IEEE Solid-State Circuits Magazine - Summer 2015 - 18

A TALE OF TWO DACs: HYDRAULIC AND ELECTRONIC
It is difficult to determine exactly when the first data converter was made
or what form it took. One of the earliest recorded digital-to-analog converters (DACs) known to the author of this article is not electronic at all,
but hydraulic. Turkey, under the Ottoman Empire, had problems with its
public water supply, and sophisticated systems were built to meter water.
One of these, dating to the 1700s, is shown in Figure S1. An example of an
actual dam using this metering system was the Mahmud II Dam built in the
early 1800s near Istanbul and described in [3].
The metering system uses reservoirs (labeled header tank in the figure
diagrams) maintained at a constant depth (corresponding to the reference potential) by means of a spillway over which water just trickled
(the criterion was that it be sufficient flow to float a straw). This is
illustrated in Figure S1(a). The water output from the header tank is controlled by a series of gated nozzles of different sizes submerged 96 mm
below the surface of the water [3]. The output of the nozzles feeds an
output trough as shown in Figure S1(b). A photo of the nozzle system
is shown in Figure S2.

The flow rates were measured in the basic unit of 1 lüle (= 36 liter/min
or 52 m3/day). Details of the metering system using the weighted nozzles
are shown in Figure S1(c). This is functionally a DAC with manual (rather
than digital, no doubt) input and a wet output, and it may be the oldest
DAC in the world.
With the expansion of electrical power in the 1800s, one of the first electronic DACs was invented by Lord Kelvin (William Thomson) and C.F. Varley
and is shown in Figure S3. The first resistor divider stage is simply called a
"Kelvin divider" or, in modern terms, a resistor "string DAC." The Kelvin-Varley
divider consists of a number of stages of precision resistors interconnected with
switches or relays to generate a precision output voltage.
The Kelvin-Varley DAC's relative accuracy is determined only by the accuracy of the precision resistors, assuming that the switch resistance is negligible
and the output is buffered. Modern instruments such as the Fluke 720A use
this technique and achieve 0.1 ppm resolution (7 decades) and 0.1 ppm absolute linearity. Variations of this architecture are found in modern IC DACs and
are often referred to as "segmented " string DACs .

Nozzles
96 mm

Water
Level

Spillway

96 mm Header
Tank

Header
Tank

Water
Input
from
DAM

Weighted
Nozzles

Header
Tank

Output
Through

Output Trough

Nozzles

Water
Input
from
DAM

Spillway
(a)

(b)

(c)

Note-The Spillway and the Nozzles Need Different Outlets

Figure S1: Early 1700s weighted water metering system: (a) header system, (b) sectional view, and (c) top view. Adapted from Kâzim
Çeçen, Sinan's Water Supply System in Istanbul, Istanbul Technical University/Istanbul Water and Sewage Administration, Istanbul,
Turkey, 1992-1993, pp. 165-167.

patent was discovered years later
after many other PCM patents had
already been issued.

The Mathematical Foundations
of PCM (1924)
In the mid-1920s, Harry Nyquist studied telegraph signaling with the objective of finding the maximum signaling
rate possible over a channel with a
given bandwidth, W. His results are
summarized in two classic papers

s u m m E r 2 0 15

published in 1924 [19] and 1928
[20], respectively.
If the telegraph signal is bandlimited to a frequency W by the
transmission channel, Nyquist's
conclusion was that the telegraph
pulse rate, 1/T, could not be
increased beyond 2W pulses per
second without the loss of information. Another way of stating this
conclusion is if a signal is sampled
instantaneously at regular intervals

IEEE SOLID-STATE CIRCUITS MAGAZINE

at a rate at least twice the highest
significant signal frequency, then
the samples contain all the information in the original signal. This is the
basis of sampling theory. Except for
a somewhat general article by Hartley in 1928 [21],there were no significant additional publications on
the specifics of sampling until 1948
in the classic papers by Shannon,
Bennett, and Oliver [22]-[25], which
solidified PCM theory for all time.

Table of Contents for the Digital Edition of IEEE Solid-State Circuits Magazine - Summer 2015