High Performance Tubed DAC Output Stage, Part 1

By Jukka Tolonen

During the past decade, most audiophiles have migrated to the CD player as their main signal source, although the vinyl still has it's devoted supporters. For an enthusiastic tubephile like myself, this presents a dilemma regarding the "purity" of the signal chain. Only the CD player remains as the last solid state fortress in my system. For the most part, it will gladly remain so; indeed, digital logic is an excellent use for transistors. But tubes are the way to go from the output of the digital-to-analog converter downstream.

Ever since I read Norman Tracy's DAC article¹, I have considered building my own outboard DAC with a tubed output stage. However, all published D-to-A converter designs I have seen this far have had two major deficiencies. They lack the low-pass filter and they load the DAC with too high a resistive load.

A technique called oversampling is commonly used in CD players to simplify the low-pass filters necessary in reconstructing the analog audio signal from the 16-bit digital samples². Special digital chips or digital signal processors (DSPs) perform the oversampling. With 8x oversampling, the sample frequency raises from 44.1kHz to 353kHz. This permits the use of a reconstruction filter with a much gentler cut-off slope. Many older players also use four times oversampling, with the sample frequency of 176 kHz.

Lacking low-pass filter

In their application notes, some chip manufacturers recommend the use of high order Sallen-Key or GIC active filters. These filters require several op amp stages, which seems way too much to be replaced by tubes. For the sake of simplicity, the low pass filter has been discarded completely in simple tube-based designs^1,3.

Superficially, a separate filter may seem unnecessary, since the sampling noise is far beyond the human hearing. Furthermore, a simple tube output stage with relatively low bandwidth automatically attenuates supersonic frequencies. The attenuation of such a stage at 353kHz can be 20dB at most. But even if you cannot hear the residuals of the sampling frequency, some intermodulation products may be produced by the amplifier nonlinearities in the audible frequency range. Effective low-pass filtering is thus essential to attenuate the undesired frequencies.

In his article "Passive Filters for Digital Audio" ⁴, Kalman Rubinson reintroduces a simple passive filter configuration that shows over 40dB attenuation at 353kHz. The phase shift is less than 40 degrees at 20kHz, much less than with conventional active filters. The response is reasonably insensitive to component variations and the impedance remains constant on the whole passband.

Table 1 lists component values for two such filters proposed by Mr. Rubinson. The maximum practical impedance for this network is 10kohms. Beyond that, the inductor values become unrealistic and hard to obtain. The 1kohm version is the most interesting, since this output impedance is sufficiently low to drive an interconnecting cable of reasonable length (say 6´) without a separate output buffer. The 10kohm filter requires an output buffer, since the capacitance of an interconnect cable would otherwise have a noticeable effect to the frequency response.

Enigmatic DACs

Simple tube output stages^1,3 cleverly use a humble resistor as a current-to-voltage converter at the DAC output. The value of this resistor is chosen so that ample output voltage is available from the output.

Modern, high-performance current-output audio DACs are invariably designed to drive the virtual ground node of an inverting op amp used as current-to-voltage converter. Thus the converter sees a virtual short circuit as its load plus a constant offset voltage, normally less than 10mV. Unfortunately, the manufacturers do not specify how the chip output behaves with a purely resistive load. It probably never occurred to the designers of these high-tech chips that somebody would want to interface them to such archaic devices as tubes.

The internal structure of these devices is not specified in data sheets, but they appear to contain an internal protection diode across the output and ground that limits the voltage of the current output to about 0.6V. To prevent distortion, the output voltage must stay well below the diode conduction threshold. Norman Tracy used 500 ohms in his design¹ with PCM58 (1mA output current) and Sheldon Stokes³ used 150 ohms with PCM63 (2mA current). Both seem dangerously high to me; I definitely would not exceed 100mV DAC output voltage under any circumstances.

To my chagrin, I do not have the necessary measuring instruments to determine that the same performance specs are met with a 100 ohm load resistor as with the recommended op amp output. The difference might be a subtle change in distortion, low level linearity, and so on. When a component is clearly designed for a certain circuit topology (op-amp output stage in this case), it is precarious to use it in a radically different way. To ensure the specified performance, you should keep the load impedance of the converter as low as possible. An ideal solution would be a tube circuit closely imitating an inverting op amp.

Figure 1 shows a state-of-the art semiconductor DAC output stage including current-to-voltage converter, low-pass filter and output buffer. I have used this circuit in my recent DAC designs, and I am very satisfied with its performance. It has only one fault: it does not glow in the dark! Consequently, I set myself the challenging goal to match the performance of this circuit using tubes.

Virtual tube circuits

I have neither the time nor the persistence to manually build a set of different tube stages in order to analyze their suitability for this application. Instead, I used the PSpice analog simulator from MicroSim Corporation. I have spent countless hours submerged in the realms of virtual tube circuits, changing a small detail and seeing immediately the effect in frequency response, output impedance, distortion or some other performance parameter. And I didn't get any nasty shocks when fiddling with live high-voltage power supplies or changing plate resistors on the run!

MicroSim is distributing a demo version from the PSpice simulator (presently part of the DesignLab product) free of charge. You can download the software (over 11MB!) through the Internet (http://www.microsim.com/). The CD contains a fully functional simulator and comprehensive documentation. The demo software includes only a very limited semiconductor model library, and the circuit complexity is confined to 25 schematic symbols or 64 network nodes (approximately 10 transistors or two op amps). Even within these restrictions, you can simulate quite substantial tube circuits.

The results of any simulation are only as good as the component models used. Since reading Scott Reynolds' article⁵, I have used his simple triode model with minor variations. To get results as realistic as possible, I fine tuned the model constants so that the resulting device models make a close match to the values given in "The Audio Designer's Tube Register"⁶. The special value of this wonderful tube-data book is the fact that its contents were developed by measuring actual devices. Thus it describes the performance of real tubes as manufactured today.

Fortunately, other GA readers have also been busy with computer simulation. Norman Koren had an excellent article⁹ in GA 5/96 that updated all my tweaks to the simple triode model. His improved triode model (see figure 2) , with a number of new parameters, provides much improved simulation accuracy. This is demonstrated in figure 3, which shows the correlation in transfer characteristics between measured data and both the old and new simulation models for 6DJ8. I chose the transfer characteristic curves for this comparison, because they clearly display the correlation of grid voltage and plate current.

Mr. Koren's model agrees closely with measured values when plate voltage is between 75 and 25 volts. Indeed, with this revised model the match can be tuned to occur on any limited operating area by tweaking the parameters. A spreadsheet such as Excel is very useful in tuning the model parameters. Excel's solver tool is able iteratively to find parameter values that minimize a user-given error criterion. I have used Norman's 12AX7 and 6DJ8 models as they are, and I have calculated parameters for the12AT7 and 6922.

Simulation's value

I am not claiming that simulation could substitute prototyping in modern tube design, but even though simulation results are not absolutely accurate, they enable you to compare various solutions and find their relative merits and weaknesses. Properly used, these studies can be even more reliable than results achieved with real prototype circuits. Moreover, simulation results are repeatable from run to run, and they are not subject to measurement errors or component parameter variations (unless you specifically request such variations).

The old models produced very optimistic harmonic distortion results. Figure 3 clearly reveals that the old tube model is more linear than real devices; hence, the harmonic distortion figures were consistently too low. The new models should produce quite realistic distortion results, provided that the operating point of the simulated tubes stays on the area accurately modelled. Unfortunately, I have not been able to verify this assumption in practice with a distortion meter.

Anyway, the distortion figures between various circuit topologies are comparable, and they reveal differencies in their behavior. The simulation can thus be an effective tool for comparing the inherent linearity of various amplifiers. Just don't expect the distortion figures to be exact.

I could not simulate the noise performance of tubes, for not enough data was available to set up a noise model. In view of its ancestry in TV tuners, the 6DJ8 should be top-notch performer in this application. You must test noise behavior with a real prototype.

The Candidates

In order to substitute a tube amp effectively for IC1 (figure 1), you need a unit with high gain and wide bandwidth. Good linearity up to several MHz is essential to minimize intermodulation products with sample frequency residuals. To keep the circuit simple, you should achieve the gain with as few stages as possible. I analyzed the topologies depicted in figure 4 with various tube types and operating parameters. The results are summarized in table 2.

I determined gain and distortion results for three load resistances: 100kohms, 10kohms, and 1kohm. The highest one demonstrates a typical load for tube circuits, the other two represent the loads of the passive filters in table 1. RDAC is the DAC load resistor required for 3V peak output voltage at 1mA output current. Ideally, this value to be as low as possible.

A common-cathode amplifier using 12AX7 (circuit A in figure 4) is the most elementary solution. A cathode follower must accompany it to achieve low output impedance. This circuit has excellent distortion figures, but rather low bandwidth and power supply rejection.

12AX7 mu follower⁷ (circuit B) has outstanding PSRR and even lower distortion at 100kohm load, but it clips on low impedance loads due to the low plate current. Thus it is not able to drive even the 10 kohm passive filter without an auxiliary cathode follower. The bandwidth is about the same as with circuit A. Mu followers 12AT7, 6DJ8, or 6922 (circuits C, D and E) drive 10kohm loads well and the have a wide bandwidth, but distortion is high with a 1kohm load.

The Cascode Connection

Cascode connection is a special two-tube combination capable of high gain and wide bandwidth. The lower tube operates as a transconductance amplifier with constant plate voltage. The upper tube is a common grid amplifier with very low input impedance and high output impedance. This combination performs like a pentode, the grid of the upper tube behaving like the screen grid.

A cascode connection has very high output impedance, so it needs an output cathode follower. Any noise in the power supply is directly connected to the output. I tried different tube combinations and plate currents to find the highest amplification (circuits F-J). 6DJ8 is the clear winner in gain and bandwidth - hardly surprising since this tube was originally developed for cascode use. Using 6922 instead of 6DJ8 provides a slight improvement in gain, but the difference is marginal.

The transconductance of the lower tube and the plate load of the upper one are the key parameters in attaining highest possible gain. In his article "Cascode Construction"⁸, Denzil Danner used 400V supply voltage and fixed bias without a cathode resistor, achieving 47dB gain. Circuits J has lower gain, because I wanted to use a lower supply voltage and cathode bias by resistor R2, enabling a DC connected input. Using a higher supply voltage would be impractical, since the output cathode follower would then demand a separate lower supply voltage to limit the tube plate dissipation to an acceptable level.

Trick and Treat

I was able to tweak 11dB more gain from circuit J by using special tricks. I got rid of the cathode resistor R2 by selecting the bias voltage VB for the desired plate current with zero grid voltage. This works only with currents well over 10mA (see Figure 3). You can reduce the plate current of the upper tube with a bypass resistor (R5 in circuit K of Figure 4). It unbalances the plate currents by supplying extra current for the lower tube. This is possible because the cathode of the upper tube is nearly at a constant potential. High current in the lower tube increases its transconductance, while a low current in the upper tube enables a large plate-load resistor, with consequent increase in gain.

There is a price to pay, as always. The power-supply rejection is very poor - this version actually amplifies the power supply noise. Luckily, this is easy to fix by splitting R5 into two resistors and bypassing the midpoint with an electrolytic capacitor, thus preventing any hum and noise from entering the cathode-plate junction.

Deceptive Distortions

The distortion figures in table 2 need some further attention. Note how ambiguously the simulated distortion results differ as function of the load resistance for various circuits. In all mu followers, the distortion steadily rises with decreasing load impedance, which is normal. But in some cases, notably with circuits F and G, the lowest load resistance boasts also the lowest distortion.

All cathode followers are identical 6DJ8 based circuits with 10mA bias current. With 3V peak signal and 1kohm load, the peak signal current is 3mA. Thus the cathode current varies between 7 and 13mA, almost an 1-2 deviation. With 5mA bias current this would be much worse, an 1-4 variation.

In real tubes, the transconductance increases strongly with increasing plate current, as figure 3 clearly shows. This is the reason for the increased distortion. Figure 5 demonstrates how the simulated distortion in a cathode follower increases with increasing signal current. Even a constant-current bias does not improve the situation appreciably.

It is now obvious that the distortion with 100kohm load represents that of the front-end circuit, whereas the distortion of the CF stage dominates with 1kohm load. Explanation for the diminishing distortion with lower loads is that the CF stage cancels some of the front-end distortion. In any case, this phenomenon is more of a windfall than an actual feature. I would not count on this occurring as well with real-world devices.

The results in table 2 helped me to design a practical, general-purpose DAC output kit with regulated power supplies and a printed circuit board. It can replace semiconductor output stages in CD players or outboard DACs that are using 8x oversampling and current-output DAC chips. In Part 2 of this article, you will see that the most straightforward solution is not necessarily the best.

References

1. "A Tube DAC", Norman Tracy, GA 1/94, p. 14

2. John Watkinson, The Art of Digital Audio, p. 147

3. "DAC Designs", Sheldon Stokes.

4. "Passive Filters for Digital Audio", Kalman Rubinson, TAA 4/94, p. 30

5. "Vacuum-Tube Models For PSpice Simulations", Scott Reynolds, GA 4/93, p. 17

6. "The Audio Designer's Tube Register, Volume 1, common low-power triodes", compiled by Tom Mitchell, Media Concepts 1993.

7. "The Mu Stage", Alan Kimmel, GA 2/93, p. 12

8. "Cascode Construction", Denzil Danner, GA 2/94, p. 1.

9. "Improved Vacuum-Tube Models for SPICE Simulations", Norman Koren, GA 5/96, p. 18.

ABOUT THE AUTHOR

Jukka Tolonen has over 20 years experience in designing medical instruments, industrial measurement and control systems, and integrated circuits for several Finnish companies. His audio hobby started at the age of 15, when he built his first amplifier. He has been a tube addict since 1992. He can best be contacted by email at . He also maintains a personal World Wide Web site at http://www.megabaud.fi/~jtolonen/.

Listing 1: PSpice models for some tubes. ECC81 is equivalent to the American type 12AT7.

Figure 1: Solid state high performance DAC output stage

Figure 2: Triode simulation model⁹

Figure 3: Measured⁶ and simulated transfer characteristics

Figure 4: The circuit topologies used in table 2.

Figure 5: Cathode follower distortion.

Comments, questions and feedback are highly appreciated:

This page was last modified on 24.08.97.