1 Introduction

        Toroidal transformer is a large type of electronic transformer, which has been widely used in home appliances and other electronic equipment with high technical requirements. Its main use is as a power transformer and an isolation transformer. Toroidal transformers have a complete series abroad and are widely used in computers, medical equipment, telecommunications, instruments and lighting.

        The toroidal transformer is a competitive electronic transformer because of its excellent performance-price ratio, good output characteristics and anti-interference ability. This article will introduce its characteristics.

2 Characteristics of toroidal transformers

       The core of the toroidal transformer is made of high-quality cold-rolled silicon steel sheets (generally below 0.35mm in thickness), which are seamlessly rolled, which makes its core performance better than the traditional laminated core. The coil of the toroidal transformer is evenly wound on the core, and the direction of the magnetic field lines generated by the coil almost completely coincides with the magnetic circuit of the core. Compared with the laminated type, the excitation energy and core loss will be reduced by 25%, which brings the following series of The advantages.

High electrical efficiency, the core has no air gap, the stacking coefficient can be as high as 95% or more, the magnetic permeability of the core can be 1.5-1.8T (the laminated core can only be 1.2-1.4T), and the electrical efficiency can be as high as 95% or more.

The no-load current is only 10% of the laminated type.

Small size and light weight Toroidal transformers can be half the weight of laminated transformers. As long as the cross-sectional area of the core is kept equal, the toroidal transformer can easily change the ratio of the length, width and height of the core, and can be designed to meet the requirements.

The magnetic interference is small. The toroidal transformer core has no air gap, and the windings are evenly wound on the toroidal core. This structure leads to small magnetic leakage and small electromagnetic radiation. It can be used in high-sensitivity electronic equipment without additional shielding. Examples are low-level amplifiers and medical equipment.

Less vibration noise The iron core has no air gap, which can reduce the noise of the induced vibration of the iron core, and the windings evenly and tightly wrap the annular iron core, effectively reducing the "hum" caused by magnetostriction

Low operating temperature Because the iron loss can reach 1.1W/kg, the iron loss is very small, the temperature rise of the iron core is low, and the winding is well dissipated on the iron core with a lower temperature, so the temperature rise of the transformer is low.

Easy to install The toroidal transformer has only one mounting screw in the center, making it especially easy to quickly install and remove in electronic equipment.

3 Classification of toroidal transformers

       According to the introduction of foreign literature, toroidal transformers can be divided into three types: standard type, economic type and isolation type. The characteristics of each type are:

The standard power transformer product series has a capacity of 8 to 1500VA, has a small voltage regulation rate, and the full-load operation temperature rise is only 40 °C, allowing short-term overload operation, suitable for high-demand applications. The primary and secondary windings are insulated with B-grade (130°C) polyester film, and at least three layers of insulating tape are required to withstand the withstand voltage test of AC 4000V for 1min.

The economical power transformer product series has a capacity of 50 to 1500VA, and strives to reduce the cost on the basis of ensuring performance. It is suitable for continuous operation without overloading. The operating temperature rise is 60 ℃, and the insulation material grade is Class A (105 ℃). The output voltage error is less than 3% at full load.

The isolation transformer product series has a capacity of 50 to 1000VA, and can be divided into two series: industrial and medical equipment. The isolation transformer focuses on its insulation performance. The primary and secondary are wrapped with at least 4 layers of B-class insulation polyester film, and the breakdown voltage is greater than 4000V. All primary leads must be double-insulated wires. The maximum temperature rise of the transformer is lower than 45℃. In addition to meeting the above requirements, the isolation transformer for medical use should also meet the UL544 standard, that is, the primary and secondary windings should have thermal protection, and the distance between the winding and the ground copper shield should be greater than 13mm. In addition, the isolation transformer for medical use also requires a temperature protection switch on the primary winding. When the core temperature reaches 120°C, the temperature protection switch is disconnected. When the temperature returns to normal, the switch is automatically reset and closed.

4 Problems that should be paid attention to in the application of toroidal transformers

4.1 The power capacity of the transformer

       The power capacity of the transformer is the main basis for determining the size of the iron core. Transformer loads are intermittent in many occasions, such as power transformers in audio equipment. At this time, the volume and weight of the transformer are much lower than those in continuous operation. As shown in Figure 2, the load section A is a smaller section than the entire B section. At this time, the working cycle of the transformer is much shorter than its thermal time constant. Use formula (1) to calculate the rated power of the transformer. PN=PL(VA) (1)

In the formula: PN——transformer rated power (VA);

PL——Transformer load power (VA);

A——on load time;

B——The working cycle of the transformer.

Figure 2 Transformer intermittent load situation

4.2 Voltage Regulation

        The voltage regulation rate is an important indicator to measure the load characteristics of the transformer. The voltage regulation rate refers to the relative change of the output voltage U2 when the input voltage remains unchanged and the load current rises from zero to the rated value, usually expressed as a percentage, as shown in formula (2):

ΔU=×100% (2)

In the formula: ΔU——voltage regulation rate;

U20——No-load output voltage (V);

U2——The output voltage (V) at the rated load of the transformer.

4.3 Toroidal Transformer Efficiency

       Because the transformer has iron loss and copper loss, the output power Po is always smaller than the input power Pi.

Fig.4 Relationship between toroidal transformer efficiency and load rate

4.4 Autotransformer

       The use of an autotransformer is appropriate when only step-up or step-down is required, and isolation of the primary and secondary windings is not required. The autotransformer has the advantages of small size, low cost, and high transmission power. The autotransformer wound with a toroidal core does not require insulation for the primary and secondary windings, so it is very convenient to process, smaller in size and weight, and lower in cost. It should be noted that the common terminal (COM) of the primary and secondary windings of the autotransformer should be connected to the neutral line, so as to be safe.

      The autotransformer circuit is shown in Figure 5, and its rated power PAH is calculated according to formula (4).

PAH=PAO(UH－UL)/UH(VA)（4）

In the formula: PAO——autotransformer output power (VA);

UH - high voltage winding voltage (V);

UL - low voltage winding voltage (V).

Figure 5 Autotransformer circuit diagram

4.5 The problem of temperature rise

      The temperature rise characteristic curve of the toroidal transformer is shown in Figure 6. It can be seen from Figure 6 that the temperature rise of the toroidal transformer is relatively low. For the standard series, even if the overload is 120%, the temperature rise does not exceed 70℃.

       The temperature rise of the transformer is determined by the iron loss and the copper loss. For the laminated transformer, the two parts are basically equal, but the toroidal transformer is wound with high-quality cold-rolled silicon steel sheets and cooperates with a good annealing process. The loss is only (10-20)% of the total loss, so the temperature rise is mainly determined by the copper loss of the winding. A reasonable design is that the power consumption of the primary and secondary windings should be basically balanced.

       The temperature rise is also closely related to the heat dissipation area. Due to the low temperature rise of the toroidal transformer core, the windings are wound evenly on the entire core, and the heat dissipation area and heat dissipation conditions are relatively good, so a lower temperature rise can be obtained.

4.6 Closing current

       Generally, the transformer will generate a large closing inrush current when closing, while the toroidal transformer will cause a larger closing current due to its lack of air gap and high magnetic permeability. The toroidal transformer below 300VA can be protected by a general fuse, but in order to prevent the closing current from blowing the fuse, the current of the selected fuse should be 8 to 10 times larger than the primary current of the transformer. For toroidal transformers above 300VA, slow fuses or thermal fuses should be considered for protection. Sometimes, in order to reduce the inrush current, the B value of the transformer magnetic flux density can be lower.

4.7 Transformer and Rectifier Circuit

      Most of the toroidal transformers used as power supplies are connected to the rectifier circuit. The relationship between the most commonly used rectifier circuits and transformer secondary voltage U2, secondary current I2 and DC voltage Ud and DC current Id is listed in Table 3 for reference during design. .

Table 3 Rectifier circuit and transformer parameters Circuit name Circuit diagram Transformer secondary voltage

U2/V transformer secondary current I2/A

Double rectifier circuit 0.8(Ud+2)1.8Id

Bridge rectifier circuit 0.8(Ud+2)1.8Id

Full wave center tap 1.7(Ud+1)1.2Id

5 Design calculation of toroidal transformer

       By designing a power transformer for a 50Hz quartz lamp, the primary voltage U1=220V, the secondary voltage U2=11.8V, the secondary current I2=16.7A, and the voltage adjustment rate ΔU≤7%, to illustrate the calculation method and steps .

1) Calculate the transformer secondary power P2

P2=I2U2=16.7×11.8=197VA (5)

2) Calculate the transformer input power P1 (set the transformer efficiency η=0.95) and the input current I1

P1=207VA (6)

I1=0.94A

3) Calculate the core cross-sectional area SS=K(cm2) (7)

In the formula: K——the coefficient is related to the power of the transformer, K=0.6～0.8, take K=0.75;

Po——transformer average power, Po=202VA. Then S=0.75=10.66cm2, take S=11cm2.

According to the existing iron core specifications, the iron core size is selected as follows: height H=40mm, inner diameter Dno=55mm, outer diameter Dwo=110mm. Calculate the cross-sectional area of the selected iron core S=H=×40×10-2=11cm2

4) Calculate the number of turns N10 per volt of the primary winding and the number of turns N1N10=(turns/V) (8)

In the formula: f-power frequency (Hz), f=50Hz;

B-magnetic flux density (T), B=1.4T. Substitute N10==2.9 turns/V, take N10=3 turns/V, then N1=N10U1=3×220=660 turns.

5) Calculate the number of turns N20 per volt of the secondary winding and the number of turns N2N20=(turns/V) (9)

Substitute N20==3.23 turns/V, then N2=N20·U2=3.23×11.8=38.1 turns, take N2=38 turns.

6) Select the wire diameter

The wire diameter d of the winding wire is calculated according to the formula (10) d=1.13 (mm) (10)

In the formula: I——the current through the wire (A);

j——current density, j=2.5～3A/mm2.

When taking j=2.5A/mm2 and entering formula (10), d=0.72(mm), then the primary winding wire diameter d1=0.72=0.69mm, and the outer diameter of the enameled wire is 0.72mm. The diameter of the secondary winding wire is d2=0.72=2.94mm, and two wires of d=2.12mm (considering that the maximum outer diameter of the insulating paint is 221mm) are wound in parallel. Because the cross-sectional area of the 2.94 wire is Sd2=6.78mm2,

The cross-sectional area of the d=2.12mm wire is 3.53mm2. The cross-sectional area of the two wires in parallel is: 2×3.53=7.06mm2, which fully meets the requirements and has a large margin.

6 Structural calculation of toroidal transformer

       The winding of the toroidal transformer is wound by the winding ring of the winding machine in the iron core, so the size of the inner diameter of the iron core is very important to the processing process. how much space. If the calculated inner diameter space is too small and does not meet the winding requirements, the size of the iron core can be modified. As long as the cross-sectional area remains unchanged, the electrical performance is basically unchanged.

      It is known that the inner diameter of the iron core is Dno=55mm, the thickness of each insulating layer in Figure 7 is to=1.5mm, and t1=t2=1mm.

1) Calculate the inner diameter Dn2 after winding the primary winding and wrapping insulation Calculate the number of turns of each layer of the primary winding n1n1=(turns) (11)

In the formula: Dn1——the inner diameter of the iron core after insulation, Dn1=Dno-2t0=55-(2×1.

5)=52mm;

kp——winding coefficient, kp=1.15. Substitute n1==197 turns

Then the number of layers Q1 of the primary winding is Q1===3.35, taking an integer Q1=4 layers

The primary winding thickness δ1 is

δ1=Q1d1kp=4×0.72×1.15=3.3mm

Then the inner diameter Dn2 of the primary winding after insulation is

Dn2=Dn1-2(δ1+t1)=52-2(3.3+1)=43.4mm

2) Calculate the thickness δ2 of the secondary winding

Calculate the number of turns n2 of each layer of the secondary winding, considering that the secondary winding is wound with 2×d2=2×2.21mm wires in parallel, then n2===27 turns

Then the number of layers Q2 of the secondary winding is Q2===1.41, taking the integer Q2=2 layers.

The secondary winding thickness δ2 is

δ2=Q2d2kp=2×2.21×1.15=5.08mm

3) Calculate the inner diameter Dn4 after winding the primary winding and wrapping insulation

Dn4=Dn2-2(δ2+t2)=43.4-2(5.08+1)=31.24mm

It can be seen that after the winding is wound, the inner diameter still has a margin, and the selected iron core size is appropriate.

7 Performance testing of toroidal transformer samples

In order to check the accuracy of the design method, the toroidal transformer samples made according to the design parameters are tested for performance, and the results are as follows.

7.1 No-load characteristic test

The measurement circuit is shown in Figure 8. The measured data are listed in Table 4. According to the data in Table 4, the no-load characteristic curve shown in Figure 9 is drawn.

From the no-load characteristics of the transformer, it can be seen that the design meets the requirements. When the rated working voltage is 220V (operating point is A), the no-load current of the transformer is only 13.8mA. Even if the power supply voltage rises to 240V, the core of the transformer is not saturated at point B. There is a large margin.

7.2 Voltage Regulation Measurement

The secondary no-load voltage U20=12.6V measured when the transformer is no-load, when the rated current I2=16.7A is applied, the secondary output voltage is U2=11.8V, and the voltage adjustment rate is calculated according to formula (2).

ΔU=×100%==6.4%

The transformer voltage regulation rate reaches the target of ΔU<7%.

7.3 Temperature rise test

The temperature rise test of the transformer winding is carried out by the resistance method, and the test is carried out after the temperature rise of the transformer is stable after energizing for 4 hours, and the average temperature rise Δτm of the winding is calculated according to the formula (12).

Δτm=(k+t1)-(t2-t1)(12)

It can be seen from the temperature rise test results that the designed transformer has reached the standard temperature rise standard, that is, Δτm<40°C, and the temperature rise of the primary and secondary windings is basically equal, that is, the power consumption of the two windings is relatively balanced.

7.4 Insulation performance test

1) Insulation resistance

Use a 500V shaker to test the insulation resistance, and the insulation resistance between the primary and secondary windings is greater than 100MΩ under normal conditions.

2) Electric strength

The transformer can withstand 50Hz, 4000V (effective value) electricity between the primary and secondary windings