A 24 Bit DAC

by Stefano Perugini

This article appeared originally in Glass Audio nr. 6/1998   

The  Vacuum Tubes Renaissance appears more and more as an

intrinsic characteristic of every sector audio; as well as in realizations

"tout-court" you can see this fascinating and bright glassy bulbs in  

increasing symbiosis with the youngest products of the solid-state

technology.

The presence of vacuum-tubes into solid state amplifiers (hybrid

amplifiers) and in the output stage of the dac converters or in the musical

"processors" of the pro-audio sector  (where in few cm² of PCB you can

see gathered DSP IC's and electron tubes)  is symptomatic, in my

opinion, of the convicement that attributes to valves the ability to

compensate the asperities produced by the solid state devices  and  allow

therefore the reproduction of a sound less straining for the human ear.

The musicians for instance seem to have a preference for the presence of

vacuum-tubes in  power amplifiers  as well as in the analog signal

processing and pre-amplification unities, while in the High-End sector

the Audiophile Community  reserve a great attention  to

dac's  with valves in output.

In this article I'm going to introduce the project of a DAC converter

that uses the recent Crystal's CS4390. This component that you can see as a

CS4329's up-grade is a complete 24 bit stereo digital-to analog converter,

that in addition to  the traditional D/A function, include a digital

interpolation filter and a 128X oversampled delta-sigma modulator.

The sigma modulation  [1]  has  now  come also to a technological

maturation and  can quietly rivalry both sonically and technically  with the

most traditional multibit modality.

In this project I have reserved great importance to the designing of

the power supplies even featuring the eccentric use, for this context, of a

vacuum-diode rectifer. The output stage, thanks to the versatility of the

'90, can lend  to the most varied designing interpretations. In this specific

case you will see the implementation of a passive unity realized with a

signal transformer.

Inside the Blocks.

Fig.1  shows  the  full block-diagram of the converter. The signal

coming from the transport unity of CD-Player is submitted to an initial

conditioning, that consists in an amplification and slope front

amelioration , Block 2. The Block 2 output is the input of the Interface

Receiver, Block 3. I have used here another Crystal's device, the

evergreen CS8412. The CS8412 receive an decode audio and digital data

from a digital audio transmission line according to the AES/EBU,

IEC958, S/PDIF and EIAJ CP-340 standards. The (low jitters) clocks

generated are:

MCK        = 256 X Fs

SCK        =   64 X  Fs

Fsync      = Fs or 2 X Fs

where Fs is the sampling frequency.

SDATA the fourth produced signal, is correlated directly with the audio

information.This data flow  is input to the DAC, Block 4, realized with

the CS4390. The 90's full Block-Diagram is shown in Fig. 2.

The interpolator, Block1, is a 128X interpolation filter that because the high

oversampling factor permets the selection of an output filter based on out-

of-band noise attenuation requirement rather than anti/image filtering [2].

The delta-sigma modulator, Block 2, convert the interpolation filter 

output into 1 bit data @128X Fs. This data flow is input to the DAC

converter, Block3, where the digital world bridge the analog world and

the digital word translated into analog signal. Block 4 perform a low-pass

filtering and allows two analog output with a phase difference of 180

degrees, Fig 3. Each output produces 1 Vrms for a full scale digital

input. In differential mode, where you can exalt the cancellation of

common mode errors, noise, distortions and offsets, you can get up to 2

Vrms.

The output Stage

The noise spectrum in output from the 4390 presented in Fig.4, shows

clearly the uselessness to apply  a strong low-pass filtering. In fact for this

operation the same Crystal recommends the implementation of a 2nd

order filter,  however some experimental tests show that good results can

already be got with an a simple 1st order filter. Nevertheless the

4390's good characteristics don't have to let think that the output filter is

superfluous because some measures, that have found full confirmation in

listening tests, have put clearly in evidence the presence of small levels of

distorsions when the signal in output of the DAC is input to the

rest of the audio-chain directly. In this project the filtering process has

been realized resorting to the natural low-pass characteristic that a real

audio transformer exhibits in the region of the high frequencies. This has

allowed the realization of an output stage, Block 5 for the L-channel

and Block 6 for the R-Channel in Fig. 1, with excellent sonic characteristics.

The output stage schematic is in Fig. 5.

Since you can see this circuit as:

a) a differential mode-to single ended mode converter;

b)   a low-pass filter;

it's very simple to profit some correlated advantages with the architecture

of the output stage internal to  the CS4390 .

Unfortunately the simplicity of this stage is only apparent since a lot of

energies can be dissipated for the search or the realization of a

transformer that answers to our specifics and for the circuit optimization;

the load seen by the transformer  is in fact very complex because you

usually have here a shielded cable that connects the output of the

conversion unity with the input of the preamplifier. The knowledge of the

interactions between the parasitic elements of the transformer,  the

connection cable  and the preamplifier input circuit ,  it's of primary

importance in order to establish the position and the entity of all the

resonances, certainly out audio band, that would be able to move by

intermodulation noise and distortion into the high region of the

audio frequencies.

I have conducted with profit this investigation entrusting me, as

usual, to the circuit simulation [3]. The circuit used for the

simulation is shown in Fig. 6. The components designated with an

asterisk represent the parasitic elements of the real transformer.

More precisely [4]:

Rti1*, Rti2*, Rti3*, Rti4* are the windings DC resistances;

L_leak_sc1*, L_leak_pr1*, L_leak_sc2*, L_leak_pr2* are the leakage

inductances;

C_lmpd_p*, C_lmpd_s* are the equivalent lumped capacitances between windings.

The  connection cable (the Signal Cable black-box)  has been

schematized as transmission line  [5], Fig 7.

I have extracted the numerical values of the parasitic elements experimentally examining a

large sample of the High-End and Consumer production; by measurements

I have extrapolated a real model of worst  cable  with

(Lp, Cp, Rp) = (3uH, 300pF, 0.1ohm)

that I have used for the simulations. Fig.8 is a Monte Carlo

analisys related to the frequency  response of the circuit in Fig. 6 when R1

and C_pre have 5% and 100% tolerance rispectively. Fig.9

show a histogram evaluated with respect to Bandwidth("node", 1db) Goal

Function [3], extrapolated from Fig.8. You can see that the

bandwidth @1dB always falls between 21.6kHz and 23.5kHz, therefore

this output stage well "defend" the correct frequency response from most load

variations.

This last results are not accidental or  causal since with a transformer of

smaller quality the results won't be so good. From these simulations

a peculiar behavior of the used transformer emerges:

the low-pass characteristic  that you can observe in

Fig.8, typical of every audio transformer, has been wanted

acting, during the transformer building, on the values of  leakage inductances.

Simulations have shown that this parameter has to lie between 10mH and

20mH. Lower values of 10mH produce an excessive extension of the

bandwidth worsening the DAC's noise levels. Greater values of 20mH

produce a premature cut of the frequency response reducing the

informative content of the audio high frequencies. Simulations and

measures have shown an optimal behavior when the leakage inductance

assumes a value of 16mH.

Alternative roads

Naturally a lot of equally valid variations to the scheme of Fig 5

exist. If in this context you don't desire to renounce to vacuum tubes  you

could take in consideration the simplified scheme of Fig. 10; as electron

tubes I recommend the followings:

437A, 3A167M, EC8010, E810F in pseudotriode, 417A, E55L

in pseudotriode.....

that is small valves with high mu, high gm and a comforting plate

dissipation in order to make easier the search or the construction of a

suitable transformer, to get a better impedance matching and to produce,

in case of necessity, also a meaningful output power . If you love to listen

to music with headphone this  can be the road to follow for achieving

excellent sonics results. Moreover  since a lot of Sound Card have a

S/PDIF output, you can use this circuit to improve the sound reproduced

by the speakers of your Computer dramatically.

By renuncing to the elegant

simplicity of a transformer output stage  (active or passive),  you can

entrust yourself to the natural tendency of an op-amp to the differential-to

single_ended mode conversion.

In Fig. 11  the scheme of a 2-pole analog filter with differential input [6] is present . Fig.12 is the

frequency response. This filter has been designed  with a cross-frequency

of 50kHz, a  40dB/Dec slope and 6dB gain. Obviously the circuit of Fig.

11 can be implemented with vacuum tubes technology getting good results

however, Fig. 13.

 You can find  the grounds of this circuit in GA 1/95

[7]. Nevertheless in comparison to the original version this schematic use only 6cg7's

and, in order to simplify the realization I have chosen a SRPP as output stage. Besides  is

C10>C3

to limit  instability phenomenae in sub-sonic band that this modifications can produce.

In fact Fig.14 shows what happens in the frequency response

when, with C3=4uF, C10 is varying between .2uF and 10uF with .2uF

step . When C10 <C3  overshoots are present in subsonic band. As

first steps you can for instance choose C10=3.3uF and C3 = .22uF and

continue with a following tuning on the real circuit. Unfortunately the

choice of a low value for C3 introduces some disadvantage; Fig.15

shows the simulated frequency response when Rl varies between

500ohms and 20Kohms with step of 500ohms. A minimal value of

8Kohms is necessary to avoid an excessive limitation of the low

frequencies. In this context, since the realization of a vacuum-tubes op-

amp is less critical than that  of a wide-band transformer , the influence of

the parasitic elements can consider some more negligible and therefore the

electric results more satisfactory.

Completion

The full schematic of the 24 bit DAC is show in Fig. 16.

The vacuum rectifier selected is the EZ81 since although reduced in

dimensions and  consumptions  it features  a good ability to supply

current. You don't have to worry about the elevated capacitive value of C35 and C36

since the repetitive peak current, even in the most serious condition of

operation is lower of the maximum value, as Fig 17 show.

L1..L4 act in the decoupling of the high frequencies residuals; nevertheless their

small values doesn't engrave heavily on the resonances of the power supplies filters,

Fig. 18.

The shunt-type regulator for the voltage of the ' 90 have been chosen because it effects

a small degrade  of the sonic performances in comparison to the series

regulation;

then whereas audio analog stage are present , the load is not onerous and,

as in this case, it is not possible  to renounce to  the power supply

regulation , I prefere it to the serie-type regulator.

The hands "in pasta"

I have realized a first prototype of this converter with a point-to-

point wiring, using  small Teflon clippings as support, Photo 1.

Photo1

Although this solution is sonically effective , lately I have opted for

a PCB realization in order to furnish in briefer times copies of this

converter to the friends of the audiophile cenacle remained  fascinated by

his intrinsic sonic characteristics,  Photos 2, 3, 4, 5.  

Photo2

Photo3

Photo4

Photo5

Unfortunately this approach determines an increase in the difficulties. In

fact as every High-Resolution Mixed-Signal PCB Layout you will have to

respect the followings constraints:

a) Separate analog and digital circuits and segment by functionality and speed;

b) Distribute power supplies and grounds taking care to minimize loop area and return current paths;

c) Isolate noisy return current paths from more sensitive analog circuits;

d) Minimize interference from clocks;

e) Decouple ALL IC power supply pin;

f) Minimize emissions;

g) Reducing the effects of capacitive and inductive couplings;

h) Minimize return current path impedances to reduce ground bounce

effects.

For instance with reference to c), the splitting of the ground into separate

analog and digital grounds is the best way to guarantee that noisy digital

currents will not flow in the sensitive analog area.

You can see the adopted solutions in the Figgs. 19..22 that  shows the

PCB artworks of the DAC.

Conclusions

The ambitious objective to make the digital source timbre similar to

that of an analogic source, or more simply to make harshless the resultant

sound, is pursued generally acting entirely on the output stage side.

Most of the high-end converters builders  realize this circuit using vacuum

tubes and the results they get  are good. Nevertheless, also using an output

stage with vacuum tubes, I think that a margin of improvement still exists

if we also re-consider the constructive philosophy of the power supplies.

In this light you can see the presence of a vacuum rectifier  and  a shunt-

regulator in the circuits of this converter.

Certainly the presence of a vacuum rectifier into a low-voltage

power supply can appear a bit " freak ", nevertheless I invite you to

experiment a similar solution, not necessarily in this same context, since,

I am sure, the results will impress you positively.

This project was conceived initially two years ago thinking at the

CS4329  (the predecessor of 4390, with the same pin-out). During the

time continuous improvements have been effected in order to get both

a minimalist and well sounding object . A possible evolution of

this object could foresee power supplies  with  choke input filter and

vacuum-tubes shunt regulators.

References:

[1] T. Tanaka, T. Sugimoto, C. Kubomura

18-bit D/A converter with integrated digital and analog filters

91st AES convention, October 1991, New York, Pre-Print

#3113(y-1);

[2] Crystal Semiconductor Corp.

24-Bit, Stereo D/A converter for Digital Audio

DS264PP1, May '97;

[3]  Microsim Corp.

Microsim DesignLab Eval. 8, 1997;

[4] Radiotron Designer's Handbook, Fourth Ed.

pags. 204-206;

[5]  Douglas Self

Cable Sonics?

Electronics World, Vol. 103 No. 1738, October 1997;

[6] Crystal Semiconductor Corp.,

Evaluation Board for the CS4329

DS153DB2, Aug. '95;

[7] Fred Forsell

A Vacuum Tube Op Amp

Glass Audio, Vol. 7 No. 1, 1995;

[8] Norman Koren

Improved Vacuum-Tube Models for PSpice Simulations

Glass Audio, Vol. 8 No. 5, 1996;