Anatoly Likhnitsky



(Preamplifier with RIAA phono correction on the X-transformer)


Fig.1. Passive correcting RC-circuit.

Perform the following experiment. Disconnect the RC-circuit (see Fig.1) in your pre-amplifier, the one that is responsible for correction of amplification according to RIAA standard, and then listen through few of your favorite Lp. For the first few moments it will sound squeaky and harsh; however, in about 10 minutes you will get used to this audio disbalance. When you don’t perceive the sound as annoying any longer, turn on the correction again. You will notice that the sound becomes “rotten,” “hazy,” slightly “rough,” and coarse. The energy, dynamic shading, especially in the upper register will disappear, and bass will become “wadded.” Partially my observations were described in “AM” Vol.3 (4) 95, p.71.

At first I thought that the increase of high frequencies and the reduction of low frequencies favors the perception of music by masking the highs with the lows; however, later I adhered to another hypothesis: it is the capacitor of the correcting circuit that is responsible for the deterioration of sound. I tried numerous capacitors of foreign and domestic brands. Though all of them sounded differently, I noticed the “signature” of the dielectric in this variety of sounds. This signature is shown in the Table below:



The type of the domestic capacitor

The signature of sound



Coarse and harsh in upper register



Clarity at low frequency, roughness at high frequency



Tender, but artificially detailed high frequency



Clarity in all range of sound frequencies, together with the coarseness



Brightness in combination with “viscous” sound

Oil paper


Poor clarity and faintness of sound



Clarity of high in combination with artificial sound of low and middle frequencies


Besides the dielectric, a capacitor contains conductors and dozens of meters of aluminum foil. The role of the resistors in the correcting circuits cannot be neglected. Either way, the main part in this ensemble is played by the dielectric of the capacitors.

I stopped experimenting with the dielectrics as soon as I listen the music with the correcting circuits with air capacitors. The last experiment turned out to be quite difficult. In order to carry it out, I had to dig out two bundles of AC capacitors from antique German radio sets. The relatively small capacitance of one section (~ 500 pF) and its enormous size caused the large background noise at the AC output of the corrector. Unfortunately, this obstacle is yet to be eliminated completely.

However, the result of “sound” of air-correcting RC-circuit was far beyond my expectations. It turned out that the air-filled circuit doesn’t deteriorate the sound. It remains detailed, clear and energetic as with no RC-circuit. By the way, the effect of “rottenness” disappeared completely.

I verified it by myself that the main source of evil in the corrector is due to the dielectric in the capacitors. The results of this pure experiment were so impressive that I decided to figure out the nature of the physical processes taking place in the dielectric. I was interested in understanding why dielectrics are so important for the quality of sound and why this effect in the capacitors of the correcting circuit is so drastic. Many times before I have noticed the fact that connecting the capacitors in different part of the circuit affects the sound considerably less[1].

For now, I have only a hypothesis regarding the influence of dielectric on quality of sound. I hope that this hypothesis will sooner or later become a theory and a basis for a doctoral thesis. The idea of this hypothesis consists of the following.

Unlike the capacitors used to transfer or to block the power source functions (where the AC component between the plates is kept close to zero), the capacitors of the correcting RC-circuit (see Fig.1) function with a continuous change of voltage between the plates. This means that all the processes in the dielectrics can be observed on the atomic and molecular levels. They are also observed, but less pronounced in other circuits. Therefore, these processes turn a capacitor into far from the ideal element of the sound track.

Among those processes the first to be mentioned is the dynamic neutralization of the charges on the plates[2]. The neutralization occurs due to dipole orientation parallel to the electric field lines. By dipoles we refer to polarized atoms, molecules, molecular conglomerates, etc. Such neutralization has a positive impact on the engineers since it enhances the optimal capacitance of the capacitors hundreds of times. However, there is no free lunch.

When AC voltage is being applied, the dipoles in the dielectric are in continuous rotating motion because of the search for the right orientation. Their behavior can be compared as of the religious fanatics; on the one hand, they are unanimous, on the other hand, they interfere chaotically. This interference, and hence, non-linear and inertial dipole interaction [1,2] takes place every time the voltage between the plates changes fast. As a result of such neutralization, a capacitor with a dielectric becomes a source of frequency-independent inertial non-linear distortions when used in the correcting circuits.

I have previously been warned by Winer [3] about the danger of such a distortion for the perception of music. Those distortions are similar to cancer. Neither a human ear, nor analytical devices are capable of differentiating these distortions from the musical signal. In addition, they are not easily detected in a sine wave signal. Therefore, one can only guess about the presence of inertial non-linear distortions in the musical signal and its sources.

For example, audiophils generally believe that the frequency cut at 500 kHz is easily audible. Since there are no reasonable explanations for this phenomenon, I connected it to the formation of mid-frequency inertial non-linear distortions in the dielectric that limit the broadband of the capacitor [4]. By the way, this supposition was totally confirmed in the course of experiments with the air capacitors.

Fig.2. Passive correcting RL-circuit.

Having lost all hopes to find the non-distorting capacitors for RIAA correcting circuits, in 1994 I decided to build a pre-amplifier with the use of RL-correcting circuit (see Fig.2). It was not a pioneering idea. Already in early 1970-s, the Japanese self-educated engineers have been publishing the schematics of several RL-correctors. No one has explained yet why the Japanese preferred the more complicated RL-correctors to RC-correctors. I will try to fill in the blanks. First, let’s compare the two physical processes which take place in RC- and RL-correcting circuits.

It’s a known fact that the dipoles in the dielectric of the capacitor of correcting RC-circuit are in the state of inertial rotation, which reveals itself in non-linear electric effects.

Magnetic materials, which are used for the induction cores in RL-correction circuits, have a similar behavior. They are full of “lazy” magnetic domains that tend to orient themselves along the force lines of magnetic field. Such orientation results in the magnetization of the core material. The high magnetization is favorable in this case, because it enhances the magnetic field created by the inductance. This enhancement can be characterized by magnetic susceptibility of the core material. It is known that the magnetic susceptibility, on the one hand, is non-linear for AC current in the inductor and, on the other hand, is inertial or complex according to the technical terminology. The theory of complex magnetic susceptibility was developed as early as in 1913 [5].

It is understandable that the complex, i.e. inertial magnetic susceptibility of the core material and non-linearity of permeability are the reason for formation of inertial non-linear distortions in RL-circuit. Why are RL-correcting circuits preferable to RC-correcting circuits then?

It turned out that the inertial non-linear distortions in RC-circuits almost do not depend on frequency, whereas in RL-circuits the distortions fade with the increase of frequency. I’m not going to provide the proof of this statement due to its complexity.

There is another important circumstance: the use of RL-circuit gives engineers some freedom in design. They get the possibility to decrease the inertial non-linear distortions by utilizing the cores of larger dimensions in the inductances. They can also make the cores from different materials, say, amorphous iron, or creating air gaps in the inductors, etc.

At the same time, the RL-circuit does not present an ideal technical solution. The use of RL-circuit doesn’t exclude the creation of inertial non-linear distortions sensible for ear[3].

In order to prove my suppositions, some tests were performed on home-made RL-corrector. However, the results of the first “hearing” showed that my concerns were exaggerated. The corrector was much more superficial in energy, dynamics, clearness of sound, clarity of high frequencies and bass articulation than RC-corrector.

Since I was so very much astounded by the quality of sound of the new corrector, I couldn’t understand why this technical solution hadn’t been used by the advanced western audio manufactures. Seven years have passed since, and I do not ask such silly questions any longer. Some of the predicted sound effects, which I related to the creation of inertial non-linear distortions in RL-corrector were also observed. They were sensed in a hardly audible artificiality of the sound. It was then when I decided to continue the research.

The inspiration came suddenly when I was studying the pre-war papers written by German engineers from the “Telefunken” company. Why don’t we try to use the leakage inductance at the output of the windings of the transformer as elements of the correcting circuit? Really, it was an unexpected enlightenment. In an instant, everything became obvious, whereas the advantages of this idea of mine took me long time to comprehend.

My work on the creation of this device lasted for about two months. Finally, the device was built. Due to the ambiguity of the used reactances, the device was named RX-corrector. Its schematic is shown in Figure 3.

R1 - 47kOhm

R2 - 47kOhm

R3 - 1,5kOhm

R4 - 47kOhm

R5 - 62kOhm

R6 - 5,1kOhm

R7  - 300kOhm

R- 100Ohm/1Wt

R9  - 64kOhm

R10 - 5160Ohm

C1 - 100μF/350V

C2 - 220μF/16V

C3 - 2,2μF/250V

C4 - 0,25μF/300V

C5 - 200μF/350V

L1 - EF86 (6Æ32Ï)

L2 - EL34

Parameters of RX-corrector (according to IEC 268-15)

Nominal EMF source

5 mV

EMF source at the input overload (1000 Hz)

130 mV

Nominal output voltage

0.5 V

Output resistance

6 kOhm

Load resistance at the output

> 250 kOhm


Fig.4. AFC of the correcting circuit based on RIAA standard.

My X-transformer became the heart of the new corrector. Together with the resistive loads, it corrects the AFC (Amplitude-Frequency Characteristic) according to the RIAA standard (see Fig.4). This is achieved by the signal addition from the two secondaries of transformers II and III in parallel. Each of the secondaries forms a certain part of AFC, turning on one pole. Such poles are produced by the interaction of leakage inductors and resistive loads at the output of the secondaries. Those are the resistor R9 for the secondary II and the resistor R10 for the secondary III.

 The pole at the output of III appears at 50 Hz. Above this frequency, the AFC falls with the slope of 6 dB/oct. At this frequency AFC changes to plateau-like, developed at the output of the transformer II, which in its turn changes to the falling part again with the slope of 6 dB/oct at 2120 Hz.

The frequency 500 Hz of “zero” is created when the transformation coefficient of II is 9 times larger than of III.

Now, when we understand the operational principle behind RX-corrector, it’s time to find the necessary leakage inductances for AFC bands.

One can easily obtain the pole at 2120 Hz. Moving a little ahead, I can notice that it’s sufficient to wind the secondary of II on the top of the primary of I. It’s much more difficult to form a pole at 50 Hz. For this purpose, the output inductance at III should be on the order of 20 H.

How to obtain such large leakage inductance? In the mind-boggling search for the answer, I was urged to solve the problem opposite to that faced by all electrical engineers of the world. It was required to significantly increase the leakage inductance. The time has come to “turn your back to the enemy” as a general gave the order in the movie “Fanfan the Tulip”.

Using this approach, I have succeeded in creating X-transformer with the main characteristics listed below:

1.         The required inductance of the primary I needed to obtain the pre-set threshold frequency of the corrector can be determined as:

 H              (1)

where is the internal resistance of the lamp EL34 working as a triode (= 800 Ohm);

       is the optimal load resistance of the triode, Ohm ( Ohm);

      is the pre-set lower threshold frequency of the transformer stage (assume  = 1.63 Hz).

2.         Transformation coefficients K2 and K3 at the output of the secondaries II and III are chosen such that RX-corrector provides the amplification equal to 100 at 1000 Hz according to IC 268-15 [6].

Since the signal at 1000 Hz corresponds to the plateau part of the AFC created by the winding II, the amplification of the corrector is defined at the output of this winding.

Taking into account[4] (see Fig.3) that the voltage amplification of the first stage of the corrector built on lamp EF86 equals 90, and that of the next stage built on EL34 (in a triode regime with the anode load ) equals 7.8, one can easily find the transformation coefficients. At the output of the winding II K2=0.141, and at the output of the winding III K3=0.141x9=1.27.

3.         The minimal load resistance for the windings II and III can be found provided that the total reduced load of X-transformer should be larger than 2 (i.e.  > 1,600 Ohm) and the contribution of the loads of both secondaries to the load of that stage should be equal. Then:

K22  Ohm;

Ê32  Ohm;

4.         The values of the leakage inductance at the output of the windings II and III can be found according to:


where is the leakage inductance at the output of the secondary, H;

                    is the RIAA correction pole frequency;

                  is the resistance parallel to the leakage inductance . This resistance includes the reduced to the secondary internal resistance of EL34, and also the resistance (wind) of the primary and secondary windings of the transformer, Ohm.

For the winding II:  K22 +  +.

For the winding III: K32 + .

The resistance of the windings is not known yet; hence for now we assume that they give a 10% contribution to the total resistance . In this case, in accordance to eq (2):



Now we have reached the ultimate point: determination of the designing parameters of the X-transformer. The leakage inductance at the output of the winding II, as has been mentioned above, can be obtained by winding of the II on the primary. The parameters of I and II can be calculated by the well-known empirical formula [6]:


where  is the average loop length of the windings I and II, m;

 is the number of the loops of the winding II;

 is the width of the windings, m;

 is the thickness of the dielectric between the windings I and II, m;

 and  are the thicknesses of the windings I and II, m;

 = 0.8 (for non-sequential windings).


We see that the formula (3) doesn’t include the parameters of the magnetic core (the average length of the magnetic field lines, their crossection and magnetic permeability). This means that (3) defines an ideal inductance , free from the inertial non-linear effects, caused by the change of the magnetic cores.

The next step is to design the part of the transformer that provides the leakage inductance equal to 21.7 H at the output of the winding III. It is not possible to solve this problem the traditional way, i.e. using formula (3) with a reasonable size of the X-transformer. I had to call for inspiration once again. I tried to visualize how the leakage inductance is created: when the magnetic flux created by the primary doesn’t cross the secondary completely [8]; that part of the missed flux has to come back to the primary anyway, most probably through air. What if one could build an artificial channel (some flux guide), which would allow the part of the flux to miss the secondary.

This insignificant, at the first glance, but quite valuable flash of intuition occurred suddenly. As it always happens, this flash of intuition pushed me to hard and tedious work. It became necessary to design an artificial channel for the part of magnetic field in the schematics of the transformer. It was practically impossible to visualize it, in a long run I had to use a second breath. In fact, it was necessary to make use of the dimensionless coupling coefficient K3, which is equal to the ratio of the magnetic flux through the primary and the secondary to the total flux created by the primary. This coefficient in its simplest form relates the inductance of the primary and the leakage inductance of the transformer reduced to the winding III [8]:

 Ê32                                                                                               (4)

Since the values  and  are given, we can easily find the value of K3 by reversing this formula:

Fig.5. Design of the X-transformer.


The value K3 = 0.87 means, from the physical point of view, that 13% of the magnetic flux created by the primary (and this is not a small number) should miss the secondary. Having become positive about the truth of this statement, I moved further towards another designing solution: to split the magnetic flux right in E-core of the transformer. In order to achieve this goal, I decided to place the windings I and III apart from each other, on the side strip of the core, but not on the center one, as it’s typically done (see Fig.5). In this case, the part of the magnetic flux of I doesn’t reach III, but is looped back through the center strip and a specially constructed gap.

The width of this gap can be determined through the coupling coefficient K3 as a function of the ratio of magnetic resistances[5] , , of the different parts of the flux guide in the transformer (see Fig .6):


Let’s express the resistance of this part of the flux guide via the magnetic parameters of the core according to the formula [9]:


where is the average length of the magnetic flux through this part of the flux guide,m;

 is the the crossection of the flux guide (gap), m;

  is the magnetic permeability of vacuum ( = 1.256x10-6 H/m);

* is the equivalent magnetic permeability of the material of the flux guide with DC current in the primary of the X-transformer[6].

Let’s change the in (5) to , to  and the magnetic resistance  of the gap to .

Also we will use the typical relations for the E-type core:


As a result, we will get a simple equation for calculating the gap:


For the X-transformer which has =0.87, =450, =0.1 m (the typical value in our case), the gap equals to m.




Fig.6. The distribution of the magnetic fluxes and magnetic resistances in E-core of the X-transformer; red lines define the magnetic fluxes, blue lines show the magnetic resistances, black lines (in parentheses) show magnetic force lines corresponding to the magnetic resistances.

The details in the derivation of the equations (1) through (7) are skipped, in order to facilitate the explanation.

For example, the two gaps marked with cross in Fig. 6 are not taken into account, though they provide the normal performance of the flux guide of the X-transformer in the anode current regime of EL34. The interturn capacitors of transformer’s windings are not taken into account, though they should be accounted for in the process of fabrication of the transformer. It is important that this capacitance in combination with the leakage inductance wouldn’t limit the frequency band at the output of the winding II lower than 20 kHz, and at the output of the winding III lower than 5 kHz.

Due to mentioned simplifications, the equations for the leakage inductance can give an uncertainty up to 15%. However, this uncertainty shouldn’t become an obstacle when setting the poles on the AFC of the corrector.  This can be done exactly by choosing the values of the resistors  and/or .

The frequency values of the poles and zeroes on the AFC of the corrector remain unchanged until the load resistance of the corrector is larger than 250 kOhm.

The reader should be able to select the size of the magnetic core, the number of turns and the wire diameter for X-transformer by him/herself using standard methods [10,11].


The formula of inspiration


The key idea of the RX-corrector is in the utilization of the leakage inductance as correcting AFC elements. The large value of the leakage inductance that takes part in the formation of the lower pole of AFC was obtained by splitting the magnetic flux created by the primary in two parts, one of which misses the secondary completely.

For this purpose the E-shaped core was used, where the primary and the secondary windings of the transformer were placed apart from each other on the opposite side strips of the flux guide. The part of the magnetic flux created by the primary in this configuration misses the secondary through the central strip of the E-shaped core and the air gap.

The advantage of RX-correction over RL-correction, technically speaking, is related to the reduction of the dependence of inductances on the magnetic parameters of the core.

The leakage inductance at the output of the winding II that is responsible for the range 500Hz – 20kHz doesn’t depend on the magnetic parameters of the core, as it can be seen from the equation (3).

Slight dependence on the core magnetic parameters is exhibited by the leakage inductance at the output of the winding III, which is responsible for the range below 500 Hz. However, this dependence is much weaker than the one observed in typical inductors.

In order to prove this statement, let’s compare the classical formula for the inductance of the winding of III:


(where  is the number of turns in III), with the formula obtained from the equations (4), (5) and (8) for the leakage inductance at the output of III:


Since 2(+)>>,  then


The comparison of the equations (8) and (9) yields the linear relationship between the inductance  and the magnetic permeability of the core material; in case of the leakage inductance  this relationship is times weaker. In our case this coefficient equals approximately 27.

The magnetic induction[7], responsible for the leakage inductance on the strips of the core, is about 6.5% from the magnetic inductance in its side strips. Hence, the central strip, which is responsible for the creation of the leakage inductance works in lighter duty than the strips used for the signal transformation from the primary to the secondary.


The principle electric circuit of the RX-corrector


Fig.7. The picture of my RX-corrector.

The principle electric circuit of my RX-corrector slightly deviates[8] from the one shown in Fig.3. This difference can be explained by the fact that initially it was designed for controlled AFC correction on 78 rpm. It was made using rare lamps, magnetic cores and other antique parts that had been manufactured by the “Telefunken” company in 30-40-ies, and the “magic” chassi, which I dismantled from the radio “D770.” Mostly owing to all this, my RX-corrector (see Fig. 7) is very much distinct from any device made by the contemporary audio manufactures. Most likely, it reminds the handicapped person of the World War II. However, this cripple by its vigor and substantiation of sound takes over all contemporary (including the expensive ones) correcting amplifiers by all means. The invincibility of my RX-corrector I can explain, first of all, by the application of the described correcting principles. There is no other mystery in my correction, except for the cited above.

I’m also going to please the readers. Using my RX-corrector and the technique of the “shortest path of musical signal,” I plan to record and release two new CDs. They contain old audio recordings, as there were on my previously recorded CDs. The readers will have an opportunity to compare the sound of RC-, RL- and RX-correctors.

Using the RC-corrector, I recorded CD “Nikolai Pechkovsky Singing,” “Porgy and Bess” by Gershwin (starring Louis Armstrong and Ella Fitzgerald), using RL-corrector (1st version) “AudioMagazin Test CD1,” using RL-corrector (2nd version with “Telefunken” parts) “Fedor Shalyapin” and “AML Test CD+” (the picture of the 2nd version of RL-corrector you can find on the insert to the last CD).

© Likhnitskiy, 2001

(The first publication the author of this article has taken place in AudioMagazine ¹ 5 (40), 2001, pp.167-173 )


1. Jung W.G., Marsh R., Selection capacitors for optimum performance. Part 1&2, Audio, Feb-March 1980, p.52-62 & 50-63.

2. Hippel A.R. Dielectrics and their application, M-L, 1959, p.336.

3. Likhnitsky A.M., The relativity formula of sound, “AM” Vol.4 (33), 2000, p.155.

4. Likhnitsky A.M., ibid, p.151.

5. Arkadiew W., Phyzik Z., Vol.14, 1913, p.928.

6. Likhnitsky A.M., Power. On the correlation parameters of audio components. “AM” Vol.6 (17), 1997, p.96.

7. Tsykin G.S., Low frequency transformers, Moscow, 1955, p.314 (in Russian).

8. Lendi Z., Davis D., Albrecht A., The handbook of radioengineer, M-L, 1961, p.373 (in Russian).

9. Alpatov N.I., Ferrites in electronic circuits, Moscow, 1962, p.9 (in Russian).

10. Tsykin G.S., ibid, pp.369-373.

11. Lendi Z., Davis D., Albrecht A., ibid, pp.384-398.

[1] The capacitors used in RC- and RL- low pass filters are the exception from this rule.

[2] The capacitor, where re-polarization of its plates takes place, is also an effective non-linear transformer of electric power into mechanical power; it makes sense to address this phenomenon separately.

[3] Only inductors without any magnetic core are free from any inertial non-linear distorsions; however, like air capacitors, they are not practical in correcting circuits.

[4] Since in this regime the transconductance of the lamp EF86 is 1.8 mA/V, and its anode load resistance is 50 kOhm.

[5] Magnetic resistance is the resistance of the magnetic circuit (or part of that circuit), where the magnetic flux is created by applied magnetomotive force. The units are A/Wb. The magnetic resistance, magnetic flux and magnetomotive force are counterpart of the electrical quantities: electric resistance, electric current and electromotive force.

[6] For the core made of common steel, μ=450 (for comparison: magnetic permeability of the air gap equals one).

[7] Magnetic induction equals the ratio of the magnetic flux to the area which is perpendicular to the direction of that flux. The units are Tesla.

[8] I have used two regulated X-transformers in my RX-corrector