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This Issue We were hoping to let the Circular/Balanced/Bridge amplifier rest and not make an appearance this issue, but it is here in an article on tube buffers. Expect more on this topology next month as well, for we are not nearly done excavating this vein. The circuit from the July article, "Unbalancing Acts," is back in the same buffer article. In this same article you find the secret to optimizing the White Cathode Follower as a Class A output stage. Headphone fans take note. I have found that many tube circuit neophytes and, unfortunately, far too many tube gurus have only the Grounded Cathode amplifier under their belt, so to speak. Good as this circuit is, a bigger repertoire is welcome. (I am saddened by sights such as the earnest tube fancier wasting his time trying different brands of the same valued plate resistor in an attempt to make the 12AX7 based line stage he owns better drive the 15 feet of high capacitance interconnect to the amplifiers.) The aim of this journal is to increase the vacuum tube circuit vocabulary of the readers. Reader Rowan has asked for some direction in building a tube microphone preamplifier. Two topologies are shown. In the last issue, reader Ian made a great suggestion: a tube amplifier that would mimic the mixed class of operation of the Pass Labs Aleph amplifier (SE / pushpull Class A). This month we have a brief follow up by presenting a current source alternative to using a choke. Remember, if you have a request or suggestion of your own for either an article topic or circuit, please email: Editor The Cathode Follower A Quick Overview Right after the Grounded Cathode amplifier, the second most common tube circuit in use is the Cathode Follower. The simplest buffer that can be made with tubes, it is used to match a signal from a high impedance source to a low impedance load. In This Issue 1 4 8 9 11 14 18 Cathode Follower White Cathode Follower Plate Follower Broskie Cathode Follower Circular/Balanced/Bridge amplifier Tube Microphone Preamplifier E-Mail Publishing Information Glossary of Audio Terms The circuit is single-ended and Class A by design, as there is only one active device. The plate is, in AC terms, but not in DC terms, grounded and thus the Cathode Follower other name: the Grounded Plate amplifier. www.tubecad.com Copyright © 1999 GlassWare All Rights Reserved NEXT > The assumption here is that the B+ connection has the same signal content and impedance as the ground. The input signal is given to the grid while the cathode is loaded by a resistor that leads to ground or a negative power supply. The gain is always less than unity, the output impedance is roughly the reciprocal of the transconductance, and the PSRR is roughly equal to the inverse of the mu. An intrinsic distortion correcting mechanism known as degenerative feedback keeps the Cathode Follower's distortion low. It works this way: any departure from the desired output voltage will subtract from the input voltage and result in a countervailing change in current flow. In other words, if the cathode is forced more positive, the grid will effectively become more negative relative to it and thus less current will flow through it, which works to decrease the output voltage; on the other hand, if the cathode is forced less positive, the grid will effectively become more positive relative to it and thus more current will flow through it, which works to increase the output voltage. In other words, the Cathode Follower relies on the tube's transconductance to keep its output voltage in line with the input voltage. Thus, the greater the transconductance, the lower the output impedance. many solid-state devices, as they exhibit such very high transconductance figures that running them at an equally high current for any length of time would melt the devices. In addition to running a Cathode Follower with too little current, many make the mistake of not using a grid stopper resistor. Cathode Followers can exhibit some wild oscillations that result from long inductive leads connecting to the grid that are easily stoppable with a 100 ohm resistor soldered right at the grid's socket tab. Bad Rap Unfortunately, in spite of low distortion, a cathode follower can sound bad if sloppily designed or improperly used. One advantage a Grounded Cathode amplifier has over the Cathode Follower is that the plate resistor and the cathode resistor (if it is not capacitor bypassed) both lower the transconductance of the triode. This would seem to constitute a disadvantage, but a high transconductance that is not matched to a high current draw, in my opinion, worsens the sound. I like to use as much current as there is transconductance, which is not possible with <PREVIOUS www.tubecad.com Copyright © 1999 GlassWare. All Rights Reserved pg. 2 NEXT > Another mistake often made is to over-estimate the driving ability of a Cathode Follower. For example, don't expect a 12AX7 based Cathode Follower to drive a 600 ohm load to 10 volt peaks just because it has a 600 ohm output impedance. Let us assume that half of the 1 mA of idle current through this Cathode Follower can be delivered to the 600 ohm load. The resulting peak voltage is disappointing: .0005 x 600 = .3 volts. An idle current of 33 mA would be needed to make the 10 volts peak figure easily possible. The key point here is not to make the mistake of thinking solely in terms of voltage--current is equally important in a buffer's design Sometimes too high a current draw leads to a compressed sound. Actually, this fault has nothing to do with the design or function of the Cathode Follower, but with sloppy power supply practice. For example, let us imagine a common tube lineup: a 12AX7 configured as a Grounded Cathode amplifier with a 150k plate resistor that then cascades into a 12AU7 based Cathode Follower with a 15k cathode resistor. Makes sense. Does it not? A high gain, low current amplifier at the front, followed by a high current, low output impedance buffer. < PREVIOUS pg. 3 Everything looks good until we see that the both stages tie together at a power supply connection with relatively high series output impedance. So when the 12AX7 tries to pull its plate voltage down, the 12AU7's cathode will follow, but as the 15k resistor is ten times smaller in value than the 150k resistor, the change in current it produces in response to the input signal will tend to swamp out the change in current the 150k produces in response to the same signal. The key point here is that while the Cathode Follower works in voltage phase with its input signal, it works in negative current phase to the Grounded Cathode amplifier. So while the 12AX7 tries to pull down its plate voltage by the increased current conduction, the 12AU7 lets go of ten times more current, which allows the power supply connection to drift upwards, which subtracts from the output. Conversely, when the first stage tries to push up its plate voltage by the decreased current conduction, the Cathode Follower conducts ten time more current, which pulls the power supply connection downwards. Of course, if the power supply were perfect, i.e. zero impedance, this cancellation effect could take place. The obvious strategy is to use a regulated power supply. A more subtle move is to match the Cathode Follower cathode resistor to the value of the plate resistor of the first stage so as to cancel any net variation in current presented to the power supply. The final setback to the Cathode Follower is that because it is intrinsically a single ended circuit, it can only aggressively drive the output in one direction: up. If presented with a difficult load, i.e. low impedance, the Cathode Follower can be driven into twice or three times its idle current, but it can only decrease its idle current to zero conduction. This makes for an asymmetrical output drive potential. A popular myth is that this problem can be overcome by using a negative power supply. But a negative power supply only allows for a larger valued www.tubecad.com Copyright © 1999 GlassWare All Rights Reserved NEXT > Get our 1999 catalog absolutely Over 10,000 square feet of: Tubes, books, transformers, sockets, friendly folks, capacitors, resistors, literature, cabinet restoration materials, friendly folks, wire, grill cloth, gifts, tools, information...and did we mention the friendly folks? free! 68 pages of products and information (most of which is also available on our web site). It's all here! tubesandmore.com cathode resistor, which would serve to better approximate a current source, but would do nothing to increase the idle current limit to the negative current swinging of the Cathode Follower. White Cathode Follower The White Cathode Follower Mr. White's improvement on the Cathode Follower was to create a buffer that boasted a much lower output impedance and the ability to sink as well as source current, i.e. push-pull operation. The lower output impedance results from the use of a feedback loop from the plate resistor to the bottom tube and the use of two tubes allows the buffer actively to draw current in both directions. Because of the increased complexity of the circuit, the math is much more complicated than that of a simple Cathode Follower: Gain = As an example, given a setup that consists of a 6DJ8 with a bypassed cathode resistor of 200 ohms and a 10k plate resistor, the results are Gain = 0.97 Zo = 3.44 ohms PSRR = -65 dB. mu² + murp/Ra (mu² + mu + 1) + (mu+2)rp/Ra Zo = 1 / [ (1 + mu)/(rp + Ra) + 1 + mu(mu + 1)/(1 + rp/Ra) ((mu + 1)Rk + rp) ] PSRR = 2rp + (2mu + 2)Rk [2rp+(2mu+2)Rk+Ra+murp+(mu²+mu)Rk] [(Ra+rp)/(mu+1)+rp+(mu+1)Rk)/(muRa)] <PREVIOUS www.tubecad.com Copyright © 1999 GlassWare. All Rights Reserved pg. 4 NEXT > If this seems too good to be true, that's because it is too good to be true. Yes, the gain is almost unity and the Zo is amazingly low, yet the circuit cannot deliver very much current into a low impedance load, such as a Grado headphone, 32 ohms. Imagine a car with 340 horsepower, yet which could only do 10 miles per hour. Surprisingly, if we try to output more than a few millivolts into the 32 ohm load, we will overdrive the circuit, as we will break out of Class A operation. Here is what happens in detail. Any variation in the current flowing though the top triode will produce a variation in the voltage developed across the plate resistor. In turn, this voltage will be transmitted to the bottom triode's grid, which can only see a few positive volts before it is driven into positive grid voltage or, if the voltage swings negatively, it is completely turned off. The greater the value of the plate resistor, the easier it is to overdrive the bottom triode, as a smaller amount of current is needed to develop a large voltage change across the plate resistor. On the other hand, if we make the plate resistor smaller in value, we gain dynamic headroom, but lose the stellar specifications. In fact, if we set the plate resistor to zero ohms, we end up with a classic Cathode Follower with an active load, i.e. the bottom triode. Of course, if the load we wish to drive is not a punishingly low 32 ohms, the headroom issue is much less of an issue. But if the load is a high impedance one, such as a 100k potentiometer, then we must ask: Why do we need to use a super low output impedance buffer? Optimal White Cathode Follower We found that too large a value plate resistor limits the potential output current from this buffer and that too low a value reduces the buffer's specifications. So the question is what would be the optimal value for a given load and a given desired out voltage swing? < PREVIOUS pg. 5 www.tubecad.com Copyright © 1999 GlassWare All Rights Reserved NEXT > This was the question I had asked myself, when I was disappointed by the results of an experiment wherein I had built a White Cathode Follower with the aforesaid tube and resistor values for driving a much more reasonable load: the Sennheiser headphones, which have an impedance of 300 ohms. After only a few millivolts, clipping occurred. My expectation was that the circuit should be able to deliver the idle current of at least 10 mA into this load, if not almost 20 mA, which would conform to classic Class A, push-pull amplifier standards. I then replaced the plate resistor with a 10k potentiometer with its center tab connected to one of its outside tabs, which allowed for easy adjustment of the plate resistor value. After adjusting the potentiometer, I found the optimal value according to the trace on the oscilloscope to be 100 ohms. The lowness of the value surprised me. I then wondered what the optimal value would be for the 32 ohm load represented by the Grado headphones. Even more surprising was that the same 100 ohm plate resistor value yielded the best performance into the 32 ohms, in spite of this load being 10 times lower in value than the previous load. Moving to the other extreme, I replaced the 32 ohm resistor with a 3k resistor and retested. The 100 ohm plate resistor value once again made for the biggest and most symmetrical voltage swings. After some mathematical introspection, everything made perfect sense to me. For any push-pull tube amplifier to work well, there most be an almost identical signal presented to each tube. (The signals must differ in phase.) In this circuit, if the top triode sees an increase in its grid-to-cathode voltage, then the bottom triode must see an equal decrease in its grid-to-cathode voltage. How do we ensure equal drive voltages for top and bottom triodes? Let us start our analysis with the severest load possible, not Grado headphone, but 0 ohms, in other words, a dead short to ground via a large valued capacitor. <PREVIOUS White Cathode Follower with a shorted output The top triode now functions as a Grounded Cathode amplifier and does see the bottom triode at all. The amount of current flowing from ground into the capacitor then into the cathode of the top triode is given by the formula: Ip = VgGm´, where Gm´ = (mu + 1) / (Ra + rp). Now as the bottom triode current flow is governed by the top triode's current flow into the the plate resistor, the amount of current flowing from the bottom triode's plate into the capacitor is given by the formula: Ip = VgGm where Gm is the transconductance and Gm = mu / rp. By rearranging the formulas for current we get Vg = Ip / Gm´ for the top triode and Vg = Ip / Gm for the bottom triode. Obviously, the only way that the two grid voltages can match is if Gm´ = Gm. Expanding this formula out yields: (mu + 1) / (Ra + rp) = mu / rp, which when we solve for Ra becomes (Ra + rp) / rp = (mu + 1) / mu Ra = rp(mu + 1) / mu - rp Ra = (rpmu) / mu + rp / mu -rp Ra = rp / mu and as rp / mu = 1 / Gm Ra = 1 / Gm. www.tubecad.com Copyright © 1999 GlassWare. All Rights Reserved pg. 6 NEXT > Thus, the only way the Vg of the top triode can equal Vg of the bottom triode is if the plate resistor equals the inverse of the transconductance of the triodes being used. (The test to put any tube circuit equation through is to try the equation with a 6AS7 and then with a 12AX7 to check the equation for absurdities.) What happens if we chose to start with infinite ohms as a load instead of 0 ohms. The answer is the same, the optimal value for the plate resistor is the reciprocal of the Gm of the triodes used, or what is the same quantity, rp/mu. White Cathode Follower with an infinite impedance output load Now let us step back and look at what is happening with this circuit in broad terms. Without an external load the rp of the bottom triode will define the sole load impedance for the top triode, remember we had defined an infinitely high impedance load. Since the gain of this circuit is less than unity, the cathode voltage will slightly lag the grid's and this gap is the change in the grid-to-cathode voltage that will prompt a change in current flow through both the top triode and plate resistor, which in turn will give rise to a change in voltage across that resistor, which will then be relayed to the bottom triode's grid. We need to ensure that that bottom tube receives an identical gridto-cathode voltage signal as the top tube. < PREVIOUS pg. 7 The math can become quite thick here, but if we think abstractly enough, it will not be too difficult to follow. We know that if the top triode sees a +1 volt pulse at its grid, its cathode will follow to some degree less than +1 volt. Whatever this outcome may be, we will refer to it as "Vg." Now Vg/rp equals the increase current (Ip) flow through the entire circuit, as all components are in current series with each other. Ip times the plate resistor (Ra) equals the voltage pulse that the bottom triode sees, which times the Gm of the bottom triode will equal Ip, if the right value of Ra has been chosen. Thus, VgRa/rpmu/rp = Vg/rp, which when we solve for Ra equals: muVgRa/rp² = Vg/rp muRa/rp = 1 muRa = rp Ra = rp/mu. Okay, what if we choose a load impedance somewhere between zero and infinity, say, 10k. Same result, Ra = rp/Gm. In this case, the load impedance is in parallel with the rp of the bottom triode. So Vg/(rp||RL) equals the increase current (Ip) flow through the top triode and IpRa equals the pulse voltage to the bottom triode. In this case, like the one with a shorted output, we have true Class A output current swing capability, so as the bottom tube approaches cutoff, the top tube's current conduction will near twice its idle value. And, of course, vice versa for negative input voltage swings. Thus, VgRa/(rp||RL)mu/rp = Vg/(rp||RL), which when we solve for Ra equals: VgRa/(rp||RL)mu/rp = Vg/(rp||RL) VgmuRa/rp = Vg muRa/rp = 1 muRa = rp Ra = rp/mu. Optimization and Zo We can use the stock, long, complex equation for output impedance for the White Cathode Follower or we can realize that we have www.tubecad.com Copyright © 1999 GlassWare All Rights Reserved NEXT > stipulated that Gm´ = Gm as a condition of satisfaction in the quest for the optimally valued Ra, and we found that Gm´ = (mu + 1)/(Ra + rp). In effect, what we have actually done by specifying the correct value for Ra is to balance the push-pull aspect of the circuit, which includes each triode offering the same output impedance to the load. Consequently, Zo = 1 / 2Gm, or Zo = rp / 2mu. Conclusion We find once again that we cannot get something for nothing: spectacularly low output impedance came at the price of a disappointingly low input overload voltage and a miniscule output current ability. But what we did get, when we gave the White Cathode Follower the optimal plate resistor value to work with, was a buffer circuit twice as good as a textbook Cathode Follower: half the output impedance and a symmetrical output current swing with twice the output current swing than a single triode Cathode Follower. <PREVIOUS The Plate Follower Also known as the Anode Follower, the Plate Follower is in many ways the inverse of the Cathode Follower. The Cathode Follower preserves the phase of the input signal; the Plate Follower, inverts. The Cathode Follower's output is taken at the cathode; the Plate Follower's output, at the plate. The Cathode Follower's input impedance is extremely high; the Plate Follower's input impedance, relatively low, as it is equal the value of resistor R1. And finally, where the Cathode Follower can only aggressively pull the output more positively; the Plate Follower, can only aggressively pull the output more negatively. Still, the Plate Follower makes a fine buffer and boasts some very desirable features: a ground potential input, adjustable gain, and low heater-to-cathode differentials. The need for a coupling capacitor or a connection to a high voltage input is eliminated in the Plate Follower, as the grid is, in DC terms, at the ground voltage. Unlike the Cathode Follower, whose gain always falls short of unity, the Plate Follower can achieve unity gain output, or if www.tubecad.com Copyright © 1999 GlassWare. All Rights Reserved pg. 8 NEXT > desired, less than unity or more than unity gain. This is a great help when cascading stages and just a bit more gain is needed. Because the cathode is not floating at some high voltage, the issue of maintaining a low heater-to-cathode voltage difference does not arise. The first step is to determine the open-loop gain (a) of the Grounded Cathode amplifier and then the ratio of resistors R1 and R2. Thus, R = Ra||RL||R2 a = muR/(muR + rp + (mu + 1)Rk), if Rk is bypassed, then a = muR/(muR + rp) Ratio = R2/R1 and finally, Gain = aRatio/(a + Ratio + 1). Now that we have the gain, we can determine the output impedance. Zo = (R||(rp + (mu +1)Rk))(Gain/a) if Rk is bypassed, then Zo = (R||rp)(Gain/a). The Broskie Cathode Follower Plate Follower circuit The negatives for this buffer are that its bandwidth is compromised by the low pass filter created by resistor R1 working into the Miller Effect capacitance of the triode and this same resistor defines the input impedance of the circuit and serves to load down the previous stage. Increasing the value of R1 unburdens the previous stage, but worsens the high frequency response. Additionally, the circuit requires three extra resistors and, potentially, a bypass capacitor for resistor Rk as well. The Math Since the Plate Follower is functionally equivalent to the inverting Op-Amp circuit, the mistake that is commonly made is to assume that the gain is given by R2/R1. This formula works for Op-Amps as they have near infinite open loop gain, whereas the Grounded Cathode amplifier, which is at the core of this circuit, has a very finite gain that can never exceed the mu of the triode. Consequently, the formula for the gain of the Plate Follower must include the relatively weak gain of the triode used. < PREVIOUS pg. 9 Although this circuit was covered in the June Issue in the article on converting a balanced signal into single-ended one, it deserves to be reexamined as a buffer circuit. As a balanced to SE converter, the circuit function is the subtract signal B for signal A. Because balanced signals consist of two phases, the function effectively becomes A + B. A signal common to both A and B, let us call it C, is canceled, as the function C - C obtains. Noise is usually equally shared between two balanced signals and is thus eliminated in the single-ended output. So far, the circuit mimics a transformer in function, which was the goal. But this circuit, which I have been testing and I have found to work so very well that I have named it the "Broskie Cathode Follower," differs from a transformer in that it does not reflect impedances, but rather provides a low output impedance and a symmetrical current swing, i.e. it can aggressively pull up or down like a White Cathode Follower. The Broskie Cathode Follower is like a Cathode Follower wedded to a Plate Follower, but not quite. www.tubecad.com Copyright © 1999 GlassWare All Rights Reserved NEXT > A normal Cathode Follower does not have a pair of resistors wrapped around its input and output. Resistors R3, R4 were added to better balanced the circuit's output impedance. Broskie Cathode Follower Once again, the easiest path to understanding what the output impedance of a circuit is to imagine connecting a 1 volt battery to the output (or any portion of the circuit to determine the impedance at that point) and then to calculate the resulting current flow into or out of the battery and then taking the inverse of the current as the output impedance. If we calculate the output for the bottom half of this circuit and then do the same for the top half, we will have, once we parallel the two results, the output impedance for the entire circuit. Starting with the bottom half first, the 1 volt pulse at the output will be relayed through the resistor string of R2 and R1 to the grid of the bottom triode. As resistor R1 and R2 define a voltage divider, only 0.5 volts of the original 1 volt will present itself to the grid. This 0.5 volt signal is then multiplied against the transconductance (Gm) of the triode, which, if its cathode resistor is not bypassed, equals mu/(rp + (mu + 1)Rk), otherwise just mu/rp. <PREVIOUS For a 6DJ8, the result would be 5 mA greater conduction, as 0.5 V x 0.01 A/V = 5 mA. Moving to the top triode, the 1 volt pulse at the output will be relayed through the resistor string of R4 and R3 to the grid of the top triode. As resistors R1 and R2 also define a voltage divider, once again only 0.5 volts of the original 1 volt will present itself to the grid. But the cathode has not remained at a fixed voltage as was the case in the previous example, but instead has moved up +1 volt with the connection of the battery. Thus the cathode voltage must be subtracted from the change in grid voltage, in this case 0.5 V - 1 V = -0.5 V. Then this negative going signal is multiplied against the transconductance (Gm) of the triode, which much as in the previous case, if its cathode resistor is not bypassed, equals (mu +1)/(rp + (mu + 1)Rk), otherwise just (mu +1)/rp. For a 6DJ8, the result would be 5.15 mA less conduction, as -0.5 V x 0.0103 A/V = -5.15 mA. If the mu of the triode is large, we can ignore the difference, as it will be less than the variation between triodes anyway. But if the mu is small, say 2, as it is for the 6AS7, then resistor R4 should be made (mu +1)/mu times larger in value. Why the difference in Gm from the top section to bottom? When a signal is applied to the cathode rather than the grid, we have more than just a change in the grid-to-cathode voltage, we have a change in cathodeto-plate voltage as well. Do not forget that the triode, unlike the transistor or MOSFET, has rp, a change in cathode-to-plate voltage will mean a change in the flow of current through the triode. So, effectively, the cathode has an amplification factor of mu + 1 and a transconductance figure of (mu + 1)/rp, while the plate has an amplification factor of 1/mu and a transconductance figure of 1/rp. www.tubecad.com Copyright © 1999 GlassWare. All Rights Reserved pg. 10 NEXT > Uses for this circuit are more numerous than just the one of converting balanced into single-ended. For example it could be used to buffer the output of a Cascode amplifier. The Cascode suffers from a virtually nonexistent PSRR, whatever is on the power supply connection, will appear at the output. Now if we connected the non-inverting input of the Broskie Cathode Follower to the power supply connection and the inverting input to the plate of the top triode in the Cascode circuit, we will have scrubbed the power supply noise from the signal. Like a transformer, if only one half of the input signal is used, the gain will fall by half as well. Of course, the inputs could be switched if the inverted output of the Cascode was desired. Another example would be to use two Broskie Cathode Followers for the output of a balanced preamplifier. This way we could achieve a clean, low output impedance, balanced output. The topology of the Broskie Cathode Follower can be easily transposed to FETs for they are depletion mode devices like the vacuum tube. With the addition of appropriate biasing circuitry the topology can be implemented with transistors or MOSFETs. microphone preamplifier. To a rough sketch of two directions he could travel is found in this month's Design Idea. The Circular/Bridge Amplifier This circuit counts as a buffer in that offers a low output impedance and no voltage gain. As the last few issues of this journal have dealt with this circuit, we will not go over the how's and why's, but rather what to expect from this circuit as a buffer. Circular/Bridge Amplifier The easy mistake to make is to assume that this circuit is just two Cathode Followers in series with each other and that as a consequence the output impedance would equal twice that of one Cathode Follower. Do not forgets that the power supplies are effectively dead shorts to AC signals. It helps to redraw the circuit so that the two power supplies are shown shorted. = A sweet microphone preamplifier or phono headamp could easily be made from four FET's and a few resistors. On the other hand, one of our readers, Rowan, has asked for some direction in building a tube and only tube based < PREVIOUS pg. 11 Connecting a 1 volt battery across the output terminals will shift one terminal +0.5 volts higher and the other -0.5 volts lower than at idle. The grids of both triodes have not moved and remain fixed at the negative bias voltage. Consequently, the tube whose cathode was forced 0.5 volts negative sees a +0.5 volt increase in its grid-to-cathode voltage and conducts more current. www.tubecad.com Copyright © 1999 GlassWare All Rights Reserved NEXT > Conversely, the tube whose cathode was forced 0.5 volts positive sees a -0.5 volt decrease in its grid-tocathode voltage and conducts less current. You can readily see that the mid-point ground halves the voltage presented to each triode, effective halving the Gm of the triodes. But as the triodes are effectively in parallel with each other, the total Gm sums to unity. "But wait, there's more!" Remember what you just read in the section on the Broskie Cathode Follower, "When a signal is applied to the cathode rather than the grid, we have more than just a change in the gridto-cathode voltage, we have a change in cathode-toplate voltage as well. Do not forget that the triode, unlike the transistor or MOSFET, has rp, a change in cathode-to-plate voltage will mean a change in the flow of current through the triode." So it would seem that the Gm of the triodes in this circuit is effectively increased by (mu + 1)/mu because of the signal is being applied to the cathode rather than the grid. But this is not quite right. For right now, let us forget the addition of the plate transconductance and move our attention to the grid-to-cathode voltage relationship. We do not receive the full transconductance from both triodes, as the grid's voltage is fixed and the applied voltage is split between cathodes. In other words, only half the Gm per tube is available to buck the applied voltage, so we would expect the Gm to be halved to Gm = mu/2rp. "But wait, there's more!" The power supplies are floating in this circuit and represent (ideally) zero ohms impedance to AC signals and they are attached to the cathodes and move with the cathodes. Thus, while one triode's cathode was being forced 0.5 volts positive by the addition of the battery, its plate was being forced 0.5 volts negative by the relayed signal through the power supply connected the other tube's cathode. <PREVIOUS Thus, the total plate transconductance (Gp) of the triodes must be added to the half the effective Gm of the tube: Gm´ = mu/2rp + 1/rp. While this circuit is still being run in strict Class A, the triodes are effectively in parallel, as the power supplies represent zero impedance to AC signals. Consequently, the Gm is doubled to: Gm´ = 2( mu/2rp + 1/rp) which reduces to Gm´ = (mu+2)/rp. Warning, do not be fooled into believing that the Circular/Bridge amplifier has in some respect departed from the more conventional totem pole configuration. It hasn't. In a properly designed Totem Pole amplifier, the same effective transconductance obtains: Gm´ = (mu+2)/rp. = Totem Pole vs. Circular/Bridge In the case of the 6DJ8, the increase in Gm´ will be slight as the mu (33) will predominate, but in the case of a 6AS7 or a 12B4 or 6C33, the increase will be dramatic as the these tubes have very low mu's. In spite of the complexity of the circuit, the math for the output impedance is simple: Zo = 1/Gm´ or what is equivalent, Zo = rp/(mu +2). If multiple pairs of output tubes are used, then Zo = rp/[n(mu +2)], where n = the number of pairs used. For example, if one 6AS7 is used to supply both triodes for this circuit, the output impedance would be 280/(2 + 2) or 70 ohms. www.tubecad.com Copyright © 1999 GlassWare. All Rights Reserved pg. 12 NEXT > And if eight 6AS7's are used, the output impedance would be 280/[8(2 + 2)] or 8.75 ohms. Not nearly as low as we had hoped. "But wait, there's more!" the assumption being made here is that the rp is constant; alas, it is not. Nor is the mu. Both vary with plate voltage and current. (Of the two the mu is closer to being an actual constant.) The RCA Receiving Tube Manual lists the mu as 2 and the rp as 280 at 135 volts of plate voltage and 125 mA of plate current. If we reexamine the tube at 100 volts and 340 mA, with a grid voltage of -10 volts, we find that the mu has climbed to 2.5 and the rp fell to 148 ohms. Now, if we redo our calculation, the output impedance is 148/[8(2.5 + 2)] or 4.1 ohms, which, when placed in parallel with the 8 ohm load, becomes 2.7 ohms. (Yes, using the load to lower the advertised Zo is cheating, but common.) Not bad, but then not great. Once again, these formulas assume true Class A operation. This makes sense, for if a triode stops conducting, its Gm falls to zero and it offers no resistance to applied voltage. 8 0 8 0 -32v 0 +32v Here is where we can see that amplifier classification is more than just pedantic taxonomy. If we desire a flat, i.e. a consistent output impedance from 1 watt to full output, then this amplifier output stage or the rearranged version, the standard Totem Pole, must either be run in strict Class A, strict Class A2, or optimized Class AB. Optimized Class AB means that the bias point has been carefully set so that the overlap of the two output devices occurs where each device has half its normal transconductance so that when paralleled, a constant transconductance is realized. This means that the optimized Class AB amplifier will have twice the output impedance of the same amplifier run in pure Class A. //JRB Audio Gadgets is software for the technically minded audiophile. The quickest way to understanding what Audio Gadgets is all about is to imagine a programmable calculator designed for the audio enthusiast. Audio Gadgets does far too much to fit in even a 21" monitor; consequently, the notebook metaphor is used to hold ten pages of audio topics. Stepped attenuators to tube circuits. Windows 3.1/ 95/98/NT Shown above is the stepped attenuator page, which is only one of ten audio pages. < PREVIOUS pg. 13 www.tubecad.com Copyright © 1999 GlassWare All Rights Reserved NEXT > Design Idea: Tube Microphone Preamplifier Will a differential input plate follower configuration create a low Z in, low enough to work as a transformerless input pre? Also instead of using a split rail I want to use a JFET in a grounded gate setup with something like 500 ohms on the drain. So far it sounds terrific. Tube CAD helps a lot but some things need the attention of the algorithmic genius himself. Your response will be appreciated. By the way I made the February Circuit of the Month regulator and all I can say is it's a serious thing indeed. Rowan Thanks for the new title. I like it, but it will not fit on a personalized license plate. In spite of the title, I have to admit that I know very little about the requirements for a microphone preamplifier. How much gain is needed? Balanced outputs or a single-ended output? So those in the know do please E-mail the required specifications. Still, a microphone preamplifier cannot differ too radically from an MC pre-preamplifier. Low noise is the requirement. A Plate Follower feedback arrangement would provide a low impedance input, but one triode would not provide sufficient gain to both sustain the feedback and provide a high gain output. This means we must cascade two triodes to increase the total gain from the preamp. <PREVIOUS Your disdain for negative power supplies is understandable, particularly, if you wish to use tube rectifiers. Nonetheless, I do not see the FET working. You see FETs have a resistive region where the drain impedance is significant. This occurs up to a few volts and then the FET enters its saturation region, with its nearly infinite drain impedance. The 6DJ8 requires about a 2 volt cathode bias to draw 10 mA of current. In other words, the point at which the FET becomes a current source is too high to bias up a 6DJ8. Even a small negative power supply voltage (-5 volts) would greatly help. Finding the right FET can also be problematic, as a high IDSS will be needed so that the idle current can be cut back by using a source resistor. The only FET I can think of that would prove quiet and beefy enough is the 2N4391. (Look for the metal can version: TO-18.) On the other hand, using a negative power supply has some real advantages. The most important of which is that the ground is freed up from having to support both the signal and amplifier circuit currents. This is a much better arrangement, as all the active circuitry is maintained by the plus and minus legs of the power supplies and the input and output signals have the ground bus to themselves. Add to this advantage the fact that active current sources really are not needed, as large valued cathode resistors are easy to implement. One advantage to split-rail power supplies is never mentioned, but should be. A split-rail power supply is 1/4 as dangerous as the same total voltage single rail power supply. How so? Let us say that you are fiddling with a chassis with a +/1 200 volts power supply. Your left hand is turning the metal volume knob, while your right hand is attaching a scope probe to a resistor. But back of your right hand also hits a part charged to +200 volts. A shocking experience. www.tubecad.com Copyright © 1999 GlassWare. All Rights Reserved pg. 14 NEXT > Now if the same thing happened with a single rail +400 volt power supply, the shock would be four time worse, as the danger is equal to the voltage squared. The last advantage to a split rail power supply is that it allow for some of the noise canceling tricks that I am so fond of in this journal and in the GlassWare website's Circuit of the Month articles. Look carefully at the two resistors and one capacitor network that serves as the common cathode resistor for the Differential amplifier at the input of the circuit below. It is required to inject more negative power supply noise current into the Differential amplifier so that the noise at the plate will be cancelled. Plate Follower based microphone preamplifier Plate Follower based microphone preamplifier in AC terms < PREVIOUS pg. 15 www.tubecad.com Copyright © 1999 GlassWare All Rights Reserved NEXT > A vacuum tube microphone preamp that uses multiple tubes in parallel to lower the noise level and Broskie Cathode Follower to both buffer the output and convert the balanced signal into an unbalanced output. Differential amplifier based microphone preamplifier An Alternative Tube Noise Now, if a single rail power supply must be used and FET current sourcing is not an option, the alternative might be something less fancy, such as the above circuit. This circuit is quite simple: a Differential amplifier handles the balanced inputs and the parallel triodes lower the noise. The buffer output stage, the Broskie Cathode Follower, is described both in this issue and in June's article on Unbalancing Acts. Basically, it mimics a transformer by converting the balanced input signal into an unbalanced output. It also provides a low output impedance of about 450 ohms, which if too high for your application, can be lowered to about 130 ohms by capacitor bypassing the two 287 ohm cathode resistors. Unfortunately, ultra low noise and tubes seldom go together. Two issue arise with using tubes in low noise applications: electrical noise from within the tube and microphonic noise generated from outside the tube. A floating sub chassis can make an otherwise unlistenable amplifier quiet. I like to use L channel extruded aluminum, which is easy to punch and drill. Sorbathane sheeting works well at isolating the vibrations, as do eyeglass rubber bands. Assuming that the mechanical design is adequate, we still have the problem of noise intrinsic to the tube. High transconductance helps as it reduces the thermal resistor noise of the tube, but other issue are evolved in the generation of tube noise. The only answer is to hand pick quiet tubes. I have used a small testing jig to test 6DJ8 type tubes. It consisted of a small chassis with one socket and two BNC connecters for mating with an oscilloscope. The circuit within consisted of a FET current source load for each triode section and a regulated heater power supply. The grid was grounded and the cathode returned to ground via a bypassed 200 ohm resistor. The trick was to look at the shape of noise as well as the amplitude. Extruded aluminum drilled and punched to accept tube sockets makes an excellent platform for a tube based project. <PREVIOUS www.tubecad.com Copyright © 1999 GlassWare. All Rights Reserved pg. 16 NEXT > Click image to see enlargement Sharp, chaotic, jagged mountain ranges were much worse sounding than foggy fuzz. A wood pencil was used to ring the tube to its susceptibility to microphonics. Phantom Power Supply Condenser microphones often require a 48 volt power supply to charge up their elements. Many solidstate microphone preamps use electrolytic capacitors to isolate this voltage from the preamp's delicate transistors. Tubes, on the other hand do not fear high voltage and 48 volts is almost laughably wimpy. Still, be careful. I once looked the lowest voltage capable of killing someone under normal conditions and I was shocked to find it to be an amazingly low 42 volts! Since tubes do not fear 48 volts, even if we do, why not dispense with the cheap capacitors altogether. A two-pole switch can be used to connect the junction of the two 6.8k input resistors to either ground or 48 volts and change the value of the cathode resistor of the first stage to match the shift in grid DC voltage. (Actually, I would use a three pole, four position rotary switch to cover the two aforesaid tasks and to mute the output while switching from one mode to another.) The power supply should be very clean and probably regulated. The heaters definitely should be fed a regulated voltage that is floated at + 48 volts; yes, you can use the same 48 volts used to bias the condenser microphone. One danger with 3 pin regulators, whether they be fixed or adjustable, is that the internal gain falls with frequency, so the declining effective feedback ratio defines an inductive element, which when in series with the wrong capacitance value produces oscillation. The easy workaround is to place a high wattage resistor in series with the regulator's output before connecting the output to the heaters. This means something like a 10 volt regulator should be used to make up for the loss through the resistor. Besides keeping the regulator from oscillating, a series resistor will extend the tube's heater life, as the resistor will absorb the inrush current that flows into a cold, i.e. low resistance heater element. A large valued capacitor can still be used and probably should be used to shunt the heaters themselves. Rowan, good luck with whichever direction you choose to follow and keep us posted. //JRB Condenser microphone preamplifier < PREVIOUS pg. 17 www.tubecad.com Copyright © 1999 GlassWare All Rights Reserved NEXT > E-mail Part 2 to last month's Ian's E-mail Subject: SE / PUSH-PULL First of all kudos to you and to your fine magazine. At first, I only understood a third of Issue 1, but now that I just reread it, I understand about 90% of it. I don't know if I will ever hit 100%, but I'll try. So here is my question. I love the idea you have of converting a ST-70 into a para feed, SE amplifier using tubes instead of chokes. I have a pair of MK 3's that I would like to convert to style of amplifier. So my question is: Would it be possible to make the amplifier work like the Nelson Pass solid-state SE, the Aleph, which is SE up to a certain amount of wattage and then switches to push-pull Class A. amplification for the rest of output power? I know the solid-stage guys have a huge advantage in that they are willing to use IC's in the signal path, which we tube purist aren't, but at the cost of less design flexibility. So is this worth pursuing? Thanks in advance. Ian until the desired break voltage was reached and the amplifier switched over to being a Class AB push-pull one. This time we will look into using a current source made out of discrete parts. The advantage this approach holds over the first is that high quality chokes are both hard to find and expensive, not to mention physically large. A further advantage is that active current source can made to track the current flow in the other tube so as to ensure a better balanced idle current. Additionally, this arrangement works a little more easily with a mono-polar power supply, i.e. one without a negative voltage for biasing the output tubes. An Op-Amp based current source could be used and it would yield the tightest current balance, but at increased complexity and expense. The simplest circuit would be made out of a few resistors and capacitors and two MOSFETs. Last month we covered a modification to the Dynaco MK 3 that resulted in an SE/AB amplifier. That modification required the addition of placing a choke in series with the cathode of one of the output tubes. The choke made a constant current source out of the tube, as its cathode would follow its grid's voltage movement so well that no variation grid-to-cathode voltage occurred, The output stage of a Dynaco MK 3 converted into an SE / PUSHPULL amplifier. Editor <PREVIOUS www.tubecad.com Copyright © 1999 GlassWare. All Rights Reserved pg. 18 NEXT > Click to move to previous page Click to move to home Click to move to next page Moving about in the Tube CAD Journal Tube CAD Journal Publishing Publisher GlassWare, creators of Audio Design Software Our Purpose The Tube CAD Journal is a monthly online magazine devoted to tube audio circuit design. Each month we will present some fresh looks at some old tube circuits and some altogether fresh tube circuits as well (yes, new tube circuits are possible). Circuits and more circuits. While we plan on covering complex tube circuits, like phono preamps or power amplifiers, our focus will be primarily on elemental circuits. Elemental circuits are the primary topologies, or part configurations, arrangements that can stand on their own as recognizable functional circuits although they may be part of a larger circuit. A power amplifier circuit, such as the famous Williamson, comprises several sub-circuits: the Grounded Cathode amplifier, the Split-Load phase splitter, the Differential amplifier and finally a push-pull output stage. Just as we must understand how a resistor or a capacitor functions in a simple circuit, we must understand the function and logic of these elemental circuits before we can understand more complex compound circuits. Why a Webzine? The original intent was to print a conventional magazine. We knew there was a need. A query on our Tube CAD registration cards that a magazine devoted to tube circuit design drew an overwhelmingly loud "YES." Still, we knew the difficulty and impracticality of starting yet another underground tube audio magazine. The Web offers the publisher some great advantages over the traditional approach: worldwide distribution, free subscriptions, no paper (for those who must own a paper version, the size of the journal has been left small enough to be printed on A4 or 8.5" by 11" three-hole punched paper for compilation in a threering binder), live forums, no Post Office, color, motion, a glossary. Schematics can now evolve, as the web allows for the easy display of animated GIF's, which display color and motion. Schematics can now show more than just part connections, they can reveal voltage potentials, current flow directions, and possibly, relative impedances. Math errors and typos will not live indefinitely on a paper page; once spotted, the Web page can be corrected quickly. We look forward to your letters, suggestions and contributions. Editorial Staff Editor: John E. R. Broskie Copy Editor: Anna Russomano Broskie Mailing Address P.O. Box 67271 Scotts Valley, CA 95067-7271 E-Mail Address [email protected] Letters to the Editor The Tube CAD Journal welcomes letters from its readers. Please share your views, opinions, design ideas, and critiques with us. Letters should be brief and accompanied by your name, e-mail address (please indicate if we can publish your e-mail address), city and country. All letters become the property of Tube CAD Journal and will be edited for length and clarity. Please send letters to the POB or our e-mail address. Article Submission A self addressed, stamped envelope must accompany all mailed editorial submissions. We are not responsible for unsolicited materials. Advertising Please contact us if you are interested in placing an ad in the Tube CAD Journal. Printing While no portion of Tube CAD Journal can be reproduced for profit without the written permission of the publisher, we encourage the reader to print one copy of each Web page for easier reading and personal archiving. First, click "File" and then "Page Setup" on your browser menu bar and set the left page margin to ½ inch. Tube CAD Journal is published monthly by GlassWare. ©1999 All Rights Reserved. < PREVIOUS www.tubecad.com Copyright © 1999 GlassWare All Rights Reserved NEXT >