An audio oscillator is intended for use in audio, therefore the frequency range of its sine wave output should lie between 20Hz and 20kHz. A widened, for example 5Hz-100kHz, range is more preferable, it allows also to investigate some audio circuits whose behavior can be explained by their amplitude and phase responses at the frequencies just outside 20Hz-20kHz. However, this standard audio range is quite sufficient for distortion measurements, it's only important to maintain the oscillator own distortion as low as possible in the whole range, down to 20Hz and up to 20kHz. The main sources of this distortion are the oscillator's active components and some specific passive components in its controlling path.
     An audio oscillator usually consists of one or several amplifiers and a loop of the positive feedback. Applying this feedback forces the amplifier(s) to start generation which, without control, produces the signal being far from a sinusoid, the signal amplitude quickly reaching a maximum determined only by the supply voltage. To turn the wild generation into stable sine wave oscillation, the negative feedback should be used. It tries to suppress generation, but both opposite processes act simultaneously and, as a result, their equilibrium is finally achieved. The control is performed by the system of amplitude stabilization containing the elements of negative feedback and all the associated circuitry which helps to set the above equilibrium at any desired level of the sine wave output and maintain this level stable.
     In most simple form, the oscillator can be built around a single operational amplifier, its inputs being the points of applying the signals of positive and negative feedbacks. Both are taken from the oscillator output , the first passes through the Wien bridge network and initiates generation at a certain frequency, the second is regulated by the elements of amplitude stabilization, it makes the amplifier operation linear and its output sinusoidal.
     All this is illustrated in Fig.1.
Fig.1. Wien bridge oscillator.

     First of all, assume that the op amp A is ideal, i.e. its inverting and non-inverting inputs have the same potential VIN and their input currents are negligibly small.
     At the negative feedback side we have a simple voltage divider, so

     At the positive feedback side, the Wien bridge network, consisting of the elements R and C, has the following transfer function:

     Rearrangement of the above expression leads to its final form:

     Oscillation takes place when the resulting loop gain becomes unity: K-× K+ = 1                                        (3)
At the oscillation frequency ω0 = 1/RC the Wien bridge network's behavior is very simple:

     The regulated element R1 of the negative feedback can be therefore calculated from (1) and (4).

     This element is included in the system of amplitude stabilization whose detector produces from the oscillator output a DC voltage compared then with a reference voltage V0 . The system acts on R1 and allows to establish any desired, depending on V0 level of the output VOUT , after that this level being maintained stable. Usually, R1 is a junction of constant resistors and the electronically variable resistance of such devices as a FET or an optocoupler. In this mode the latter devices are principally non-linear, so it's difficult to minimize distortion contributed by them. The necessary for that reduction of the voltage applied to these devices immediately results in worse static and dynamic stability of the oscillator output.
     Therefore, the main target of an audio oscillator design is to find a reasonable compromise between low distortion and good stability of its sinusoidal output. It's also important to make the right choice of op amp for the oscillator, but now this seems to be not a problem because a good modern op amp easily ensures its own distortion being well below 0,01% in the whole audio range. Moreover, such op amps are available in packages containing two and four identical devices, so the oscillator can be built on several op amps without notable increase in cost. Advantages of the multistage oscillators are apparent and further I would like to consider such an oscillator with no compromise in performance at all.
     The chosen topology of this oscillator (see Fig.2) represents its oscillating loop consisting of three op-amp stages - two phase-shifting and one inverting.

Fig.2. Phase-shifting oscillator.

     As usual, assume all the op amps are ideal and start the circuit analysis from the first phase-shifting stage.
Relationships between its input VIN1 and output VOUT1 voltages can be written with the help of potential V01 being equal at the inverting and non-inverting inputs of A1

     The potential V01 is directly obtained from VIN1 :

     The same expression in the frequency domain:

     At the corner frequency (ω = ω01)   K1 = 1×e = 1×ej90°.
     One extreme frequency value (ω = 0) gives K1 = -1 = 1×ej180° , other extreme frequency value (ω ) gives K1 = 1 .
Thus, the magnitude of K1 is always equal 1, while the phase angle between input and output is varying within 0 - 180° according to the following formula:

     The exact value φ1 = 90° is reached at ω = ω01 .
     Similar relationships can be written and for the second phase-shifting stage, on op amp A2 .

     The third stage of the oscillator contains only resistors plus op amp A3 (see Fig.2). The latter has at its non-inverting input

     All the three stages are connected in the closed loop, so oscillation will be initiated, if the resulting transfer function or, in other words, closed loop gain becomes equal unity
                                             K1 × K2 × K3 = 1 .                                                                                         (10)

      To satisfy this condition, K3 must be equal -1, given that earlier calculations have yielded

                                             K1 × K2 = 1×ej90°× 1×ej90° = 1×ej180° = -1.

     Replacing K1 and K2 by their expressions (6) and (8) gives an equation for determining the oscillation frequency ω0:

     The same after rearrangement          R1R2C1C2s2 = -1 .         Substitution    s = jω0   leads to    R1R2C1C2ω02 = 1 .

     When R1 = R2 = R    and    C1 = C2 = C ,    ω0 = 1/RC .
     To make the oscillation reliable and optimal in all its parameters, a system of amplitude stabilization is used. Unlike other elaborate systems, it doesn't inject any correction or controlling signal to any point of the circuit, the only element it regulates is a composite resistance R34 (see Fig.2).
Just this resistance is responsible for satisfying the above condition K1 × K2 × K3 = 1 , the automatic variation of R34 takes place around the value determined from (9) when putting K3 = -1 :

     The amplitude stabilization is purely parametric and two-channel (precision and dynamic), it's why all characteristics of the output - settling time, long-term stability, distortion and noise - are predictable and therefore easily controllable.
     Of course, the oscillator excellent performance first of all should be credited to its topology. Each of the stages has a stable magnitude of its transfer function (K1 = K2 = K3 = 1) regardless of the equality between ω01 and ω02 of the phase-shifting stages. This makes it much more easier to maintain the oscillation dynamically stable in amplitude while varying its frequency ω0 even by a single resistor or capacitor, according to expression (11).
     If C1 = C2 = C and R1 = R2 = R, the oscillator delivers the whole set of sinusoids of equal amplitude with relative phases of 0°, 90° and 180°. These outputs can be used for various purposes, in this oscillator they just come in handy in the amplitude stabilization system.
     The oscillation frequency is usually adjusted by a two-ganged element, potentiometer for example. If this potentiometer has the difference between R1 and R2 within 10% (R2 = 1,1R1), the phase shift φ1 , calculated from (7), will be:

     Here a phase error of 3° is quite tolerable.
     The third most important feature of this oscillator is that all its regulated elements, both frequency setting (R1, R2) and amplitude stabilizing (R34) , are connected to ground. This means a programmable oscillator can be easily built by replacing the ganged potentiometer with fixed resistors which are switched electronically, with the help of MOSFETs, from a quad SD5000 device for example.
Fig.3. Programmable oscillator - fragment.

     Given that all the MOSFETs have their sources connected to ground and their RON< 50-Ohm is much lower than the switched resistors, the signal applied to their drains doesn't exceed several millivolts, so resulting distortion of the output can be expected within 0,001 - 0,01%. Control circuitry drives the MOSFETs' gates according to the required program.
     Smooth variation of the oscillator frequency can be carried out electronically too, the role of R1 and R2 may perform here a twin optocoupler (two photoresistors + LED) or a matched pair of FETs, the latter case being attractive if low distortion isn't of prime importance.
     In my voltage-controlled oscillator, the twin optocoupler's resistors are involved simultaneously in two processes - the AC process of oscillation and DC process of controlling the frequency of this oscillation. To realize such controlling, two current sources produce equal stable currents I0 which flow through R1 and R2 and create DC voltages V1 and V2 across them (see Fig.4).

Fig.4. Voltage-controlled oscillator.

so it is determined by these DC voltages which therefore can be used for its accurate setting. Each of them (V1 and V2) is compared with the same controlling voltage Vc , both differences are amplified and the outputs of op amps A4 , A5 are summed and filtered. The output stage of the frequency setting system, a non-inverting integrator A6 , feeds the optocoupler's LED whose light acts on R1 and R2 , closing the control loop.
The relationship the system maintains with high accuracy is Vc = (V1 + V2)/2 and combining it with the above relationship (13) will be simple, if we assume that

To provide optimum parameters of the controlling process, a network of dynamic correction is used. The achieved result is striking - a rapid (within 1-2sec) exponential variation of Vc from 4V to 4mV causes an immediate, exact log response of frequency from 20Hz to 20kHz. This is particularly important, as the oscillator first of all is intended for use in various sweeping modes.
     In the VK-1 ultra-low distortion oscillator, the frequency is set manually, on the octave principle which is natural for an oscillator intended for use just in audio. Frequency can be selected from the accurate (1%) basic frequency sequence 20Hz, 40Hz, 80Hz, 160Hz, 315Hz, 630Hz, 1,25kHz, 2,5kHz, 5kHz, 10kHz, 20kHz with the help of an octave rotary switch simultaneously replacing equal capacitors C1 = C2 = C of the two phase-shifting stages (see Fig.2).
     Their resistive elements R1 and R2 are switched independently by two additional frequency controls, each of them providing frequency variations in accurate (1%) 1/6, 1/3 or 1/2 octave steps. Joint action of these additional controls gives the resulting variation from the selected basic frequency, it's only should be remembered that the exact 90° phase shift between the oscillator two outputs is guaranteed if R1 = R2 , i.e. both frequency variations are equal. Choosing both of them, for example, +1/6 octave allows to obtain the next selectable frequency sequence 25Hz, 50Hz, 100Hz, 200Hz, 400Hz, 800Hz, 1,6kHz, 3,15kHz, 6,3kHz, 12,5kHz, 25kHz. And, at last, two +1/3 octave variations give the third standard sequence 31,5Hz, 63Hz, 125Hz, 250Hz, 500Hz, 1kHz, 2kHz, 4kHz, 8kHz, 16kHz, 31,5kHz.
     Total number of all the spot frequencies is 70 (from 16Hz to 44,8kHz), it's therefore very easy to plot amplitude-frequency responses of the device under test without using a frequency meter.
     Variation from any above spot frequency can be accomplished within one octave also continuously, by choosing a +(0-1)-octave position of the second additional frequency control switch and turning a fine frequency knob. The varied here is only R1 , a wirewound high-quality potentiometer is used for this purpose. Fine frequency adjustment can be useful, for example, in determining the cut-off frequency of a filter whose behavior in the stop-band area is then investigated by one- or third-octave stepped varying from this frequency. All manipulations with the frequency controls don't cause any notable amplitude bouncing of the output, it is the result of using dynamic amplitude stabilization in the VK-1 oscillator.
Typical amplitude stabilization suggests detection of the output sinusoid, filtering and comparing the obtained signal with a DC reference V0 and then control of the amplitude regulating element, R1 in the Wien bridge oscillator Fig.1 and R34 in the phase-shifting oscillator Fig.2. Filtering must be good enough, otherwise the remaining double-frequency ripple modulates the controlling voltage and hence the regulated resistance that leads to appearing the second harmonic of distortion, particularly at the lowest frequencies.
     Averaging solves this problem, but it introduces a time delay in reaction of the system to a change of amplitude, the regulating element adding to that its own delay (0,1-0,4sec for a photoresistor). The gain within the control loop is very high and the process of amplitude settling hardly can be provided optimal in the whole audio range. To damp appearing oscillation in the amplitude settling at the lowest frequencies, the filter time constant should be increased, but that makes the settling process too slow at high audio frequencies.
     In oscillators with the decade frequency range selection, a compromise may be found by switching the filter's capacitors according to the chosen frequency range, so the amplitude controlling process always is maintained close to optimum.
     Another approach is used in my VK-1 oscillator and the described above voltage-controlled oscillator. Each of them contains two channels of amplitude stabilization (precision and dynamic) which act on a single regulating element - resistance R34 (see Fig.2).
     In the VK-1 oscillator (Fig.5), this resistance is composite, it represents a series connection of stable resistor R30 , photoresistor RPH and the drain-to-source resistance RDS of a FET T1 . Operation of the precision channel is similar to that of the considered earlier typical amplitude stabilization system. Much more higher is its performance, particularly in obtaining the mean-rectified value of the oscillator output. The used precision full-wave synchronous detector contains fast electronic switches which turn on and off exactly at the moments of the output sinusoid zero-crossing.
     Therefore, the detection accuracy is high in a wide range of voltages (2mV-2V) and frequencies (10Hz-200kHz), the characteristics unreachable when using ordinary diode detectors. The synchronous detector is controlled by a square wave shaper which is built on discrete components and produces two balanced, square wave, very symmetrical outputs with fast rising and falling edges and regulated bipolar swing.
     The loop of precision amplitude stabilization is closed by the optocoupler LED+RPH , being the most critical element in achieving both the lowest distortion and highest stability. The main thing here is to make the right choice of the optocoupler type and to find its optimal working conditions.
     The dynamic channel of amplitude stabilization consists of a buffer and a sample-and-hold circuit built around op amp A6 and controlled by a strobe generator. The latter is triggered by the rising edge of the square wave voltage VSW and produces a short pulse closing an electronic switch S just at the moment the buffer's output sinusoid reaches its maximum. The rest of the period the charged capacitor C4 serves as a memory of the output amplitude which after buffering (A6) and proper attenuation (RAT) is applied to the gate of the p-channel FET T1 . An increase of amplitude makes the FET biasing voltage and its drain-to-source resistance higher, that via the control loop leads to reducing the amplitude to its former value. Such compensation is carried out without delays, it takes place in each period of the output frequency and helps the precision channel to maintain the output amplitude stable just during transient periods of operation, ensuring its settling process to be always fast aperiodic.

Fig.5. VK-1 audio oscillator.

     In the voltage-controlled oscillator, dynamic operation of the amplitude stabilization system is impressive indeed - its two channels act on a single regulating element, a FET T (Fig.4), which performs so tight control of the output, that even this output's fast (1-2sec) frequency sweep from 20Hz to 20kHz doesn't cause any slightest notable disturbance of its amplitude.
     The precision channel of amplitude stabilization establishes the oscillator output at the level of its mean-rectified value, this level is determined by the reference V0 and for the VK-1 oscillator it normally equals 2V, for the voltage-controlled oscillator - 0,4V. The time constant of integrator A5 (Fig.5) doesn't heavily affect the system's dynamics anymore, so capacitor C3 can be chosen for the best filtering the products of detection to eliminate the associated distortion at all.
     Just the precision channel provides a long-term and temperature stability of the outputs VOUT1 and VOUT2 and their very flat amplitude-frequency characteristic, the accuracy of maintaining these outputs is better than 0,3% under all possible, even extreme conditions. Of course, blameless operation of the amplitude stabilization system requires right and careful adjustment of each its channel and both of them in interaction. Fortunately, the chosen oscillator topology allows to perform this adjustment without any trade-off between low distortion and good stability.
     The oscillator outputs VOUT1 and VOUT2 have a 90° phase shift between them and each of them can be smoothly variable within 0-2V with the help of a wirewound high-quality potentiometer whose resistance shouldn't be too low to avoid excessive loading of the op amp and rising distortion, at the same time it shouldn't be too high, as it determines the oscillator output impedance. The main output VOUT1 can be also attenuated in 10dB steps from 0dB (1V) down to -60dB (1mV), its output impedance being in this case exactly 600-Ohm that keeps the attenuation correct regardless of loading.
     So far, such characteristics of the generated sine wave signal as its amplitude and frequency have been analyzed in detail. It's time however to focus on one more characteristic - distortion being most disputable in audio and even ignored by some respected manufacturers who declare only output power and frequency range of their audio products.
     Assume that we have a nearly ideal automatic rejection filter completely suppressing the fundamental harmonic and leaving absolutely untouched the residuals, an amplifier bringing these residuals, distortion and noise, to a sufficient, within 0,1-1V level, a band-pass 20Hz-100kHz filter, a RMS-millivoltmeter, an oscilloscope and, at last, a computer with a decent soundcard and the SpectraLab 4.32 software installed. Connection of this equipment according to Fig.6 gives a typical test scheme for the accurate and thorough distortion analysis.

Fig.6. Distortion measurement scheme.

     The test scheme works excellently while distortion of the oscillator under test is higher than 0,002%. The corresponding curve on the oscilloscope screen looks clear and still, the RMS-millivoltmeter reading THD+N (V) is confidently confirmed by the result of spectrum analysis performed by the computer program, the obtained harmonics of distortion are displayed on the monitor, measured and then combined in a root-sum-square fashion:

     Here the oscillator output noise N, measured in a 20Hz-100kHz bandwidth, is negligible in comparison with the total distortion which in many practical situations can be represented only by its first four harmonic components VH2 , VH3 , VH4 , VH5 . To specify distortion in %, it should be expressed with respect to the fundamental signal VS :

     When investigating distortion below 0,001%, the oscillator noise becomes the main interfering factor. The observable on the oscilloscope screen distortion curve acquires a noise cover which is getting thicker if distortion is reduced and the vertical sensitivity of the oscilloscope is proportionally increased. In the end, the distortion may become undistinguished at all in the noise background, just this picture is seen when testing the VK-1 audio oscillator at all its frequencies. Only spectrum analysis can discover such vanishingly small distortion and the SpectraLAB 4.32 software allows to register the amplitude of its harmonics down to -145dB. The expression for THD+N (%) should be used here in its full exact form:

     The RMS-millivoltmeter directly (in %) measures the above total harmonic distortion and noise, if the whole signal VS is maintained constant at a 1V level. This normalization can be carried out within the oscillator itself or with the help of input circuitry of the automatic rejection filter, the obtained measurement result is:

     When the total distortion component and noise component VN of the oscillator output are comparable in magnitude, their separation can be done indirectly, by making two measurements. First of them is performed with the normal maximum output defined by the amplitude stabilization reference V0 (see Fig.1,5) and with the necessary normalization settings, the millivoltmeter reading being
      To make the second measurement, the above reference and hence the oscillator maximum output should be notably, say in 4 times, reduced (from 2V to 0,5V in the VK-1 oscillator), all other settings left the same. At this level of oscillation, the measured is practically only the unchanged noise component VN - the total distortion component is buried well under the noise and therefore can be neglected at all. The root-square difference between these two readings gives the exact THD value:

     When testing the VK-1 oscillator, the absolute difference between the readings obtained by the above method doesn't exceed 0,00002% at any frequency within 20Hz-20kHz, for example (0,00041 - 0,00040)% at 1kHz, that gives the THD of
Checking the noise reference VN can be done at any moment simply by pressing a 2V/0,5V button on the VK-1 front panel.
     Taming distortion and minimizing noise are equally challenging when designing the ultimate audio oscillator. Each stage of the phase-shifting oscillator Fig.2 contributes noise which is produced by its active (op amps) and passive (resistors) components. In a typical application circuit of the phase-shifting stage (Fig.7), two equal 3kOhm resistors, connected to the op amp inverting input, set the unity gain and generate an equivalent input thermal noise VNR which can be calculated by the Nyquist formula:

Fig.7. Phase-shifting stage noise.

     Equivalent input noise VNA of the op amp itself is determined in the same bandwidth, for NE5532 with its noise figure of
5nV/(Hz)0,5 this noise equals:

     Each noise component should be multiplied by its individual gain, all they are then properly summed to get the total output noise VN of the stage:

     The oscillator three stages multiply this figure by 30,5 , so the whole noise of its output will be 4,43×1,73=7,66μV, that gives -108,3dB relative to the oscillation 2V signal. There are two ways of reducing this noise - using a less noisy op amp, AD797 for example, and lowering the values of the gain setting resistors. The latter measure has a strong limitation - it's inadmissible to load the op amp by less than 600-Ohm in total, including the gain setting resistors, output attenuator etc, the penalty being increased distortion.
     To resolve this problem, the VK-1 audio oscillator is built on original, all-discrete class-A operational amplifiers which guarantee the harmonics of distortion being less than -130dB for a 2V output signal applied to a 300-Ohm load. A remarkable feature of the oscillator topology is that all its three stages are configured as the unity gain op-amp blocks with the maximum amount of the applied feedback and hence with the minimum of distortion achieved. In a Wien bridge oscillator (Fig.1), the generating op amp has the closed loop gain of 3, the feedback amount is therefore three times smaller that reduces distortion less effectively under all other equal working conditions.
    The oscillator full circuit diagram is represented in Fig.8.

Fig.8. VK-1 audio oscillator - full circuit diagram.

    The used in this circuit optocoupler is a Tesla 3WK163-43 device, it exhibits the best linearity among other models I’ve tried. Replacing the BC546-BC556 transistors in the amplifying stages with the complementary 2N5089-2N5087 has resulted in reducing distortion too, at least by 10dB. These transistors also provide better noise performance and here the struggle carries on for each reduced dB.
     The oscillator features a synchronous detection of the generated sinusoid in order to get an enhanced accuracy of the output amplitude characteristic in a wide frequency range. The employed for this purpose are precision fast MOSFET switches from the quad SD5000 device, one of the switches performing also the amplitude sample-and-hold function in the dynamic channel of amplitude stabilization. The switches can normally operate only with the signals of positive polarity, this condition is provided by diodes D7,D9,D10 (see full schematics). In simulation circuits I use an equivalent analog switch array ADG442 which accepts the signals of either polarity and whose simulation model is available.
     The full-wave synchronous detector is controlled by a square-wave shaper built on discrete components (transistors Q31-Q36). Performance of this shaper deserves to be described in a separate article, here I would like only to show how it handles a sine-wave 1V-1MHz signal applied to its input (see Fig.9).

Fig.9. Conversion of sine-wave input to square-wave output.

     At audio frequencies it at all demonstrates both phenomenal input sensitivity and output square-wave symmetry. This simple circuit produces two balanced rectangular outputs which feature an unprecedently high slew rate (450V/µs at 1MHz) and can be easily made unipolar or bipolar by regulating their swing and offset with the help of a single resistor (R110 in Fig.8). In the VK-1,2 instruments, this shaper not only plays the important role in synchronous detection. Being applied to the instruments’ rear panel jacks, its ideal square-wave outputs become available for various external applications.
     Another discrete part of the VK-1 oscillator, greatly improving its characteristics, is its transistor amplifying block. This circuit is excellently simulated by the Multisim 10 software and the results of virtual measurements completely confirm its blameless operation within the real oscillator. The simulation graphs of Fig.10 represent the second and third harmonics of distortion taking place in the amplifier 2V output loaded by a 330-Ohm resistor. A slight rise of distortion at frequencies above 5kHz is explained by the internal frequency compensation of the amplifier to ensure its absolute stability under various loads and feedback amounts. The investigated configuration is a unity gain inverting amplifier – just how it is used in the oscillator stages.

Fig.10,11. Amplifying block of the VK-1 oscillator – distortion, amplitude characteristic.

     Amplitude-frequency response of the inverting amplifier with the gain of 5 is depicted in Fig.11, the AC analysis shows that this discrete amplifier can be successfully used at frequencies up to 10MHz.
     Of course, I don’t insist on building the oscillator with the help of the above discrete blocks. Its oscillating circuitry can be simply realized on the best integral op amps, for example LM4562, and this alternative is worth to be tried.
     Real distortion measurements of the VK-1 audio oscillator were conducted according to the test scheme Fig.6 , the rejection filter, amplifier and band-pass filter being realized as a complete instrument - the VK-2 distortion meter. The obtained measurement result is total and it's very difficult to separate the distortion originated from the oscillator and the meter, especially at the final stage of development, when both of them are completely swamped by the total noise. If the distortion curve becomes slightly emerging from the noise background, the initial step in troubleshooting is to fix exactly where does this distortion occur. The next question is how does it occur and, at last, what should be done for its elimination. But first of all, it's necessary to minimize the number of possible sources of distortion and to prevent any cause of its appearing.
     There are three main sources of distortion in the phase-shifting oscillator - the op amps of its oscillating loop and two elements of its amplitude stabilization system - a photoresistor and a FET. The use of super-linear modern op amps doesn't necessarily guarantee extremely low distortion, the cause of appearing distortion may be a parasitic high-frequency oscillation in one of the stages, excessive loading of the op amp and simply a faulty resistor around it. The mentioned above electronically varying resistances are inherently non-linear components, but that doesn't mean we should refuse to use them. Most decisive here is to make the right choice of their types and to set the right voltages across them, because minimizing distortion requires this voltage to be as less as possible, while good stability can be achieved only at a certain sufficient voltage level.
     The series connection of a stable metal-film resistor R30, photoresistor RPH and the drain-to-source resistance of a FET T1 is the most critical part of the VK-1 oscillator circuitry (Fig.5). A voltage of 170mV across this connection (point P) and its portions of 50mV and 20mV, applied correspondingly to the photoresistor and the FET, is just the case, when the non-linearity of these amplitude stabilizing elements practically doesn't influence the oscillator output. Thanks to the oscillator topology, this voltage can be easily set and reset with the help of four resistors according to the relationship (12):

     Accurate adjustment allows to bring this distortion component of the oscillator down to -130dB, it is mainly the second harmonic.
     In the VK-2 distortion meter, the sources of distortion are two - its input normalizing amplifier and photoresistors included in the elements of the T-twin notch network, they perform here fine automatic tuning of the rejection filter to the fundamental frequency. Again, the consequences of the photoresistors' non-linearity can be dramatically minimized by a reasonable reduction of the voltage applied to them without any loss of the effectiveness the filter tunes itself to the fundamental, its -130dB suppression is reached in 4sec at any audio frequency and distortion contributed by the filter doesn't exceed -130dB.
     The normalizing amplifier is built on the described above discrete op amp too, but its operating condition is more comfortable than that of the oscillator - its stable 1V output signal is passing to the input of the T-twin notch network which doesn't appear to be a heavy load. Normalization is carried out by a distortionless wirewound potentiometer and the amplifier is usually configured as a unity gain non-inverting op amp, therefore its distortion can not be registered even by the spectrum analysis, I suggest the distortion figure being less than -140dB.
     The considered above distortion components of the oscillator and distortion meter are normally added to each other, their partial compensation is possible within one instrument and only under some conditions, the effect taking place, for example, in a narrow frequency range, with certain harmonics of distortion, it brings rather misunderstandings than practical usefulness.
     Final testing of the combination VK-1 oscillator + VK-2 distortion meter was conducted some years ago, since then investigations concern mainly the suitability of several models of the optocouplers for use in these instruments. Graphs in Fig.12 represent the spectrums of the VK-1 + VK-2 combination output at the oscillation frequencies of a standard sequence, the oscillator output set normally 1V (right vertical graph row) and reduced to 0,25V by pressing the noise reference button (left vertical row). In the latter case, the harmonics of distortion can not be revealed at all by the SpectraLAB 4.32 software, so the RMS-millivolmeter measures and oscilloscope shows practically the pure total noise of the system.

Fig.12. Spectrums of the VK-1 oscillator + VK-2 distortion meter combination output, obtained with the help
of SpectraLAB 4.32 software: left - VK-1 output is set 0,25V, right - VK-1 output is set 1V.

     That is also illustrated by the lower curve in Fig.13 where the upper curve represents the RMS-millivoltmeter reading THD+N (%) corresponding to the oscillator 1V output. The absolute difference between these two readings is barely perceptible - less than 0,00001% at any frequency within 20Hz-20kHz, so the root-square difference (16) can not give here exact figures of total distortion, it may only confidently indicate that this distortion is less than 0,0001%. Evaluation of distortion between -120dB and -150dB can be done easily and accurately by the spectrum analysis and the adduced graphs demonstrate that.

Fig.13. Distortion plot of the VK-1 oscillator + VK-2 distortion meter combination:
1 - THD+Noise (%) for measurement bandwidth of 100kHz (0,00041% at 1kHz);
2 - only Noise (%) for measurement bandwidth of 100kHz (0,00040% at 1kHz).

     The VK-1 oscillator and VK-2 distortion meter were designed and built more than ten years ago and since then these real instruments have been employed in numerous real measurements both when self-checking each other and when designing and testing various audio equipment. I'm very scrupulous about my electronics designs and consider them uncompleted and not suitable for public disclosure until their circuitry operation is successfully simulated by such a trustworthy program as Multisim 10. The last two years I've carried out strict and comprehensive virtual testing of the whole VK-1 oscillator and its separate parts, all that has convinced me in remarkable properties of the Multisim 10 software and confirmed the validity of the oscillator design and impeccability of its operation. Here I would like to represent a fragment of the simulated circuitry, the virtual oscilloscope screen shows the oscillator main output (orange trace), the synchronous detector output (green trace) and the process of settling the output amplitude (see Fig.14). The measurement probes placed at some points of the circuit monitor the simulation process at these points and give detailed time-varying information about its main parameters (voltage, current, frequency).

Fig.14. Simulation of the VK-1 oscillator circuitry.

     The virtual distortion analyzer reads <-100dB THD, the -100dB being a minimum limit of this interactive distortion measurement. The Multisim function of distortion analysis allows to evaluate distortion down to -160dB at once in the whole audio frequency range, but in our case it can be used only by opening the oscillating loop and testing the oscillator as a three-stage amplifier fed from the program’s ideal 2V RMS sine-wave source. The modified for that oscillator circuit is shown in Fig.15.

Fig.15. Simulation circuit for the Multisim distortion analysis.

    The obtained are the second and the third harmonics of distortion at the outputs of each stage within 20Hz-20kHz. The generated by the Multisim 10 simulation graphs are presented in Fig.16,17.

Fig.16,17. Distortion analysis results.

     The aim of this virtual testing was to check the linearity of the VK-1 oscillating circuitry (its three discrete amplifying stages) separately from distortion contributed by the elements of amplitude stabilization (optocoupler and FET). Normally, the oscillator’s two outputs are taken from its first and third stages, each loaded by a 680-Ohm potentiometer. Here the stages' total loads are set correspondingly about 300-Ohm and 600-Ohm, the applied to them output voltages are 2V RMS.
     The obtained vanishingly small distortion figures can be confirmed in reality only by a precision spectrum analysis, and I am happy that the results of all latest virtual measurements match the results of the same measurements performed earlier with the help of real instruments.
     In conclusion, some words about the oscillator construction which adds to its outstanding characteristics two very important features - the instrument's portability and convenience of its use. The front view of the VK-1 oscillator and VK-2 distortion meter is shown in Fig.14, dimensions of each instrument are 200×180×65mm, so both of them can be easily placed inside a briefcase and transported just to where you need to perform the test. The front panels aren't overloaded with controls, handling of these controls is simple and understandable, the number of manipulations with them is minimized when making basic audio measurements.

Fig.14. Front view of the VK-1 oscillator + VK-2 distortion meter set.

     The interior view of both instruments is represented in Fig.15. Constructions of the oscillator and distortion meter are very compact, that has required great care in making their printed circuit boards, placing components on them and finally mounting all parts of each instrument inside the case. In the oscillator, the two-inch neighborhood of its mains transformer and the lower board containing the oscillation loop doesn't negatively affect the output sinusoid characteristics.
     The oscillator configuration has excellent immunity from picking up interferences and hum, but decisive is of cause the used screening of the lower board and the components mounted around the control switches. The photo of Fig.15 shows the instruments in their exposed state being convenient for troubleshooting - the screens are removed and the upper boards are unscrewed, turned 180° outwards and fixed on the rear panels, giving easy access to any element within the devices. The upper boards don't require screen protection at all.
     Mandatory conditions for successful operation of the oscillator are also the right grounding and the right, optimal connections between all its parts, particularly those delivering the power supply voltages. These bipolar ±15V voltages are produced by a stabilizer built on discrete components.

Fig.15. Interior view of the VK-1 oscillator + VK-2 distortion meter set.

     I don't enclose the lists of components each instrument consists of, because here I don't offer a DIY (do it yourself) project. I simply would like to share all information that concerns this type of audio oscillator - its theoretical background, practical realization on the example of the VK-1 instrument and, at last, minimizing and measuring distortion. There is no still commercial version of the VK-1 audio oscillator, but I hope it might appear in the near future.
                                                                                                                                                            pdf version here
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