John Broskie's Guide to Tube Circuit Analysis & Design 
25 december 2016 (updated dec 27 2016) 幸运28计划软件appmerry christmas! i didn't plan on posting today, but i didn't want to miss a chance to use the following image, one of my favorites. see to read about her.
PushPull Minus Push Equals SingleEnded My pick is Leonhard Euler's Identity Equation. 幸运28计划软件app It is short and sweet, filled with all the important things, such as zero, the primary integer, pi, i, e, addition, multiplication, exponentiation, and equality. Returning to the world of electronics, What happens to a pushpull circuit when we subtract pushing half? Answer: we get singleended operation. Here is an example, which converts a nominally pushpull output stage into a singleended one.
The triode on the right functions as a constantcurrent source, as its cathode is loaded by one. The triode on the left does all the amplifying. Understand that plate load impedance has fallen, as only half of the primary is loaded. In other words, if the winding ratio had been 20:1, it's only 10:1 now, which means that that primary impedance has fallen to one fourth its platetoplate value, as the winding ratio squared equals the impedance ratio. Now, if you are running 16ohm speakers, you could attach them to the 4ohm output tap on the secondary, so the old load impedance is restored. 幸运28计划软件app by the way, what happens if we remove the remaining electrolytic capacitor from the above circuit? we get no amplification at all. what happens if we add a second the electrolytic capacitor to the above circuit shunting the right constantcurrent source and drive both grids with a balanced input signal? we get pushpull operation in classa. well, we can actually push the output stage past classa, but we risk overcharging the two electrolytic capacitors, which will lead to under biasing the output tubes, which if severe enough, can turn them off altogether for a short period, resulting in momentary loss of output, i.e. blocking distortion. classa means living within our idle current. Here is a fun pushpull setup, wherein each triode gets its own constantcurrent source to set its idle current, while the nonpolarized electrolytic and film capacitors bridge the two cathodes to AC signals. 幸运28计划软件app Now that we have mentally warmed up, we can move on the three reflexive circuits, i.e. the SRPP, White cathode follower, and SRCFPP. All three belong to a triumvirate of lazy pushpull circuits, circuits that achieve classA pushpull operation without receiving a balanced pair of input signals, making use of a single unbalanced signal at just one triode's grid. How does the other triode get its own signal at its grid? Each circuit uses a currentsense resistor to develop the needed antiphase signal to drive the opposing triode. All three circuits are entirely load dependent; a different load impedance requires a different currentsense resistor value. The SRPP is the darling of tube fanciers, as it is super simple and it solves the problem of what to do with the extra triode found in dualtriode tubes such as the 6DJ8, 6SN7, and 12AU7. The SRPP's formula for the optimal currentsense resistor value is easy enough:幸运28计划软件app Rs = (rp + 2Rload) / mu in fact, this same formula is used with the other two lazy circuits. With a cathodetoplate voltage of 75V and 10mA of idle current, an ECC99 exhibits a plate resistance of 2700 ohms and a mu 22, which the above formula decrees that a 150ohm currentsense resistor be used. SPICE simulations conformed the formula's prediction. the ecc99 is a robust twin triode tube that can dissipate an amazing amount of plate dissipation, i.e. 5w per triode. in the above circuit it idles at 10ma, which means that the peak output current swing is 20ma, which in turn means a peak voltage swing of 6v into the 300ohm load. if we replace the currentsense resistor with constantcurrent source, we end up entirely undoing the pushpull operation, leaving only singleended operation. it is no longer an srpp, as we have undone the pushpull operation. some call this circuit a mu follower. many either believe that this is the ultimate expression of the srpp topology or that this actually how all srpp's work. ah, distinctly i remember it was in the bleak late 1990s; and each separate angry email wrought its ghost upon my soul. the same three pained expression of dissatisfaction and resentment. "all circlotron must by necessity operate exclusively in classa." "bruce rozenblit's patented otl circuit had been vouchsafed by the luminaries at the us patent office, so no debate was permissible." "the srpp holds no pp, as it is purely a singleended effort, the top triode functioning as a constantcurrent source and as a cathode follower at once, achieving the miracle by varying the current flow through the top triode, which is a great trick for something that draws a constant current." all three claims were repeated over and over, like some deranged magical enchantment. then it ended. somewhere mid 2000's, the three claims grew silent. why? super good question. 幸运28计划软件appmy guess is that enough readers had access to a spice program and they were able to perform their own tests. in the simulations, no exclusive classa operation could be found, just everyday classab; bruce's patent didn't ensure equal but opposite phase conduction for the otl's output tubes; and the srpp pushed and pulled, true to its name. thus, spice won over those for whom reasoned arguments left unpersuaded. at the same time, however, spice allowed many to create impossible circuits. for example, the above currentsourceladen circuit works perfectly well in spice, but would prove impossible to reproduce in reality with the same performance. Seriously? Why? in spice, a current source is magical device that finds no equivalent in reality, as it produces current flow in the absence of a power supply; it is a power source in its own right. the above is a screen capture of a spice current source in action. note that no power supply or battery is present. 幸运28计划软件appin reality, constantcurrent sources are actually current regulators or current limiters; they do not produce current out of thin air. moreover, they cannot work below some relatively high voltage, say 1v to 3v. is this a problem? yes, it is, as this means that the circuit shown above will choke with a real current source, such as the lm334, as only 1.5v of voltage spans from the bottom triode's plate to the top triode's cathode. think about, let's say that the lm334 could, miraculously enough, work down to 0v across its leads. then the maximum positive gridvoltage swing the top triode could experience would be 1.5v, the voltage drop across the current source at idle. but a real lm334 will stop working once its voltage differential falls below 1v. in contrast, a spice current source can swing the grid up past its cathode voltage, as the following spice generated graph shows. the thick, blue line reveals the top triode's gridtocathode voltage. after a 1ms delay, a 1vpk sinewave is presented to the bottom triode's grid. the constantcurrent source sets a strict negative voltage swing into the load of 3vpk, as 10ma against 300 ohms equals 3v. the top triode is not limited by the constantcurrent source; indeed, the constantcurrent source performs the magic trick of swinging the top triode's grid 4v more positive than its cathode. unfortunately for us living in the nonvirtualreality world, this magic trick is just a fantasy. 幸运28计划软件appthe workaround would be to add an internal coupling capacitor and a few extra resistors and fet or mosfet—and bump up the b+ voltage to something closer to 160v. another possible workaround is to use a largevalued inductor, say at least 20h) with a dcr of 150 ohms. the inductor can swing the top grid several volts more positive than the top cathode, but it, too, imposes an idlecurrent limit to negative voltage swings into the load impedance, the same 3vpk limit. okay, returning to the virtualreality spice version of the srse, the top triode experiences all the current variations, while the bottom triode sees a constant current flow. the 300ohm load impedance sees the difference between the top triode's conduction minus the 10ma of steady current flow. for example, in order to swing +/10ma of current into the load, the top triode must increase its conduction up from 10ma to 20ma and then drop its current flow to zero to allow the constantcurrent source to deliver all its flow into the load. 幸运28计划软件appthe great advantage to the srse topology is that gain increase from 1.9 for the resistorbased version to 15 for the constantcurrentsource version. in the distortion contest, the winner is clear.
幸运28计划软件appforgive the christmas color scheme. ho ho. the srpp with the currentsense resistor puts out far less than 0.1% distortion, whereas the srse with the constantcurrent source, the spice bestcasepossible current source, does a little better than 1%. the srpp can swing up to 6vpk into the 300ohm load, while the srse can only swing 3vpk. 幸运28计划软件appokay, was this a slam dunk? did the srpp with currentsense resistor totally kick butt? maybe, maybe not. note that the srse delivered more 2nd harmonic distortion. i can easily imagine many preferring the sound from the srse, finding it far more musical and warm sounding. of course, even this scenario can be flipped. the same listener who reveled in the srse's romantic presentation of an old verve jazz lp may prefer the srpp with a thick orchestral recording, finding the clearer presentation well suited to complex, hundredinstrument performances. sometime you fell like a nut; sometimes you don't.
SingleEnded White Cathode Follower many, if not most, do not want to use the optimal white cathode follower setup shown above, preferring to make the currentsense resistor's value as high as possible, which logically ends in using a constantcurrent source instead. placing a constantcurrent source in series with the triodes means that we have departed pushpull operation, as the top triode must constantly draw a fixed amount of current, which means that the bottom triode must do all the work, swinging up to twice the idle current and then swinging down to zero conduction. with a 10ma constantcurrent source, the maximum output voltage swing would be 3vpk into 300 ohms. in contrast, the optimal pushpull version will swing 6vpk into 300 ohm, as each triode can deliver twice the idle current into the load. 幸运28计划软件appin terms of performance, the constantcurrent source version offers a closer appropriation to unitygain (0.94 versus 0.8, in this example), far lower output impedance (5 ohms versus 45 ohms), insanely improved psrr (near negative infinity versus 9.3db). what about the all important harmonic distortion? here is the spice generated results. 幸运28计划软件appthe optimal pushpull version of the white cathode follower delivers lower 4th and above harmonics, while the constantcurrent source version offers lower 2nd and 3rd harmonics. so which won? i cannot say. i can say, however, that if you need stellar psrr and low output impedance, but not heavy power delivery, say driving a passive lcr riaa eq network, then the constantcurrent source version clearly wins. or does it? in the absence of a dc feedback mechanism to keep the dc voltage inline with our desires, placing a constantcurrent source in series with an ultrahigh impedance termination, which the top triode's plate presents in this topology (in dc terms, not ac terms), creates huge headaches. trust me. placing constantcurrent source in series with an ultralow impedance termination, such as a cathode, however, works well. The solution is to use one of my compliantcurrent sources幸运28计划软件app (CCCS) instead. The
is a highvoltage (500V) MOSFET in a TO92 package. It is rated for 0.89W and two can be bought for less than $1. Now, the idle is set by the 150ohm cathode resistor, not a constantcurrent source.
SingleEnded SRCF like the white cathode follower, the srcfpp is a unitygain buffer, a buffer which can swing twice the idle current into the load. here is a fun arrangement, which uses a 12au7 as the input tube and an ecc99 as the output tube. 幸运28计划软件appthe output impedance is about 80 ohms; the psrr, about 60db; and the gain, about 6 (+15.5db). this makes a truly sweet headphone amplifier for 300ohm headphones, such as those made by sennheiser. (i plan on building a headphone amplifier based on this circuit with two s and two , one per channel. overkill? yes. i want to not share ground connections between the channels in the enclosure, only in the signal source, so i welcome the balanced output. the idea behind this project is to prevent a shared ground that would allow signal currents to travel down the wrong channel's ground connection.) undoing the pushpull operation requires replacing the currentsense resistor with a constantcurrent source. unlike the srpp and white cathode follower, the constantcurrent source in series with the cathode and ground is no problem. what might prove to be a problem, however, is the constantcurrent source starving for voltage. one workaround would be to place a 2m in parallel with the 0.68µf capacitor. 幸运28计划软件appnote the high b+ voltage (250vdc) and the high idle current (20ma), both of which allow 6vpk output voltage swings into 300ohms, compared to the pushpull version's 12vpk swings. unlike the previous shootout, the gain, output impedance, and psrr are pretty much the same between the pushpull and singleended versions. what does differ, however, is the harmonic distortion, as the following graph shows. the pushpull version offers significantly less harmonic distortion. How can this be, John, constantcurrent sources always make things better? 幸运28计划软件appactually, they don't. for example, a cathode follower's psrr worsens with a constantcurrent source load over a resistor load. 幸运28计划软件appfor those who must use the treecontact headphone plug, the following variation could be used. 幸运28计划软件appthe output transformer allows us to either run a balanced output or a regular sharedground output. in addition, it allows easy phase reversals and the ability to use either high or lowimpedance headphones. a winding ratio of 2:1 results in an impedance ratio of 4:1, so 300ohm loads will be reflected at the primary as 1,200ohms loads. assuming 50ohm headphones as the lowimpedance load, the winding ratio should be 5:1, as 25 times 50 is 1250, close enough. i ran some spice simulations on the above circuit and the results were so fine, i am too embarrassed to show them.
SE Vs PP Update
幸运28计划软件appthe singleended versions with a constantcurrent source delivered half the peak output swing. the white cathode follower improved the most, as its output impedance and psrr fell considerably; its distortion was more than halved. across the board, the srcfpp suffered from using a constantcurrent source over a currentsense resistor. and the srpp delivered a mixed bag of results, as the output impedance fell greatly, while the psrr improved and the gain climbed, but the distortion substantially worsened by twentyfold. note that the srcfpp circuit was the straight version shown below, except that no rk resistor or coupling capacitor at the input. instead, we can use the aikido version of the srcfpp, which offers a significantly improved psrr. by inject a small portion of the powersupply noise into the bottom triode's grid, we create a powersupplynoise null across the load resistance.
//jrb
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幸运28计划软件appso many have asked that i had to do it. WARNING: THESE THREE PROGRAMS WILL NOT RUN UNDER VISTA 64Bit or WINDOWS 7 & 8 or any other 64bit OS. 幸运28计划软件appi do plan on remaking all of these programs into 64bit versions, but it will be a huge ordeal, as programming requires vast chunks of noisefree time, something very rare with children running about. ideally, i would love to come out with versions that run on ipads and androidos tablets. //jrb 
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