantly evolving.

    Harvard...........5F10................1956 - 62.......................................................................................250V..........6V6

    Deluxe .............5E3.................1955 - 61.......................................................................................250V..........6V6

    Vibrolux..........5F11................1956 - 62.......................................................................................260V..........6V6

    Super Amp......5E4, 5E4A......1955...............................................................................................300V..........6V6

    Pro Amp..........5E5, 5E5A......1955 - 60.......................................................................................300V..........6L6

    Twin................5E8, 5E8A......1955 - 57.......................................................................................300V..........6L6.

    Super Amp......5F4..................1957 - 60.......................................................................................332V..........6L6

    Bandmaster.....5E7..................1955 - 60.......................................................................................332V..........6L6

    Bassman..........5E6, 5E6A......1955 - 57.......................................................................................335V..........6L6

    After the next update of the range, Fender changed all the amps over to long tailed pair phase inverters, but it was decided to use the cathodyne in the new 1961 6G2 Princeton, which changed from being a single 6V6, to becoming a push-pull amp, with the new tremolo circuit. At this time, Fender also decided to change the cathodyne bias resistor from 1500 to 1000 Ohms, (although the schematics voltage references remain showing an unchanged 1.5V bias, which is likely to be wrong) and to lower the supply voltage through the successive releases until the AA1164 set the standard at around 250V, where it remained for almost 20 years.

    Princeton.........6G2, AA964, AA1164, B1270, Reverb w/boost,..1961 - 82....+ R.I...........240 - 290V.........6V6

    In 1982, when a LTP was used for the Princeton II phase inverter, the cathodyne was then used in the new Champ II & Super Champ push-pull 6V6 amps, keeping the same P.I. circuit used for so long in the Princeton's, with the 1K resistor, but re-raising the supply voltage to the higher level as used in the 6L6 amps of the mid 50s.

    Champ II & Super Champ........1982 - 86...................................................................................335V.........6V6



    Although still common in very many different Hi-Fi tube amplifiers the world over, where it use never has been truly superseded, the use of the cathodyne in guitar amplifiers has been rather limited. Here are a few exceptions;

    Ampeg - AC12, B12-XY & XT, B15-N & ND, B18-X & N, B22-Y, B25, B42-X, G -12, 15 &20, GU12, GV12, EJ12-A,, V3 and the mighty STV, all of which are AC coupled, and the DC coupled J12.

    Epiphone - EA-8P

    Gibson - GA-30RV, GA-25RTV, GA-88S, Hawk, Titan-Medalist,

    Harmony - H-311, 322 & 415.

    Kay - 720, 830

    Jim Kelley - His innovative amps used a fixed bias, AC coupled cathodyne.

    Magnatone - 413, 415, 421, 422, 425, 431, 440, 441, 460, 260-A, 280-A, M-2 through to M15, MP-1, 2, 3, & 5

    are all AC coupled, and the DC coupled 450 & 480.

    Orange - 1970's amps used both AC or DC coupled cathodyne.

    Rickenbacker -B-16

    Silvertone - Many amps, mostly AC coupled, but they also sometimes used a DC coupled cathodyne.

    Sunn - Beside their transistor amps, quite a few tube amps, most P.I.'s of which where DC coupled.

    Zodiac - Twin 30 & 50
     
    Last edited: Aug 4, 2017
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  3. Bendyha

    Bendyha Friend of Leo's Silver Supporter

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    The cathodyne, a simplified explanation of how it works.

    How they work 1 upload_2017-8-3_22-37-55.png

    Shown in the diagram, is the cathodyne phase inverter from the Fender Princeton Reverb PRRI-65

    with the supply and idle voltages shown. There is also an AC test signal voltage given for the grid and at the plate and cathode, I have drawn in a wave form to show the reversed phase of the signal coming from the plate, and the cathode wave form in phase with the control-grid signal.

    The voltage at the control-grid is not shown on the schematic, due to the fact that most people do not own a high-input-impedance multimeter to be able to read the voltage correctly. It will be near enough to identical to that shown sitting on-top of the cathodes load resistor, as the 1M grid leak resistor, carrying no current, will be dropping no voltage, and have the same voltage on both ends.


    If the 56k cathode load resistor is dropping 55V then it has 0.982mA across it. …......(55 / 56000 = 0.000982 )

    as will the 56k plate load resistor, as the current across the tube is consistent at all points.

    Therefore the 1k bias-resistor will be dropping 0.98V…...............................(1000 x 0.000982 = 0.98 )

    which is now the bias between control-grid and cathode.


    If we put a 20V positive signal voltage on top of the 55V at the control-grid, we then have this positive signal also at the cathode, making the 56k resistor drop (yes an upwards drop) 75V, then there is 13.4mA across the tube, and the bias voltage across the 1k bias-resistor increases to 1.34V.

    The plate-load resister will also drop 75V instead of the previous 55V, swinging the plate voltage down from 195V to 175V.

    So a positive signal voltage causes the cathode voltage to go up, and the plate voltage down, Phase Inversion.

    If we had a 20V negative signal instead, then the cathode drops to 35V, across the tube is 6.25mA, and the bias swings down to 0.65V.

    So a 40V swing at the input control-grid, causes inverted swings of 40Vat both the plate and cathode...... well almost, some loss will be incurred by the circuit, the creation of the bias voltage by a voltage drop in the middle of the circuit being the main cause.

    These figures match with what is being shown on the loadline further down, which I will discuss later.

    A 40V positive signal put 95V on the cathode resistor, 16.96mA across the tube, bias shifts to 1.696V, plate drops to 155V.

    A 40V negative signal, 15V Cathode resistor 235V Plate, 2.68mA current, bias 0.268V


    If we tried to swing from the idle 55V down to 0V and up to 110V then the bias would swing from 0V up to 1.96V, but one would normally never swing this far to the limit.

    So this is how a 1V idle bias is enough to handle large input and output voltages.



    As I said, a version that I hope is simplified enough to help understand what's happening in a cathodyne, yet near enough to the actual somewhat more complex workings so as not to be misleading.
     
    Last edited: Aug 4, 2017
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  4. Bendyha

    Bendyha Friend of Leo's Silver Supporter

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    The Fender Cathodyne.

    Now a look at the schematic of a Fender cathodyne, here from the Princeton reverb reissue '65. Although in some aspects not quite the same as the original AA1164, its cathodyne has the same circuit, & it shows the voltages one would expect to see when designing this stage.
    upload_2017-8-3_22-40-20.png
    2 SCHEMATIC

    And the load characteristics for the 12AX7 Phase Inverter would look like this.
    upload_2017-8-3_22-40-44.png
    3 SINGLE DC LOADLINE GRAPH

    The load line is drawn connecting the point given by the supply voltage of 250V on the 0mA horizontal line, to the point of calculated current of 2.21mA given on the 0V vertical line.

    This figure of 2.21mA is calculated by dividing the supply voltage by the added values of the plate, cathode and bias-setting load resistors. 250 / (56000 + 56000 + 1000 (= 113000)) = 0.00221A . (With the bias setting resistor only making up less than 1% of the total load resistance, it could be left out of this calculation with little discernible difference in the results.)

    Then draw the load line given by the bias resistor. This can be calculated by joining the points found by choosing a milliamp setting level on the current scale, and multiplying this by the value of the bias setting resistor, then moving along the chosen ampere line to the point where it crosses the grid bias (negative) voltage curve that matches the result. Repeat the procedure for a higher current setting, then join the two point found with a line.

    For a 1KΩ resistor at 1mA this would be; 1000 x 0.001 = 1V. (-)

    For a 1KΩ resistor at 2mA this would be; 1000 x 0.002 = 2V. (-)

    Or if you prefer, you can go the another way; for a 1K5 cathode resistor

    -1V grid curve line; 1/1500 = 0.666˙ mA

    -2V grid curve line; 2/1500 = 1.333˙ mA


    Or with the third option that Ohms law gives us, V/I = R, we could choose a point on the load line and read-off the -V of the grid curve line and divide this by the mA on the plate current scale to find the required bias resistor. For example;

    1.4 / 0.000795 = 1761, so a 1K8 resistor would be really close in this case.


    The set-up for the Princeton has the 1mA, -1V & 1K all crossing the plate load line very neatly at the same point, our quiescent bias point; this makes the calculations very easy. Tracing from this Q-point down to the plate voltage scale, we see we have 137V. This figure could also be calculated by knowing that the load resistors cumulative value of 113K will at the 1mA setting, be dropping 113V from the 250V supply, leaving 137V. Also we could expect to find 250 - 56 = 194V on the plate, 57V on the cathode, and the 1K bias resistor giving 1V less; 56V being fed through the 1M to the grid. As there is no current flow through this grid leak resistor in normal operating conditions, there is no voltage drop of the bias supply caused by it. (this changes in an over-driven condition, when the grid draws current)


    To calculate the available output swing we must now plot an AC loadline.

    For this we need to know the total AC load placed on the tube. This load impedance is made up of not only the two 56K, but also of the two 220K grid loading resistors for the following 6V6 power tubes.

    So for each parallel pair we get 56K ∥ 220K = 44K64 , doubling this for the total = 89K3

    upload_2017-8-3_22-41-40.png
    4 AC LOADLINE GRAPH

    Finding the angle of a 89K3 loadline, (at any suitable nearby point 200/ 89300 = 2.2mA) and sliding it over until it passes through the Q-point that we have already established, we see that it is slightly more revolved around in a clockwork direction than the DC loadline. Reading down from this new loadline at the 0V grid bias crossing point we find it to be at 77V, subtracting this from the Q-point voltage, we get; 137 - 77 = 60V

    Swinging upwards in the other direction amount from the -1V Q-point at 137V we see that -2V places us at 190V.......53V up, with an additional 60V of clean swing available before cut-off; well off a central / maximum swing bias.

    The Princeton schematic shows us that the output tubes are biased at -40V, so the available drive delivered is just enough to push the 6V6's into a mildly over-driven state, with the cathodyne working comfortably inside it's "clean", non-distorting limits.


    But if you want more.........

    One often finds sited on forums, a mod suggested for boosting 5E3 style Deluxe amps, and many Princeton owners seem to have directly copied the idea, rather than adapting it to properly suit the conditions found in their amp. It suggests reconnecting the cathodyne plate 56K resistor to the next higher voltage node, which on the 5E3 is the 320V supply for the 6V6 screens. On the Princeton though, there is an untapped 345V node in the power supply (seemingly made for this purpose) that one can use instead of the 250V node where it is normally tapped off from. ( It may well then drop to be nearer 340V due to the increased current draw caused by raising the PI voltage.) NOTE: This higher node will be less well filtered, and contain more residual noise. Due to the design of the cathodyne, it will have this power-supply ripple mostly amplified one-sided rather than symmetrically in opposing phase, therefore this will not be cancelled-out by the power tubes. Nonetheless, I've shown this mod on a schematic further down. Raising the voltage does not change the near-unity gain, but does extend clean headroom, thereby allowing it to pass more gain from the proceeding stage.


    The 5E3 Deluxe uses a 1K5 bias resistor, rather than the 1K that can be found in all of the Princeton's. A load-line for the 5E3, with its lower voltages, shows that the 1K5 resistor makes it more centrally biased than the Princeton. In fact the 1K5 appears to be an acceptable alternative for the Princeton as well, left at the lower voltage, or raised. If the voltage is raised and the 1K left in place, this might give you about 25V more downward swing, (added to the 60V unmodified swing) and thereby more headroom, whereas changing to a 1K5 would give you about 43V more downward swing before grid current limiting, and therefore lots of extra drive and headroom. This added headroom seems to be popular with Deluxe owners wishing to have more drive, and over-drive, potential; especially useful for those who go that step further and put 6L6 tubes in their amps like Neil Young.

    How symmetric the output of the phase-inverter is, due to the choice of Q-point, makes a noticeable difference when one side starts clipping long before the other. It is a matter of personal taste and preference as to how to set the bias, dependent upon many factors that the player must decide for themselves.


    To show what settings the other Fender amplifiers have used for the cathodyne's, I include this following diagram. What do we see here? That by increasing the bias-setting resistor from 1K to 1K5 we achieve a cooler bias, we get closer to the point of maximum available swing, & that raising the supply voltage also increases the potential maximum swing. This is why the Fender 6L6 amps used higher voltages and the 1K5 resistor.
    upload_2017-8-3_22-42-16.png
    5 MULTI DC LOADLINE GRAPH
     
    Last edited: Aug 4, 2017
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  5. danlad

    danlad Tele-Meister

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    I think your spellchecker has corrected paraphase to paraphrase!

    Are the Zodiac amps not Selmer?

    Having said that, am enjoying this write up
     
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  6. Bendyha

    Bendyha Friend of Leo's Silver Supporter

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    Critics are quick to point out the weaknesses of the cathodyne phase inverter;

    1. That it has no gain, at the best slightly below unity.

    But that is what the other half of the tube is free for.

    2. The two outputs are unbalanced at high frequencies & have differing impedances

    Irrelevant for guitar amps.

    3. Prone to motor-boating due to low frequency phase shifts when in a high level negative feedback loop.

    Not a problem in our amps, any knowing the problem, means it can be easily avoided.

    4. When over-driven, they can have unpleasant distortion characteristics.

    Well....this is to a degree a matter of taste, and may or may not be a problem. There are two main independent scenarios to be dealt with here, both originating from the cathode side, but effecting the anode side of the P.I.


    A - The first is usually before the P.I. itself distorts due to reaching a state of grid-limiting & current draw, but the output tube being driven by the cathode reaches such a state. This can cause the plate of the P.I. driving the other output tube to create a spiked response - BUT, in a normally biased Princeton with reasonably matched 6V6's, the tube receiving this spike should be in cut-off due to the AB bias-setting. A hotly biased 5E3 would be more likely to suffer from this ailment, but a quick modification can alleviate the likelihood of it happening.


    B - The second is when the P.I. itself distorts due to reaching a state of grid-limiting & current draw. If driven harder, so much current flows into the cathode that the tube saturates as the cathode reaches a fixed limit, and any additional grid signal input will now suddenly cause the plate signal to follow it, switching it from its normal function of inverting the input. A swap of input signal phase will cause the equally sudden return of the cathode & plate to their normal functioning. This sudden switching back & forth of phase creates sharp twin-peaks in the output signal, having twice the input frequency, but with intervals of varying regularity, dependant on the shifting shape of the fundamental wave form and interacting unpredictably with the riding waves of the overtones. There are cases where this can sound harmonious and "swirly", but generally this will add disharmonious overtones sounding like they are coming out of a slightly out of tune, buzzily farting transistor radio, or blatting - not good, but fortunately these conditions are easily controllable.


    For detailed explanations of how & why the cathodyne distorts, take a look at Merlin Blencowe's site, or better still buy his excellent book for an extensive analysis, and a lot, lot more. http://www.valvewizard.co.uk/cathodyne.html


    Fortunately, there are modifications that can be made to the basic Fender circuit, that are so easy to do, and make such a marked improvement to the hard driven clean tone, and even more so to an over-driving lead tone, that it could almost be classified as mandatory for achieving a good tone. Not only are there absolutely no negative side effects to the mods, it is clear and simple to do, quickly done, and cheap. They are also easily reversible, if one so chooses.



    So... what are the modifications? Simply add a grid-stopper resistors to the cathodyne, and to the output tubes.

    1. Add a 1M Ohm grid-stopper resistor to pin 7 of the 12AX7. This will prevent any frequency doubling. The easiest way would be just to solder it straight onto the tube socket. Although this is placed between the tube and the 1M grid-leak resistor, it will make no difference to the grid-leak resistor function, or to the amps previous sound. Although data sheets vary in the limit given for maximum grid circuit resistance, with Q at 1mA and 2M Rg, a 12AX7 should be alright. If, alternatively, the grid-leak resistor is between the grid-stopper and the tube, we then form a 1:1 voltage divider, and input strength will be effected.

    I did this mod on my Super Champ, along with a few others, and found that it improved the amp's sound. It added a creaminess to the tone by loosing the buzzy, blatty edge the amp had at high volumes. It helped improve the feeling of touch sensitivity, and transition into the onset of distortion, as it seems that it extended gain levels are available to drive the power tubes without the sound mushing-out. Add to this a more singing sustain when everything is dimed, and the easing of that tip into harmonic wails in the right places. As I mentioned, I have done some other mods as well.


    2. Add grid-stopper resistors to pin 5 of the 6V6 power tubes. This will help prevent any nipple distortion, which maybe isn't too much of a problem in a class AB amp like the Princeton, as the 6V6 should be biased into cut-off when the spike occurs, and will therefore it not be audible. Nonetheless, the potential for improvement to the tone achieved by avoiding the cathodyne's cathode from being clamped, along with the other advantages of using large grid-stopper resistors on the output tubes (that I won't go into here), make this quick, cheap mod well worth implementing.

    The Princeton PRRI 65 as shown above, has 1K5 grid-stopper resistors already added to the circuit, that where not present in the various original models of Princeton's between 1964 & 82. Only the 6G2 from 1961 - 64 had them.
    I have installed 33K grid-stoppers to my amp (1980's Super Champ). Although even larger resistors might be desirable, it must also be noted that these control grid resistors become part of the already high circuit resistance, and so lowering the value of the bias feed resistors is probably not a bad idea. I piggy-backed 1M resistors in parallel onto the two 220K bias feed resistors, making them effectively just over 180K. This was at first just as a trial set of values, but the results sounded so good, with no discernible treble loss or lack of power, that I have long since left it so. The Data-sheets for 6V6 tube state that the maximum grid circuit resistance should not exceed 100K in fixed bias setup, or 500K when cathode biased such as the 5E3, so our Fender standard 220K is already pushing it, and maybe shouldn't be exceeded even more, for risk of high current flashovers sending the tube into a run-away condition, & burning out the delicate grid,. (more likely to happen in older, gassy tubes) ( That being said, the Silvertone 1344 used 430K grid stoppers & 430K bias feed resistors on the 6V6GT's, but I don't know to what success. )

    Here is a schematic showing all of these mods that I have just mentioned.
    upload_2017-8-3_22-44-12.png
    6 PRRI 65 Mods

    The effect on the AC loadline; 56K ∥ 220K = 44K6 verses 56K ∥ 180K = 42K7, for the full load doubling this = 85K4. This does revolve the AC loadline a bit more clockwise than before, but with the raised voltage, this still leaves us with a downward swing potential of 82.5V, just over double the 40V bias, so capable of very heavy overdrive.
    upload_2017-8-3_22-44-43.png
    7 Here is a loadline showing this set-up.
     
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  7. Bendyha

    Bendyha Friend of Leo's Silver Supporter

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    Something else that one reads about, but seems to be more of a Hi-Fi thing than a guitar amp issue, is the concern that there could be a possible signal imbalance sent to the power tubes owing to the 1K bias resistor being added on to the load on the cathode making it a 57K ohm load vs the 56K plate load. This is a difference of 1.8% ! The carbon-compound resistors in all older amps are at best + 5% tolerance when new, and likely to have drifted off-spec. over the years. Measuring my amp, I found the anode resistor to be 59K and the cathode to be 57K. (which was closer than I expected) No harm would come from blue-printing all the components, but it really isn't necessary, the cathodyne is very much a self biasing circuit that will adapt to find its own working point somewhere in the middle. One could shift the coupling cap connection from the cathode end of the 1K biasing resistor, to the end where it joins the 56K load resistor. Set up like that, the 1K bias resistor could help smooth the tone by adding a bit of local negative feedback. I tried this on my OR100/2 Orange amp, but could hear no discernible difference. Some people recommend bypassing the bias resistor with a cap, but then there is no LNFB.
     
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  8. Bendyha

    Bendyha Friend of Leo's Silver Supporter

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    More things to try with a Cathodyne ? How about a fixed supply voltage for the grid.

    A common mod that many people seem to have tried on Fender cathodyne P.I. amps such as the 5E3 Deluxe and the various Princeton's, is to change the stock self bias set-up to what is referred to as a fixed bias arrangement. The idea being that, if the bias point is correctly chosen, it leads to the cathodyne voltage swing being more stable, thus having a more symmetrical clip when over-driven, thereby giving a smoother sounding breakup, with an increase in headroom that comes through the larger voltage swings before the phase splitter clips, and also to eliminate (or at least somehow limit) the degenerative feedback coming from the cathode bias. As to whether it fulfils all or any of these expectations, or indeed sounds better than stock, I will not judge. Many people seem to have tried it, some liking the results, others not. Many people seem to have just blindly followed and copied what is referred to a "Paul C mod." and used a 1M & 2M2 resistor as voltage dividers, rather than working out the correct values for the tubes, resistors and voltages in their amps. So I guess many have unintentionally created a super-asymmetrical Fuxed-bias rather than an efficient and symmetrical fixed-bias; maybe the reason that many seemed to dislike the mod, or maybe the reason that some liked it ?

    The Deluxe 5E3, and all the Princeton's (with the exception of the G2) all have approximately 250V phase inverter supply voltage. In all other aspects, the phase-inverter circuits are the same - a 12AX7 tube with 56K cathode and anode resistor loads, a 1K bias setter, and a 1M grid (leak) feed. This method will work for all of them, regardless of supply voltage, as the fixed-bias is a fixed proportion of it.

    This is what one should do to change the exemplified Princeton into a fixed bias cathodyne set-up.

    First I'll work out the bias setting that would deliver the maximum voltage swing, which will probably also represent the coolest bias-setting advisable for a 12AX7, due to its fairly limited current delivering capabilities.



    First plot the D.C. load-line onto the "anode voltage vs cathode current" characteristic grid bias curves sheet.

    The 56K plate and cathode resistors form an accumulative load of 112000 Ω ( I'll ignore the 1K resistor)

    Supply voltage is 250V.

    250 / 112000 = 0.00223A...........= 2.23mA

    The load-line (RED) joins the 250V to the 2.23mA



    Where this crosses the 0V grid-curve, we can read off the cut-off voltage 72V & current 1.58mA (GREEN)

    For a central bias we can either halve the current reading of 1.59mA = 0.795mA

    or find the swing centre; 250V - 72V = 178V......../2 = 89V.........+72 = 161V.

    Plotting (BLUE) from 161V or 0.79mA towards the load-line, brings us to the idle bias voltage of -1.4V.



    Now working backwards again, to see how everything lines up, we can get the grid voltage.

    The Bias point voltage is subtracted from the supply voltage tells us how many volts altogether are being dropped over the two 56k resistors. Halving this figure leaves us with the idle voltage to be found on the cathode.

    250V - 161V = 89V....................89V / 2 = 44.5V



    Alternatively, multiply the idle bias Amperes by the Ohmage of the cathode resistor to get the voltage drop.

    .000795 * 56000 = 44.5V..................The answer is the same.



    To find the grid voltage required, subtract the idle bias voltage from the cathode voltage.

    44.5V - 1.4V = 43.1V



    Subtracting the grid voltage from the supply voltage, we can then extract the ratio between the two;

    250V - 43.1V = 206.9...............43.1 / 206.9 = 0.208



    Using this ratio, as it is the same as the ratio between the voltage divider resistors we require;

    R+ connected to the HT supply, and R- connected with ground, we can get the three optional calculations to help us find suitable resistors to join together at the grid, to set the bias;

    R- / 0.208 = R+

    R+ * 0.208 = R-

    R- / R+ = 0.208



    Using standard values, and keeping R+ as small as possible to limit thermal noise, but big enough not to load down the supply chain too much, and at the same time also keeping R- big enough to not load down the previous stage more than necessary, a fairly good compromise and combination could be 3M3 with 680K :

    Bouncing this around the three calculations above, we get;

    680000 / 0.208 = 3269230

    3300000 * 0.208 = 686400

    680000 / 3300000 = 0.206



    So 3M3 / 680K are a fairly good matching choice, an would yield = 42.7V..... less than 1% off the aim of 43.1V.

    Remembering that the combined impedance of the resistors will be loading down the previous stage, we could use any one of these following combinations, sometimes having to run two resistors in series to make up the needed value.


    3M3 / 680K = 42.7V = 564K load

    2M5 + 2M5 / 1M + 47K = 43.3V = 866K load

    2M2 + 2M5 / 1M = 43.8V = 825K load

    2.2M / 470K = 44V = 387K load is probably a bit low.

    3M3 / 750K = 46.3V = 611K load

    2M2 + 2M / 1M = 48.V = 808K load

    3M3 / 820K = 49.75V = 657K load

    4M / 1M = 50V = 800K load

    3M3 / 910K = 54V = 713K load

    4M4 / 1M + 270K = 56V = 985K load



    Now say I wanted to have the same bias point as the stock Princeton. We have already seen it has the 1mA, -1V & 1K all crossing the plate load line very neatly at the same point, and that the cathode has 57V on it, and so we want 56V on our grid. Supply is 250V.

    250 - 56 = 194.................56 / 194 = 0.28866

    4400000 * 0.28866 = 1270104..................we'll have to build that value............(2 * 2M2) / (1M +270K)

    I couldn't find single standard values that come near to matching the requirements, but this is very close to perfect.

    250 * (127 / (440 + 127)) = 55.99V..............The option on the bottom of the list above.


    The combination 2M2 + 2M / 1M = 48.V. is about what a 1K5 self-bias resistor would give you.



    Interestingly, but not so surprisingly, running these computations through for a 350V supply instead of for a 250V supply, the proportions for the two resistors for the voltage divider work out to be almost exactly the same, so long as the two 56K resistors remain unchanged.

    If a Princeton owner where to change the plate supply voltage up to the higher node, then shifting the voltage divider supply at the same time, would require no additional changes to be made.



    The cathodyne is a fairly forgiving circuit, with the tube floating around somewhere in the middle of it. Even in this so called fixed bias-setting, due to the inherent cathode current feedback, it will always be self-adjusting.

    The cathodyne is quite linear down to lower currents, as it is not effected by the bunching together of the grid voltage curves in the same way as common cathode gain stage would be. Being a (near) unity-gain stage, to get 100V of output swing, the input will have to be slightly more than 100V. So the amplified grid voltage swing is not the grid voltage bias change shown by the grid curves, but the input voltage swing matching that shown on the plate voltage scale at the bottom, minus the grid bias voltages shown. The spacing of the plate voltage scale is linear, and subtracting the few extra grid volts at lower currents has little effect upon this. None-the-less, we don't want to be to far into this low current area when biasing, as it can lead to other problems......

    I would recommend the point of maximum swing, and the equivalent of the standard Princeton setting, to be about the two outer limits that one might aim for. So let's say a fixed bias feed of between 42 & 58V.

    BUT...Going back to the 2M2 & 1M that some modders seem to have opted for in the past. This bias combination is way off from being suitable for a decent headroom.



    So how might Paul C have come up with this strangely inadequate resistor combination?

    If he had calculated what this combination gives you, he would have seen;

    1M /(1M+ 2M2) = 0.3125.................................0.3125 * 250 = 78.125V

    and realized that this was unsuitable. But maybe he then tried to measure his results.



    So what was the input resistance of his voltmeter? 10M maybe?

    Put that in parallel with the 1M resistor he would have been measuring the voltage drop over;

    10Meg || 1Meg = 909090, so he would actually be measuring the voltage drop over a 909K resistor.
    909090 / (909090+2200000) = 0.2924 .............0.2924 * 250 = 73.1V.

    Still unsuitable.


    But what if he used a 1M input impedance meter, like many of the cheaper multimeters have?

    1M || 1M = 500K

    500000/(500000 + 2200000) = 0.185...............0.185 * 250 = 46.3V

    Then he would be getting the falsified reading of 46.3V, which is very close to what the bias should be, and maybe what he thought he had actually got. In fact due to bias shift within the tube, his meter probably showed an even lower voltage.

    I think this very easily made, but basic error, might well have been the origin of this often copied, but inadvisable modification.



    BUT.....the thing is, this unruly set-up will still work, nothing like intended to maybe, but work - it does. Instead of creating an efficient fixed-bias set-up, the tube will instead have to self-adjust with help of its equal loads on both cathode and anode, and swing itself into a new state of equilibrium. This requires it approximately doubling its previous pre-mod current draw, stressing the tube more, and dropping twice the previous voltage over each of the two 56K resistors (keeping them nice and warm). This way the tube pulls its cathode voltage up so as to be back within a few volts of the fixed grid voltage. So instead of freeing the cathodyne to work more effectually, it has instead become more limited in its potential output swing. Nonetheless, very strangely, some people who have tried it seem to be happy with the results.
     
    Last edited: Aug 3, 2017
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  9. Bendyha

    Bendyha Friend of Leo's Silver Supporter

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    It may be noted that Jim Kelley, who's 4*6V6 amplifiers used a fixed bias 12AX7 cathodyne PI with a 375V supply divided by a 5M6 / 1M5 to deliver 79.22V to the grid.

    The cathode and anode load resistors where 68K. Drawing up a load-line for this 136K, one finds that the centrally biased point of maximum swing is almost exactly where a 1K5 resistor would bias the tube if in a self biasing configuration, this is at 1.14mA and with a 1.7V bias.

    The 68K cathode resistor at 1.14mA would drop................0.00114*68000 = 77.52V

    77.52 + 1.7 = 79.22V Exactly what the voltage divider is supplying.

    This delivers a potential output swing of 120V for each output tube pair.
     
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  10. Bendyha

    Bendyha Friend of Leo's Silver Supporter

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    We are not finished yet, there are still some other considerations;

    As to whether the lower load of 564K when using the 680k resistor is problematic for the previous stage and the input signal, or if any thermal noise from a 3M3 resistor injected straight into the grid is deemed to be to loud. Well.......there is an easy fix that will ensure avoiding both these possible problems. Instead of connecting the bias voltage directly to the grid, decouple this node with a 1µF capacitor to ground as a filter, and a 1M resistor as the grid leak resistor, to act as a new higher grid load. The added 470k grid resistor is an optional grid current limiting resistor. The recommended maximum grid circuit resistance for a 12AX7 is 2M2, so I wouldn't go much bigger than the 470K here.
    upload_2017-8-3_23-55-42.png
    8 Fixed Bias Mod.

    Although the 1K bias resistor is no longer needed in the cathode circuit, and many argue that its presence can upset the symmetry of the phase inverter, it is actually not a bad idea to leave it there to help buffer the tube from following load capacitance. So either remove the 1K, or just shift the output connection to the 22nF coupling capacitor to the lower end of the 1K resistor as shown above. Although this makes the combined cathode resistance somewhat larger than that of the plate, the cathodes source impedance is much lower, so the added series resistance will make very little difference to the balance.


    To avoid the unwanted effect of frequency doubling, a grid stopper should also be added to limit the grid drawing current in the way that I've described further above. In conjunction with the 1M that is feeding in the bias voltage, a grid resistor of 470K shouldn't attenuate the ample driving signal to much, but still suffice in limiting current draw and unwanted distortion.

    -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------

    The correct measuring of the higher impedance parts of the power supplies in tube amp can be a tricky task, as the measuring voltmeter becomes an active part of the load on the supply. This leads to the measured voltage being lower than expected of the original source voltage. If measuring a fairly stable part of the power supply, one can make compensating calculations to correct the measured voltage; if the input impedance of your meter is known, and the source impedance of the supply being measured.

    But the control grids of tubes can present a difficult problem, as they do on the self-biasing cathodyne P.I. With its 1M grid-leak resistor, as soon as a multimeter is connected, not only does the voltage drop due to the voltage divider being formed, but this drop will cause the tube to re-bias itself, drawing different currents, thereby dropping different voltages.....and as a result, the grid voltage reading could read as little as 1/3 of what it is in an unmeasured state. With a fixed biased cathodyne, the grid supply voltage will be more stable, but will still need to be recalculated if actual working voltage for some reason needs to be correctly recorded.

    To be able to take "real" measurement, the voltmeter must have an extremely high input impedance. One could make up a very high ohmage voltage divider by adding a 1GΩ resistor to the input of your meter, and then multiply up the measured millivolts to get closer to true reading.

    But usually it is not necessary to measure the grid voltage, as the readings at the cathode and plate will show if anything is amiss.
     
    Last edited: Aug 4, 2017
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  11. Bendyha

    Bendyha Friend of Leo's Silver Supporter

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    It's all a matter of personal taste as to whether a guitar amp sounds better with a balanced phase inverter, or if an asymmetry in the signal being sent to the output tubes improves the amps tone by adding an increase in even order harmonic distortion. How much headroom do you want/need? In the end, it perhaps depends more on all the tubes around the phase inverter. Why ? Because the tube driving the cathodyne might have to put 100V of voltage swing into the grid, to get two inverse outputs of slightly less voltage swing on the other side. The cathodyne, with its very high negative feedback, has very low distortion, unlike the tube driving it, which will be distorting to quite high levels long before the cathodyne. The same goes for the power tubes being driven by the phase-inverter.

    Just how hard one wants to drive the output tubes, and whether there are adequate current limiting measures being taken to cater with these demands, this is what is deemed to damn the sound as being perceived as either the Good, the Bad or the Ugly. But as the man with no name said "Every gun makes its own tune."



    Here are some measurements taken from the Fender Cathodyne family of amps. Make of it what you will.

    upload_2017-8-3_22-52-6.png
     
    Last edited: Aug 4, 2017
  12. Tommy Gereg

    Tommy Gereg Tele-Meister

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    Thank you so very much Bendyha! This is absolutely fantastic reading. I've converted forty old tube Hi-Fi and PA amps to guitar amps over the last few years and I used the Fender AA964 style Cathodyne PI on every one of them.

    The low wattage amps (6V6, 6BQ5, 6AQ5) all sound great but the higher wattage 6L6, EL34 amps have strange issues. I think the Cathodyne PI may be the problem with the biger amps.

    Perhaps the LTP PI would be a better choice????
    Thanks again!
     
  13. D'tar

    D'tar Friend of Leo's

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    That's a ton to chew on and will take me some time but thanks B! You fellas have impeccable timing:). Your patience and generosity are remarkable.
     
  14. Old Tele man

    Old Tele man Friend of Leo's

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    Hey, Bendyha! To those nit-pickers complaining about the 1kΩ bias-resistor, tell them to simply add a complimentary 'balancing' 1kΩ resistor to the plate-side path. Of course, doing so will NOT correct the inherent impedance differences of the plate- and cathode-outputs, but it will "balance" the plate/cathode voltage-split (wink,wink).
     
    Last edited: Aug 3, 2017
  15. robrob

    robrob Poster Extraordinaire Ad Free Member

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    Bravo! Great post Bendyha.
     
  16. fmmlp

    fmmlp TDPRI Member

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    55v/56k= 982uA or 0.982mA
     
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  17. Bendyha

    Bendyha Friend of Leo's Silver Supporter

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    Fixed, thanks...I often have problems counting when too many 0.000000 are in a row. Sometimes I feel i'm missing the point:D
     
    Last edited: Aug 4, 2017
  18. fmmlp

    fmmlp TDPRI Member

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    I think it's a good analysis. I will read it through this night. Thanks for sharing
     
  19. Commodore 64

    Commodore 64 Friend of Leo's

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    Thank you for this great amalgamation of data. I've subbed, so I can easily find it so I can easily reference it in the future.
     
  20. robrob

    robrob Poster Extraordinaire Ad Free Member

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    The sections on creating load lines are the best I've ever read. Really nice work Bendyha.
     
    Last edited: Aug 4, 2017
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