Time-Compressing Infrasonic Recordings to Discover New Sounds, by Clark Huckaby
Water Theremin: Circuit Description and PerformanceTheremin as Transducer. As introduced in Overview Part 4, my water
surface wave pick-up is based on the theremin, a musical instrument. For playing music, the distance between a
theremin's pitch-control antenna and the player's hand determines the output
The instrument mixes (sums) two radio-frequency (RF) signals and
outputs the audio-frequency
difference (heterodyne or "beat") signal. Two separate oscillators
make the RF signals: one has a fixed frequency, while the other is
proximity-sensitive due to an antenna hooked to its L-C resonant
network. The antenna
acts as one plate of a capacitor, the player's hand the other, and air
dielectric. The distance between plates affects total capacitance in
resonant circuit, and hence RF frequency. Since the audio output is a
difference signal, small capacitance changes translate into wide pitch
swings (one reason a theremin is so notoriously hard to play in tune).
In my Water Theremin (WT) transducer, the antenna is insulated and
water serves as one capacitor "plate," so immersion depth determines
output frequency. Water surface waves modulate that frequency, so the
output is a FM analog of those waves.
WT Construction. Photographs of the WT are shown in Figures 9 through 11 of Overview Part 4. The oscillators are wired point-to-point on separate 0.6-inch square ground plane-clad perfboard
squares (after using a small router to clear immediate copper from holes for
the non-grounded leads). I cut a standard perfboard to fit inside a 2x3x1-inch plastic project box. This "mother board" hosts the oscillator modules
and all other components, and is wired point-to-point. A small perfboard glued
to the outside of the box has three solder terminals for the power
responds to sub-millimeter depth changes, so it needs a stable physical
support. Ideally, the support should not interfere with the water surface waves
being recorded. I used salvaged laboratory
"ring-stand" hardware for the 5-1/2-inch long, 3/8-inch diameter horizontal arm terminated with a right-angle coupler. The vertical
support for bench tests was an old laboratory stand with a 12-inch post and a Bakelite base. I made a vertical
support for field recordings by pushing a 30-inch length of 1/2-inch
(O.D.) aluminum conduit into a 32-oz plastic funnel, then filling the
funnel with about
five pounds of concrete to serve as
the base. The metal support hardware grounds the WT to
the water, which is essential as I will describe below. My WT's enclosure is
not water-proof (however, the cable is). A water-proof enclosure would be
an improvement--it would allow accidental immersions and recording in all
Circuit Description: Oscillators. Figure 1 shows a schematic diagram of the WT (figure and component numbers are specific to this page). I based
the two identical Colpitts-type RF oscillators on a design by Aurthor Harrison
(within http://home.att.net/~theremin1/ navigate to "144 Theremin"). Each uses a common-base-wired PNP transistor (Q1) with an L-C
resonant network (L1, C2, and C3) in its collector circuit. Positive feedback
links a capacitance "tap" (C2-C3 junction) to the emitter, which
develops the output voltage across R3.
external capacitors, the oscillators run at about 1.2 MHz. But C4-C6 (reference
oscillator) and C7-C8 (depth-sensitive oscillator) make this about 1.0 MHz. I
tweaked C5's value for a null heterodyne (equal RFs) when the antenna tip is
about 2 mm deep. You may need a different value. Stray coupling tends to
synchronize a theremin's oscillators when their frequencies nearly match. To
minimize this, I physically separated the oscillators as much as possible and included
power supply decoupling (R4 and C1) in each. As discussed below (see Figure 3), however, the normal operating range avoids frequencies close to the null heterodyne. The individual oscillators are sensitive to temperature changes, but the overall WT is remarkably temperature-stable. Heating it
with a hair dryer for 5 minutes caused a mere one-percent change in output
frequency. Presumably this is because the identical oscillators drift the same way, rejecting common-mode temperature changes.
Figure 1. Schematic diagram of the Water Theremin, a transducer for water surface waves.
Circuit Description: Mixer and Envelope Detector.
outputs AC-couple through C9 and C10 to two-input CMOS NOR gate U1A,
as a mixer. Resistor network R5 through R9 biases the signals into the
gate's ersatz "linear" range. I picked R5's value empirically. You may
need a different value, or better yet, design a better mixer (see
"Resolution: Room for Improvement," below). The envelope of U1A's output is "beats"--bursts of pulses
when input signals reinforce each other (positive interference). Threshold
response by U1B helps square up the envelope.
next stage, timer LM555 (U2) acts as an all-or-none envelope detector. It is wired as
a re-triggering monostable multivibrator. R10 and C12 set the hold time at 10
microseconds. Individual input pulses re-trigger the timer since they make Q2
discharge C12 (E.A. Parr  "IC 555 Projects"
Bernard Babani Publishing LTD, London; ISBN
0-85934-047-3). The result: U2's output is continuously
"high" during input pulse bursts (beats) plus an extra 10
microseconds. Wired in parallel, gates U1C and U1D serve as an output buffer that drives a 30-foot waterproof
cable leading to male XLR plug J1. This plug connects to the Interface Unit, which
needs a 6-VDC power supply for the WT. With perhaps excess caution to minimize voltage sag, I used a heavy-duty lantern battery
for field recordings. However, I found that a 0.1-V decrease in supply voltage changed the WT's output frequency by
only 0.15 percent.
maximum output frequency is about 75 KHz. The duty cycle depends on frequency, due to
mixer non-linearity and the 10-microsecond detector hold time. However, frequency
division in the Interface Unit is routinely used, converting the duty cycle to 50 percent.
Antenna Trials. I
bench-tested the WT with a jar of water containing a ground electrode. My first
antenna was a 6-inch length of 1/8-inch diameter steel welding rod,
shrink-wrapped and sealed at the bottom. The insulation did not shed water
reliably; after a few minutes in water, it became "wetted" and did
not respond well to small, rapid changes in depth. I cut most of it off,
leaving a one-inch stub to serve as a solder terminal for other antennas.
wire types I tested, enameled copper magnet wire performed best. I
straitened samples (about 3.5 inches long) by stripping the top
soldering) and sealing the bottom end with a tiny bead of epoxy cement.
carefully cleaned the antenna with alcohol and a soft cloth before each
use. The water also needs to be clean; good results are not
there is pond scum or an oily film.
Effect of wire guage on Water Theremin performance in static tests
(immersion depth versus output frequency). Guage is related to
conductor diameter according to the inset table. All wire samples were
enameled copper, sealed at the bottom end with a bead of epoxy cement.
Immersion depth is measured from the bottom of epoxy bead (i.e., 0
depth is when bead just makes contact with water).
shows WT output frequency versus water depth for enameled-wire antennas of
three different diameters. The thinnest wire (36 AWG) gave the largest depth
range, so I used it on further experiments and all recordings. The source of this 36-AWG wire was an old-stock spool labeled "Heavy Formvar," manufactured in 1944 by SX Wire Products, Ft.
Antenna Model. For the
WT's antenna to act as a water depth-dependent capacitor, the water must
be grounded and contain charge carriers. I bench-tested the WT with distilled, tap, and brine
(saturated salt; NaCl) water. In distilled water, the WT completely ignored
depth. Instead, it was sensitive to the distance between antenna and ground
electrode--like a musical theremin. In Figure 3, square and round data points are my observations for brine and tap water,
respectively. I calculated the well-fitting curves using the model in Figure 4, which is equivalent to the resonant network of the WT's depth-sensitive
oscillator. Cosc combines this oscillator's fixed capacitors (C2, C3, C7, C8 in Figure 1) and includes a
fudge-factor within the 5% component tolerances. Losc is L1 (see Figure 1), and I ignore its minimal DC
resistance. Cant is the depth-dependent capacitance due to the
36-AWG antenna, and Rant is the resistance
between this antenna and ground, due to the water.
Observed (data points) and modelled (curves) Water Theremin static
characteristic in brine versus tap water. The model is shown in Figure 4
The maximum practical depth range, which is the expected maximum surface wave
height (crest-to-trough), is indicated for tap water. The "equilibrium
depth" is the operating point: the optimum immersion depth for a quiet
water surface corresponding to f0
, a 32-KHz WT output which is the FM carrier frequency. The Interface Unit
was thus normally set to divide the WT frequency output by 32, down-converting f0
to 1 KHz to match the nominal operating point of the Data Converter
demodulator. The 200-1800 Hz lock range of the demodulator sets the
expected maximum surface wave amplitude marked in this Figure.
The model in Figure 4 (which fits the observed data; see Figure 3) suggests that each 1-mm increment of 36-AWG antenna immersion increases Cant by 1.12 pF. In saturated salt water, Rant is indistinguishable from zero ohms at all immersion depths. In tap water, as depth increases, Rant
decreases by a factor of 55 K-ohms divided by the depth in mm. As long
as the ground connection to the tap water has a large suface area
compared to that of the antenna, the distance between the ground and
antenna has a negligible effect (at least for distances relevent to this experiment). For the normal WT operating range,
the antenna surface area in contact with the water is small, and
apparently this is the limiting factor for Rant in tap water. Rant behaves like an array of 55-K resistors combined in parallel, in which the number of these resistors equals the depth in mm.
Model of Water Theremin antenna which fits observed performance in static ("bench") tests, in
context of simplified resonant network of depth-sensitive oscillator. Cosc represents the net fixed capacitances associated with the depth-dependent oscillator (C2, C3, C7 and C8 in Figure 1). Losc is the oscillator's inductor (L1 in Figure 1). Cant is the immersion depth-dependent capacitance of the antenna. Rant is is the resistance between the antenna and the water's ground connection.
Amplitude Range and Linearity. Against its
tap water static response curve in Figure 3, I marked the WT's largest practical depth range. Five stages of frequency division (25 = 32) in the Interface Unit matches this range
to the lock range of the Data Converter's demodulator. It suggests a maximum input wave height of
30 mm crest-to-trough. My sidebar on the physics of water surface waves helps put this in the perspective of water
surface waves found in nature.
useful range, the WT's non-linearity error is about six percent. All classic-design
theremins are non-linear: equal changes in capacitance do not change output
frequency equally across the working range. Review the equation for L-C
resonance to understand the "root" cause of this (pun intended). Since it's a
known error, one could compensate for it in recording software. Or one
could try a more linear water level sensor (such as the non-theremin water level-to-frequency converter described in: P.J. Ross  "A Water-Level Sensor
Using a Capacitance to Frequency Converter"
J. Phys. E: Sci. Instrum. 16: 827-828).
Resolution: Room for Improvement. WT
resolution can be defined as the smallest change in depth that consistently causes a proportional
change in output frequency. For minimum noise, it should be smaller than the Data Converter's resolution limit (12-bit, or 1/4096th of full scale in my case) after any
gain is applied. My WT design falls short, as I will explain.
care-free "parts-on-hand" approach, I used digital gates as an analog
mixer--the U1A and U1B cascade. This is a "square (digital) peg for a
(analog) hole." The gates' threshold response (i.e., non-linearity)
cause stepped (not smooth) frequency output versus depth. Envelope
periods are quantized in one-microsecond steps (period of the 1-MHz
time-averaging due to frequency division (by 32), there are 4416 frequency
"steps" for the 30-mm range shown in Figure 3. But their
distribution is not uniform. There are 1250, 54, and 16 steps per millimeter at
the minimum, equilibrium, and maximum depths, respectively. A 1/54-mm
resolution at the operating point doesn't seem too bad at first glance, but note that
it's equivalent to less than 11-bit resolution (referred to a 30-mm range). A better WT would be designed around a linear mixer.
Distortion: Water-Antenna Interaction. As
noted above, the old-stock 36-AWG enameled wire for my antenna came
from an old spool labeled, "Heavy Formvar," which is probably a trade
name for the insulation. Using a microscope, I was impressed by the
appearance of the insulation surface. For
another way to assess smoothness, I watched light reflected from a water
surface while drawing wire samples up and down. Any visible jitter of the
reflection at the surface-wire interface would expose a source of noise and
distortion. I saw no jitter during motion in either direction. But I
noticed a different problem: The wire attracted a small positive meniscus
(about 0.2 mm high). Apparently, the insulation is slightly hydrophilic (has some affinity for
water). The meniscus was shallower during insertion than withdrawal.
slight, water adhesion to the WT's antenna should distort surface
waveforms, affecting low-amplitude signals the most. This is a likely
cause of the distortion highlighted in Figure 12 of Overview Part 4. In that experiment, I recorded water surface waves resonating in a sink (Figure 11 in Overview Part 4 is a
photo of the set-up). I excited the quiet water with an impulse. It took nearly three minutes for the surface to settle
down (damp out) completely. A minute or two into this decay, the crests of low-amplitude waves begin to appear
clipped, likely due to antenna-water stickiness.
distortion source is flexing of the antenna by the waves themselves. Water
particle motion is circular as surface waves pass a fixed point (see sidebar on physics of water surface waves). If
antenna insertion depth is small compared to wavelength, the crests exert net
lateral force on the antenna in the direction of wave travel, and troughs do
the opposite. Thus, a flexible antenna records crests that lag, and troughs
that lead, their actual timing. This effect should increase with amplitude. One
possible solution might be to attach a mass (sinker) to the tip of the antenna
wire using fishing line.
General comments and discussion about the Water Theremin are in Part 4 of the Overvierw, along with links to recordings made with this transducer.
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