EE 300W 001 Lab 2: Optical Theremin. Cole Fenton Matthew Toporcer Michael Wilson
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1 EE 300W 001 Lab 2: Optical Theremin Cole Fenton Matthew Toporcer Michael Wilson March 8 th, 2015
2 2 Abstract This document serves as a design review to document our process to design and build an optical Theremin using LabVIEW software. An optical Theremin is a light sensitive electronic musical instrument that allows the user to produce music by controlling the frequency and amplitude of the output. The output is produced based on the amount of ambient light absorbed by the photodiodes, which is controlled by the user. The photodiodes produce a small amount of current, which is related to the intensity of light being absorbed by the photodiode. The current produced is then converted to voltage and amplified using a trans-impedance operational amplifier to meet the 0-10 Volt specification of the mydaq Analog Input terminals. After the current has been converted and amplified, the mydaq reads the voltages and interprets them separately. LabVIEW then isolates the two input voltages and normalizes them to control the range of the output. The autotune function takes the signal related to frequency and compares it with an array of predetermined frequencies and then coerces the signal to the nearest discrete frequency. The autotuned value, in combination with the controlled volume, is then sent to the audio output of the mydaq. The frequency and amplitude are related to the pitch and volume and are a result of different levels of ambient light permitted to reach the photodiode by the user. Introduction A Theremin is a musical instrument that can be played without any physical contact. A Russian physicist and engineer named Leon Theremin invented it in A thereminist plays the instrument using only their hands to fluctuate the pitch and volume of the sound generated. Theremins usually include oscillators and antennas to determine where someone s hands are. The downside to these types of designs is that they can be very expensive to develop. One way to make the instrument at low cost is to develop an optical Theremin that uses ambient light as an input. Ambient light is introduced to two photodiodes that correlates the amount of photons received to the fluctuations in pitch and volume levels. This design is simple and cost effective compared to the more expensive Theremins on the market. Rationale The optical Theremin circuit design consists of two OPTEK OP906 photodiodes connected to a TI TL047CN operational amplifier (op amp.) We chose to set the op amps up as transimpedance amplifiers to convert and amplify the current to voltage. The current is generated by an ambient light source and a photodiode is then used to convert this signal to a voltage and amplify it before being input to the Analog Input terminals of the mydaq. Each photodiode has a specific role; one controls the frequency while the other controls the amplitude. Once the voltage is input to the mydaq, it is used in the LabVIEW program to control the two outputs, volume and pitch. The voltages are first read by the LabVIEW program and then normalized to a
3 3 range defined by the user. The normalized signals as well as the input signals are available so the user is able to monitor the changes in each signal depending on the ambient light available. The user has the option to autotune the pitch signal, which is done using the Autotune sub VI. If selected, the autotune function takes the pitch (frequency) signal and compares it with an array of predetermined frequencies, 20Hz to 20kHz, and then the signal is coerced to the nearest frequency. The two signals then go to the Distortion sub VI, which adds clipping to the original waveform that is at some frequency and volume. The final signal is sent to the audio output port on the mydaq. Initial Block Diagram and Justification Following the basic diagram known as POSaM: The high-level diagram for the project is: Figure 1: Generic POSaM Diagram Figure 2: Applied POSaM Diagram Figure 2 was configured to strictly follow the design specifications of the project and served as the guide to its basic functional requirements. The Transformation block is further defined in Figure 10: Expanded Transformation Process and is the result of research and development of the product and its features at a deeper level than this initial block diagram.
4 4 Bill of Materials Part Quantity Price Per Unit (USD$) OPTEK OP906 Photodiode TI TL047CN Op. Amp MΩ Resistor NI mydaq Breadboard Total Description of Design Modifications Figure 3: Bill of Materials Modifications to the design specifications are not applicable as all aspects of design were met. The basic structure of the project s inner workings (code and hardware) was modified several times due to technical or practical concerns. Technical concerns included the revision of the original design of the feedback resistor in the transimpedance amplifier. The primary analysis estimated a resistor value close to 100k ohm but through trial and error, due to the lack of knowledge of our ambient light conditions, we chose a 9.1M ohm feedback resistor to provide the full swing of voltage, 0-10 volts, for the very little amount of light received at the photodiode. Another technical problem involved the distortion subvi. Developers found it difficult to implement some of the more simple candidate functions that could have more easily supplied the distortion the design specifications called for. It was chosen by the developers to take on a ground-up approach and construct a full sub VI to handle distortion based on elementary principles. The sub VI entails creating the original signal, generating an array of square waves that are used to hone in on parts of the sine wave that need to be modified or clipped and simply apply superposition to reconstruct these signals to the final clipped signal. Practical concerns included adding simulated inputs to the front panel to allow the user to more easily troubleshoot the hardware, if it is suspected to be at fault. This made independent coding less prone to downtime and increased flexibility in schedule as developers could simulate inputs without the hardware.
5 Optical Theremin 5 DAQ Assistant Setting Parameters & Observations Input Settings: Output Settings: Output data Input data Voltage_0 VoltageOut Voltage_1 Signal Input Range: -2 to 2 V Signal Input Range: 0 to 10V Acquisition Mode: Continuous Samples Acquisition Mode: Continuous Samples Samples to Read: 440 Samples to Read: 100 Rate (Hz): 1 Rate (Hz): 1000 Capture of all LabVIEW Virtual Circuit Block Diagrams from Parts 1, 2 & 3 Figure 4: Main VI (note each case structure s true/false selection) Figure 5: Main VI (note each case structure s true/false selection) Figure 6: Raw to Regulated ( Raw to Reg ) Sub VI (Taken from the pitch channel)
6 Figure 7: Distortion ( Clip ) Sub VI Optical Theremin 6
7 7 Front Panel Capture of the Final Product Figure 8: Autotune ( AT ) Sub VI Figure 9: Optical Theremin Front Panel
8 8 Block Diagram Analysis An expansion on the Transformation block includes how the device acquires, regulates and generates the output. Figure 10: Expanded Transformation Process Progressing through the most detailed from left to right, a description of each process block follows. Light intensity incident on photodiode produces current signal Using the OP906 photodiode, the incoming light can be interpreted as a current signal proportional to the amount of light received. The diode acts as a dependent current source across a range of light intensity. A strong amount of light correlates to a high amplitude current signal on the order of 35 ua, according to the manufacturer s datasheet. Transimpedance Op Amp converts current to voltage signal Using the TL074CN operational amplifier (op amp), the current signal from the photodiode is used in a transimpedance op amp configuration to convert the current signal to a proportional voltage signal. Optimally, the scale of the voltage signal should be in the range of the MyDAQ s Analog Input (AI) channel s acceptable range of zero to ten volts. By trial and error, a resistor value of 9.1M was chosen to act as negative feedback to generate a signal of reasonable sensitivity to detect an obstacle blocking ambient light from reaching the photodiode. See Figure 11: Operational Amplifier Configuration for Signal Conditioning for a schematic of the circuit at the input to the MyDAQ AI.
9 9 Figure 11: Operational Amplifier Configuration for Signal Conditioning DAQ Assistant calls for sample data at Analog Inputs (AI0+ & AI1+) To acquire the voltage signal at the input to the MyDAQ s AI channels, a DAQ Assistant application is utilized. Each channel has information collected about its voltage level that is produced by the transimpedance opamp circuit. Fit raw input voltage data to user specified range per channel In a two-step process, transform the raw input voltage amplitude to a suitable pitch/volume for their respective channel. The first step is to perform a sequence of comparative and logical tests to force the raw input value into a range defined by the user. If an input exceeds the user-defined maximum, force the output to this maximum value. If an input exceeds the user-defined minimum, force the output to this minimum value. For Step 2, let:
10 10 This step is to perform a mathematical scaling of the I Range value to a Normalized Output value. Eq. 1 demonstrates this scaling. (Eq. 1) The derivation is encapsulated in the function described by Figure 6: Raw to Regulated ( Raw to Reg ) Sub VI. Calculate user-defined output signal requirements This process incorporates two functions that add user-adjustable characteristics to the output signal before outputting the sine wave signal. These features add the ability to give the project an interesting sound quality. One function is the Autotune feature that forces a continuous spectrum of frequencies to be represented by a discrete set of frequencies. Choosing an arbitrary frequency of 440 Hz, the Autotune VI establishes an array, iterates 151 discrete values of frequency (as a result of a function defined by Eq.2) into the array and chooses which discrete bin a particular frequency belongs to. The input frequency to this VI is the output of the Normalized Output Pitch. For a complete list of frequencies by n value, see the appendix for Figure 14: Discrete Frequency Bins for Autotune Sub VI. f n = 440 Hz * (1/12) (n-76) (Eq. 2) The second function is the Distortion feature that uses the original sine wave (at the specified frequency and unit amplitude of 1) and superimposes a group of modified square waves to distort the signal. The process begins by calculating and establishing necessary values for duty cycle and phase shift for each square wave at a given frequency. Figure 12: Visual Aid for Derivation describes an example sine wave with amplitude of 1 at 20 Hz. Let us consider applying a hard distortion at 90% unit amplitude, or ±0.9. Along the bottom of the graph the variables t (rise time to reach 90%), T (period of the sinusoid), φ (Phase shift relative to t) and the full range of the sine wave in degrees.
11 Optical Theremin 11 Figure 12: Visual Aid for Derivation (20 Hz Sine Wave) Solving for all parameters used in the LabVIEW code for the example of a 20 Hz sine wave: Solving for the period, T: (Eq. 3) Solving for the rise time, t: (Eq. 4) where Course is the input that defines 30-90% hard distortion Solving for the Duty Cycle: (Eq. 5) Solving for the Phase Shift of Square Wave B: (Eq. 6) Solving for the Phase Shift of Square Wave G: (Eq. 7) This series of calculations is used to render all possible hard distortion waveforms in the range of 20 to 20kHz. The original sine wave undergoes a battery of alterations by selectively eliminating the parts of the waveform that the designers wish to qualify as hard distortion. Figure 13: Distortion Overview graphically displays the main parts of this process while Figure 7: Distortion ( Clip ) Sub VI provides the full model used to produce hard and soft
12 12 distortion. Eq.8 explains this mathematical process. (Eq. 8) where: A is the original sine wave K, B, L and G are the square waves at the frequency of A Fine is the value that specifies the type of clipping (soft, hard or normal on the front panel) Scalar is the waveform of hard clipping amplitude Soft distortion is achieved by scaling the modified peak by the Fine variable. Figure 13: Distortion Overview Generate Signal This process is made inherently simple, even for developers, as LabVIEW eliminates a lot of the work of producing a sinusoid. Given the inputs from the Normalized Output from each respective channel, the information is fed to the Simulate Signal block in the Clipping Sub VI that produces the signal, a dynamic data type. DAQ Assistant prepares signal for output This process is also very simple as LabVIEW handles all aspects of generating the output signal for the 3.5mm headphone jack to output to a speaker. The input for this process is the dynamic data type signal that was generated in the previous step. The output is the sound at the headphone or speaker. Conclusions The Gold team designed and developed an optical Theremin under the constraints of using a set of photodiodes in conjunction with an operational amplifier. We came to the consensus that a transimpedance amplifier was ideal to develop the Theremin in order to convert the current generated by the photodiodes into voltage that would be read by the mydaq. Once we realized that we needed to use a transimpedance amplifier, we had some trouble figuring out what resistor values would give us the best response for both diodes. At first we picked a 100K
13 13 ohm resistor pair, however the amplification wasn t enough to fully see the fluctuations in the waveforms. We then decided to pick a much higher resistor value and went with a 9.1 Mega-ohm resistor pair in which the waveform response was much more sensitive. It was decided that we also add a simulate function to our VI for additional functionality which separates us from the other team designs. We wanted to make sure that even when we were working separately, we could still work on the code and see if it worked. It was a great debugging technique to insure that our waveforms were responding accordingly and limit any problems to the data acquisition from our circuit. The team ran into some trouble when we were interfacing with LabVIEW. The DAQ Assistant Setting Parameters were difficult to handle because the Samples to Read and Rate values were giving us a slow acquisition. Using trial and error we came to the specifications mentioned above to get an appropriate acquisition pace. Once we addressed these issues, we were then able to successfully complete the Theremin in the time period given to us. Appendix: Octave Scale Figure 14: Discrete Frequency Bins for Autotune Sub VI
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