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Theremin

23/05/2009

Abstract

The theremin was invented nearly 100 years ago. This instrument captivated audiences worldwide when it was first demonstrated by its inventor, Lev Sergeivich Termen. Despite mainstream interest in the theremin had faded by 1938, the instrument remained popular amongst electronics enthusiasts and hobbyists alike. Fortunately, building a simple theremin is not an expensive enterprise; anyone with moderate electronics skills can build one for themselves. This article will demonstrate an analogue theremin that also incorporates a contact-less volume control feature, as seen on the original instrument. The theremin circuit performs quite well, considering the choice of components are of cheap variety, not to mention accessible. However, the design also leaves a lot of room for improvement—perhaps that will be revisited on another day.

1 Introduction

1.1 Historical Background

A theremin is an electronic musical instrument that can be played without physical contact by the operator. The operate a typical theremin, the user is required to interact with two metallic control rods mounted at some distance apart on the instrument. The rods are designed to sense the proximity of the operator's hands, which affect the instrument's pitch and volume respectively. The pitch is manipulated with one hand and the volume is controlled with the other hand.

The instrument was invented in 1919 by a Russian physicist named Lev Sergeivich Termen [19]. Not long after inventing the theremin, Termen demonstrated his new invention to Lenin. This gave him the opportunity to showcase the instrument to the rest of the world, particularly in Europe and in the United States. During his travels in the West, Termen acquired the familiar Westernised name, Léon Théremin. He filed a U.S. patent for his invention in 1925 [1]. Four years later, the instrument was commercialised for the first time, under the brand name RCA Thereminvox. Today, the instrument is generally known as the theremin.

Since the invention of the theremin, the instrument was used in many notable films and by musicians. Examples of films include The Day the Earth Stood Still, The Thing from Another World and The Ten Commandments. From the music category, Good Vibrations by The Beach Boys and Whole Lotta Love by Led Zeppelin are classic examples; even the Beastie Boys are known to use theremins in their music tracks.

1.2 Theremin Circuits Today

Despite mainstream interest in the theremin had faded by 1938, the instrument remained popular amongst electronics enthusiasts and hobbyists alike. Today, an entire range of theremin kits are available through various vendors. Popular examples include the Etherwave Theremin by Moog Music [2], the Theremax Theremin by PAiA [3], the theremin kit by Silicon Chip [4, 5], the Harrison Instruments 151 Theremin [6], and the Junior Theremin [7].

Of course, not all theremins are in kit form. Many enthusiasts researched vintage theremin circuits and built their own. Some individuals even managed to replicate the original RCA Thereminvox with great success [8, 9]. While there is no doubt that efforts behind building replicas is impressive, other theremin projects based on valve technology are equally remarkable [10, 11, 12, 13, 14]. Having said that, theremins designed with semiconductor technology should not be overlooked either [15, 16, 17, 18]. Transistors and intergrated circuits perform extremely well in theremin applications. More importantly, they operate at safer voltages and they are more accessible to hobbyists.

1.3 Dom's Version

This document will detail my attempt at designing and building a complete theremin. Admittedly, perfection is not a strong point in this theremin, a number of flaws and problems have been discovered which can affect the overall performance. Having said that, the theremin works quite well for the most part, despite the shortcomings in this circuit. (Problems and possible solutions will be discussed in the Results section.) Sample audio files, including a video footage demonstrating the theremin, is listed in the Appendix section. The project should be a valuable educational experience for anyone undertaking basic RF electronics.

The theremin was built with discrete components. All components are of common variety, they should available at most electronics outlets. The construction did not involve winding coils, nor building exotic components. Most parts can be substituted with alternatives if required. The circuit can be modified to some extent, due to the modular approach of the design. The final construction utilises a chassis fashioned from a recycled ATX power supply case. The case was slightly modified to accommodate the extra connectors and the tuning capacitors required by the theremin circuit.

This project will require test equipment, such as an oscilloscope. Nothing fancy, a cheap 10 MHz oscilloscope should do the job fine. If an oscilloscope is not available, a good multimeter can be used to test key points within the circuit, albeit with limited debugging potential.

The rest of the document will discuss the circuit diagrams, the construction and debugging process. The document will conclude with discussions on performance results and possible future work. Schematics, PCB artwork and other related files will be available to download in the Appendix section.

2 The Theremin Circuit

2.1 Units and Terminology

In order to avoid confusion, the following list is a clarification on how units will be interpreted in this document:

  • VP = Peak Voltage, maximum half-wave amplitude swing from the DC point of reference.
  • VPP = Peak to Peak Voltage, maximum amplitude swing from the lowest point of the waveform to the highest point.
  • VRMS = Root Mean Squared Voltage, the DC voltage equivalent of an AC waveform, ideally for sine waves.
  • V AC = Alternating Current Voltage, measured in VRMS.
  • dB = Power gain, expressed in decibels.

In this project, the majority of the waveforms are roughly sinusoidal, therefore Equation 1 provides a suitable representation of relationship between VRMS and VP.

1 (1)

Equation 2 calculates the power gain (dB), where P0 and P1 is the output power and input power respectively (both given in WRMS).

2 (2)

The following terminology will be used in this document:

  • Instrument — Implies the theremin musical instrument.
  • Detector — Refers to either the theremin's pitch detector or the volume detector circuit.
  • Control rod — Also known to as the "antenna" on the theremin, which acts as a proximity sensor.
  • Mixer — Frequency mixer, also known as a multiplier.
  • Zero beat — Occurs when the theremin's pitch (or volume) detector is tuned; the difference frequency at the mixer output is 0 Hz.
  • Resonator — Refers to a resonant L-C tank circuit.

2.2 Circuit Overview

In a nutshell, the theremin circuit consists of three main sections: The pitch detector, the volume detector and the output amplifier. The complete block diagram for the circuit is illustrated in Figure 1. The pitch detector generates the audio signal, which varies in frequency in accordance to the hand proximity from the control rod. Likewise, the volume detector employs the same operating principle, although in this case the detector controls the actual gain of the output amplifier.

Figure 1
Figure 1: Block diagram for the theremin circuit.

When the operator moves his or her hand closer to the pitch control rod, the pitch frequency increases. To control the volume, the operator is required to perform similar gestures on the volume control rod. Moving the hand closer to the volume control rod will decrease the gain in the output amplifier; and therefore reduces the overall volume of the pitch signal. Table 1 summarises how a theremin responds to various hand gestures. It is worth noting that the pitch response and the volume response of this particular theremin is non-linear. For example, the frequency for the pitch will increase exponentially as the hand is moved closer to the control rod (see the Results section for details). This kind of behaviour is analogous with many existing theremin designs [20].

Hand Proximity
Close Far
Pitch High Low
Volume Low High
Table 1: Theremin response.

Both the pitch and the volume detector circuits are functionally identical. Therefore, only the pitch detector circuit will be described in detail. The pitch detector consists of the following fundamental circuits: The LO (local oscillator), the VFO (variable frequency oscillator) and the mixer. The LO runs at a fixed frequency, which serves as a reference signal to the rest of the pitch detector circuitry. The VFO is a tunable oscillator and it is adjusted to operate at the LO frequency. The VFO is also connected a pitch control rod, making the oscillator very sensitive to the parasitic capacitance introduced by the control rod. When a large electrically conductive object is placed near the control rod, the parasitic capacitance in the rod changes and thus detunes the VFO, causing it to drift out in frequency. The difference in frequency between the LO and VFO is detected by the mixer circuit.

The mixer circuit operates in a heterodyning principle [21, 22]—it multiplies the input frequencies from the LO and the VFO, and produces an amplitude modulated signal at the output. The modulated signal is basically a combination of the sum, the difference and both original frequencies of the input signals. In this particular application, only the difference of frequencies will be utilised. All other frequencies present will be removed in the subsequent stages of the circuit.

Before operating the theremin, it is necessary to tune the VFO in such way that difference frequency at the mixer output is 0 Hz. Tuning is done while no conductive object is near the control rod. This is also known as tuning for the zero beat frequency. In most theremin circuits, the tuning oscillators tend to lock onto each other when they are almost synchronised [23]. Therefore, once tuned, the VFO will remain stable and synchronised until the parasitic capacitance in the control rod changes significantly enough to nudge the VFO out of tune. Likewise, if a zero beat occurs in the volume control circuit, the instrument will play at maximum volume until its own VFO is detuned in a similar fashion, which in turn decreases the pitch volume (more on this later). In this particular theremin design, it is possible to detune the pitch VFO by as much as 1.9 kHz, which defines the frequency range of the pitch (i.e. 0 to 1.9 kHz).

As mentioned earlier, both the pitch detector and the volume detector is identical in functionality. However, one discrepancy remains; each detector operates at a different LO frequency. The LO frequency in the pitch circuit runs at 1.06 MHz, whereas the volume circuit operates at 715 kHz. This was deliberately done to minimise interference between the two detectors.

Figure 2
Figure 2: SPICE simulation of the modulated (green)
and demodulated signal (orange).

The green plot in Figure 2 is a simulated example of what a modulated signal looks like at the frequency mixer output. The plot predominantly consists of the LO frequency signal, shaped by a low frequency modulation envelope. The the LO frequency is too high for the graph to reveal, hence plot appears to be shaded in solid green colour. However, the feature of interest is actually the low frequency modulation envelope.

The modulated signal is fed into a diode envelope detector circuit. This detector's purpose is to trace the low frequency contour of the waveform and discard the remaining high frequency components. Essentially, the envelope detector functions as a demodulator, which produces a near-sinusoidal signal, as illustrated by the orange plot in Figure 2. Such demodulation techniques are commonly used in AM radio circuits [24].

Ideally, the demodulated signal should be sinusoidal. However, the true waveform will be always distorted to some extent, particularly when the VFO and LO converge towards the lock (or zero beat) frequency. The distortion is due to electrical and magnetic coupling between the oscillator circuits, causing their waveforms to create harmonics in the difference frequency [23]. The demodulated signal will also retain some of the LO frequency noise. Therefore, a LPF (low pass filter) is needed at the end of the detector circuit chain to eliminate the LO noise.

That said, eliminating distortions in the pitch waveform is not critical in this application. Indeed, many theremin circuits do not output pure sinusoidal signals at all; distortions tend to give the instrument "character" [23]. Some theremins generate half-rectified waveforms, others incorporate effects, such as timbre, velocity, and other special waveform manipulation filters [3]. The waveform purity for the volume detector output is even less critical, because the signal is used for charge pumping purposes in the frequency to voltage converter.

The final stage of the theremin circuit consists of a VCA (voltage controlled amplifier) and a F2V (frequency to voltage) circuit. Volume control is performed by the F2V circuit. It converts the frequency from the volume detector to a particular voltage level, which is fed to the VCA gain control circuit. Changes in the volume detector frequency will shift the F2V output voltage level, which in turn increases or decreases the gain of the VCA. The VCA also acts as a simple buffer between the sensitive pitch detector and the external device connected to the theremin.

Figure 3
Figure 3: The complete theremin schematic (click image to enlarge—warning, large image).

The complete circuit diagram is illustrated in Figure 3. A PostScript version of this schematic diagram is also available to download in the Appendix section. The following sections will explain the theremin circuit in greater detail.

2.3 The Local Oscillator

An oscillator is basically a limiting amplifier that feeds itself a phase shifted input signal, through a feedback network consisting of a resonating L-C tank circuit [24, 28, 29]. To sustain an oscillation in the circuit, the amplifier must overcome losses present in the feedback path, stabilize the amplitude of oscillation, and it must re-excite the resonator. The rate at which the lost energy is replenished in the tank circuit will determine the operating frequency of the oscillator.

The theremin operates on four L-C oscillator circuits. It uses two LOs (local oscillators) and two VFOs (variable frequency oscillators). As mentioned earlier, the pitch and the volume detector is functionally identical. Therefore, only the pitch detector LO will be described in detail. The schematic diagram for the volume detector LO is illustrated in Figure 3.

Figure 4
Figure 4: Pitch local oscillator.

The pitch LO, as illustrated in Figure 4, is based on the Vackář (Vackar) oscillator [25, 26, 24]. The circuit uses a Colpitts type resonant tank [27], formed by capacitors C2, C5, C7 and the inductor L2. The capacitive voltage divider, formed by C12, C10 and C14, is a feedback path that drives the transistor, Q2. The transistor operates as a low gain Class A amplifier and produces a 180° phase shifted signal at the drain pin. The output signal is used to maintain oscillation by exiting the resonator via the feedback loop at L2 and C2.

What makes the Vackář oscillator unique is the feedback system formed by C12, C10 and C14. The capacitive voltage divider introduces extra stability against frequency drift (and phase noise) by isolating Q2 from the resonator. This arrangement provides the right voltage transformation ratio at the transistor gate without loading the tank circuit too much [25]. Oscillator stability is an important factor in tuning circuits, particularly in the VFO described later in this document.

The pitch circuit resonates at 1.06 MHz ±10%, as defined by the component values of C2, C5, C7 and L2. The volume detector resonates at 715 kHz ±10%. The margin of error indicates the maximum shift of the operating frequency point. This shift is caused by the uncertainty in component values used by the tank circuit. To minimise this error, choosing components with a good tolerance is important, typically 10% for inductors and 5% for capacitors (or better). However, it is not critical for the LO to operate exactly at the theoretical frequency, provided the LO frequency lies well within the tuning range of the VFO.

The significance of the capacitors C5 and C7 being in parallel is to allow crude tuning of the resonant circuit; capacitors can be mixed and matched in the hope of improving the operating frequency point, as long as their combined value remains close to 150 pF. That said, substituting C5 and C7 with a single 150 pF capacitor is perfectly reasonable. As for the capacitors in the feedback circuit, the parallel combination of C10 and C14 should be close to 600 pF in order to attain the recommended 1:6 divider ratio with C12, as suggested by Vackář [25].

The inductor L4 is part of the impedance coupling network at the oscillator output and also serves as a load for Q2. The zener diode D7 stabilises the oscillator's power supply, roughly at 5 V DC. The supply also uses R-C decoupling (R7 and C18) to minimise noise propagating into the power supply. Finally, the output is fed to the buffer amplifier stage through an AC coupling capacitor, C19. The output is a pure sine wave, with a peak amplitude of anywhere between 1.5 VP to 2 VP. An example of the output waveform is depicted in Figure 5.

Figure 5
Figure 5: Pitch local oscillator output;
0.2 µs/Div, 1 V/Div.

2.4 The Variable Frequency Oscillator

Figure 6 illustrates the VFO used by the pitch detector. At first glance, it is apparent that the circuit is very similar to the Vackář local oscillator described earlier (Figure 4). In fact, both circuits are almost identical, except the VFO has a tuning capacitor and a control rod (or a pitch antenna) present in the resonant tank circuit. The VFO has two roles in the theremin: It allows manual tuning for the zero beat frequency (that is, to synchronise with the LO frequency); and it also allows predictable detuning through hand gestures near the control rod. The volume VFO employs the same design as the pitch VFO and thus it will not be discussed here (see Figure 3 for the volume VFO circuit diagram).

Figure 6
Figure 6: Pitch variable frequency oscillator.

Vackář oscillators are considered to be extremely stable; they are robust against phase noise and amplitude variations across a rather large tuning range of fMAX:fMIN = 3:1 [26]. The pitch VFO in Figure 6 has a centre frequency close to 1.06 MHz. The tuning capacitor C8 is able to vary the VFO frequency from 969kHz to 1140 kHz (with the control rod disconnected), giving it a theoretical tuning range of 1.18:1. The volume VFO has a tuning range of 682 - 735 kHz, or 1.08:1. The range can vary dramatically by as much as ±10%, again due to the uncertainty in the component values, and due to the type of tuning capacitor is used. Similar to the LO circuit, it is possible to improve the operating frequency point by matching capacitors C4 and C6 to equal 120 pF. This Vackář oscillator is stable enough to operate with a cheap tuning capacitor for C8, the type commonly found in AM/FM radios.

When the control rod is attached to the circuit (through C3), the L-C tank sees a parasitic capacitance as high as 5 pF in parallel with C4, C6 and C8. This parasitic capacitance varies depending on the rod's size, shape and the proximity of electrically conductive objects nearby. Slight changes in parasitic capacitance will shift the resonant frequency of the L-C tank and thus detunes the VFO. The capacitor C3 provides DC decoupling from the L-C tank and it also influences the control rod's sensitivity. The VFO produces a 1.5 VP to 2 VP sine wave as depicted in Figure 7.

Figure 7
Figure 7: Pitch variable frequency oscillator output;
0.2 µs/Div, 1 V/Div.

2.5 Buffer Stages

Each oscillator in the theremin is isolated by a buffer amplifier. Isolation is required to prevent the mixer circuit from interfering and loading the oscillator. Loading can significantly affect the frequency stability of the oscillator. Therefore, the buffer amplifier should have a high impedance at the input and be able to drive a load with lower impedance. All buffer amplifier circuits in this theremin are identical (see Figure 3); therefore, only the one buffer amplifier belonging to the pitch LO will be described.

Figure 8
Figure 8: Buffer for the pitch local oscillator.

The circuit in Figure 8 is a type of source follower J-FET amplifier, originally implemented by Harris [30]. Typical source follower amplifiers have a unity gain close to 1, whereas this circuit has a gain of 2, due to the output stage acting like a balanced line driver. The inductor L6 provides an untuned impedance coupling for the output signal [32]. Basically, this kind of coupling behaves like an output transformer under unbalanced conditions. In other words, L6 outputs a balanced signal with a reference to ground, rather than a floating output as one would expect with a transformer. Buffer amplifiers with a balanced output will have gain of 1 for the positive line and a simultaneous gain of 1 for the negative line (the ground reference in this case), hence a net gain factor of 2 [31].

The output amplitude should be 3.5 VP to 4 VP immediately after the AC coupling capacitor C28, as shown in Figure 9. This signal drives the mixer circuit directly, as described in the next section below. The buffer circuit also uses a zener diode D12 to stabilise power supply and a R-C decoupling network (R13 and C25) to minimise supply noise.

Figure 9
Figure 9: Pitch buffer amplifier output;
0.2 µs/Div, 1 V/Div.

2.6 The Dual FET Mixer

The mixer circuit is what makes the theremin actually useful. It takes the signals from the LO and the VFO respectively, and electronically multiplies them together to obtain their difference in frequency. Of course, the mixer will output other signals that will be discarded in the later stages of the detector circuit (such as the sum of frequencies, the LO and VFO signals, and so on). The frequency mixer is identical both for the pitch and the volume circuit (see Figure 3). Hence, only the pitch mixer will be described in detail.

Figure 10
Figure 10: Dual FET mixer for the pitch detector.

Figure 10 is an active transconductance mixer, formed by two discrete transistors (Q6 and Q7) in a cascode-like arrangement [33, 34]. The two transistors are connected in series to behave like a monolithic dual gate transistor. The mixer circuit is arranged in the same fashion as a source follower amplifier, but in this case it has two input ports and an impedance coupling at the source pin of Q7. Mixing occurs when the VFO and the LO signals are applied to the two separate gates, through R20 and R21 respectively. The LO waveform drives Q7, where its transconductance is modulated by the VFO signal applied at Q6 [35].

The modulated signal emerges at the source pin of Q7, which is connected to a tuned impedance coupling tank, formed by L7 and C30. This L-C tank resonates at the LO frequency of each respective mixer: 1.06 MHz for the pitch detector, 715 kHz for the volume detector. The tank also operates as a filter, which discriminates the LO frequency in the amplitude modulated form, as shown in Figure 11. The feature of interest is the low frequency envelope in the output waveform. The output should have a peak amplitude at about 4 VP—enough to overcome signal losses in the envelope detector and in the low pass filter.

Figure 11a Figure 11b Figure 11c
(a) (b) (c)
Figure 11: Examples of modulated output signals from the mixer, with a frequency difference of (a) 33 Hz (10 ms/Div, 1 V/Div); (b) 208 Hz (1 ms/Div, 1 V/Div); and (c) 500 Hz (1 ms/Div, 1 V/Div).

Couple of notes: R20 and R21 are place holders for attenuation resistors, which form a voltage divider with R22 and R23 respectively. Attenuation is only needed if either (or both) oscillators happen to have a very high Q and causes the buffer amplifiers to overdrive the mixer. If necessary, R20 and R21 should be chosen to attenuate the signal down to 3.5 VP (maximum of 4 VP) at each transistor gate in order to reduce distortions and clipping in the modulated output.

2.7 Envelope Detector and the Low Pass Filter

The next stage in the pitch (and volume) detector circuit deals with the extraction of the difference frequency from the modulated waveform. The circuit also employs a low pass filter to clean up the output signal. This section will only detail the pitch envelope detector, as the volume envelope detector uses the same design (see Figure 3).

Figure 12
Figure 12: Pitch envelope detector and low pass filter.

The modulated waveform obtained from the mixer is fed to the envelope detector, such as the one illustrated in Figure 12. The detector is an extremely simple circuit, consisting of three components, D13, C32 and R25. The diode D13 is a half-wave rectifier, which only lets through the negative part of the modulated waveform. The rectified signal is filtered by capacitor C32, it smoothes the negative side of the envelope by eliminating most of the LO frequency components. R25 is serves as a load for the rectifier. The envelope detector produces a well formed difference frequency signal at 1 VP with a DC offset of -1.6 V (see Figure 13a). The PI-filter network, C33, R26 and C34, removes the remaining LO noise left by the envelope detector. The filter has a -3 dB cut-off point at 22.5 kHz. C35 is an AC coupling capacitor and outputs the final signal at 0.5 VP (see Figure 13b). Note: The signal depicted Figure 13b was offset by 3 V DC, due the input biasing for the voltage controlled amplifier. This bias should be absent (0 V DC) for voltage detector circuit.

The envelope detector and the filter attenuates the signal by -29 dB, which is a significant drop. However, the voltage controlled amplifier in the next stage has a 27 dB gain, which recovers most of the aforementioned losses at the pitch audio output. The -29 dB drop is not critical for the volume detector, because it uses a frequency-to-voltage conversion circuit that relies on the frequency aspect of the signal, and not so much on the amplitude.

Figure 13a Figure 13b
(a) (b)
Figure 13: Waveforms after (a) the envelope detector (1 ms/Div, 1 V/Div);
and (b) after the filter and AC coupling capacitor (1 ms/Div, 1 V/Div).

2.8 Frequency to Voltage Converter

In order to control the volume of the theremin, it is necessary to convert the frequency signal from the volume detector circuit into a control voltage that manipulates the gain of the pitch amplifier. The frequency to voltage converter shown in Figure 14 consists of three main stages. The first stage is a comparator circuit that converts the weak AC signal from the volume detector into a series of trigger pulses. The second stage is a charge pump that makes the frequency to voltage conversion happen. The final stage is an inverting buffer amplifier that drives the gain control circuit for the voltage controlled amplifier.

Figure 14
Figure 14: Frequency to voltage converter. The circuit is rearranged in this figure for a better fit.

The op-amp U1A in Figure 14 operates as a comparator. The large feedback resistor R3 sets the amplifier's gain to about 40. The non-inverting input of the amplifier references the ground. With this arrangement, the amplifier turns on hard every time the input voltage crosses the zero point and becomes negative. Therefore, the small alternating signal present at the input (approx. 0.5 VP) will produce a series of 5 VPP trigger pulses at the output (Figure 15a). The pull-down resistor R1 is required to centre the input signal at 0 V, which ensures the comparator is triggered with a duty cycle roughly at 40 to 50%.

Figure 15a Figure 15b Figure 15c
(a) (b) (c)
Figure 15: Waveforms produced by the frequency to voltage converter: (a) comparator output (1 ms/Div, 2 V/Div); (b) charge pump capacitor output (1 ms/Div, 2 V/Div); and (c) reservoir capacitor voltage level (1 ms/Div, 0.5 V/Div).

Charge pumps are commonly used in circuits that require frequency to voltage conversion, examples include FM demodulators [36], phase locked loops [37], and of course theremins [3]. In Figure 14, the frequency to voltage conversion is performed by the diode charge pump circuit, formed by C15, D5, D8, C21 and R8. The comparator feeds capacitor C15 with a pulse train (see Figure 15b for C15 output), and pumps charge into the reservoir capacitor C21. When the comparator output is +5 V, the reservoir capacitor C21 will charge up through C15 and D8. As soon as the comparator output drops close to 0 V, the pump capacitor C15 discharges through the comparator and D5. Diode D8 does not conduct at this point and cuts off the reservoir capacitor C21 from the pump circuit. In the meantime, the reservoir charge bleeds steadily through the load resistor R8 and the buffer amplifier through D9.

The average voltage level maintained at C21 will depend on the frequency of the comparator—that is, pumping rate of the diode-capacitor network. Figure 15c illustrates an example where the reservoir charge is replenished at a frequency of 650 Hz and maintains a steady voltage around 1.75 V DC. The component values in the charge pump circuit were chosen carefully to attain 2.5 V DC at C21 when the pumping frequency reaches 1 kHz. When the frequency drops, the average voltage level in the reservoir will drop accordingly, making electronic volume control in the theremin possible. In a nutshell, the difference in LO and VFO frequency obtained from the volume detector circuit is translated to a voltage level via the charge pump, which will ultimately control the gain of the pitch amplifier.

The NPN transistor Q5 acts as an inverting buffer amplifier and is driven by the charge pump circuit through diode D9. The diode prevents the transistor's biasing network from influencing the voltage level in the reservoir capacitor. The transistor is biased to perform linearly for input voltages between 0 and 2.5 V DC. The output will be an inverted voltage, with a range of 0.2 to 5 V DC. Capacitor C29 filters out the sawtooth noise caused by the charge pump. The resulting control voltage is attenuated by the trimmer RV1. Attenuation is necessary because the voltage controlled amplifier requires a gain control voltage of 0 V DC for maximum volume, and 3 V DC for minimum volume. Therefore, RV1 should be calibrated to output a maximum of 3 V DC when the volume detector circuit is at zero beat.

2.9 Voltage Controlled Amplifier

The final stage of the theremin circuit consists of a voltage controlled amplifier. This amplifier combines the pitch and volume control functionality of the instrument, and it also serves as a vital buffer between the pitch detector and the external equipment connected to the theremin.

Figure 16
Figure 16: Voltage controlled amplifier (click image to enlarge).

The voltage controlled amplifier in Figure 16 is an inverting op-amp (U1B), which is setup to operate in a single-supply environment. In order to handle signals with a negative voltage, the op-amp must be biased in such way that the output AC signal is centred at mid-supply voltage. Otherwise, the op-amp would clip the negative cycle of the amplified signal against the ground reference. Midpoint biasing is achieved by fixing the non-inverting input at 3 V DC through a voltage divider, R28, R31 and C37. From the amplifier's perspective, this midpoint becomes a new ground reference, called the virtual ground [38, 39, 40]. Resistors R28 and R31 are chosen to provide adequate current for the op-amp and its gain control circuit, while C37 stabilises the virtual ground against AC noise. The amplifier input is connected to an AC coupling capacitor C35 (Figure 12), which isolates the pitch detector from the 3 V DC bias.

The gain control circuit in Figure 16 uses Q8 and Q9 as part of the amplifier's feedback loop. The transistors behave like a voltage controlled resistor, which affects the transfer function of the op-amp [41]. When a 0 V DC control voltage is applied at R29, the transistor gate-source voltage VGS becomes -3 V DC and the drain-source resistance RDS becomes high. In this mode, the amplifier will operate with a maximum gain of 4.5 (27 dB). If the control voltage at R29 is set 3 V DC, the transistors will see 0 V across VGS and the drain-source resistance drops to a minimum. The drop in RDS will shunt the feedback loop to virtual ground and reduces the amplifier's gain by -26 dB. The transistors are arranged in parallel to keep net RDS small when the transistors are fully turned on.

Resistor R34 eliminates amplifier crossover distortion by a adding bias current to the output. C40 acts as a decoupling capacitor for the bias resistor. C36 is also used for decoupling purposes across the power pins of U1. The amplifier should output a signal anywhere between 1.5 to 2 VP during maximum amplification, and around 0.2 VP at minimum amplification (see Figures 17a and 17b). The coupling capacitor C41 is a bipolar electrolytic type. The amplifier should be able to drive external equipment with a load resistance of 3 kΩ.

Figure 17a Figure 17b
(a) (b)
Figure 17: Waveforms for the voltage controlled amplifier at (a) maximum gain (1 ms/Div, 0.5 V/Div);
and (b) minimum gain (1 ms/Div, 0.5 V/Div).

2.10 The Power Supply

The circuit in Figure 18 provides a 6 V DC power supply for the rest of the circuit. The theremin is fairly efficient, hence a 1 W power transformer should be sufficient. The circuit uses a standard 6 V regulator (U2) for the VCC power rail. The regulator IC only needs a small heat sink, because the unregulated input voltage is about 12 V DC, and the whole circuit draws a current at 72 mA. The VCC rail was chosen to operate at 6 V DC in order to minimise energy dissipation by the 5 V zener diodes in the LO and VCO circuits. The 1 V drop by zener diodes generates less heat and hence less wasted power.

Figure 18
Figure 18: The power supply (click image to enlarge).

Analogue circuits, particularly circuits used in audio applications tend to be sensitive to noise in the ground rail. This noise generally manifest themselves as a hum in the audio output, often caused by eddy currents in the chassis (or in the copper tracks), or by magnetic field ground loops, or by rectifier current spikes. These aforementioned noise problems can be minimised by connecting every ground reference in the circuit to a single point, called the star point [42, 43]. The designated star point is at the negative pin of the power supply filter capacitor, C20.

In reality, running all ground connections to the star point would be impractical, because the total number of connections required would be quite large. Therefore, a hierarchical grounding system is used instead. Basically each sub-circuit in the theremin is isolated, grounded locally and given a dedicated connection to the star point. This arrangement can be seen in the final PCB layout. Other ground points, such as RCA audio connectors and tuning capacitors must be electrically isolated from the chassis. The chassis has its own dedicated connection to the star point.

2.11 Component Selection/Variations, Circuit Modifications and Other Notes

This section will discuss the possible variations and some of the constraints within the circuit. Every effort was made to build the circuit out of conventional and readily available components. Some parts can be substituted with equivalents, while other parts do not offer that flexibility. Substitutes should be chosen carefully, because changes can degrade the performance of the whole circuit, particularly the oscillators. It is a good practice to prototype new designs and changes first. In fact, half of this theremin was successfully built and tested on a breadboard as shown in Figure 19.

Figure 19
Figure 19: Prototyping one half of the theremin. Click to see the labelled version.

Notes on component selection:

  • Inductors - Every inductor in this circuit is an epoxy encapsulated axial type. They are very compact, cheap and resistant to mechanical stress and humidity. Radial leaded type inductors are also suitable, provided they fit the PCB footprint given in the Appendix below. Do not mix inductor types, the coil form factor should be consistent throughout the whole circuit. Tolerance should be 10% or better.
  • Capacitors in oscillators - Large NP0 type ceramic capacitors are the most suitable. They offer the best temperature stability—an important attribute in tuned circuits. All resonant L-C circuits should use capacitors of similar physical size (applies to C4, C6, C5, C7, C30, C45, C64, C67, C63 and C65). This keeps the Q consistent for all oscillators. Tolerance should be 5% or better; they generally also have a J marking. The accuracy of the operating frequency point for each oscillator can be improved when matching parallel capacitors in the resonant tanks. All oscillators should output a sine wave in the vicinity of 1.5 VP to 2 VP. If that is not the case, try using capacitors from a different manufacturer.
  • Control rod decoupling capacitors - Capacitors C3 and C66 provide DC decoupling (up to 40 V DC) and influence sensitivity of the control rods. Sensitivity can be reduced by substituting these capacitors with a value less than 100 pF.
  • Tuning capacitors - Cheap AM/FM tuning capacitors work well with this theremin (C8 and C62). They are also known as miniature film variable capacitors, most radios use the two gang type as shown in Figure 20. The centre pin is usually ground, one pin taps the 10 - 60 pF variable capacitor, and the third corresponds to the 15 - 140 pF capacitor (actual specifications can vary between manufacturers). Only the 10 - 60 pF range will be used, the other pin should be shorted directly to the middle ground pin. Unfortunately, AM/FM variable capacitors can be sensitive (and fiddly) when it comes to tuning for the zero beat frequency. Therefore, it might be worthwhile to invest in quality air variable capacitors, preferably the ones with reduction gearing built in.
Figure 20
Figure 20: Cheap AM/FM tuning capacitor.
  • Limiting oscillator output - Not all inductors are equal, neither are capacitors. Specifications can vary between manufacturers, which can affect the Q factor of the components. High Q factors can make oscillators operate more efficiently, and potentially overdrive the buffer amplifier, or the mixer. Therefore, attenuation may be necessary. All oscillators should output 2 VP maximum; attenuation is possible by substituting output AC coupling capacitors C17, C19, C53 and C55 with values less than 100 pF. The same strategy can be used for the buffer amplifier coupling capacitors C27, C28, C46 and C47 to attain a 4 VP output signal. If necessary, further attenuation is possible at the mixer input ports; one could increase the input resistance for R20, R21, R41 and R42 to set their respective gate voltage around 3.5 VP.
  • Charge pump reservoir capacitor - Capacitor C21 is listed as a 0.1 μF electrolytic type, although just about any type of capacitor with the same value will do.
  • Op-amp AC coupling capacitor - C41 is a bipolar electrolytic. If this capacitor is substituted with a polarised version, its positive terminal should be connected to the op-amp output.
  • PI-filter - The PI-filter circuit after the envelope detector can be omitted all together in order to reduce signal loss. In that case, capacitors C33, C34, C39 and C42 can be left out. However, the voltage controlled amplifier will not be able to attenuate the output volume completely due to the increased input signal strength.
  • Transistors - Just about every J-FET transistor in the circuit can replaced with a candidate from the 2N548x family, such as 2N5485 and 2N5486. Substitute J-FETs from a different family can be also used, provided they possess similar transconductance, frequency and VGS(off) characteristics. Substitutes should be identical for all oscillators, buffers and mixers. If transistors Q8 and Q9 is replaced in the gain control circuit, the biasing resistors R29 and R32 may need tweaking. The volume response of the voltage controlled amplifier could be also affected for the better or worse, depending on the drain-source resistance characteristics of the substitute Q8 and Q9. Transistor Q5 in the frequency to voltage converter can be replaced by any device from BC54x family, such as BC547 and BC549. If Q5 is replaced by a bipolar device from another family, the biasing network around the transistor will have to be reworked to attain a linear output response between 0.16 and 5 V DC at the collector.
  • Power supply - The voltage regulator U2 is a heavy duty type, capable of delivering a 1 A current, and accepts input voltages anywhere between 8 - 35 V DC. This design uses a 12 V AC power transformer, allowing the regulator to operate reasonably efficiently with a small heat sink. The transformer also includes an internal thermal fuse. Substituting the transformer is possible, provided the regulator is mounted with a heat sink, especially if the rectified voltage reaches 9 V DC and above. Also pay attention to the voltage rating for the filter capacitor C20. If the substitute transformer lacks an internal fuse, a suitable fast blow fuse will be needed for added safety. The fuse should be connected in series just before the mains switch.

3 Construction

3.1 The Printed Circuit Board

Both the schematic and the PCB was designed with open an source software, called KiCad. KiCad offers surprisingly advanced design features, considering it is a free software. Design examples are shown in Figure 21. The PCB and silk screen art work is available to download in the Appendix section.

Figure 21a Figure 21b Figure 21c
(a) (b) (c)
Figure 21: PCB design with KiCad: (a) pcbnew editor, (b) pcbnew 3D Viewer, and (c) the final product.

The PCB was etched using the toner transfer method [44, 45, 46, 47, 48, 49]. The general idea is to use the toner from a laser printer as an etch resist. The artwork is printed onto paper as usual, then a clothes iron is used to fuse the toner onto the PCB copper surface. The paper is eventually removed, leaving the toner behind. Unfortunately, the toner also sticks to paper, making the paper difficult to remove. This crucial step usually involves soaking the paper in water and rubbing the pulp away from the board. Removing the paper is a hit-and-miss affair, peeling and rubbing can ruin the toner resist. Success will often depend on the type of paper used.

Fortunately, there is a better way to transfer toner onto copper. After experimenting with various types of paper, backing paper generally found on stickers (and adhesive labels) worked the best. The backing paper has a smooth surface that prevents strong adhesive bonding with the sticker; and in this case, with the toner. The process involves printing the PCB artwork on the smooth side of the backing paper, then ironing the toner onto the copper. The backing paper is separated from the board by peeling. No soaking required. Surprisingly there is little discussion about this technique in the wider community, bar one small reference on an online forum [50].

Of course, the backing paper method is not flawless either. The smooth surface of the backing paper will cause the toner to smudge or flake off. To remedy this problem, the smooth surface can be rubbed with an abrasive sponge to attain a matte finish. The matte surface allows the toner to stick better. It may take several attempts to get the balance right—the toner should stick on the paper, while allowing easy separation once fused onto copper. Once perfected, the technique works quite well, as illustrated in Figure 22a. The PCB artwork was delicate, hence the toner broke away in some areas with the backing paper (Figure 22b). When correcting the etch resist, the backing paper can serve as a useful guide for locating damaged toner on the board (Figure 22c). Figure 22d illustrates the board just before etching.

Figure 22a Figure 22b
(a) (b)
Figure 22c Figure 22d
(c) (d)
Figure 22: The toner transfer method, using sticker backing paper. (a) Board with a good toner transfer, placed next to a paper hard copy for comparison. (b) Some toner did not stick properly, hence correction is needed. (c) The actual backing paper after peeling from the board. (d) Etch resist corrected.

Figure 23a shows the board immediately after the etching process. The toner acts as a very good etch resist, none of the tracks were broken, and the number of holes in the copper was trivially small. In Figure 23b, the board was cleaned up with acetone and the solder pads were drilled. The toner transfer process is equally useful for applying silk screen artwork onto the component side of the board, as shown in Figures 23c and 23d. The component layout diagram can be tremendously helpful for minimising mistakes made during the board assembly. Unlike the copper artwork, the toner transfer quality of the component layout is not critical, provided the result is still readable.

Figure 23a Figure 23b
(a) (b)
Figure 23c Figure 23d
(c) (d)
Figure 23: The board (a) after etching, (b) after drilling, (c) and (d) with the component layout artwork applied.

The PCB was designed to fit a recycled ATX power supply case, as described later in this document. Therefore, the drill holes and board dimensions are tailored for a specific power supply case. The drill holes in this design may not align with other power supply cases. If you wish to use your own ATX power supply case, some board modifications will be necessary.

3.2 Soldering Components and Testing

Populating the board and soldering components is probably the most critical stage of the building process. The sheer number of components involved and the small feature size of the solder pads can make construction difficult. Components can be oriented the wrong way, or mounted in the incorrect location. Solder can bridge tracks and neighbouring pads. Correcting solder bridges, or attempting to desolder components can be destructive due to overheating and mechanical stress. To prevent mistakes, it is a good idea to assemble the theremin in a modular fashion.

The common practice for assembling circuits is to mount low lying passive components first, followed by radial components, then semiconductors last. However, it is highly recommended that the theremin is constructed in stages, and routinely tested with a quick power-up cycle. Once powered, various test points can be observed with an oscilloscope. Problems can be identified quickly this way.

When picking components, double check reference numbers against the parts list. Special attention should be paid to diode orientation. It is good practice to test resistors with a multimeter before soldering—this step may seem redundant for some people, but this precaution can eliminate unpleasant desoldering jobs later on. Note that most resistors and inductors use a vertical footprint, hence one of the leads must be bent backwards into a U shape, close at the base of the component.

The assembly procedure is as follows:

  1. The power supply should be constructed first before building the rest of the circuit. The power supply can be tested this way before subjecting the rest of the circuit to power-up tests. The diodes are soldered first, followed by the capacitors, the resistor and the power LED. Mount the voltage regulator IC last. Connect the power—any 9 to 12 V DC (or AC) bench power supply will do, and measure the voltage output at the regulator IC. The voltage should be steady at 6 V DC.
    Figure 24
    Figure 24: The power supply: It works!
  2. One of the local oscillators can be constructed next. In the following example (Figure 25), construction started with the pitch local oscillator. Start by soldering the capacitors, followed by the resistors and inductors. The zener diode is one of the few components that is mounted horizontally. Finally, solder the J-FET transistor. Check for short circuits and power up the circuit. Use an oscilloscope to test the oscillator output. The voltage level is expected to be 4 VP at the transistor's drain pin, and should be oscillating within ±10% of the theoretical frequency. The signal will be 2 VP maximum after the coupling capacitor (Figure 5).
  3. The buffer amplifier can be constructed in a similar manner as the oscillator in the previous step. The correct buffer output voltage level is between 3.5 and 4 VP (Figure 9). Repeat the whole process for the volume local oscillator and its respective buffer amplifier (Figure 26).
    Figure 25 Figure 26
    Figure 25: Pitch local oscillator. Figure 26: Volume LO and buffer amplifier.
  4. The variable oscillators can be assembled in identical fashion as the local oscillators, see Figure 27. The voltage output levels are also similar, about 2 VP after the coupling capacitor (Figure 7). The completed VFO buffer amplifiers is shown in Figure 28. The correct VFO buffer output is also between 3.5 and 4 VP (Figure 9).
    Figure 27 Figure 28
    Figure 27: Variable frequency oscillators. Figure 28: VFO buffer amplifiers.
  5. Once all the oscillators and their respective buffers are assembled, both mixer circuits should be built next. The mixer circuit can be tested by attaching the variable capacitor to the VFO for the purpose of tuning the circuit (Figure 29). The mixer will produce a modulated waveform as shown in Figure 11, with a maximum peak voltage of 3.5 to 4 VP. At this stage, it should be possible to find the zero beat frequency between the LO and VFO. If that is not possible, the LO frequency is outside the tuning range of the VFO. In such situations, attach the control rod to see if that will make the VFO tuning range overlap the LO frequency. Failing that, the value of the tank capacitor(s) in the VFO (or the LO) should be adjusted. If all is well, repeat this step for the other mixer circuit (Figure 30).
    Figure 29 Figure 30
    Figure 29: Testing the dual FET mixer. Figure 30: Both mixers completed.
  6. The envelope detector and the low pass filter are very simple circuits. Therefore, their assembly should be straightforward (see Figure 31). When testing the envelope detector and the low pass filter outputs, their signal levels will be 1 VP and 0.5 VP respectively (see Figure 13).
    Figure 31
    Figure 31: Envelope detector and LPF.
  7. Use a socket for the dual op-amp IC. The socket will make IC replacement easier in an event of failure. Also mount the voltage divider resistors R28 and R31, including the filter capacitor C37. The decoupling capacitor C36 should be also mounted. Finally, plug the op-amp into the socket, while paying attention to its orientation.
  8. Next, start constructing the frequency to voltage converter. Solder the resistors around the op-amp, R1, R2 and R3. The charge pump should be assembled next. Take extra care with the diode orientation for D5, D8 and D9. Not all diodes face the same way, D5 and D9 are oriented upwards, while D8 downwards. Assemble the inverting amplifier Q5 and its resistor biasing network. Finally add the filter capacitor C29 and the calibration pot, RV1.
  9. Calibrating RV1 - Before powering up, turn the wiper of RV1 completely towards ground (test with multimeter to make sure). Disconnect the volume control rod, power up the unit and tune volume detector so that it outputs a 1 kHz signal at C38. If everything is well, the charge pump should maintain a voltage around 2.5 V DC at C21, while the collector of Q5 should be 0.16 V DC. Now tune the volume detector for the zero beat. The reservoir capacitor C21 will be discharged to 0 V, and the Q5 collector should be anywhere between 4 to 5 V DC. At this point RV1 must be calibrated so that its wiper pin will output 3 V DC.
  10. The final step involves the assembly of the voltage controlled amplifier (Figure 32). The bulk of this circuit is the resistor feedback network and the gain control transistors, Q8 and Q9. Before testing the voltage controlled amplifier, disconnect all control rods from the circuit. Next, tune the pitch detector so that it outputs a 1 kHz audio signal. Meanwhile tune the volume detector for the zero beat—in other words, the comparator output at pin 1 of U1B should be 0 V DC. If everything is well, the voltage controlled amplifier will output a maximum signal anywhere between 1.5 and 2 VP (Figure 17a). Now detune the volume detector so that the comparator output at pin 1 will be a 2 kHz square wave. The voltage controlled amplifier will output a minimum signal at 0.2 VP (Figure 17b).
    Figure 32
    Figure 32: Completed theremin circuit.

That sums up the circuit board construction and testing. The next section will deal with mounting the circuit board into a chassis.

3.3 The Chassis—Recycled ATX Power Supply Case

The theremin circuit board was housed in a recycled ATX power supply case. This case was ideal, because it included a mains connector and a power switch. Furthermore, it also facilitated slots and mounting screws for the PCB. The metallic chassis was mechanically robust and provided some shielding against external interference. Most of all, the case was free.

Figure 33 Figure 34
Figure 33: Mechanical testing. Figure 34: Mechanical testing, bottom view.

During the final phases of the schematic capture and PCB design, the copper artwork and the component layout diagram was printed to scale. Both printed artworks were cut to size and glued together on a cardboard paper, back-to-back. The cardboard cut-out offered a physical representation of the PCB's size, which helped with the mechanical testing. This also ensured that final PCB would fit into the chassis and the components had enough clearance from the other parts in the case (see Figures 33 and 34).

The case was slightly modified to accommodate extra connectors and the tuning capacitors. The capacitors were mounted on the front cage and electrically isolated with a plastic sheet (Figure 35). This insulation was necessary to conform with the star point grounding methodology, as discussed earlier in this document. As shown in Figure 36, additional modification was required to mount the RCA audio connectors and the banana sockets for control rods. Banana plugs allow the operator to connect arbitrary shaped metal objects to the theremin. Again, all connectors were electrically insulated to the chassis for the same star grounding reasons.

Figure 35 Figure 36
Figure 35: Tuning capacitor insulated from the case. Figure 36: Side view, showing the RCA and the control rod connector.

Figure 37 shows how the circuit board was mounted and wired to the transformer. Just about every connection on the circuit board used recycled cabling and LED plugs from an old PC case. The green ferrite choke bead located on the mains cabling was also reused from the original ATX power supply circuit.

Figure 37
Figure 37: Completed theremin circuit mounted in the ATX power supply chassis.

Finally, Figures 37 and 38 depict the theremin fully assembled and ready to go. Admittedly, this theremin is probably the silliest looking thing I have ever constructed, resembling that robot's head from the Intergalatic music clip by the Beastie Boys.

Figure 38 Figure 39
Figure 38: Fully assembled theremin. Yes, it looks like a robot's head. Figure 39: Side view with the control rod plug and the RCA audio leads.

3.4 Grounding and Safety

Adequate grounding and mains safety should be a high priory when wiring the theremin circuit. Figure 40 illustrates how the chassis was grounded to the mains power connector. The ATX power supply case provides a convenient grounding point. The thinner green cable connects the grounding network located on the circuit board. As mentioned earlier, a star point grounding strategy is used, and hence all connectors and tuner capacitors should be electrically isolated from the metal case.

When wiring up the mains connector, use heat shrink tubing to insulate all exposed metal terminals in order to minimize potential electrical hazards. All mains cabling should be kept far away from the board to reduce mains interference. Use cable ties if necessary. The same cabling strategy should apply for the 12 V AC power output from the transformer.

Figure 40
Figure 40: Grounding the ATX power supply chassis.

4 Performance and Results

4.1 Pitch Frequency Response

Figure 41 illustrates two regression plots for the pitch frequency response of theremin at various distances. The data in the blue plot was recorded when the circuit was still prototyped on the breadboard. The red plot represents the data obtained when the theremin was fully completed and housed in the metal chassis.

The procedure for collecting the data was simple. For taking frequency measurements, an oscilloscope was attached to the output of C35 (that is, at the pitch envelope detector and low pass filter output). The pitch detector was connected to a telescopic control rod (FM radio antenna), approximately 50 cm long. The control rod was erected upright on a non-metallic base and mounted on top of a wooden desk. The theremin was situated behind the control rod with respect to the user. The pitch detector was tuned for the zero beat frequency, while making sure the user was situated far away. In order to take distance measurements, a plastic ruler was placed on the table, with its origin (0 cm) coinciding with the location of the control rod. Frequency measurements were taken by progressively moving the hand closer to the control rod at 2 cm intervals.

The plots in Figure 41 clearly reveal that the theremin had a frequency response that followed an inverse-square-law of hand capacitance. As the hand moved closer to the control rod, the frequency increased exponentially. This behaviour was analogous with other existing theremin designs [20]. Reliable frequency measurement was not possible beyond distances of 18 to 20 cm. The oscillators locked onto each other and produced zero beat frequency beyond the 20 cm threshold. The maximum measured pitch frequency was between 1.5 and 2 kHz, at about 1 to 2 cm away from the control rod.

The closeness of both regression lines indicate that the completed theremin performed similarly to the breadboard prototype. The metal chassis did not inhibit the theremin's sensitivity, nor did it change the theremin's frequency characteristics in a significant way.

Figure 41
Figure 41: Pitch detector frequency response.

4.2 Volume Response

The volume detector response curve is illustrated in Figure 42. The data was collected in a similar manner as in the pitch detector test discussed earlier. However, measurements were only collected for the completed theremin. In this case, the oscilloscope was connected to C38, the output stage of the volume frequency envelope detector and low pass filter.

The regression curve in Figure 42 shows the volume detector also exhibited an exponential response, as expected. The volume detector was clearly less sensitive compared to the pitch detector; reliable frequency measurements could not be taken beyond 10 cm. The maximum frequency response for the volume detector was just over 1 kHz with a hand distance of 1 cm. The lower sensitivity in the volume detector can be explained by lower operating frequency of its oscillators. Parasitic capacitances in the control rod introduces smaller frequency shifts at 715 kHz, compared to the pitch detector operating close to 1.06 MHz. Such behaviour was to be expected.

Figure 42
Figure 42: Volume detector frequency response.

In addition to volume detector frequency measurements, the actual peak voltage levels were also measured at the voltage controlled amplifier output. This data is plotted in Figure 43. The procedure for making these measurements was as follows: The pitch detector control rod was completely disconnected and the pitch frequency was tuned to generate a 1 kHz signal at the theremin audio output. The volume control rod was connected using the same setup as the pitch frequency measurements described earlier. Peak voltage measurements at the RCA connector were taken by progressively moving the hand closer to the control rod at 2 cm intervals.

Figure 43
Figure 43: Voltage controlled amplifier response.

The plot in Figure 43 shows an interesting linear response for the majority of the measurements. However, there were two outliers for measurements made at 1 and 2 cm. The voltage response also started to drift away from the linear regression at 4 cm. Therefore, an assumption was made that the volume response for the theremin is most likely logarithmic. This assessment seemed to agree with preliminary SPICE simulations of the charge pump circuit, which also exhibited a logarithmic voltage response. Having said that, considering how difficult it was to obtain stable measurements close to the control rod, large errors may have contributed to these outliers, and hence one could also assume the volume response was linear for the most part.

4.3 Problems and Possible Improvements

Perhaps the most significant problem observed in this theremin is poor immunity to noise. More specifically, the presence of mains hum, despite efforts made for implementing star point grounding throughout the circuit. It seems the pitch detector picks up interference from the mains transformer mounted above it. Presumably the alternating magnetic field from the transformer injects 50 Hz noise (and its harmonics) into the mixer and the oscillators, resulting in a choppy modulated output waveform.

Figure 44
Figure 44: Theremin pitch locked at 50 Hz due to interference.

The noise is more dominant in the low frequency range, as shown in Figure 44. The pitch frequency tends to lock onto the 50 Hz hum when the detector goes out of zero beat, thus limiting the low frequency range of the theremin. The 50 Hz harmonic noise makes the instrument sound very 'electric' in nature, almost like sound made by an arc discharging from a high tension transformer. (Sample audio files are available to download in the Appendix section.) The actual noise floor at zero beat frequency is illustrated in Figure 45, which further highlights the problem.

Figure 45
Figure 45: Theremin noise floor. Very hairy.

To remedy the mains interference problem, the transformer should be isolated from the detector circuits somehow. Perhaps a better solution is to use an external 12 V DC power source, rather than an internal one. Another possible solution is to use a different case that allows space partitioning and shielding for sensitive components. This is definitely an area for improvement.

Each dual FET mixer circuit also introduces some distortion in the modulated signal, such as low frequency clipping and other harmonic artifacts as seen in Figure 11. To address this problem, a variable capacitor could be introduced for each mixer's tuned impedance coupling tank; that is, in parallel with C30, L7 and C45, L8 respectively. This way the mixer's sensitivity can be controlled with the variable capacitor, and hopefully would shape the envelope of the modulated output signal a little better. The use of double-balanced passive mixer, such as the diode quad-ring mixer, could also improve performance, albeit at the cost of signal loss and the need of two baluns [33]. Another option is to use an active balanced mixer, such as a Gilbert Cell [28]. Unfortunately, most active balanced mixers have a high component count and also require a negative power rail.

There are also significant signal losses at the envelope detector and the low pass filter in both detector circuits. Such gain losses could be eliminated with the use of buffer amplifiers between the envelope detector and low pass filter. Again, this solution comes at a cost of higher circuit complexity and component count. It is possible to leave the low pass filter out all together if the envelope detector is good enough to remove the LO and VFO noise.

The gain control for the voltage controlled amplifier is not perfect either. The theremin pitch sound is still audible at minimum volume. There is also a noticeable delay in volume reaction time introduced by the charge pump circuit. The gain issue could be solved with a dedicated voltage controlled amplifier IC, that has better signal attenuation characteristics. The volume response delay could improved by using a smaller reservoir capacitor in the charge pump; however, that comes at a cost of increased gain control voltage fluctuations due to pumping noise.

Finally, the detector sensitivity for the theremin could be also increased, particularly for the volume control. One quick remedy is to allow the volume detector oscillators to operate at higher frequencies, perhaps at 900 kHz. To attain this new frequency, the capacitors should be decreased to something more suitable in the volume detector resonant tanks. Experiments with different types of inductors, particularly increasing their inductance, may also improve sensitivity. These oscillator design ideas will be left for future work.

5 Conclusion

The purpose of this project was to explore the possibility of building a theremin using cheap and conventional electronic components. The instrument featured RCA audio outputs, banana sockets to attach control rods of various shapes and sizes, plus a rigid metal chassis to resist wear and tear. The circuit was designed to allow contact-less pitch and volume control, which was conceptually similar to the original theremin. Special emphasis was made not to use exotic, or custom components during the design stage. The need for RF transformers, baluns and hand-wound coils was deliberately avoided.

The theremin operated by heterodyning signals from two Vackář oscillators in each detector circuit. The frequency mixing was performed trough a dual-FET mixer. The modulated waveform was then processed by an envelope detector and a low pass filter, which extracted the desired difference signal. For the pitch circuit, the difference signal served as the actual theremin pitch. The volume detector circuit used the difference signal to control the instrument volume though a frequency to voltage converter and a voltage controlled amplifier.

During the construction phase, the well known toner transfer method was used to etch the printed circuit board. The toner transfer method was slightly modified by utilising backing paper from stickers and adhesive labels with relative success. Unlike conventional methods, backing paper can be peeled off once the toner fused to the copper; therefore, soaking in water was not required. The assembled circuit was housed in a recycled ATX power supply case. The case provided a convenient and rigid housing for the circuit, complete with PCB mounting points, a chassis mains socket and a switch.

The performance of the theremin was far from perfect, the instrument was plagued by mains interference. The culprit was the mains transformer mounted inside the theremin chassis. The noise floor at zero beat frequency exhibited a 50 Hz hum, including some harmonics at 100 Hz and 150 Hz, at about -10 dB. This hum was a significant problem, which can be addressed by powering the theremin from an external DC power supply. Despite all the noise issues, the theremin worked quite well for the most part. The instrument's pitch frequency response surpasses 1.5 kHz and is able to detect hand gestures as far away as 18 to 20 cm. The volume detector's sensitivity is somewhat less, about 10 cm maximum. The voltage controlled amplifier can attenuate the pitch signal by -26 dB, although the pitch signal can be still heard at minimum volume.

As mentioned earlier, the oscillator and mixer circuits were sensitive to electromagnetic interference, hence good isolation from mains wiring is essential. Other improvements in regards to noise could include adding tuning capabilities in the mixer circuit. The ability to tune the mixer would allow shaping of the modulated output envelope a little better. Signal losses are rather high in the low pass filter. If the envelope detector was designed a little better, the low pass filter could be eliminated all together. Another solution is to insert an amplifier just before low pass filter to compensate for the gain losses. The voltage controlled amplifier could be redesigned to achieve better attenuation at minimum volume. Sensitivity in the pitch and volume detector could be improved by increasing inductance and by decreasing the capacitance in the resonant tank circuits. These modifications and improvements will be reserved for future revisions for this theremin.

For the most part, the project was a valuable educational experience. If anyone is interested learning something about RF electronics, perhaps building a theremin should be given consideration.

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Appendix

Theremin Operating Characteristics

Characteristic Symbol Min. Typ. Max. Unit
Unregulated operating voltage VU 8 12 30* VRMS
Unregulated current draw IU 72 mA
Power consumption (VU = 12 VRMS) P 432 mW
Regulated power rail VCC 6 V DC
Pitch detector operating frequency (±10%) fPitch 965 1061 1179 kHz
Volume detector operating frequency (±10%) fVolume 650 715 795 kHz
Tuned pitch detector frequency response fD Pitch 25 1900 Hz
Tuned volume detector frequency response fD Volume 100 1200 Hz
Effective tuned pitch detector range dPitch 1 20 cm
Effective tuned volume detector range dVolume 1 10 cm
Maximum isolation voltage for pitch and volume control rod input 40 V DC
Audio attenuation at minimum volume GdB -26 dB
Audio output voltage range VOUT 0.2 2 VP
Audio output load impedance RL 3000 74000 Ω
* The regulator IC will need a bigger heat sink for unregulated voltages greater than 12 VRMS.
Table 2: Theremin operating characteristics.

KiCad Project Files

Schematic Diagram

PCB Artwork

Parts List

Sample Audio Files

Video Clips

Copyright

KiCad Project Files

The actual hardware is licensed under the Creative Commons Attribution-ShareAlike 3.0 Unported License.

Documentation

This document, including schematic images, PCB diagrams and miscellaneous images is released under GPL conditions. Reproducing, building, or replicating the information presented here is permissible for any purpose you see fit. This notice may not applicable for every aspect of the circuit design, due to prior art. See citations in the Reference section.

This electronic project was published in the hope that it will be useful, but without any warranty; without even the implied warranty of merchantability or fitness for a particular purpose. The author will not be held liable for any direct, or indirect damages, data loss, financial loss, injury, death, total world annihilation as a result of using this information.