24 Bit Digital to Analog Conversion

High Speed Low Noise High Precision Converter

From douzzer Sat Feb 15 13:49:41 EST 1997
From: Daniel Pouzzner <douzzer.mit.edu>
Newsgroups: rec.audio.tech
Subject: 24 bit D/A
Sender: <douzzer.mit.edu>
Organization: (private)

I've been puzzling for a month over how to build a 24 bit DAC that is
inherently linear, capable of "oversampling" (rendering of
interpolations) 64x above a 96KHz sampling rate, exhibits an
Smax/(THD+N) >120db, and a noise floor 130db below full
signal. Reading data sheets off the web has primarily convinced me
that the industry leaders (notably Burr Brown) are missing
something. There is much talk about the inherent linearity and
inherent noisiness of "bitstream" DAC's, and much talk about the
quietness but pesky nonlinearity of resistor ladder DAC's.

So, let me get this straight: all that's needed to achieve 24 bit
linearity is a voltage ladder with precise power-of-two relationships
between the elements of the voltage ladder. Bitstream DAC's dispense
with the ladder completely, and simulate it with pulse density
modulation. Conventional DAC's, like the Burr Brown PCM1702, use a
resistor ladder to generate the reference voltages.

The Burr Brown PCM1702 is capable of sampling 8x above 44.1KHz, and in
the literature a 40KHz low-pass filter is mentioned as a component in
the production testing apparatus. Though Burr Brown calls it a 20 bit
convertor (and it does use 20 bits and have a 20 tier resistor
ladder), it delivers only 17 bits of real accuracy, despite
laser-trimming. This chip is the state of the art in monolithic DAC
designs.

The problems with bitstream DAC's are that they become very noisy in
the bottom few bits, and that their design precludes serious
oversampling (44.1KHz*(2^15) == 1.445GHz, hence the BiCMOS design of
bitstream DAC's and the infeasibility, at least in 1 bit designs, of
the kind of "oversampling" (lagrangian interpolation) used with
resistor-ladder DAC's). Bitstream DAC's can be designed to use "noise
shaping" to fake the interpolations to a certain degree, but the
noisiness is inherent. Since their internal clocks already run balls-
to-the-wall, the only way to push past the 16 bits of resolution is by
changing to a hybrid scheme combining a resistor ladder with pulse
density modulation (clocking a multibit DAC at a very high rate), or
by summing multiple one-bit DAC's (I think this is how Matsushita's
"MASH" converter works). The noisiness is never abated.

But "all that's needed to achieve 24 bit linearity is a voltage ladder
with precise power-of-two relationships." Bitstream or bitstream-
hybrid DAC's can achieve this if their output is fed into a low-pass
filter. A second-order low-pass filter that rolls off starting at 10hz
is >130db down at 20KHz. A 10 bit DAC clocked at 200MHz is sufficient
to produce dithering trains that, after passing through the low-pass
filter, yield any of the 24 reference voltages with noise >130db below
full signal. The FET's whose gates are connected to the outputs of the
low-pass filters can be clocked at any speed desired; 64x above 96KHz
is 6MHz but there is no reason it can't be clocked higher. The output
of the FET's is then summed, fed into a current-to-voltage converter
(a resistor), and that voltage feeds an amplifier which produces the
final output of the converter.

There is not, of course, a 10 bit 200MHz DAC dedicated to each of the
24 reference levels. There is a single resistor ladder. A small forest
of control transistors associated with each resistor appropriately
switches that voltage level into the inputs for the 24 low pass
filters (first they become a currents, which are then summed and sent
across an IV converter which feeds the LPF).

The big questions in my mind are how to put 24 10hz second-order LPF
filters on a chip, and how to keep signals sufficiently isolated.  The
lowest sampling frequency in the system will be about 22KHz, which is
basically ultrasonic, but considering the application it's a little
close for comfort.

-Daniel Pouzzner
 System Architect

p.s. If someone has already come up with this design, who is producing
it? If not, I got proof of prior invention - woo hoo!