Optical Theremin Critical Design Review

Transcription

1 1 Optical Theremin Critical Design Review EE 300W Team Laplace: Richard Michael Sean Solley Ye Zhang 10/23/15

2 2 Abstract: Team Laplace successfully designed a working Optical Theremin with equalizing and auto-tune functionality. The Theremin uses two circuits containing photodiodes, resistors, and operational amplifiers to generate a voltage signal in response to light incident on the photodiodes. A user can vary the light intensity the photodiodes sense by shielding them with their hands, thus varying the voltage output of the circuitry. The voltage signals are measured with a National Instrument s mydaq, a data acquisition device which can interface with a PC running LabVIEW. A LabVIEW VI, or virtual instrument, processes the two signals from the photodiode circuits to control the amplitude and frequency of an audio tone. This tone is outputted through the mydaq s Audio Out port, making this interconnection of devices and software a fun, user-friendly musical instrument. In addition to the standard abilities of the Theremin, additional features were incorporated to help customize the outputted signal. An auto-tune function allows the user to play in a number of musical keys by restricting the output frequency to the frequencies of notes within the selected key. The Theremin also contains an equalizer which permits adjustments to the amplitudes of different frequency components. Introduction: The Theremin is a musical instrument invented in 1919 by a Russian named Lev Termen. The instrument was named after the Americanized version of Lev s name, Leon Theremin. Unlike other instruments, the Theremin does not require physical contact with the player. The original Theremin contained two antennas used to control the pitch and frequency of the audio tone respectively. These antennas act as the positive plates of capacitors and the player s hands act as the grounded plates. Varying the distance from the antennas to the hands varies the capacitance, resulting in a change in the audio tone. A variation on this design replaces the two antennas with two photodiodes. The design, therefore, operates in a similar manner, but on different principles. This variant is known as an Optical Theremin. The Optical Theremin exhibits several advantages over its predecessor. As a result of the digital back end processing, the settings of the Theremin can be adjusted through an easy to use computer interface. This means the frequency range, amplitude, and amplification of different frequency components can by altered by the push of a button, as opposed to reconfiguring analog circuitry. In addition, as we already possess breadboards, mydaqs, and LabVIEW licenses, we required few additional resources for the implementation. Finally, the size of the Optical Theremin (the size of one or two breadboards) proves significantly smaller than that of the original Theremin. Exploiting these advantages resulted in a fun and easy to use Theremin design.

3 3 Rationale: The keystone of our design, the sensing circuitry, was implemented using two sets of photodiodes and trans-impedance amplifiers. The photodiodes are responsible for generating a current in response to photons incident on their surface. Incident light and current produced are positively correlated, meaning when a user varies the amount of light reaching the diode they vary the current produced. Appendix B shows a plot of photodiode light current vs. irradiance. The produced current can be transformed into a voltage by using the trans-impedance amplifier found in Appendix A. Kirchhoff s Current Law at the inverting op-amp terminal yields: This results in a gain of 0 V out R f + ( I P ) = 0. V out I P = R f, (1) (2) where R f denotes the resistor in the amplifier. The MyDAQ can detect an analog voltage signal for processing by a LabVIEW VI. Therefore, using two of the MyDAQ s analog input channels to measure the voltage signals produced by each circuit would be advantageous. Employing LabVIEW s signal processing capabilities, these inputs can be used to control the amplitude and frequency of a generated audio tone. In addition to the amplitude and frequency variations induced by the Theremin player, further adjustments could easily be made available to the user through the LabVIEW front panel, such as auto-tuning and equalizing capabilities. Due to the wealth of tools offered along with the ease of designing a user interface, LabVIEW proves to be an indispensable software program for this design. From the preceding arguments, an initial block diagram was formulated to describe our design. This block diagram can be found in Appendix L. At the N=0 level, we realized the inputs and outputs of the device and considered the transformation in between. For the simple Theremin design, ambient light along with frequency, amplitude, and light intensity range settings are used to produce an audio signal. In the N=1 level, or the main design architecture, the transformation is further divided into the circuitry to sense the ambient light level and LabVIEW processing to generate the audio tone from the circuitry signals. The light sensing circuit obtains the light intensity input, and the LabVIEW processing receives the other settings. For the N=2 level, the aforementioned modules are disassembled into a stage resembling the detailed design level. The light sensing circuitry branches into photodiodes, resistors, operational amplifiers and the mydaq analog inputs. The physical portion of the design can be broken down no further. The LabVIEW Processing module divides into read data, normalization, generate waveform, export data, and mydaq analog outputs. The only step remaining for these

4 4 modules is division into their constituent functions and subvis. As for the inputs in the N=2 level, the light intensity is measured by the photodiodes, and the settings are directed to the normalization module. This block diagram meets all high level design requirements. Implementation: Appendix N contains a photograph of the ambient light sensing circuit. The circuit contains two Optek OP906 photodiodes along with a Texas Instruments TL074CN operational amplifier. The feedback resistors were 1.2 MΩ. This resistance was selected to ensure the output voltage of the amplifier would remain below 10V (maximum rated input voltage for the mydaq) when subjected to an LED flash light. After passing this test, we could be certain our circuit would operate without failure in any light condition encountered. When the resistor, photodiode, and op-amp are connected in a trans-impedance amplifier configuration, they produce an output voltage ranging from 0 to approximately 1.2V under lab lighting conditions. The mydaq s analog input A0 reads the voltage from the circuit controlling the audio signal amplitude, and analog input A1 reads the voltage from the circuit controlling frequency. After conditioning in our physical circuit, the photodiode light intensities are ready to be processed by our LabVIEW VI. In order to use the measured voltages in our code, a DAQ Assistant express VI is required. This express VI controls the mydaq s sampling circuitry and converts the input data into a waveform datatype. The DAQ Assistant samples the analog lines at a rate of 1 khz. Furthermore, the signal input range is set between -1 and 2 volts. A smaller input range results in a higher resolution for the analog to digital conversion. The selected range provides a high degree of accuracy while offering a safety margin for larger than expected light intensities. The DAQ Assistant is encapsulated within a while loop and is configured to read one hundred samples from each channel on every loop iteration. These samples are then averaged before undergoing normalization. The sub VI for normalizing signals can be found in Appendix E. The front panel of the VI allows the user to input the desired amplitude and frequency range of the output signal, along with the expected output voltage range of each light sensing circuit. The output voltage range will change depending on the ambient light intensity. In a brighter environment, the circuit can output a higher voltage than in a darker environment. The normalization process takes into account the change in output voltages for varying ambient light levels. The first step of the normalization process is performed according to the following formula: S n = (S avg S min )/(S max S min ). (3) S avg represents the average of the samples produced by the mydaq. S min represents the minimum voltage the light sensing circuit can produce (usually set to zero). S max represents the maximum voltage the circuit will produce, and S n represents the normalized signal. One can easily see that when S avg equals S max, the normalized signal is one. If S avg equals S min the

5 5 normalized signal is zero. In the event that the average lies external to the S max and S min boundaries, the normalization process uses an In Range and Coerce function to saturate the output at zero or one. This normalization is identical for both the frequency and amplitude signal. The normalized value can then be shifted to produce values within the ranges of the set maximum and minimum values of amplitude and frequency. This shift is implemented using: S n2 = (Max_Value Min_Value) (S n ) + Min_Value. (4) S n2 denotes the normalized and shifted value of the signal. The meanings of the other variables are explicit. The normalization sub VI was instantiated twice within our main VI. One instance serves to normalize the amplitude input voltage and the other to normalize the frequency voltage. The normalized values for frequency and amplitude are then directed into a Simulate Signal express VI which generates a sine wave with frequency and amplitude equal to the inputted values. The output of this VI connects to another DAQ Assistant responsible for generating an output voltage on the MyDAQ s Audio Out terminal. This VI continuously samples the input sinusoid at a rate of 40 khz. Sampling at 40 khz, allows the DAQ Assistant to sample the full range of frequencies produced by the Theremin (up to 20 khz) without aliasing. The voltage outputted lies within the range of -2 to 2 V, the rated values for the Audio Out port. Additionally, a maximum of 100 samples can be stored in the VI s buffer. Following implementation of the basic Optical Theremin functionality, an auto-tune feature was added. The auto-tune feature accepts the normalized input frequency from the Theremin and rounds it to a frequency on the equal tempered scale to be played instead. In addition to simply playing notes from the equal tempered scale, an enumerated control allows the user to select different major keys for the Theremin to play. The auto-tune feature can be initiated with the auto-tune switch on the front panel. The auto-tune sub VI can be found in Appendix F. Depending on which key the user selects, a case statement switches state to output a 1D array with the lowest frequency notes in the key. This array is then inputted into a for loop responsible for generating the next 10 octaves of the key. On each iteration, the for loop accepts the original base frequencies and multiplies each by 2 n, where n represents the iteration count of the loop plus one. Using shift registers and an Insert Into Array function, the arrays multiplied by 2 n are concatenated together to create a larger array containing each frequency of the selected key. A Threshold 1D Array function compares the value of the normalized frequency to the ten octave array. This function outputs a value corresponding to the index of the array closest to the normalized frequency. Special attention was required for this output due to its double format. The output value is not rounded to the index of the note closest to the normalized frequency, but instead remains in double format to indicate the closeness to an index value. For

6 6 example, if the first and second values in the 1D array were 2 and 6, and the normalized frequency was 5, the output of the Threshold 1D Array function would be 0.75 instead of simply 1. For this reason, a Round To Nearest function rounds the double to the closest whole number value. This value becomes type casted to an integer and enters an Index Array function to select the correct frequency component from the ten octave array. The auto-tune switch on the front panel controls the output of a Select node which switches between the original normalized frequency and the auto-tune frequency. The final addition to the Theremin was the equalizer. The equalizer allows the user to vary the amplitude of different frequency components. The user can adjust the frequency ranges of the different bands (i.e. treble, mid-tones, and base) from the front panel, along with the desired amplification of each. A later addition to the equalizer introduced the ability to process.wav files. Two separate but similar equalizers can be found in our VI. The first, which can be seen on the final Theremin block diagram in Appendix J, was placed between the Simulate Waveform express VI and the DAQ Assistant on our original VI. This equalizer processes the sound produced by the Optical Theremin. The waveform leaving the Simulate Waveform express VI divides into three branches which are each routed through a third order butterworth filter. The topmost filter on the VI performs high pass filtering. The filter in the center acts as a band pass, and the bottom filter is a low pass. The cutoff frequencies of each filter can be configured by the user on the front panel. Upon exiting the filters, the modified waveforms pass through a Multiply function. The additional inputs to the Multiply functions are derived from user controlled sliders on the front panel. The sliders in conjunction with the Multiply functions serve to intensify or suppress their respective frequency components. After each of the three frequency components undergoes filtering and amplitude modifications, they are superimposed using Add functions. Before this waveform is played, it encounters one final Multiply function with another user adjustable slider input. This serves as a master volume control for the Theremin. The signal then enters a Divide function which divides by three to suppress frequency components which may have passed through multiple filters with minimal attenuation. The final waveform transitions to the same DAQ Assistant used for the part one design. A Spectral Measurements express VI is used to generate a front panel graph of the frequency spectrum of the audio waveform. A case statement governed by the tab control on the front panel surrounds the Theremin code. Until this point, only page 1 of the tab control has been discussed. Examining Appendix I reveals a second page. This page is the control panel for the.wav file equalizer. Appendix K displays a code resembling that of the Theremin equalizer. Instead of processing the Theremin output, however, this equalizer derives its input from a.wav file stored on the host machine. A series of small, square shaped VIs run along the bottom of the case statement. Collectively, these VIs are responsible for extracting the.wav file s information, opening the file, reading a set number of samples on each iteration of the while loop, and closing the file after

7 7 processing completes. The VI reads the audio signal from a file using the Sound File Read VI. The signal then becomes subjected to an equalizer identical to the one previously explained. The output of the.wav file equalizer, however, differs from that of the Theremin equalizer. A case statement surrounds the DAQ Assistant which is responsible for outputting the signal. This case statement allows the equalizer to operate on.wav files containing either monaural (single channel) or stereophonic (dual channel) sound. A front panel enumerated control allows the user to select whether the inputted.wav file is single or dual channel. The case statement, driven by the enumerated control, switches between two DAQ Assistants configured to handle single and dual channel outputs respectively. In addition to the extra channel added to the dual channel DAQ Assistant, these express VIs were required to have a different configuration from the one used for the Theremin. The buffer size had to be increased drastically in order to prevent it from overflowing when performing background tasks on the host machine. Also, in order to prevent aliasing in the wide variety of.wav files which could be read, the DAQ Assistant express VIs read the sampling rate value outputted by the Sound File Info VI and alter their sampling rate accordingly. The final component of both equalizers which has yet to be mentioned is the LED outputs. Before the superposition of the different frequency components, each individual component is sent to a Tone Measurements Express VI, which outputs the respective amplitudes. These amplitudes are compared with an arbitrary value selected experimentally to illuminate the LEDs when a distinguishable frequency component is present in the output audio signal. When the Treble component of the waveform exceeds its arbitrary constant, the boolean output of the Greater? VI will become true and will illuminate a green LED. Through the same process, a large mid-tone component will excite a yellow LED and a large bass component will excite a red LED. The LEDs were placed on a separate bread board to prevent interference with the photodiodes. The unaltered output of the Greater? VI will be sufficient for driving the LED indicators on the front panel which correspond exactly to the physical LEDs. An intermediate step must be taken to illuminate the physical LEDs. DAQ Assistants 5 and 6 drive the digital output lines DIO0, DIO1, and DIO2 of the mydaq which serve as voltage sources for the LEDs. When the DAQ Assistant receives a true boolean input, the corresponding digital output produces 5V, turning an LED on. When the boolean input becomes false, the digital output produces 0V turning off an LED. The DAQ Assistant produces errors when attempting to directly input the waveform datatype from the Greater? VI. Therefore, case statements were used to translate this datatype into boolean constants which were combined into a 1D array and exported to the DAQ Assistant. Both DAQ Assistants are set to 1 sample (on demand) generation mode. As a credit to the thorough design of the Theremin, few modifications were made during testing. We determined that high amplitude frequency components located near the cutoff frequencies of two filters were not attenuated sufficiently, and thus when superimposed required an output voltage exceeding the mydaq s capabilities. This generated an error

8 8 message and halted the execution of our VI. For this reason, a Divide function was inserted into the equalizers between the master volume control and the DAQ Assistant. The value of three was chosen so that in the event that the user selected cutoff frequencies for the filters which did not attenuate the amplitudes at all, a signal with three times the amplitude of the original signal would not be sent to the DAQ Assistant. Instead, the original, unabated signal would be played. The final modification made during testing was a reconfiguration of our auto-tune VI. The VI was originally created with several for loops working in parallel to create the entire ten octave 1D array for each key. These ten octave arrays would then be sent to a case statement acting as a multiplexer to decide which array would be played. After noticing a speed delay upon adding the auto-tune feature, we decided that the thirteen (number of keys playable with auto-tune) for loops operating ten times in parallel was extremely inefficient. During each iteration of the Theremin while loop, these large arrays would be generated and at most one would be used. We compressed our auto-tune VI to the current design which selects a single key s base frequencies before executing one for loop ten times. After making this change, the speed delay was eliminated. Conclusion: Using light sensing circuitry, a mydaq for data acquisition, and LabVIEW for signal processing, Team Laplace has developed an Optical Theremin which will outperform most in its class. Through robust circuit design and utilization of normalization capabilities in LabVIEW, the Theremin is guaranteed to work flawlessly in various lighting environments. Audio tones can be produced which possess an amplitude and frequency accurately reflecting the distance of a user s hands from two photodiodes. If a user prefers to play the Theremin in a certain key instead of playing any frequency in a specified range, the auto-tune feature can be activated from the front panel. This feature gives the user access to a number of major scales in addition to the equal tempered scale. To allow the user to synthesize the perfect tone, the audio signal can be manipulated with an easy to use equalizer. The flexible equalizer design allows for standard amplitude modifications on different frequency bands, and furthermore, allows the frequency ranges of the bands themselves to be changed. When the user is tired of creating the music, they can entertain themselves by processing their favorite songs with the.wav file equalizer. Although the back-end power of the design may not be evident to users, the attractive, easy to use front interface will certainly be appreciated by all. Team Laplace s thorough attention to detail throughout all stages of the design has led to the creation of a high quality, user friendly Theremin which will provide hours of enjoyment to users with all levels of musical ability.

9 9 Appendices: A. Trans-impedance Amplifier (one used for frequency the other for amplitude) B. Light Current vs. Irradiance Chart

10 C. Optical Theremin Part 1 Front Panel 10

11 11 D. Optical Theremin Block Diagram Part 1 E. Normalization SubVI

12 12 F. Auto-tune SubVI G. Optical Theremin Block Diagram Part 2

13 13 H. Optical Theremin Front Panel with Auto-tune and Equalization Functionality I..WAV Equalizer Front Panel

14 J. Full Theremin VI with Auto-tune and Equalizer Functionality 14

15 15 K..WAV File Equalizer

16 16 L. Initial Block Diagram

17 17 M. Gantt Chart N. Light-Sensing Circuitry

18 18 O. LED Circuit P. Optical Theremin Circuit

19 19 Bill of Materials Capital (Quantity) NI MyDAQ (1)..... $ Circuit Boards (2)......$21.99 (Radio Shack) OP906 Photodiodes (2) $0.59 (Mouser Electronics) TI TL074 Op-amps (1)..$0.61 (Mouser Electronics) Computer with USB Drive (1).owned LabVIEW License (1). owned LEDs (red,yellow, green) (3)...$0.27 (Mouser Electronics) 2KΩ Resistors (3)....$0.10 (Mouser Electronics) 1.2MΩ Resistors (2).. $0.005 (Newark Element 14) Spool of Wire (1). $2.50 (Adafruit Industries) Total..$ Labor Hourly Engineering Wage...$30.00 Hours Worked...50 Total...$

20 20 Works Cited 1. "What Is A Theremin?" What Is A Theremin? N.p., n.d. Web. 20 Oct "OP906 Optek / TT Electronics Mouser." Mouser Electronics. N.p., n.d. Web. 20 Oct "Universal Solderless Breadboard." Radioshack. N.p., n.d. Web. 22 Oct "Texas Instruments TL074CN. Mouser Electronics. N.p., n.d. Web. 22 Oct "Yageo Carbon Film Resistors - Through Hole 2.2K ohm 1/4W 5% Mouser Electronics. N.p., n.d. Web. 22 Oct "MULTICOMP MCCFR0W4J0125A50 Through Hole Resistor, Carbon Film, 1.2 Mohm, 250 MW, ± 5%, 250 V, Axial Leaded." MCCFR0W4J0125A50. N.p., n.d. Web. 22 Oct "Cree, Inc. Standard LEDs - Through Hole Mouser." Cree, Inc. Standard LEDs - Through Hole Mouser. N.p., n.d. Web. 22 Oct "Hook-up Wire Spool - Red." Adafruit Industries Blog RSS. N.p., n.d. Web. 22 Oct