Final Report
Analog Theremin with Frequency Detector
ECE 4007 Senior Design Project
Section L03, Team Theremin
Matt Britt, Team Leader
Ryan Adams
Yuri Yelizarov
James Lewis
William Findley
Submitted
April 29th, 2008
Table of Contents
Executive Summary ........................................................................................................................ 1
1.
Introduction ............................................................................................................................. 2
1.1
Objective ......................................................................................................................... 2
1.2
Motivation ....................................................................................................................... 2
1.3
Background ..................................................................................................................... 3
2.
Project Description and Goals ................................................................................................ 3
3.
Technical Specifications ......................................................................................................... 5
4.
3.1
Proposed Technical Specifications ................................................................................. 5
3.2
Final Technical Specifications ........................................................................................ 6
Design Approach and Details ................................................................................................. 7
4.1
Design Details ................................................................................................................. 7
4.1.1
Theremin Design ..................................................................................................... 7
4.2.2
Frequency Detector ............................................................................................... 10
4.2
Codes and Standards ..................................................................................................... 12
4.3
Constraints, Alternatives, and Tradeoffs ...................................................................... 12
5.
Schedule, Tasks, and Milestones .......................................................................................... 12
6.
Project Demonstration ......................................................................................................... 16
7.
Marketing and Cost Analysis ................................................................................................ 17
8.
7.1
Marketing Analysis ....................................................................................................... 17
7.2
Cost Analysis ................................................................................................................ 19
Summary and Conclusions ................................................................................................... 21
Team Theremin (ECE4007/L03)
i
9.
References ............................................................................................................................. 22
Appendix A: Unit Cost Analysis ................................................................................................. A1
Appendix B: Component Pricing .................................................................................................. B1
Team Theremin (ECE4007/L03)
ii
Executive Summary
Vacuum tube Theremins are rare in today’s market, making them a potentially profitable
product. The Theremin is a fully electronic musical instrument that has been around since 1919.
It is operated by moving the user’s hands closer to or further away from the antennae. The
movement of the user’s hands relative to the antennae changes the capacitance of the oscillator,
which in turn changes the frequency and therefore the sound that is produced.
The process of learning the Theremin can be difficult as it requires a trained ear to play
the discrete notes on the musical scale when the device produces a continuous spectrum of
audible frequencies. To this end, a Frequency Detector has been designed as an optional extra
for the Theremin. The Frequency Detector will only allow the frequencies of the discrete notes
on the musical scale to play, allowing users to more easily train themselves and their muscles to
achieve the correct frequencies.
A functional prototype of the Theremin in its final form is now on display in the ECE
building. A prototype of the Frequency Detector has also been created, but will require more
work before it can be sold as a marketable product. The Theremin plays audio across four
octaves, and the volume can be adjusted between 0 and 28 dB. It is contained within a 16”x10”x
6” aluminum case, with 3 foot antennae protruding from the top and left side. The Frequency
Detector currently allows only the ‘E’ musical note to play, but, with further development, can
be replicated and used to allow all musical notes and filter out all of the frequencies between
them. As the frequency detector was designed with solid state devices, it can also be tightly
packaged in a small case.
Team Theremin (ECE4007/L03)
1
Analog Theremin with Frequency Detector
1.
Introduction
In 1919, Léon Theremin invented a musical device out of vacuum tubes that created
sound by mixing two inaudible high-frequency waves together in a nonlinear device, creating
audible harmonics. The device came to be known as the Theremin for its inventor. [1].
Theremins are operated by changing the capacitance on an oscillator by moving a hand closer to
or farther from one of the antennae, causing a smooth slide from the lowest to the highest
frequency [2]. The addition of frequency-selective circuitry to the output of the Theremin may
facilitate playing discrete notes more akin to traditional instruments by filtering out the
intermediate tones produced by the action of moving the pitch control hand.
1.1
Objective
The objective of this project is to create a fully analog Theremin that can recognize and
play musical notes while filtering out the noise between them. Musicians who play the Theremin
require much time and practice to train their hands in such a way that they can locate the proper
frequencies to allow them to play a musical piece. With the frequency detector added to an
analog Theremin, a training musician will be less dependent on finding the note by ear, and will
be able to spend more time training his hands to find the correct notes.
1.2
Motivation
While analog Theremins are available on the market, the addition of a frequency detector
to the analog Theremin allows the musician to play only the notes that he or she wishes to play
by filtering out the frequencies around each note. This addition is especially useful to the novice
Team Theremin (ECE4007/L03)
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Theremin musician, because it only creates sound when the musician’s hand is in the correct
position to create the note he or she is attempting to play. By filtering out the noise around the
note, there is less need for the musician to know the exact frequency by ear. Additionally, the
choice of an all vacuum tube design tailors to the well-known tube preference in the music
production field [3].
1.3
Background
Currently there are very few types of Theremins on the market. Many models use a
single antenna and are marketed as novelty gifts, but are not operable as musical instruments.
Theremins are often sold in kit form for customers to assemble themselves [4]. Fully assembled
Theremins are mostly of transistorized construction and are housed in nondescript packaging [5].
Tube-based designs are unavailable commercially, likely due to the size, cost, and fragility of
vacuum tubes [6].
There are many sources of information related to building one’s own Theremin. This is
due to the device often being sold in kits and built by hobbyists or by musicians who wish to
fully customize the instrument to create the exact ranges and types of sounds that they wish to
play [5]. The key building blocks of the analog Theremin are antennae for pitch and volume, and
circuits for frequency mixing, volume control, and output.
2.
Project Description and Goals
The analog Theremin and frequency detector will both be prototyped using original
circuit designs created by Team Theremin and built from parts ordered and owned by the
College of ECE at Georgia Tech. The Theremin and frequency detector can be marketed to
musicians either together or separately based on the following goals.
Team Theremin (ECE4007/L03)
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Goals of the Theremin

Vacuum tube design

Safe

Adequate dynamic pitch and volume ranges

Moderate sensitivity

Tuning controls

Compatibility with other equipment

Aesthetic
Goals of the Frequency Detector

Bandpass filtering capabilities

Compatibility with other equipment
One of the two purposes of the project is to create the Theremin out of vacuum tubes,
which raises unique safety due to the high voltages required. The Theremin needs to have a
reasonable dynamic pitch range spanning several octaves, and a good dynamic volume range to
allow maximum creative expression on the part of the musician. Additionally, sensitivity to
changes in the position of the operator’s hands should be tuned to balance controllability with the
required range of physical motion to span the instrument’s capabilities. Dynamic pitch and
volume range as well as sensitivity are determined by the oscillator, volume control circuitry,
and antenna designs. The Theremin must also include tuning controls to allow the performer to
adjust the musical and tactile qualities of the instrument to suit individual playing preference. In
order to reach the market of professional musicians, it needs to be able to interface with other
audio equipment. For marketability, the Theremin needs to be designed with aesthetic in mind,
balancing this goal with the other core features as much as possible.
Team Theremin (ECE4007/L03)
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The other purpose of this project is to create a frequency detector for the Theremin that
can filter out the unwanted frequencies between notes. The detector will be implemented
separately from the Theremin due to power supply requirements. Therefore, it must be able to
interface with the Theremin and with other standard audio equipment. Since the device is
peripheral, less emphasis will be placed upon aesthetic design and its electronics will be
implemented with standard integrated circuits and transistors to reduce cost.
3.
Technical Specifications
3.1
Proposed Technical Specifications
The proposed specifications of the Theremin and frequency detector are given below in
Table 1.
Table 1. Original Technical Specifications
Goal
Specification
Vacuum tube design
Safety
Theremin – Yes
Frequency Detector – no
Safe for usage at 120+ V
Dynamic pitch and
volume ranges
Sensitivity
TBD
Tuning controls
Volume range
Fundamental Pitch
Mute
TBD
Band-pass filter
selectivity
Moderate
Compatibility
Standard
Aesthetic
Marketable yet safe
Team Theremin (ECE4007/L03)
Description
This is purely an aesthetic and marketing
decision
The power supply must be properly
grounded and there must not be large
electric potential on the antennae
The ranges depend on the nominal oscillator
frequencies and design of the antennae
Closely linked to the ranges, sensitivity is
defined as the amount of volume/pitch
change with a given change in hand position
Increase/Decrease dynamic ranges of pitch
and volume or turn off the sound altogether
without turning off the device
This determines the frequency detector’s
ability to filter out unwanted frequencies
and what frequencies it will allow
Able to interface with other audio
equipment
The package should look attractive enough
to sell, but should also meet safety
specifications
5
The Theremin itself was to use vacuum tubes as active devices, and the frequency detector would
mostly use operational amplifiers that consume much less energy and space. Safety is a primary
concern of the project, as the Theremin would require relatively high voltages across the vacuum
tubes. The specific ranges of pitch and volume in the Theremin and the specifics of the notch
filtering capabilities in the frequency detector had not yet been determined since the circuit
design had yet to be finalized. The sensitivity of the Theremin had yet to be determined exactly,
but was planned to be set such that the pitch and volume do not swing too quickly or too slowly
with each hand movement.
3.2
Final Technical Specifications
Following a decision to modify the proposed goals in order to better quantify the
objectives and results of the device, the proposed specifications have been reworded to match
their final results and the un-quantifiable specifications were removed. The final proposed
specifications and results of the Theremin are given below in Table 2.
Table 2. Final Technical Specification
Specification
Specified
Pitch range
30 Hz to 1 kHz
Volume control range
Unspecified
Sensing range
Unspecified
Heater supply
6.3 VAC, 2.5 A
High voltage supply
75 VDC, 10 mA
Output
Audio line level (1.4 VRMS
max)
Result
100 Hz to 3 kHz
30 dB dynamic range
~ 0-12/16 inches
6.3 VAC, 4A
75 VDC, 25 mA
~ 1.5 Vpp
The final assembled Theremin produces a pitch range of roughly 100 Hz to 3 kHz.
However, the lowest frequencies contain several harmonics and do not sound musical. Likewise,
the highest frequencies are spaced very close together and are difficult to play. The playable
range therefore considered to be roughly 300 Hz to 2 kHz, about 2.7 octaves. The volume range
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was simulated to be about 34 dB and was tested to be roughly 30 dB. Sense range for the pitch
antenna was measured at about 0-16 inches when properly tuned, while the range for the volume
antenna is closer to 0-12 inches.
Power supply specifications, including safety, heater supply, and high-voltage supply
were all met or exceeded and are easily demonstrated. The audio output levels depend highly on
the mixer design and thus went through several incarnations. In the final design, the maximum
output level is 1.5 Vpp, which is compatible with standard audio line levels.
The Frequency Detector successfully isolates the frequency 659 Hz, otherwise known as
the ‘Concert E’ musical note. The frequency detector did not meet its proposed goal of isolating
every note of the musical scale due to time constraints. In order to gain a full-scale frequency
detector, the current model can be replicated with the capacitances adjusted to the proper
frequencies of the notes.
4.
Design Approach and Details
4.1
Design Details
4.1.1 Theremin Design
At the outset of this project, the Theremin was envisioned as a fully analog and vacuum
tube driven design. As such, a fairly traditional Theremin topology was adopted and the details
fleshed out using hand design, simulation, and bread board testing. The functional Theremin
components are shown schematically in Figure 1.
Team Theremin (ECE4007/L03)
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Figure 1. Theremin block diagram.
Pitch is produced by mixing the outputs of two radio-frequency oscillators. One oscillator runs
at a constant, reference frequency, while the other is frequency-variable, its oscillation frequency
modified by a tuning capacitor and by the performer’s hand distance from the pitch antenna. The
two oscillators are nominally tuned to the same frequency, and the action of the performer’s hand
causes a small frequency difference between them. Originally the pitch oscillators were
designed to run at a nominal 700 kHz, but this frequency was reduced after testing to 500 kHz in
Team Theremin (ECE4007/L03)
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order to reduce pitch sensitivity somewhat. The outputs of the pitch oscillators are mixed
nonlinearly in a cut-off tube, producing sum and difference frequencies in a process known as
heterodyning. The RF oscillator frequencies are then discarded using a low-pass filter, leaving
audible audio frequencies which represent the difference between the variable and reference
pitch oscillators. Volume detection is accomplished by a third RF oscillator, tuned to a nominal
455 kHz. The output of this oscillator drives a 455 kHz ceramic band-pass filter with extremely
quick fall-off. Moving the volume oscillator frequency off its nominal value results in a large
change in the amplitude coming out of the filter. This amplitude-modulated signal is then
processed by a peak detection circuit to produce a negative DC control voltage. This control
voltage modifies the bias of the output voltage-controlled amplifier, affecting its gain and
controlling the amplitude of the audible signal produced on the output.
The design process for each circuit component began with hand calculations of potential
circuit topologies. Once a topology was selected, it was often simulated with EWB Multisim
using modified SPICE vacuum tube models developed for the project. Not all of the components
were simulated beforehand, but critical sections like the oscillators and the VCA were. In
general, simulation was found to be in reasonable agreement with the actual constructed circuit
behavior. The circuits were all prototyped on a series of bread boards, which led to some severe
RF coupling issues due to long wire leads and close spacing of components. These issues were
somewhat mitigated with careful power supply decoupling, but they were still significant enough
to prevent testing the full Theremin in its bread board form. Only the complete pitch section and
volume section with VCA were tested, independently of one another. After we were reasonably
satisfied with the breadboard circuit performance, the prototype was disassembled and rebuilt in
Team Theremin (ECE4007/L03)
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a metal enclosure which was carefully designed and built to provide secure retention of
components, safety for the user, minimize RF coupling, and afford an attractive aesthetic.
Future improvements may be made to the Theremin, especially in the physical layout and the
mixer circuitry. The physical component layout on the protoboards was designed without
considering the placement of individual tubes, and therefore often crowded wires or made them
unnecessarily long. Careful re-routing of the circuit boards could further improve the wiring
tidiness, which is essential to minimizing RF coupling issues. In addition, further tweaking of
the mixer circuitry will significantly alter the tonality of the instrument, and it may be possible to
improve the timbre at low frequencies by consideration of alternate biasing points or topologies.
4.2.2 Frequency Detector
The schematic of the frequency detector is shown in figure 1. This third order band pass
filter was designed with two operational amplifiers, three inductors, three capacitors, and nine
resistors. The circuit is divided into three uniquely designed stages: Theremin output
amplification stage, frequency isolation stage, and the desired frequency amplification stage.
Figure 2. Frequency detector design.
Team Theremin (ECE4007/L03)
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The first stage as seen in Figure 2 amplifies the Theremin’s output, which consists of multiple
frequencies. The inverting amplifier design with no input resistance theoretically provides
infinite gain. Based on equation 1, Ri = 0. Keeping the virtual short circuit theory in mind, a
1 kΩ resistor is placed at the positive terminal to ground to prevent improper biasing of the input
terminals.
Av, inv 
- Rf
Ri
Equation 1
The second stage of the design is the high Q notch filter. This third order filter provides both a
high gain and high Q. The notch frequency may be altered by manipulating the value of
capacitor C1 and C2. Increasing the C1 and C2’s value will decrease the notch frequency and
provide a slightly higher Q. Equation 3 shows that the impedance of the capacitor decreases
with increasing frequencies. Conversely, decreasing the value of C1 and C2 will shift the notch
to a higher frequency while increasing the Q. Increasing the input resistance, R3, of the notch
filter, will increase the Q and decrease the gain.
ZL  s  L  j    L
ZC 
1
1

s C j  C
Equation 2
Equation 3
The third stage of the frequency detector is intended to force, the output to reach to a level
desired by the speaker. The necessity of an excellent feedback network that will attenuate noise
was of major concern. Without it, the speaker will output both the desired frequency and the
noise associated with the circuit. The combination of a resistor, inductor, and capacitor in
parallel assure that the feedback resistance remains high at all frequencies. As illustrated by
equation 4, high feedback impedance provides a high gain.
Team Theremin (ECE4007/L03)
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Av, inv  1 
4.2
Rf
R pos
Equation 4
Codes and Standards
While no specific standards for Theremin design exist, several relevant general standards
for consumer electronics apply. FCC Title 47, Part 15 governs the operation of unlicensed RF
devices in the United States [8]. Since the Theremin will be producing RF-wavelength signals,
compliance with this FCC section must be ensured before production. Voluntary standards, such
as those published by the Underwriters Laboratories, may also be reviewed for good design
practice. Applicable UL standards which cover electronic musical equipment are UL/IEC 6500,
UL 813, and UL 60065 [9].
4.3
Constraints, Alternatives, and Tradeoffs
As noted above, most commercially available Theremins are transistor-based designs.
While transistors are inexpensive and compact compared with vacuum tubes, the Theremin’s
uniqueness as an instrument is further supplemented by the novelty of vacuum tube design.
Proper tube design adds greatly to the aesthetic of the instrument and gives it value as a visual
performance piece as well as an auditory one. Furthermore, tube design capitalizes on traditional
musician preference for the “tube sound”. It is believed that the value added by the unique
construction of the vacuum tube Theremin will outweigh the additional cost and power
requirements incurred.
5.
Schedule, Tasks, and Milestones
The projected and actual timelines for the project are presented in Table 3.
Team Theremin (ECE4007/L03)
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Table 3. Project Schedule by Date Completed
Task
Evaluation and ordering of vacuum tubes
Building prototyping board
Constructing antennae
Obtaining/writing/testing SPICE models
for circuit simulation
Designing and testing oscillators
Designing and testing mixer
Evaluating antennae with oscillators
Designing volume evaluation circuitry
Evaluating power supply requirements
and building the supply
Physical design (PCB board)
Designing and testing voltage-controlled
amplifier
Final construction and testing
Frequency detector development
Owner
Matt Britt
Ryan Adams
James Lewis
Yuri Yelizarov
Projected
Start Date
1-16
1-16
1-23
2-1
Projected
Deadline
1-23
1-23
2-6
2-11
Date
Started
1-16
1-16
1-23
2-1
Date
Completed
1-23
1-23
2-6
2-11
Matt Britt
Matt Britt
Matt Britt
Matt Britt
Matt Britt
1-23
2-18
2-6
1-30
1-23
2-11
2-24
2-18
2-11
2-25
1-23
2-18
3-05
3-22
3-22
2-11
3-05
3-12
4-2
4-9
James Lewis
Matt Britt
2-25
2-18
3-5
2-25
3-29
3-22
4-9
4-11
James Lewis
Yuri Yelizarov
3-5
1-23
3-15
2-18
4-21
4-9
4-23
4-25
It is clear that the project was optimistically scheduled. Factors that were not taken into account
when the projected schedule was made include classes, interviews, jobs, schedule conflicts,
motivation of teammates, laziness, problems in testing, time for parts to come in, and time spent
on organization and documentation. While many of the tasks were started and long after the
projected start times, the only task that we failed to complete was replication of the frequency
detector to cover the entire musical scale. Since this replication was not a scheduled task, we do
not list it as either incomplete or failed. In the beginning of the semester, we continuously ran
into issues with scheduling and finding time to work on the project, and little was achieved in
this time. As time ran out for the project and the deadlines approached, most of the team found
time or made time in order to achieve the goals of the project. The hardest and most timeintensive tasks in the project were started in either late May or early April, but were completed
before the deadline at the end of April.
Team Theremin (ECE4007/L03)
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At first, task distribution was handled in a careless manner, and the project tasks were
freely distributed amongst the team members with little regard to skill and willingness. As time
went on, the project tasks were completed by whoever had the most time and knowledge
available to do the work. Tasks were often redistributed in the weekly meetings based upon who
was present and willing to do the work. Another reason for task redistribution was to give the
task to the most knowledgeable member in the area that the task is associated with, which
ultimately saves time for the entire team and produces a better product. Table 4 below presents
the initial task assignments, and then the persons who actually took charge of and completed the
tasks.
Table 4. Project Task Ownership
Task
Evaluation and ordering tubes
Prototype board construction
Oscillator design
Antenna design
Mixer design
Power supply design
Case design
Frequency detector design
Voltage-controlled amplifier design
Protoboard layout
Final construction
Projected
Owner
Matt Britt
Ryan Adams
Matt Britt
Will Findley
Matt Britt
James Lewis
James Lewis
Yuri Yelizarov
Matt Britt
Will Findley
Ryan Adams
Completion
Owner
Matt Britt
Ryan Adams
Matt Britt
James Lewis
Matt Britt
Matt Britt
James Lewis
Yuri Yelizarov
Matt Britt
James Lewis
James Lewis
Status
Completed
Completed
Completed
Completed
Completed
Completed
Completed
Completed
Completed
Completed
Completed
The tasks listed above reflect the tasks listed in the project timeline, but some have been
condensed into one displayed task.
Matt Britt and James Lewis took on the Theremin testing, construction, and design
portions of the project itself as a team, with Matt being the analog specialist, and James as an
experienced CAD designer and as a team member with enough free time to help whenever it was
needed. The project tasks around the Theremin were estimated to be difficult due to the size of
Team Theremin (ECE4007/L03)
14
the circuit and the casual GT ECE student’s lack of experience when working with vacuum
tubes.
Yuri Yelizarov is the audio specialist and enthusiast, and he is also the webmaster. He
worked on the Frequency Detector alone most of the time due to his unpredictable and
unforgiving job schedule, but he still completed the task assigned to him from the beginning of
the class. Yuri also created and maintained the website for the team. The project tasks
concerning the Frequency Detector were estimated to be of a mid-level difficulty, because they
were to be designed using solid state devices and because once one note was isolated, the others
could be isolated through simple duplication of the circuit with different capacitances.
Ryan Adams took on the role of project manager for this project, and as such, he was not
responsible for many of the project tasks themselves. He focused instead on team
communication, organizing the team meetings, writing the weekly reports, writing the project
summary, proposal, and final papers for the group. As his role is a more administrative role, any
miscommunication or absence was problematic for the team, but James was able to fill in when
Ryan was unavailable due to unexpected conflicts or emergencies. The role of project manager
was not assumed to be a hard one, but proved to be so whenever communication between team
mates broke down due to unresponsiveness, impatience, or lack of motivation.
William Findley was supposed to take on the final product designer role. He attended
only 4 or 5 of the 15 scheduled team meetings, and either did not or very slowly completed the
tasks he had accepted. Other members of the team had to fill in for him on a number of
occasions. Towards the end of the semester, due to multiple absences, lack of communication,
and seeming unwillingness to work, he was deemed unreliable for completing the PCB design
necessary to build the final product which due to time constraints was changes to use of
Team Theremin (ECE4007/L03)
15
protoboards that required careful layout of components. The task was given to James by
unanimous agreement of the other 4 members; since, designing the final product was a critical
task in order for the team to consider the project a success, and it was projected to be a difficult
task due to limited protoboard space and problems with RF coupling of the oscillators.
6.
Project Demonstration
The Theremin with frequency detector was shown to meet specifications through a
simple demonstration. First, operation of the Theremin was explained to project advisors for
reference in future demonstrations and usage see Appendix <Theremin Manual>: Theremin
Manual. A demonstration of safety was shown by using a multimeter to test both the DC and AC
voltages on the antennae, and during the demonstration these were shown to be around 5 mVDC
and 0.1 VAC respectively. Since normal usage requires tuning the Theremin, how to tune the
Theremin was demonstrated. Next, to demonstrate a reasonable pitch and volume range a probe
line was connected from the output to an oscilloscope. The demonstration of pitch range was
done by detuning the volume so that an audible tone was generated without the users hand
present, and the user moved there right hand with respect to the pitch antenna from far away to
very close: the results of the pitch demonstration were a full range of 100 Hz to 3.0 kHz, but the
playable range was found to be generally 300 Hz to 1.5 kHz. For the volume range
demonstration, the volume was retuned and the user held their right hand on the case next to the
pitch antenna while moving their left hand with respect to the volume antenna from far away to
inside the antenna loop: the demonstrated range was a maximum of 1.6 Vpp to a minimum 50
mVpp yielding a 30 dB range. To show playability the project advisor were given a chance to
play the Theremin. The frequency detector was demonstrated by connecting it to the Theremin
Team Theremin (ECE4007/L03)
16
and showing that the output of the frequency detector was loudest at a Concert E; therefore,
allowing a layer to find a reference point for playing the Theremin.
7.
Marketing and Cost Analysis
7.1
Marketing Analysis
The Theremin has never been a popular device amongst the general public. Since its
creation, it has been viewed as something to be built by hobbyists, and the infrequent musician
every now and then. The challenge presented to the team to market the Theremin is considerable
given its history.
Though the Theremin has not been used for anything besides making music in the past,
advances in technology have driven down the prices of its components, and now make it an
affordable option in many situations. The Theremin can be used in the classroom as an
interactive demonstration of capacitance and its effects. It can also be used as a proximity
sensor, in which case it could either become louder as someone came nearer, or could trigger a
nearby device such as an alarm or a portcullis. The Theremin can also be used for its originally
designed purpose, as an instrument, but even in this field, the Theremin can be modified to create
a larger pitch range or volume range. The Theremin can be modified to include as many
antennas as the user desires, even if the user doesn’t have enough body parts to use them all at
once.
The Theremin is highly marketable and aesthetically pleasing to potential customers.
The bright glow of the LEDs beneath the retro-style vacuum tubes add a mysterious effect to an
instrument that was designed to create dramatic sounds and music. Recent advances in audio
Team Theremin (ECE4007/L03)
17
technology have led to advanced audio-editing computer software that can be used to modify a
given sound into almost anything the user desires. While most instruments are easily
synthesized by a computer or electric keyboard, the Theremin has the unique quality of being the
only instrument that can readily and continuously play the complete spectrum of audible
frequencies. Similar effects are difficult to create digitally, and do not have the same affect on
an audience when created through an electronic synthesizer.
Team Theremin (ECE4007/L03)
18
7.2
Cost Analysis
The nonrecurring cost of the project came to $63,750 as shown in Tables 5.
Table 5. Nonrecurring Cost
Description
Position Type Number
Salary/Yr
Research and Development
Months
Cost
Employees
Engineers
Non-Engineer
2
1
$50,000.00
$30,000.00
1.5
1
$12,500.00
$2,500.00
$500.00
$2,000.00
$10,000.00
Engineers
1
$50,000.00
0.75
$3,125.00
1
$50,000.00
0.75
$3,125.00
Engineers
Non-Engineer
1
1
$50,000.00
$30,000.00
0.5
1
$2,083.33
$2,500.00
Engineers
Non-Engineer
1
1
$50,000.00
$30,000.00
1
1
$4,166.67
$2,500.00
1
1
$50,000.00
$30,000.00
0.5
0.5
$2,083.33
$1,250.00
1
$30,000.00
2
$5,000.00
1
$30,000.00
2
$5,000.00
1
$30,000.00
0.5
$1,250.00
$50,000.00
1
Total Non-Recurring Cost
$4,166.67
$63,750.00
Materials and Supplies
Computer Systems
Other Capital Equipment
Documentation
Design for Testability
Engineers
Production
Setup Charges
Testing Design
Packaging
Package Design
Engineers
Non-Engineer
Marketing
Non-Engineer
Sales
Non-Engineer
Distribution
Non-Engineer
Support
Engineers
1
The capital equipment needed for research and development in a production environment was
multimeter, high voltage bench top power supply, oscilloscope, RLC meter, and function
Team Theremin (ECE4007/L03)
19
generator. The nonrecurring cost was amortized over the estimated 12,000 units sold over 4 years
shown in Table 6 shown.
Table 6. Cost Analysis
Recurring Cost
Year 1
Sales Volume (units)
Year 2
3000
Unit Price
$600.00
Sales Revenue
$11.95
$35,859.38
3000
$662.00
$1,890,000.00
$11.95
Year 4
3000
$630.00
$1,800,000.00
Non-Recurring Cost
Year 3
3000
$35,859.38
$596.00
$1,986,000.00
$11.95
$35,859.38
$1,788,000.00
$11.95
$35,859.38
Research and Development
Redesign
Engineering Change Order
$20,000.00
$20,000.00
$20,000.00
$0.00
$5,000.00
$5,000.00
$5,000.00
$0.00
Production
Parts
$213.04
$639,114.06
$191.73
$575,202.65
$172.56
$517,682.39
$155.30
PC Board
$2.00
$6,000.00
$2.00
$6,000.00
$2.00
$6,000.00
$2.00
$6,000.00
Assembly
$10.00
$30,000.00
$10.00
$30,000.00
$10.00
$30,000.00
$10.00
$30,000.00
Packaging
$5.00
$15,000.00
$5.00
$15,000.00
$5.00
$15,000.00
$5.00
$15,000.00
Testing
$5.00
$15,000.00
$5.00
$15,000.00
$5.00
$15,000.00
$5.00
$15,000.00
$3,000.00
$1.00
$3,000.00
$1.00
$3,000.00
$1.00
$3,000.00
Package
$1.00
$465,914.15
Marketing
Non-Engineer
$30,000.00
$30,000.00
$30,000.00
$0.00
Sales
Non-Engineer
$30,000.00
$30,000.00
$30,000.00
$20,000.00
Distribution
Shipping
Support
Non-Engineer
$30,000.00
125%
$1,966,440.23
$5.00
$15,000.00
Adjusted Cost
$15,000.00
$5.00
$15,000.00
$5.00
$15,000.00
$30,000.00
$20,000.00
$20,000.00
$873,973.44
$810,062.03
$742,541.76
$625,773.52
$1,092,466.79
$1,012,577.54
$928,177.20
$782,216.91
$1,822,639.57
$1,670,718.97
$1,407,990.43
Total Cost/Year
Overhead %
$5.00
Cost/Unit
Total Profit/Year
Profit/Unit
$655.48
$607.55
$556.91
$469.33
-$166,440.23
$67,360.43
$315,281.03
$380,009.57
-$55.48
$22.45
$105.09
$126.67
Total Profit
$596,210.81
Total Cost
$6,867,789.19
Profit Margin
8.7%
For the unit cost shown in the analysis see Appendix A: Unit Cost Analysis and Appendix B:
Component Pricing. The selling price of a unit is around $600 and yields a profit over the 4 year
period of approximately $596,000.
Team Theremin (ECE4007/L03)
20
8.
Summary and Conclusions
The Theremin is a success. It functions as it was projected to function, and it is contained
within a single, aesthetic box, ready to be mass produced as a final product. The Frequency
Detector that is to accompany the Theremin is completed, but is not ready for mass production.
It should be duplicated and tuned to the discrete frequencies of the musical scale.
If the project were to be repeated, the team would have collectively given all of their
effort to seeing it completed inside of two months, because the length to which it was drawn out
was inconvenient to every member in one form or another. The team would also be more
carefully chosen in order to include only members who wanted to do the project, because we
found that to be a problematic issue throughout the time spent working on the Theremin.
Team Theremin (ECE4007/L03)
21
9.
[1]
References
A. Glinksy, Theremin: Ether Music and Espionage. Champaign, IL: University of
Illinois Press, 2003.
[2]
L. S. Theremin, “Method of and Apparatus for the Generation of Sounds,” U. S.
Patent 1,661,058, 28 Feb., 1928.
[3]
R. A. Pittman, The Tube Amp Book II, Sylmar, CA: Groove Tubes, 1988.
[4]
ThereminWorld, “Guide to Buying a Theremin,” [Web Article], [cited 2008 Feb
4]. Available HTTP: http://www.thereminworld.com/article.asp?id=31
[5]
zZounds, “Theremins,” [Sales Literature], [cited 2008 Feb 4]. Available HTTP:
http://www.zzounds.com/cat--Theremins--2712
[6]
VacuumTubes, “Prices,” [Sales Literature], [cited 2008 Feb 4]. Available HTTP:
http://www.vacuumtubes.net/prices.htm
Team Theremin (ECE4007/L03)
22
Appendix A: Unit Cost Analysis
Team Theremin (ECE4007/L03)
A1
Component
CAPACITOR, 330 pF
CAPACITOR, 22 pF
CAPACITOR, 820 pF
CAPACITOR, 50 pF Air gap variable vernier
CAPACITOR, 100 pF
CAPACITOR, 22 μF, Electrolytic
CAPACITOR, 10 pF
CAPACITOR, 100 nF
CAPACITOR, 47 pF
CAPACITOR, 100 μF Electrolytic (200 V)
CAPACITOR, 220 pF
CAPACITOR, 1.0 nF
DIODE, 1N4005 Rectifier
DIODE, Blue 3 mm round LED
FUSE, 1/8 Amp MDL slow-blow
FUSE, 2/10 Amp MDL slow-blow
CONNECTOR, 1/4" Mono phone jack
CONNECTOR, IEC 60320 C14 chassis power
INDUCTOR, 560 μH Molded High-Q
RESISTOR, 68 kΩ
RESISTOR, 200 kΩ
RESISTOR, 2.4 kΩ
RESISTOR, 62 kΩ
RESISTOR, 12 kΩ
RESISTOR, 51 kΩ
RESISTOR, 1.0 MΩ
RESISTOR, 510 kΩ
RESISTOR, 200 Ω
RESISTOR, 5.1 kΩ
RESISTOR, 2.7 kΩ, 2 W
RESISTOR, 5.6 kΩ, 1 W
RESISTOR, 20 kΩ
RESISTOR, 2.2 kΩ
RESISTOR, 56 kΩ
RESISTOR, 43 kΩ
SWITCH, SPST Mute switch
SWITCH, DPDT Power switch
TRANSFORMER, Hammond 220 VCT
TRANSFORMER, Hammond 6.3 VCT filament
VACUUM TUBE, 12AU7A (ECC82) Twin triode
VACUUM TUBE, 12AX7A Twin triode
VACUUM TUBE, 6AL5 Twin diode
VACUUM TUBE, 6X4 Full-wave rectifier
VACUUM TUBE, 0A3 (VR75) Glow discharge
FILTER, Murata CFULB455KB2A-B0 ceramic filter
VACUUM TUBE SOCKET, 7 pin
VACUUM TUBE SOCKET, 8 pin
VACUUM TUBE SOCKET, 9 pin
Miscellaneous Hardware
Unit
Price
$0.67
$0.30
$0.77
$15.95
$0.36
$0.18
$0.32
$0.15
$0.33
$1.58
$0.48
$0.83
$0.02
$0.34
$1.30
$0.45
$0.64
$0.44
$0.60
$0.03
$0.03
$0.01
$0.03
$0.03
$0.03
$0.03
$0.03
$0.03
$0.03
$0.07
$0.04
$0.03
$0.03
$0.03
$0.10
$3.06
$1.28
$53.11
$26.92
$5.95
$10.95
$3.65
$6.40
$6.50
$1.01
$1.25
$1.95
$1.10
Quantity
3
1
1
2
4
5
1
3
1
3
3
5
1
6
1
1
1
1
3
2
1
1
1
1
1
6
1
1
1
2
1
3
4
1
1
1
1
1
1
4
1
1
1
1
1
2
1
5
Total Cost
Team Theremin (ECE4007/L03)
Cost
$2.01
$0.30
$0.77
$31.90
$1.44
$0.90
$0.32
$0.45
$0.33
$4.74
$1.44
$4.15
$0.02
$2.03
$1.30
$0.45
$0.64
$0.44
$1.81
$0.06
$0.03
$0.01
$0.03
$0.03
$0.03
$0.18
$0.03
$0.03
$0.03
$0.15
$0.04
$0.09
$0.12
$0.03
$0.10
$3.06
$1.28
$53.11
$26.92
$23.80
$10.95
$3.65
$6.40
$6.50
$1.01
$2.50
$1.95
$5.50
$10.00
$213.04
A2
Appendix B: Component Pricing
Team Theremin (ECE4007/L03)
B1
25
100
500
CAPACITOR, 330 pF
Component
Mouser
598-CD15FD331JO3F
$1.210
$0.970
$0.820
$0.750
$0.690
$0.670
$0.660
CAPACITOR, 22 pF
Mouser
5982-15-500V22
$0.440
$0.400
$0.370
$0.350
$0.310
$0.300
$0.300
CAPACITOR, 820 pF
Mouser
5982-19-500V820
$1.300
$1.090
$0.950
$0.900
$0.770
$0.770
$0.770
CAPACITOR, 50 pF Air gap variable vernier
oselectronics.com
AVC50VD
$15.950
$15.950
$15.950
$15.950
$15.950
$15.950
$15.950
CAPACITOR, 100 pF
Mouser
598-CD15FD101JO3F
$0.650
$0.520
$0.440
$0.400
$0.370
$0.360
$0.350
CAPACITOR, 22 μF, Electrolytic (100 V)
Mouser
647-TVX2A220MAD
$0.320
$0.320
$0.290
$0.260
$0.210
$0.180
$0.170
CAPACITOR, 10 pF
Mouser
5982-15-500V10J
$0.760
$0.580
$0.470
$0.350
$0.320
$0.320
$0.320
CAPACITOR, 100 nF
Mouser
80-C322C104J1R5CA
$0.430
$0.370
$0.270
$0.190
$0.160
$0.150
$0.140
CAPACITOR, 47 pF
Mouser
5982-15-500V47
$0.600
$0.480
$0.410
$0.370
$0.350
$0.330
$0.320
CAPACITOR, 100 μF Electrolytic (200 V)
Mouser
647-UPS2G101MRD
$6.310
$4.210
$3.150
$2.260
$1.580
$1.580
$1.580
CAPACITOR, 220 pF
Mouser
5982-15-500V220
$0.850
$0.680
$0.580
$0.530
$0.490
$0.480
$0.470
CAPACITOR, 1.0 nF
Mouser
5982-19-500V1000
$1.380
$1.110
$1.020
$0.950
$0.830
$0.830
$0.830
DIODE, 1N4005 Rectifier
Mouser
863-1N4005G
$0.050
$0.040
$0.030
$0.020
$0.019
$0.019
$0.019
DIODE, Blue 3 mm round LED
Digikey
365-1173-ND
$0.780
$0.455
$0.432
$0.377
$0.351
$0.338
$0.319
FUSE, 1/8 Amp MDL slow-blow
Mouser
576-315.125P
$2.000
$1.900
$1.800
$1.700
$1.490
$1.300
$1.300
FUSE, 2/10 Amp MDL slow-blow
Mouser
576-313.200P
$0.690
$0.690
$0.652
$0.583
$0.511
$0.445
$0.445
CONNECTOR, 1/4" Mono phone jack
Mouser
568-NYS229L
$0.820
$0.780
$0.740
$0.700
$0.660
$0.640
$0.620
CONNECTOR, IEC 60320 C14 chassis power
Digikey
Q210-ND
$0.920
$0.832
$0.668
$0.439
$0.439
$0.439
$0.439
INDUCTOR, 560 μH Molded High-Q
Digikey
DN42106-ND
$1.510
$1.290
$0.860
$0.688
$0.602
$0.602
$0.538
RESISTOR, 68 kΩ
Mouser
660-CFS1/4CT52R683J
$0.030
$0.030
$0.030
$0.030
$0.030
$0.030
$0.009
RESISTOR, 200 kΩ
Mouser
660-CFS1/4CT52R204J
$0.030
$0.030
$0.030
$0.030
$0.030
$0.030
$0.009
RESISTOR, 2.4 kΩ
Mouser
291-2.4K-RC
$0.100
$0.040
$0.040
$0.014
$0.007
$0.007
$0.006
RESISTOR, 62 kΩ
Mouser
660-CFS1/4CT52R623J
$0.030
$0.030
$0.030
$0.030
$0.030
$0.030
$0.009
RESISTOR, 12 kΩ
Mouser
660-CFS1/4CT52R123J
$0.030
$0.030
$0.030
$0.030
$0.030
$0.030
$0.009
RESISTOR, 51 kΩ
Mouser
660-CFS1/4CT52R513J
$0.030
$0.030
$0.030
$0.030
$0.030
$0.030
$0.009
RESISTOR, 1.0 MΩ
Mouser
660-CFS1/4CT52R105J
$0.030
$0.030
$0.030
$0.030
$0.030
$0.030
$0.008
RESISTOR, 510 kΩ
Mouser
660-CFS1/4CT52R514J
$0.030
$0.030
$0.030
$0.030
$0.030
$0.030
$0.009
RESISTOR, 200 Ω
Mouser
660-CFS1/4CT52R201J
$0.030
$0.030
$0.030
$0.030
$0.030
$0.030
$0.009
RESISTOR, 5.1 kΩ
Mouser
660-CFS1/4CT52R512J
$0.030
$0.030
$0.030
$0.030
$0.030
$0.030
$0.008
RESISTOR, 2.7 kΩ, 2W
Mouser
660-MOS2CT52R272J
$0.130
$0.130
$0.099
$0.083
$0.074
$0.074
$0.066
RESISTOR, 5.6 kΩ, 1W
Mouser
294-5.6K-RC
$0.140
$0.140
$0.050
$0.050
$0.036
$0.036
$0.035
RESISTOR, 20 kΩ
Mouser
660-CFS1/4CT52R203J
$0.030
$0.030
$0.030
$0.030
$0.030
$0.030
$0.009
RESISTOR, 2.2 kΩ
Mouser
660-CFS1/4CT52R222J
$0.030
$0.030
$0.030
$0.030
$0.030
$0.030
$0.009
RESISTOR, 56 kΩ
Mouser
660-CFS1/4CT52R563J
$0.030
$0.030
$0.030
$0.030
$0.030
$0.030
$0.009
RESISTOR, 43 kΩ
Mouser
660-CF1/4CT52R433J
$0.100
$0.100
$0.100
$0.100
$0.100
$0.100
$0.007
SWITCH, SPST Mute switch
Mouser
633-M201101-BA-RO
$3.600
$3.240
$3.060
$3.060
$3.060
$3.060
$3.060
Team Theremin (ECE4007/L03)
Vendor
Part #
1
1,000
2,000
B1
5,000
Component
Vendor
Part #
25
100
500
$2.550
$2.550
$1.660
$1.600
$1.340
$1.280
$1.280
546-182L110
$69.750
$59.010
$53.110
$53.110
$53.110
$53.110
$53.110
Mouser
546-167S6
$36.710
$28.840
$26.920
$26.920
$26.920
$26.920
$26.920
VACUUM TUBE, 12AU7A (ECC82) Twin triode
tubesandmore.com
T-5963_12AU7A
$5.950
$5.950
$5.950
$5.950
$5.950
$5.950
$5.950
VACUUM TUBE, 12AX7A Twin triode
tubesandmore.com
T-12AX7A-C5
$10.950
$10.950
$10.950
$10.950
$10.950
$10.950
$10.950
VACUUM TUBE, 6AL5 Twin diode
tubesandmore.com
T-6AL5_6EB5
$3.650
$3.650
$3.650
$3.650
$3.650
$3.650
$3.650
VACUUM TUBE, 6X4 Full-wave rectifier
tubesandmore.com
T-6X4_EZ90
$6.400
$6.400
$6.400
$6.400
$6.400
$6.400
$6.400
VACUUM TUBE, 0A3 (VR75) Glow discharge
tubesandmore.com
T-0A3_VR75
$6.500
$6.500
$6.500
$6.500
$6.500
$6.500
$6.500
FILTER, Murata CFULB455KB2A-B0 ceramic filter
Mouser
81-CFULB455KB2A-B0
$2.680
$2.180
$1.340
$1.240
$1.170
$1.010
$0.940
VACUUM TUBE SOCKET, 7 pin
tubesandmore.com
P-ST7-814
$1.250
$1.250
$1.250
$1.250
$1.250
$1.250
$1.250
VACUUM TUBE SOCKET, 8 pin
tubesandmore.com
P-ST8-801
$1.950
$1.950
$1.950
$1.950
$1.950
$1.950
$1.950
VACUUM TUBE SOCKET, 9 pin
tubesandmore.com
P-ST9-511
$1.100
$1.100
$1.100
$1.100
$1.100
$1.100
$1.100
SWITCH, DPDT Power switch
Mouser
108-1MD1T2B3M2QE-EVX
TRANSFORMER, Hammond 220 VCT
Mouser
TRANSFORMER, Hammond 6.3 VCT filament
Team Theremin (ECE4007/L03)
1
1,000
2,000
B2
5,000