This audio component was designed at the time of reigning the cassette tape recordings, when the first mass CDs hadn't still appeared. Cassette decks were practically in every home and every car, so copying music from tape to tape or from LP to tape was easy and widespread. A decent cassette device had satisfactory for recording characteristics: wide frequency range, low wow and flutter, it completely preserved dynamics of the original audio material. The only snag of its permormance was a notably heard noise of the obtained recordings, caused by physical processes in the magnetic tape and being therefore unavoidable.
     To fight this noise the cassette tape itself was being constantly developed and various noise reduction systems appeared. Most advanced of them used special techniques during recording (compressing) and reproduction (expansion), naturally, these processes were required to be strictly complementary, for full signal reconstruction.
     Unfortunately, none of the introduced noise reduction systems was ideal and there was a period when I ignored the cassette tape recording at all and continued to use my reel-to-reel tape machine for Hi-Fi recording from LPs, these recordings, however, suffered from noise too, although in a smaller degree. In general, the noise problem exists also when reproducing LP and early CD records, here it isn't such acute as in the case of cassette tape, but its nature is the same because of using for such records the source audio material originally saved on magnetic master tapes, vinyl recordings adding to that their own specific surface noise.
     Trying to find a universal, acting only during reproduction remedy for noise, I turned to the idea of dynamic filtering offered by Philips and realized in its DNR system which was very popular, along with Dolby systems. This noise reduction method suggests minimum intrusion to the processed audio signal, this signal simply passes through a low-pass filter whose cut-off frequency is automatically and continuously varied in response to the signal amplitude and its frequency content. When the signal is small in amplitude and has a poor high frequency content, the tape noise becomes dominating and the filter restricts the bandwidth to 1kHz, thus reducing the tape hiss during quiet musical passages or in pause. If the signal is getting increased in amplitude and rich of high frequency components, it can mask the tape noise and the filter cut-off frequency is automatically pushed up to 30kHz, thus leaving the audio signal practically intact.
     The noise reduction system based on this principle contains the regulated low-pass filter itself and a control path which produces the regulating signal for the filter. To ensure nearly ideal functioning of the system, two main conditions must be met - blameless circuitry of the filter and blameless operation of the control path. The first means that any deterioration of the audio signal passing through the filter (distortion, poor dynamics, additional noise) must be completely excluded. The second means the transitions from the lowest cut-off frequency to the highest and vice versa must be optimized just for human hearing and therefore audibly imperceptible, all the set parameters must be kept then unchanged with time, temperature and other factors. The system performance can be easily checked subjectively by turning the noise reduction on and off during reproduction of a musical program. In both these cases the audio signal and hence the reproduced sound must remain absolute the same, the only perceived by the ear difference is the reduced tape noise.
     The VK-7 noise reducer is built around my audio inverting amplifier being unsurpassed just in audio applications. Its merits are a wide frequency range, high open-loop gain, extremely low distortion, excellent dynamics and good stability. The only allowed inverting operation of this amplifier defined the choice of the filter configuration, it should be an inverting, two-order low-pass RC-filter with two equal frequency-setting resistors. This non-traditional configuration hardly can be found in popular literature, so I was forced to sit and design the filter from scratch, making diligently all the necessary calculations.
     The noise reducer circuit chosen for analysis is depicted in Fig.1. Here the audio inverting amplifier is represented as an operational amplifier A whose non-inverting input is grounded. During linear operation, and it is just the case, two main rules can be applied to the op amplifier: there are no currents flowing into its inputs and there is no voltage difference between them, therefore its inverting input has zero potential too.

Fig.1. Second-order low-pass filter.

     The circuit will be analyzed with the help of a nodal method. Considering the three node voltages V1, V2, V3 and remembering that the currents' algebraic sum in each node equals to zero, the following three equations can be written for the nodes 1, 2, 3:
     Replacing V1 and V2 by their expressions in the first equation leads to

     Filter transfer function:

     To simplify the last expression, we choose R2 = RC and R1 = R4 = m RC , here RC - constant value, m - coefficient.

     When taking R2 = RC = 430-Ohm and R1 = R4 = 2,7kOhm, the determined value of m is m = 6,3.
Variation of the filter cut-off frequency within 1,6-32kHz is carried out by RV variation from 12kOhm to 0,6kOhm (a real range for the two matched JFETs), so always RV >> RC , and further simplification of the transfer function can be done, assigning also C2 = C and C1 = nC :

     General characteristic of the Butterworth two-order low-pass filter:

     Comparing it with (3) results in the following equations:

     Their solution in relation to coefficient n gives n = 2(m + 2) = 2×8,3 = 16,6.
The filter cut-off frequency is defined from equation (5) :

     If we take F0max =32kHz and C=C2 =680pF, other circuit parameters are: C1 =nC2 =12nF and from (6) RVmin =0,63kOhm.
The lowest filter cut-off frequency F0min =1,6kHz. In this case the maximum value of the frequency setting resistors is:

                                                                 RVmax = 20RVmin = 20×0,63 = 12,6kOhm.

     Voltage V1 at node 1 can be found by substituting VOUT from (2) into the expression for V1 :

     Remembering that n = 2(m + 2), at the cut-off frequency ω0 = 1/1,4142CRV(m + 2) we have:

     At 32kHz RV =630-Ohm, RC =430-Ohm and V1 = 0,095VIN ; at 1,6kHz RV =12,6kOhm, RC =430-Ohm and V1 =0,144VIN .

     The next I would like to focus on is very low distortion which must be provided by the filter circuit. Most critical in this respect is the voltage V1 applied to the channels of two matched JFET transistors, whose varying resistance just changes the filter cut-off frequency. Distortion produced by these JFETs depends on their channel resistance and voltage applied to it. When the input signal has a sufficient, up to maximum level and rich high frequency content, the filter is open, i.e. its cut-off frequency is pushed up to the highest limit of 32kHz determined, as it follows from the above calculations, by the 630-Ohm channel resistance. Voltage drop across such a resistor isn't high and this is favorable to reducing the contributed by the JFETs distortion.
     If the input signal level and its poor high frequency content are insufficient for opening the filter, the cut-off frequency is fixed at 1,6kHz, the channel resistance being here 12,6kOhm. However, the voltage drop across the channel remains not high and it's the result of the reduced input signal. In general, the right choice of the input signal range is a decisive factor in minimizing this kind of distortion, retaining the signal within 0-100mV guarantees in this filter distortion of less than 0,001% at all audio frequencies.
     Full circuit diagram of the low-pass filter is represented in Fig.2.

Fig.2. Noise reducer low-pass filter.

     Here the inverting amplifier configuration is used with minor circuit variation - capacitor C6 is used to prevent the unwanted AC negative feedback via the biasing resistor R2. The filter RC elements have the calculated above values, the preferable type of capacitors is polystyrene. The noise reducer is powered from a unipolar +24V supply, this dictates the use of a p-channel JFET matched pair which requires just the positive voltage for its control. Originally, a 2SJ109 (K504HT2) device was used, but it can be replaced by two matched 2N5018 JFETs and simulation is performed with these transistors too. The minimum channel resistance of the chosen JFETs shouldn't be more than 300-Ohm, their gate-source cut-off voltage should optimally lie within (4-6)V. Four equal resistors R12 - R15, connected in parallel to the channels, together with capacitors C7, C8 linearize the channel resistance, thus reducing distortion, they also restrict the filter cut-off frequency when the JFETs are completely turned off.

Fig.3. Noise reducer filter - AC analysis.

     Fig.3 shows the filter amplitude-frequency responses obtained with the control voltage V2 incrementally varied from 2,7V to 4,3V. Relationship between this voltage and the cut-off frequency isn't linear, but it doesn't matter in this filter where the cut-off frequency is incessantly rushing from one limit to another. More actual here is to strictly fix these frequency limits and to prevent their drift with time and temperature.
     The filter characteristic is flat in the pass band, it exhibits a -3dB fall at the cut-off frequency and then, in the stop band region, its constant slope is -12dB/octave, it's why this two-order filter is very effective in suppressing the high frequency noise components when it is closed. That also allows to increase the lowest frequency limit up to 2kHz for better reproduction of the signal's low level mid-range frequency components. In these conditions, the achieved level of noise reduction is more than 12dB.
     The filter distortion is evaluated by the Fourier analysis of its output, carried out with the help of the Multisim 10 software. The filter is open, its 32kHz cut-off frequency is set by the control voltage of 2,7V. The input voltage chosen for this simulation is 100mV RMS, the output being 100mV too, and the analyzed frequencies are 20Hz, 1kHz, 10kHz and 20kHz. The analysis results (Fig.4) reveal distortion well below 0,001% (typically 0,0005%) at frequencies up to 10kHz. A slight (0,0014%) distortion rise at 20kHz is explained by the neighborhood of the cut-off frequency at which the voltage applied to the JFETs channels is maximum.

Fig.4. Noise reducer filter - Fourier analysis.

     Being a fraction of the input signal, the voltage V1 (net 1 in Fig.2) varies considerably over the audio range, its expression is given by formula (7) and at the cut-off frequency it equals V1 =0,095VIN =9.5mV. Its behavior is also illustrated by a simulation graph in Fig.5. As can be seen, voltage V1 is proportional to the cut-off frequency - the lower this frequency, the higher the reactive impedance of the filter capacitors C5, C9 and hence the lower the channels' current which produces less voltage drop. All that moves point 1 closer to the virtual ground and at frequencies of 10kHz, 1kHz , 100Hz the voltage V1 applied to the channels decreases correspondingly to 4mV, 400μV and 60μV. In these conditions, distortion contributed by the JFETs is vanishingly small.

Fig.5. Noise reducer filter - open state.

     Screenshot of the filter simulated circuitry is represented in Fig.6. The virtual distortion analyzer monitors the filter output, there are also measurement probes placed at some critical points of the circuit and giving detailed time-varying information about characteristics of the simulation process (voltage, current, frequency). It has become a good practice for me to perform virtual testing of the designed earlier circuits and obtain the data completely coinciding with the calculated parameters and the results of real measurements conducted years ago by using real instruments. Most helpful in this respect were my VK-1 audio oscillator and VK-2 distortion meter.

Fig.6. Noise reducer filter - simulation.

     If the range of input voltages applied to the filter is more than 100mV, say 500mV, it can be adapted to that simply by proportional increasing the value of input resistor (R1 in Fig.1), this brings the filter maximum output to the former 100mV ensuring all other circuit parameters remain the same too. To compensate this signal attenuation, an additional amplifying stage is necessary, but it may combine one more useful function, to be for example also a gain control. However, the filter can successfully handle the signals up to 500mV without any circuit modification, in this case the only compromise in its performance will be slightly increased distortion at the 500mV output (0,002% at frequencies up to 4kHz and 0,007% at 20kHz).
     This problem doesn't arise when the noise reducing filter is integrated into an audio system where its place is just after the input amplifying stage bringing the signals from various linear inputs and internal MC- and MM-head preamplifiers just to the normalized 0-100mV range.
     The filter noise performance is analyzed in the Multisim 10 too, the noise spectral density of its output being measured in a 20kHz frequency band. In the open state, the filter features a practically constant (5×10-16) V2/Hz output noise density (red line in Fig.7) that yields total output noise:

Fig.7. Filter noise analysis.

     In the closed filter state, the JFETs' channels have the increased resistance which generates higher noise, but at frequencies above 2kHz this noise is reduced by the filter as well as external noise, so its spectral density steeply (-20dB/dec) falls after 2kHz (blue curve in Fig.7). Subjectively, such weighted filter noise is hardly perceptible by the ear.

Fig.8. VK-7 noise reducer circuit diagram.

     The VK-7 noise reducer full schematics is represented in Fig.8. The device consists of the automatic low-pass filter itself (transistors Q1 - Q4), two frequency varying JFETs Q13, Q14, a control path (U1, U2) and at last an output amplifier (transistors Q5 - Q8). The filter and amplifier four-transistor configuration is suitable for a 14V or 24V power supply voltage (the only one resistor being adjustable). The VK-7 accepted input signal is 0÷500mV, but the filter performs the signal processing within 0÷100mV to keep distortion below 0,001%. After that the filter output needs therefore to be amplified to the same level as input (500mV), the output amplifier with the gain of 5 carries out this task, it also serves as a useful volume control. When the noise reduction is turned off, the input signal bypasses the filter and goes directly to the output amplifier which leaves in this case its level unchanged.
     The noise reducer control path contains a control amplifier (op amps U1, U2) which has a special amplitude-frequency characteristic and a gain of 3000 at 10kHz. There is also an output detector D3 and two independent adjustments of the filter cut-off frequency low (2kHz) and high (32kHz) limits. The noise reduction threshold level can be set by the front panel potentiometer for a concrete audio program. Of course, making the correct setting requires a certain experience, but with the help of a bypass switch and hence immediate comparison of the intact and processed program material, this procedure isn't so difficult.

Fig.9. Filter output transient characteristics.

     The output transient characteristic of a 100mV-10kHz signal is shown in Fig.9 (red color) for the filter at first getting closed and then getting open. The detector attack and release times are chosen optimal for the characteristics of the human ear, and while the attack time doesn't exceed 1msec, the release time is set up to 150msec to preserve "the air" between sounds, just its loss is typical for the majority of digital noise reducing systems.
     There are also some features of the control path design that make the filter operation practically ideal, free from any kind of noise modulation and other unpleasant effects. The processed are the filter input and output, this feedback improves the transients between the filter two states and is particularly beneficial for the subjective perception of this process.
    The final stage of development was of course a continuous uncompromising listening expertise of the noise reducer and I spent a lot of time and efforts to attain the initially set goal - to get rid of the tape hissing accompaniment presented in all cassette recordings, leaving the recordings themselves absolutely intact. Only after that I turned from breadboarding to building the finished product.
     Constructively, the VK-7 noise reducer is made as a separate compact device. It is mains powered, the internal transformer and stabilizer produce for the circuitry a 14V power supply voltage. All elements of the device’s two stereo channels are mounted on a single printed circuit board housed inside a 170×125×45mm case (see the photograph of Fig.10).

Fig.10. VK-7 noise reducer photo.

     To evaluate the VK-7 noise reducer operation subjectively, two samples containing the same audio track are offered for downloading. The track was originally recorded from my vinyl disk to cassette tape by using a Denon DRW-750A cassette deck. The record was then played, processed via the VK-7 noise reducer and converted to the digital form, the finished file was labeled as "clean record". The file "noisy record" was obtained similarly, but with the noise reduction turned off. To compare these records and investigate the difference, they should be opened with an audio editing program, Sound Forge for example, and then played alternately, starting from the same chosen point.
     The above procedure may be practiced and when comparing two recordings made from the same LP but via different audio equipment. The main requirements here are to set an equal (within 0,2dB) volume level of these recordings and equal (within 1dB) frequency content, the first can be easily done with the help of the recordings' graphically built peaks in the editing program. Only after that a difference in "live sound" content and other subtle details can be revealed, and just at the moment of switching from one recording to another.
    The downloadable clean record and noisy record have the title "Duet Besedina and Taranenko - I Like"
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