Output transformers (С.Н. КРИЗЕ)

Выходные трансформаторы, С.Н. КРИЗЕ
(Output transformers)

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I present an unauthorized translation of S.N. Krizov's book "Output Transformers," which I created for my own needs while designing output transformers. Since the book was published some 70 years ago and, to my knowledge, has never been translated into Polish, I am sharing my translation without infringing on copyright, hoping that it will be an interesting read for those interested in tube amplifiers who don't speak the language or don't have access to the book.

Grzegorz "gsmok" Makarewicz

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The output transformer is a simple yet crucial component of any low-frequency receiver or amplifier. The performance of the entire system depends heavily on its quality. An improperly designed output transformer can cause significant distortion, reduce the power delivered to the external load by the output stage tubes, and so on. Therefore, output transformer parameters should be selected in close relation to the load data and the operating conditions of the output stage: its configuration, tube type, and operating mode.

Selecting an output transformer

The output stage tube of a receiver or amplifier produces a specific oscillation power in the anode circuit corresponding to the frequency of the useful signal. This power, P₁, depends on the amplitudes of the alternating current I₁ and alternating voltage U₁ occurring in the anode circuit of the tube and is defined by the following simple expression:

Depending on the value of the DC voltage of the anode power supply U_o, the amplitude of the AC voltage in the anode circuit of the electron tube is usually:

for triodes:

for pentodes and beam tetrodes:

In this way, pentodes and beam tetrodes are characterized by better utilization of the anode voltage, which determines a much higher efficiency factor of these tubes.

The amplitude I₁ of the variable component of the anode current depends on the value of the current i₀ corresponding to the zero voltage on the control grid of the electron tube (Fig. 1) and is equal to:

for triodes:

for pentodes:

Fig. 1. Output stage tube characteristics
i₀ - anode current at zero control grid bias voltage

For low-power amplifier tubes, the I₁ value usually does not exceed 30÷50 mA. The usable power that the tube can deliver is equal to:

for triode:

for a pentode or beam tetrode:

Table 1 presents basic data characterizing the operating mode of the anode circuit of some types of electron tubes.

Table 1.

Let's assume that the voltage and current amplitudes in the anode circuit are predetermined. This requires determining the required load resistance R_a in the anode circuit of the vacuum tube, which should be equal to:

For example, for a 6F6 pentode operating in class A with anode voltage U₀=250V, the anode load resistance should be equal to:

The load resistance values ​​of the anode circuits of other types of amplifier tubes should also be of the same order (no less than several thousand ohms).

The resistance of a speaker coil is usually in the single ohm range. Such a large difference in the resistance values ​​of the amplifier's load and the optimal load of the output tube's anode circuit necessitates the use of an output transformer as a matching element. Connecting a low-impedance load resistance directly to the tube's anode circuit would significantly reduce the power delivered by the amplifier to the load. Furthermore, nonlinear distortion in the output stage could significantly increase..

For example, let's compare the operating conditions of a 6F6 pentode for two values ​​of anode circuit load resistance: R_a1 = 7400Ω and R_a2 = 10Ω. The second case corresponds to the direct connection of a low-impedance loudspeaker coil to the tube anode circuit.

For R_a1=7400Ω the useful power given off by the tube is equal to:

where: I₁=27mA – current amplitude in the anode circuit of the tube for R_a1=7400Ω.

For R_a2=10Ω we get:

where: I₁=30mA – amplitude of the anode current when the anode circuit is short-circuited.

Therefore, the effective power output of the tube at a low-impedance load decreases 60-fold. At the same time, nonlinear distortion increases from approximately 5% to 10%. Furthermore, when the load is directly connected to the anode circuit, a DC component of the tube's anode current will flow through it, which in many cases (e.g., for a speaker coil) is unacceptable.

A completely different situation occurs when a low-impedance load R_N is connected through a step-down transformer. This type of load is referred to hereinafter as an external load. The load resistance R_N' for medium audio frequencies, referred to the transformer's primary winding, is equal to:

where: n - transformation coefficient of the output transformer equal to the ratio of the number of turns of the secondary winding to the number of turns of the primary winding.

For a step-down transformer, n<1, which allows the creation of a resistance in the anode circuit equal to the most favorable one for a given tube, also for a low-impedance load connected to the secondary winding of the output transformer.

The transformation coefficient ensuring the given resistance R_a of the anode load can be determined from the following relationship resulting from expression (9):

Since usually R_N<R_a, hence usually the transformation coefficient is less than unity.

The need for a step-down output transformer can be physically explained as follows. To obtain the required effective power through the load resistance R_N, a significant current must flow through this resistance, as the resistance R_N is small. As mentioned earlier, a relatively small alternating current flows in the tube's anode circuit. By using a step-down output transformer (n<1), the current flowing in its secondary winding can be increased compared to the current in the primary winding. The operation of the output transformer can therefore be compared to that of a mechanical lever, which allows for increased force at the expense of reduced operating distance.

Fig. 2 shows the graphs of the dependence of two basic parameters of the output stage operation: the effective power P₁ and the nonlinearity coefficient γ on the transformation coefficient n. The curves were determined for the 6F6 pentode operating under the following conditions:

• anode power source voltage and screen grid voltage 250V;
• negative bias voltage on control grid (grid one) 16.5V;
• signal amplitude on grid one14V;
• load resistance of the transformer secondary winding 10Ω.

Fig. 2. Dependence of the useful power P₁ and the nonlinearity coefficient γ on the transformation coefficient n of the output transformer for the 6F6 pentode at the load R_N=10Ω.

Analysis of these curves shows that, for the assumed operating conditions, the most favorable output transformer transformation ratio lies in the range n=0.03÷0.04, with the lower value (n=0.03) providing maximum usable power, while the higher value (n=0.04) allows for minimal nonlinear distortion. Typically, it's best to choose an intermediate value, e.g., n=0.035, which corresponds to a 28-fold voltage reduction through the output transformer. In this case, a tube operating under the conditions described above can achieve a usable power of approximately 2.4W with nonlinear distortion of around 5%.

Output transformer parameters

The properties of the output transformer are characterized by the following basic parameters:

1. transformation coefficient;
2. inductance of the primary winding L₁;
3. leakage inductance L_p;
4. winding resistances (primary r₁ and secondary r₂).

These parameters, along with the tube's internal resistance R_i and the external load resistance R_N, determine the output stage's frequency response. Furthermore, knowledge of these transformer parameters is essential for practical implementation, as they determine the transformer's design data: winding wire diameters, number of turns, etc.

Let's consider the effect of transformer parameters on the output stage's performance. The effect of the transformation coefficient n on the stage's performance was discussed above. Let's now turn to the remaining transformer parameters.

The inductance of the primary winding, created by the magnetic flux of the turns forming the primary coil, influences the frequency distortion of the amplifier's output stage in the low-frequency range. To ensure that these distortions do not exceed a predetermined value, the transformer should have a primary winding inductance L₁ no less than a specified value. Of two transformers operating under identical conditions, the transformer with the higher primary winding inductance will have the better frequency response at low frequencies.

Since increasing the L₁ value can only be achieved by increasing the transformer's size, weight, and manufacturing cost, transformer design should be guided by the minimum necessary primary winding inductance. When operating a transformer with a magnetic core, the primary winding inductance can vary depending on the magnitude of the direct and alternating current in its windings. To avoid frequency distortion exceeding the permissible value, it is necessary to ensure the specified primary winding inductance under the most unfavorable operating conditions.

The influence of direct current in the transformer windings on the inductance of its primary winding will be considered later in the description.

The leakage inductance of a transformer depends on the magnetic fluxes that do not simultaneously flow through both windings. These magnetic fluxes are confined by the air, not the core interior, and are called leakage fluxes. The transformer's main magnetic flux Φ₁₂ flowing through both windings, as well as the leakage fluxes Φ₁ and Φ₂, are shown in Fig. 3.

Fig. 3. Distribution of magnetic fluxes in the transformer

Leakage fluxes and the associated leakage inductance cause frequency distortion in the output transformer at high frequencies. During amplifier operation in Class B, leakage inductance can cause nonlinear distortion. Therefore, the leakage inductance L_p in output transformers should be as low as possible. This can be achieved by improving the magnetic coupling between the windings, for example, by using windings composed of alternating sections. Despite its benefits, this transformer winding method is not always used, as it complicates the transformer design and increases its cost. Leakage inductance should not exceed a specific value depending on the assumed maximum distortion value. In good transformers, the leakage inductance L_pi does not exceed a percentage of the primary winding inductance.

The resistance of a transformer's windings influences the amount of acoustic-frequency energy losses occurring within it and determines the transformer's efficiency factor. It should be clearly emphasized that the efficiency factor also depends on core losses. However, in acoustic-frequency transformers, especially low-power ones, the core losses are always small compared to the winding losses. This allows the efficiency factor to be calculated by considering only the winding losses, while neglecting the core losses.

To better utilize the power generated by the amplifier's output stage tubes, it's always a good idea to have an output transformer with the highest possible efficiency. Increasing the efficiency can be achieved by reducing winding losses, i.e., by increasing the wire diameter used to wind the transformer. Unfortunately, this inevitably increases its size and manufacturing cost. Therefore, when designing a transformer, a compromise efficiency value should be adopted that, to some extent, meets the two opposing requirements: low losses and low manufacturing costs. Practice shows that the output transformer efficiency value can be roughly estimated based on the data in Table 2.

Table 2.

Knowing the value of the transformer's efficiency factor, it is possible to determine the actual resistance of its windings, and based on this, the diameter of the wire with which it is wound.

Defining the output transformer parameters

To define the output transformer parameters discussed above, it is necessary to know the following quantities defining the operating conditions of the amplifier's output stage:

1. The operating frequency range is limited from below by the frequency f_N and from above by the frequency f_W.
2. Permissible frequency distortion of the output stage for the lower f_N and upper f_W cutoff frequencies. The frequency distortion is characterized by the frequency distortion coefficients M_N and M_W, which are equal to: 
   
   where: K₀ – gain for medium frequencies K_N and K_W correspond to the markings in Fig.4.
3. The values ​​of the external load of the amplifier, i.e. the resistance R_N and the inductive resistance L_N.
4. The most favorable anode load resistance of the output stage tube R_a.
5. Output transformer efficiency factor η_T.

Fig. 4. Frequency response of the output stage

The parameters of the output transformer can be determined as follows.

The transformation coefficient is determined from the previously presented formula (10):

For a push-pull system, substitute twice the value of R_a.

The frequency response of the output stage in the low-frequency range depends on the inductance L₁ of the transformer's primary winding. Fig. 5 shows the frequency responses for two values ​​of the inductance L₁ of the primary winding.

Fig. 5. The influence of the inductance L₁ of the primary winding of the output transformer on the frequency response

The characteristic curve corresponding to a larger value of L₁ runs higher. Therefore, as the inductance of the output transformer's primary winding increases, the frequency distortion decreases. Physically, this phenomenon can be explained by the fact that with a larger value of L₁, the primary winding inductance shunts the tube load less. The following expression can be used to determine L₁:

where: R - resistance in the anode circuit of the tube.

In the case when the output stage uses a triode R=R_i, and in the case of a pentode or a beam tetrode:

If we assume that f_N=80Hz, M_N=1.22, the calculation formula for determining the inductance of the primary winding of the output transformer takes the simplified form:

In the case of a push-pull output stage, the inductance of the primary winding should be assumed to be twice that resulting from relations (11) and (12). If the output stage is subject to a negative feedback circuit, the value of L₁ can be assumed to be approximately half as small.

The transformer leakage inductance L_p determines the amplifier's frequency response in the high-frequency range. The effect of L_p on the frequency response is shown in Fig. 6.

Fig. 6. Influence of the leakage inductance L_p of the output transformer on the frequency response

As the leakage inductance increases, the amplification factor at higher frequencies decreases and frequency distortion increases. The maximum allowable value of the output transformer leakage inductance L_p for the load resistance of the secondary winding can be determined using the relationship:

where: f_W – upper frequency response band,
M_W – frequency distortion factor for the frequency f_W.

If we assume f_W=6000Hz and M_W=1.2, the relationship for determining the leakage inductance takes the simplified form:

If the output stage load has a significant inductive component, e.g., if the load is a dynamic speaker coil, the permissible value of the output transformer leakage inductance is much greater than the value obtained from relations (13) and (14). With an inductive load of the secondary winding, the output transformer leakage inductance can be determined from the following relation:

where: L_N – load inductance.

For dynamic speakers, the L_N value is typically (0.2÷1)·10^-3H. In a push-pull configuration, the output transformer's leakage inductance can be assumed to be twice as large as the values ​​determined using formulas (13), (14), and (15).

If the amplifier's output stage uses pentodes or beam tetrodes with high internal resistance (tens of thousands of ohms or more), the allowable leakage inductance is so high that virtually every transformer has a lower leakage inductance. Therefore, for stages using pentodes or beam tetrodes, the output transformer's leakage inductance may not need to be determined, and the transformer can be designed without taking measures to reduce its leakage inductance.

However, it should be borne in mind that when operating a tube with high internal resistance in the output stage without negative feedback, a correction filter consisting of a capacitor C_K and a resistor R_K should be connected in parallel with the primary winding of the transformer, as shown in Fig. 7. Without such a filter, the stage will produce unacceptably high distortions.

Fig. 7. Connection diagram of the C_KR_K correction circuit in a stage operating on a pentode or beam tetrode

Filter data can be determined from the following relationships:

Resistances r₁ and r₂ of the transformer windings are determined for a given value of the efficiency coefficient using the formulas:

If we assume η_T=0.85, then:

Formulas (18)-(21) define the maximum allowable winding resistances of the transformer. If the winding resistances are lower than the calculated values, this will have a positive impact on the output transformer's properties and increase its efficiency. For push-pull circuits, double the R_a value should be substituted in formulas (16)-(21).

Examples of electrical calculation of output transformersh

1. Calculation of the output transformer for an unbalanced stage operating on a pentode.

Data:

• Lower frequency response band f_N=70Hz.
• Frequency distortions in the assumed frequency range should not exceed 2 dB, i.e. M_N≤1.26.
• External load resistance R_N=4Ω.
• Load inductance L_N=4·10^-3H.
• The most favorable load resistance of the anode of an electron tube R_a=7000Ω.
• Output transformer efficiency factor η_T=0.85.

We calculate the transformation coefficient:

Primary winding inductance:

where: R=R_a (for pentode)

We find the correction filter data:

where: L_p=0.01L₁ was assumed, which is usually the case in typical transformers.

We determine the winding resistances:

primary:

and secondary:

2. Calculation of the output transformer for a push-pull stage operating on triodes.

Data:

• Operating frequency range f_N=60Hz, f_W=8000Hz.
• Frequency distortion in a given operating frequency range M_N=M_W=1.2.
• External load resistance R_N=10Ω.
• Internal resistance of an electron tube R_i=1500Ω.
• The most favorable anode load resistance of each tube R_a=4000Ω.
• Transformer efficiency factor η_T=0.9.

We determine the transformation coefficient:

Inductance of the primary winding of the output transformer:

Leakage inductance:

Winding resistances:

primary winding:

secondary winding:

Design calculations of output transformers

The purpose of a design calculation is to determine all the data necessary to build a transformer, including core dimensions, the number of winding turns, the diameter of the winding wires, etc. The input data for the design calculations are the transformer's electrical parameters found above: primary winding inductance, leakage inductance, transformation ratio, and winding resistance.

The design calculation methodology for a transformer depends on the operating mode of its magnetic circuit. The presence of direct current in the primary winding creates a constant magnetic flux in the transformer core, which significantly reduces the magnetic permeability of the core material and, consequently, the inductance of the primary winding L₁. This necessitates the use of a slightly different winding calculation methodology than for transformers operating without constant magnetic flux in the core (e.g., in push-pull configurations).

As we know from the previous description, the inductance of the primary winding of a low-frequency transformer should be sufficiently high (on the order of several Henrys or more). To achieve this inductance, low-frequency transformers always use a steel core.

A transformer consists of the following main parts:

1. core,
2. bobbin - a casing for winding the winding,
3. windings,
4. elements that compress the core and serve to secure the transformer.

A transformer core consists of separate plates ranging from 0.2 mm to 0.5 mm thick. The core plates are coated on one side with an insulating varnish or covered with thin paper. Insulating the plates from each other reduces core losses caused by eddy currents, which increases the transformer's efficiency. Transformer steel is primarily used as the core material, from which plates of specific shapes (so-called shapes) are cut. Two types of cores are used in transformers: bar/core (or O-shaped) and armored/jacketed (or S-shaped). The bar core is shown in Fig. 8, and the "shell" core is shown in Fig. 9.

Fig. 8. Rod core (type O)

Fig. 9. "Shell" core (type Ш)

In low-frequency and low-power transformers, shell cores are most commonly used. Bar cores are primarily used in higher-power output transformers operating at high voltages. Shell transformers are simpler to assemble, having a single coil within which the transformer windings are arranged. However, isolating the windings is more difficult than in core transformers, where the windings are arranged in two coils. Shell cores are assembled using shapes resembling the letter Ш, which is why shell cores are called Ш-type cores. To eliminate the gap between the main Ш-shaped leaf and its closure, the transformer shapes are assembled alternately. Core transformers consist of rectangular shapes. Once assembled, the core shapes are compressed with clamps, usually through holes in the shapes. In low-power transformers, the core is sometimes compressed with a metal support, which also serves as a mounting for the transformer.

The bobbin on which the transformer windings are placed is usually made of pressboard. The bobbin consists of a "sleeve" and "collars." To reduce costs, transformer manufacturers often use so-called bobbinless winding. The windings are wound on a sleeve without collars. Thin paper pads are placed between the winding layers, the ends of which are glued together. A cross-section of the bobbinless winding is shown in Fig. 10.

Fig. 10. Cross-section of the bobbinless winding

Bobbinless winding can only be used in transformers of relatively small dimensions, because with a larger winding height (above 20...25 mm) it is difficult to obtain sufficient mechanical strength of the coil, as there is a possibility of slippage of the upper end windings.

Transformer windings are made of copper wire insulated with enamel, paper, or silk. Enameled wire (e.g., ПЭЛ) is typically used in low-power transformers, as it is the cheapest and takes up the least amount of space on the coil. Silk-insulated wires (ПШД, ПШО) and enamel-silk-insulated wires (ПЭШД, ПШО) are primarily used in high-voltage windings (above 1000V), where there is a high risk of interwinding breakdown and where increased electrical resistance requirements apply. To protect the transformer against breakdown, the winding layers are separated by thin paper or oilcloth spacers. For enameled wire, spacers should be used for each layer, and for other wires, spacers should be used every 3-5 winding layers. To protect the transformer from moisture and increase its electrical resistance, the coils of factory-made transformers are impregnated with a special compound, such as ceresin or an insulating varnish, after winding. In some cases, after impregnation, the coil is additionally coated with a bituminous surface layer, which significantly increases the transformer's resistance to moisture.

The order in which the windings are placed on the transformer body is not critical. The preferred method is usually to ensure the windings are easy to install. The transformer's primary winding is usually placed at the bottom. However, this rule is not mandatory. The winding terminals are made of soft, multi-core wire with good insulation. They are connected to the terminals of the terminal blocks, which also serve to connect the external wires to the transformer.

Transformer windings come in two forms: cylindrical (Fig. 11) or disc-shaped (Fig. 12). Cylindrical windings are the simplest and most commonly used.

Fig. 11. Cross-section of the cylindrical winding

Fig. 12. Cross-section of the disc winding

Design calculations of output transformers for unbalanced systems

Transformer calculations begin with selecting the core type and size. Sometimes, the most desirable core shape is specified, and it is only necessary to determine the thickness of the sheet stack.

The required output transformer dimensions depend on its power. For a given core type, the characteristic value determining the maximum transformer power is the result of the expression O_sQ₀, where: Q_s=ab – the core cross-sectional area and Q₀=hc – the area of ​​the window in which the windings are placed (Figs. 8 and 9).

Increasing the core cross-sectional area Q_s allows for a reduction in the number of transformer turns while maintaining the inductance of its primary winding L₁. This, in turn, allows for the winding to be made with a larger diameter wire, thus increasing the current in the transformer windings and, consequently, its power. If, for the same core cross-sectional area Q_s, the window area Q₀ is increased, this approach allows for the construction of a higher-power transformer on a given core, as it allows for the increase of voltage (by increasing the number of turns) or current (by increasing the wire diameter) in the transformer windings.

If the transformer operates with constant submagnetism, its geometric dimensions can be determined for a given power using the following expression:

where:

• Q₀ – window area, cm²,
• Q_s – cross-sectional area of ​​the core, cm²,
• P₁ – transformer power, W,
• A – a factor depending on the operating conditions of the output stage: the type of tubes used, the adopted quality indicators (frequency band, frequency distortion).
  Additionally, the coefficient A strongly depends on the existence of negative feedback in the output stage circuit.

For different operating conditions of the output stage, the coefficient A can be determined approximately from Table 3.

Table 3.

For example, if the output stage of the amplifier uses a triode and there is no negative feedback, then for a power of P₁ = 3W the result Q_oQ_s should be no less than 30cm⁴. Therefore, a core with a cross-sectional area of ​​Q_s = 3cm² and a window area of ​​Q_o = 10cm² can be used, or a core with Q_s = 6cm² and Q_o = 5cm² can be used with the same result.

When choosing the relationship between the core and window cross-sectional areas, for a given value of Q_oQ_s, it should be noted that increasing Q_o requires greater wire consumption during transformer winding, while increasing Q_s requires more transformer steel. In most cases, it is advisable to choose approximately equal values ​​for Q_o and Q_s. Table 4 presents the basic data for some types of shell cores.

Table 4.

After selecting the type of transformer core, you can proceed to calculating the number of turns of its windings.

The number of turns of the primary winding that provides the given inductance L₁ is found from the expression:

where:

• I₀ – constant component of the anode current of the output tube, mA,
• Q_s – cross-sectional area of ​​the core, cm²,
• l_s – length of the average magnetic flux line in the core, cm.

Equation (23) gives an exact result, but the calculations using it are quite complex. In practice, when high accuracy is not required, a much simpler approximate formula can be used to determine the number of turns:

where: L₁, I₀ i Q_s are the same parameters as in the expression (23)

Number of turns of the secondary winding:

Primary winding wire diameter (in mm):

where:

• l₀ – average winding length, cm,
• r₁ – resistance of the primary winding which, as shown earlier, is defined by the transformer efficiency factor according to expressions (18) and (20).

In order to avoid overheating of the transformer primary winding, it is necessary to check the permissible current density for the wire diameter found using expression (26):

where: d₁ – in mm, I₀ in mA.

Wire diameter in mm of the secondary winding:

Finally, we determine the thickness of the gap in the core:

where: l₃ in mm; I₀ in A.

This completes the calculation process for a transformer operating with constant submagnetism. All that remains is to verify the winding arrangement within the core window.

To better explain the calculation sequence, let's consider a numerical example.

Example

Calculate the output transformer for an unbalanced amplifier using a 6F6 pentode in the output stage at a power of P₁ = 2.5 W. There is no negative feedback in the circuit. The speaker coil resistance is R_N = 10 Ω.

1. In order to select the core type, we will find the result of expression (22) assuming A=20:

2. Select the core type from Table 4. The most advantageous is the Ш-19x40 core, for which Q_sQ₀ = 59.2 cm⁴, which slightly exceeds the required value (50 cm4). Assuming a Ш-19 type fitting, we find the minimum thickness of the core pack (dimension b). Core cross-section:

and the thickness of the package:

So we choose the Ш-19x34 core for which:

3. From Table 1 for the 6F6 type pentode we find:

The most favorable load resistance is R_a=7400Ω. The constant component of the anode current (quiescent current) I₀=35mA.

4. From the relation (12) we find the inductance of the primary winding of the output transformer:

5. From the relationship (23) we determine the number of turns of the primary winding:

It will be interesting to compare the result with the result of calculations performed using the relationship (24):

As you can see, the difference in this case is small. We assume the rounded value w₁=5000 zwojów.

6. The transformation coefficient is calculated from the relationship (8):

7. Number of turns of the secondary winding:

8. Primary winding resistance:

where we assumed that η_T=0.8.

9. Primary winding wire diameter:

10. Let us verify d₁ with respect to the current density:

Since we calculated that d₁=0.15 mm the transformer will not overheat.

11. Secondary winding wire diameter:

Both the primary and secondary windings will be made of enamel-insulated wire.

12. We determine the thickness of the gap in the core:

In the clad core, the gap consists of two breaks crossing the magnetic circuit of the transformer, therefore the thickness of the spacer should be twice as small as the calculated required gap thickness:

13. We check the arrangement of the windings.

Number of turns in one layer of the primary winding:

where: d_1iz=0.17 – diameter of the winding wire taking into account the thickness of the insulation.

Number of primary winding layers:

Winding height:

Let's add 2mm for spacers between the layers (spacers made of cigarette paper). Hence, the total winding height is 5.6mm, approximately 6mm.

Number of turns in the secondary winding layer:

Number of secondary winding layers:

Height (without spacers) of the secondary winding:

The height, including the interlayer spacers, is approximately 5mm. The total height of the spacer windings between the primary and secondary windings is:

The bobbin height is 15mm. Therefore, the windings should fit within the core window.

The transformer calculated above for the 6F6 pentode can provide approximately the following quality parameters:

• frequency distortion in the band from 100Hz of the order of 1.5dB,
• frequency distortion in the 50Hz band of the order of 4.0dB,
• efficiency factor (for medium frequencies) 80%

If smaller core sizes are adopted, the frequency distortions will increase and the transformer efficiency factor will be much lower.

Design calculation of output transformers for push-pull circuits

Output transformers in push-pull circuits operate without permanent core submagnetization. Linear transformers, such as those used in wired networks for radio broadcasting, also operate under similar conditions.

The following factors determine the transformer dimensions in such cases:

1. permissible nonlinear distortions, which depend on the maximum induction in the core,
2. frequency response and permissible frequency distortion at low frequencies,
3. set value of the efficiency coefficient.

The maximum induction in the core depends on the ratio between the transformer's power and the volume of its magnetic circuit. However, in low-power transformers (up to 10 W), the induction in the core is small for practically applicable dimensions. Therefore, in the case of low-power output transformers, the geometric dimensions of the core have only a small effect on the maximum permissible induction.

The maximum power of a transformer operating without submagnetization is related to the core size by the following approximate relationship:

where:

• P₁ – transformer power, W;
• Q₀ – window area, cm²;
• Q_s – cross-sectional area of ​​the core, cm²;
• l_s – average magnetic flux path length, cm.

Relationship (29) allows easy selection of core dimensions according to the assumed effective power of the transformer P1. If the core type is given, the required cross-sectional area Q_s can be found from the relationship:

Table 4 provides approximate power values ​​for transformers operating without submagnetization, which can be obtained for various core types.

The maximum induction B in the transformer core can be verified using the following formula:

where: V_s – core volume = Q_sl_s, cm³.

To avoid significant nonlinear distortion in the transformer, the value of B should not exceed 6000÷8000Gs. As described above, in the case of low-power transformers, the inductance is lower than the maximum value, and verification using formula (31) can usually be omitted.

The maximum inductance in the core can be related to the ratio of the core dimensions. It turns out that the inductance B will not exceed the permissible value if the following condition is met:

This condition, as seen in Table 4, is met for most core types.

For amplifiers whose output stages are subject to negative feedback, the output transformer power can be assumed to be twice that calculated using formula (29), or the core area can be half that calculated using formula (30).

The number of turns in the transformer's primary winding is determined as follows:

where: L₁ – inductance of the primary winding calculated based on relations (11) and (12).

It should be noted that for push-pull circuits, Ra in equations (11) and (12) should be substituted with twice the value of the anode load resistance of one branch. In the remaining considerations, the calculation of the output transformer for the push-pull stage does not differ from the calculation presented earlier for the asymmetric stage. The cores of transformers operating without permanent submagnetization are not equipped with a gap.

Let us consider an example of the design calculation of a transformer operating without permanent submagnetization.

Example

We will calculate the output transformer for the push-pull stage, which uses 6P3S tubes, one in each branch.

1. Table 4 shows that for a negative feedback amplifier with an output power of 20 W, the best-suited core type is the Ш-19 core. We can find the core cross-sectional area using the following formula for negative feedback amplifiers:

Therefore, the thickness of the core package is:

2. We calculate the maximum induction in the core:

where: Vs – core volume equal to V_s=Q_sl_s=5.15=75cm³.

The obtained value of maximum induction is permissible.

3. We calculate the inductance value of the transformer primary winding:

where: R_a – load resistance for one branch, which for a 6P3S tube is 4000Ω. The existence of feedback allows L₁ to be reduced by half, therefore we assume L₁=11H.

4. Number of turns of the primary winding:

5. Transformation factor:

6. Number of turns of the secondary winding:

7. Resistance of the primary winding:

8. Primary winding wire diameter:

9. We check the wire diameter for the permissible current density value:

Since the condition of the permissible value of the current density resulted in a larger wire diameter, we choose a ПЭ0.21 wire for winding the primary winding.

10. Secondary winding wire diameter:

Here, as d₁ we use the value found according to the relationship for the permissible actual resistance of the windings, because no direct current flows through the secondary winding and there is no danger of its overheating.

11. Finally, we check the correct arrangement of the windings in the core window. In the case of a push-pull transformer, it is advisable to wind the coil on a coil body divided into two sections (Fig. 13). This will reduce the risk of a breakdown between the primary windings, and will also allow the primary winding halves to be made more symmetrically. With this design, each section is wound with half of the primary and secondary windings.

Fig. 13 Cross-section of the output transformer winding arrangement

We check the filling of the section with winding wire:

Primary winding:

Number of turns in section layer:

Number of layers in section:

Winding height without pads:

 

Full height of primary winding:

Secondary winding:

Number of turns in section layer:

Number of layers in section:

Winding height without pads:

Thickness of spacers between windings: 2mm

Full height of primary winding:

Figure 13 shows a cross-sectional view of the winding arrangement in the core window, which indicates that the window filling is adequate. It should be noted that the window filling analysis performed in this and the previous example is correct for layered winding: wire-on-wire. With mass winding, the windings take up significantly more space and may not fit on the coil former. It is recommended to wind transformers in layers, which increases their electrical strength and significantly reduces their geometric dimensions.

The transformer calculated above, when operated in a push-pull mode on 6P3S tubes according to a negative feedback loop scheme, allows for obtaining the following approximate quality parameters:

• frequency distortion in the band from 100Hz of the order of 1.5 dB,
• frequency distortion in the band from 50Hz of the order of 3.0dB,
• efficiency factor (in the medium frequency range) 85÷90%.

Translation: Grzegorz "gsmok" Makarewicz This email address is being protected from spambots. You need JavaScript enabled to view it.