Building a Soda Can Theremin with the Analog Discovery Studio

Remember those old-school sci-fi movies with squeaky and eerie background music? Those unique sounds were made using a Theremin, an electronic instrument that can be played without physical contact. When playing a Theremin, the operator can control volume and pitch with his or her hand position relative to two antennas.

This project is going to demonstrate how to build and debug a simple Theremin on the Analog Discovery Studio using a soda can as the antenna! With simplicity in mind, the Theremin in this project will only demonstrate pitch modulation. The design that is implemented is shown in the block diagram to the right. It doesn't take too much extra work to add volume control, so I encourage you to try it if you're looking for an extra challenge.

For the fully analog theremin:

• Analog Discovery Studio
• Breadboard Canvas
• Analog Parts Kit
  • speaker
  • audio connector
  • OP27 operational amplifier (x2)
  • OP37 operational amplifier (x2)
  • 2N3904 NPN transistor
  • 2N3906 PNP transistor
  • 1N3064 small-signal diode
  • 1N914 diode (x2)
  • 10kΩ potentiometer
  • 100pF ceramic capacitor
  • 1nF ceramic capacitor (x2)
  • 10nF ceramic capacitor (x2)
  • 47nF ceramic capacitor
  • 100nF ceramic capacitor
  • 47Ω resistor (x2)
  • 470Ω resistor
  • 4.7kΩ resistor
  • 10kΩ resistor (x5)
  • 20kΩ resistor (x2)
  • 47kΩ resistor (x2)
  • 100kΩ resistor (x3)
• a soda can
• WaveForms

For the mixed-signal theremin:

• Analog Discovery Studio
• Breadboard Canvas
• Analog Parts Kit
  • OP27 operational amplifier
  • 10kΩ potentiometer
  • 100pF ceramic capacitor
  • 100kΩ resistor (x3)
• a soda can
• WaveForms
• Python 3

Place the op-amp such that it straddles the valley of the breadboard and the notch is towards the top of the breadboard. Op-amps require +5V at one rail and -5V at the other rail. That being said, one power rail of the breadboard is designated for +5V and the other power rail is designated for -5V. In the breadboard image below, red wires are used for connections to the +5V power rail and white wires are used for connections to the -5V power rail. Connect pin 7 of the op-amp to the positive power rail (+5V). Connect pin 4 of the op-amp to the negative power rail (-5V). Connect a black wire between the ground rail and one of the breadboard rows above the op-amp.

Place the 100pF capacitor between the grounded row of the breadboard and pin 2 of the op-amp. Now we'll place the resistors. All the resistors used in the oscillator are 100kΩ. Place one resistor across the op-amp from pin 2 to pin 6. Place another resistor across the op-amp from pin 3 to pin 6. Place the last resistor between the grounded row of the breadboard and pin 3 of the op-amp.

The soda can is to be placed in parallel with the capacitor. Connect one end of a black jumper wire to the grounded rail of the breadboard. You will hold the other end of this wire in your right hand when operating the Theremin. Connect one end of a green jumper wire to pin 2 of the op-amp. Connect the other end of this wire to the soda can. A slightly longer jumper wire is easier here. I place the wire such that it is held on by the tab on the top of the can. Taping the wire to the can would work as well. Just make sure there is metal-to-metal contact. By holding the black wire in your right hand, your body is now part of the circuit. This allows you to use your left hand to act as a plate of a capacitor with the soda can.

Connect an orange wire to pin 6 of the op-amp. This will carry the output voltage from this oscillator to the next section of the circuit, the weighted summer.

To see the output of this circuit block, open WaveForms, then, in the Supplies instrument, set +5V, respectively -5V for the variable power supplies. Enable both power supplies, then turn on the V± switch on the Breadboard Canvas, to power on the circuit.

Connect the Oscilloscope Channel 1+ (orange wire) to the output of the block and the 1- (orange-white wire) to ground, then open and start the Scope instrument. As you move your hand towards the soda can, you should see the oscillation frequency changing.

For the fixed-frequency oscillator, we will be using the OP37 operational amplifier. The pin out and specifications of the OP37 can be seen in the data sheet.

Place the op-amp such that it straddles the valley of the breadboard and the notch is towards the top of the breadboard. Op-amps require +5V at one rail and -5V at the other rail. That being said, one power rail of the breadboard is designated for +5V and the other power rail is designated for -5V. In the breadboard image below, red wires are used for connections to the +5V power rail and white wires are used for connections to the -5V power rail. Connect pin 7 of the op-amp to the positive power rail (+5V). Connect pin 4 of the op-amp to the negative power rail (-5V).

Place the 1nF capacitor between the grounded row of the breadboard and pin 2 of the op-amp. Place one 10kΩ resistor across the op-amp from pin 2 to pin 6. Place another 10kΩ resistor across the op-amp from pin 3 to pin 6. Place the 20kΩ resistor between the grounded row of the breadboard and pin 3 of the op-amp.

Connect an orange wire to pin 6 of the op-amp. This will carry the output voltage from this oscillator to the low-pass filter network. This network consists of three RC low-pass filters, connected in series, the first being connected to the output of the op-amp (pin 6). The output of this block is taken from the ungrounded pin of the last capacitor.

To view the signals on different parts of this block, power on the circuit, as previously described, then connect the Oscilloscope Channel 1+ (orange wire) to the output of the op-amp (pin 6) and Channel 2+ (blue wire) to the output of the low-pass filter network. Don't forget to ground Channels 1- (orange-white wire) and 2- (blue-white wire).

As seen in the image to the right, the output signal is more a triangular wave, than a sinus, but for this application, this will be a good approximation.

Move a few holes down the breadboard from the oscillator and place the OP27 such that it straddles the valley of the board and the notched side is towards the left side of the board. Just as we did when building the oscillator, connect pin 7 of the op-amp to the positive power rail and pin 4 of the op-amp to the negative power rail. Connect pin 3 of the op-amp to one of the ground rails on the breadboard.

Connect two 47kΩ resistors in parallel as shown in the breadboard image below. The bottom side of both resistors should be connected to pin 2 of the op-amp. The left sides of the resistors should be off by one row as shown. Connect the other end of the orange wire from the oscillator to one of these 47kΩ resistors. Use another wire to connect the output of the low-pass filter network after the fixed-frequency oscillator to the other 47kΩ resistor. Place a 20kΩ resistor across the op-amp from pin 2 to pin 6. Lastly, place an orange wire at pin 6 of the op-amp, just like in step 1. This will connect the output of the weighted summer to the next section of the circuit, the envelope detector.

As the frequencies of the two input signals are very close, when they are added, they interfere, producing a beat (a specific interference pattern). At this point the output signal is still outside the audible frequency domain, but it can be visualized with the oscilloscope.

The input of the envelope detector is the output of the weighted summer. A few holes down from the weighted summer, connect the other end of the orange wire (from the weighted summer) to the orange (“positive”) side of the diode. At the negative side of the diode, place the 10kΩ resistor and 47nF capacitor in parallel. Connect the other side of the resistor and capacitor to a ground rail.

The output from this circuit is at the junction of the diode, resistor, and capacitor. Connect one side of an orange wire here.

The output signal falls in the audible domain. However, it is “weak”, having a small amplitude, but a relatively large DC offset, which can damage the speaker, so further processing is necessary.

Moving moving further down the board, place the OP37 the same way the OP27's were placed, straddling the valley of the board with the notch to towards the top of the breadboard. As with the previous two op-amps, connect pin 7 of the op-amp to the +5V rail of the breadboard and connect pin 4 of the op-amp to the -5V rail of the breadboard.

Place a 10kΩ potentiometer near the op-amp. This potentiometer will be used to set the amplitude (volume) of the signal. Connect the middle pin to pin 2 of the op-amp and another pin to pin 6 of the op-amp. Place a 4.7kΩ resistor such that one side of it is connected at pin 2 of the op-amp. The other side of the resistor should be connected a few holes to above the op-amp. Connect the other side of the orange wire from the envelope detector's output to this side of the resistor.

Pin 3 of the op-amp would normally be connected to ground through a resistor. In this scenario, it is ideal to use as large of a resistor as possible. To simulate an infinite resistance, we will leave pin 3 unconnected such that it sees an “open circuit”. No current can flow through an open circuit it so it acts as an infinite resistance.

Connect the 100nF capacitor to the output of the op-amp. Connect an orange wire to the other pin of the capacitor. This will be used to send the amplifier to the speaker, while the capacitor in series with the output will eliminate the DC offset of the signal (decoupling capacitor).

To visualize the signals, connect the Oscilloscope Channel 1+ (orange wire) to the input of the block and Channel 2+ (blue wire) to the output, after the decoupling capacitor. Don't forget to ground the 1- (orange-white) and 2- (blue-white) wires.

Connect together the emitters of an NPN and a PNP transistor. Connect the collector of the NPN transistor to +5V, the collector of the PNP transistor to -5V. Connect one 10KΩ resistor between the base and the collector of each transistor.

Connect the anode (“positive” pin) of a diode to the base of the NPN transistor. Connect the anode of a second diode to the cathode of the first, and the cathode of the second diode to the base of the PNP transistor.

The input of the power amplifier is the cathode of the first diode and the output is the emitter of the transistors.

Connect the Oscilloscope Channel 2+ (blue wire) to the middle pin of the 10kΩ potentiometer and ground Channel 2- (blue-white wire). Use jumper wires to connect one unconnected leg of the potentiometer to the positive supply voltage and the other to the ground. This potentiometer will set the volume of the theremin.

The main part of the project starts with importing the necessary modules, then defining the most important parameters of the project:

• sampling_frequency - the frequency at which analog data is sampled
• buffer_size - the number of data point in a data set (maximum is 8192)
• amplitude - this sets the amplitude of the output signal, set it in a way to get around 1V amplitude at the output
• frame_repeat - how many times should a data set be repeated
• fixed_frequency - the frequency of the fixed-frequency oscillator

These parameters, the device handle and the library of the SDK are also initialized in the modules.

# import necessary modules
import sys
import math
import numpy
import ctypes as ctp
import dwfconstants as dwfct
from scipy.signal import hilbert
 
# import own modules
import device
import supply
import scope
import wavegen
 
 
class state:
    # application parameters
    sampling_frequency = 1000000.0
    buffer_size = 8192
    amplitude = 2.0
    frame_repeat = 5
    fixed_frequency = 30500.0
 
 
# set parameters in modules
scope.state.sampling_frequency = state.sampling_frequency
wavegen.state.sampling_frequency = state.sampling_frequency
scope.state.buffer_size = state.buffer_size
wavegen.state.buffer_size = state.buffer_size
wavegen.state.frame_repeat = state.frame_repeat
 
# load dynamic the SDK
dwf = device.load()
supply.dwf = dwf
scope.dwf = dwf
wavegen.dwf = dwf
 
# open device, send handle to modules
hdwf = device.open()
supply.hdwf = hdwf
scope.hdwf = hdwf
wavegen.hdwf = hdwf

After this, the instruments are initialized.

The output of the fixed-frequency oscillator is generated. This is always the same, based on the following formula: $signal_{f_{fixed}}=sin(2*{\pi}*\frac{f_{fundamental}}{f_{sampling}}*(0:nr_{sample}))$

try:
    # setup instruments
    supply.initialize(5.0, -5.0)
    supply.enable(True)
    scope.initialize()
    wavegen.initialize()
 
    # generate fixed-frequency sine wave
    samples = numpy.arange(0, state.buffer_size - 1)
    angular_velocity = 2.0 * math.pi * state.fixed_frequency / state.sampling_frequency
    fixed_signal = samples * 1.0
    for index in range(len(samples)):
        fixed_signal[index] = math.sin(angular_velocity * samples[index])
    mixed_signal = samples * 1.0

In the main loop the data acquired on Scope Channel 1 is normalized, then added (mixed) with the generated fixed-frequency signal. The envelope of the resulting signal is extracted by calculating the absolute value of the signal's Hilbert transform. The DC offset of the envelope is removed by substracting from the samples the average of the samples, then the resulting signal is normalized again.

The second Oscilloscope Channel is read and averaged to get the potentiometer state, which determines the volume (amplitude) of the resulting signal.

As a final step, the signal is generated with the desired amplitude on both Wavegen Channels.

# loop
    while True:
        # mix signals
        variable_signal = scope.acquisition(1)
        variable_maximum = max(variable_signal)
        for index in range(len(fixed_signal)):
            mixed_signal[index] = fixed_signal[index] + \
                (variable_signal[index] / variable_maximum)
 
        # detect the envelope
        analytic_signal = hilbert(mixed_signal)
        amplitude_envelope = numpy.abs(analytic_signal)
 
        # remove offset and limit the resulting values between +1 and -1
        envelope_average = sum(amplitude_envelope) / len(amplitude_envelope)
        ac_envelope = amplitude_envelope - envelope_average
        envelope_maximum = max(ac_envelope)
        ac_envelope = ac_envelope / envelope_maximum
 
        # get potentiometer information and calculate volume
        voltages = scope.acquisition(2)
        voltage_average = sum(voltages) / len(voltages)
        volume = voltage_average * 1.0 / 5.0
 
        # output the result on the waveform generator
        wavegen.generate(ac_envelope, volume * state.amplitude)

You can stop the theremin by pressing Ctrl+C on the keyboard. The program will stop the supplies, reset all instruments and close the device, to make it available for other software (like WaveForms).

except KeyboardInterrupt:
    # exit on ctrl+c
    pass
 
finally:
    # stop the supplies and close the device
    supply.enable(False)
    device.close()

If you want to visualize the signals outputted on the Wavegen Channels, connect an oscilloscope (for example another Test & Measurement device) to any output channel, or use the matplotlib.pyplot python module and the plot() function; however, plotting will introduce significant delays, thus the results may not be correct.

It can be seen, that if the variable frame_repeat is set to 1, huge delays appear in the output signal. This happens due to the processing speed of our script: mixing and demodulating/filtering the signals requires more time than the runtime of the waveform generator for a data set.

This effect can be reduced by a small trick: we will repeat every data set a few times (around 5 is fine). As the signals are mostly periodic and because of the large sampling frequency and the reduced buffer size of the instrument, this trick isn't even audible in the resulting audio signal.

Small (around 3ms) delays still are present. These are the moments when new data sets are loaded in the Wavegen's buffer, but these interruptions add a really cool effect to the resulting sound.