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Design method of power transformer in switching power supply

1 characteristics of power transformer in switching power supply

power transformer is a very important component in switching power supply. Like ordinary power transformer, it also transmits energy through magnetic coupling. However, the magnetic circuit to realize magnetic coupling in this power transformer is not the silicon steel sheet in the ordinary transformer, but the magnetic materials such as ferrite core or beryllium molybdenum alloy with high permeability working at high frequency. Its purpose is to obtain a larger excitation inductance, reduce the power loss in the magnetic circuit, and enable it to transmit pulse energy with a wide frequency band with minimum loss and phase distortion

Figure 1 (a) shows the rectangular pulse wave added to the input end of the pulse transformer, and figure 1 (b) shows the output waveform obtained at the output end. It can be seen that the waveform distortion caused by the pulse transformer mainly includes the following aspects:

Figure 1 pulse transformer input and output waveform

(a) input waveform (b) output waveform

(1) the rising edge and falling edge become inclined, that is, there is rise time and fall time

(2) at the last moment of the rising process, there is an upward rush, and even oscillation

(3) at the last moment of the descent process, there is undershoot and oscillation waveform may also appear

(4) the flat top part falls gradually

these distortions reflect the difference between the actual pulse transformer and the ideal transformer. Considering the influence of various factors on the waveform, the equivalent circuit of the pulse transformer as shown in Figure 2 can be obtained

in the figure: internal resistance of RSI signal source UI

resistance of RP primary winding

RM core loss (for ferrite core, it can be ignored)

t ideal transformer

resistance of RSO secondary winding

RL load resistance

equivalent distributed capacitance of C1, C2 primary and secondary windings

leakage inductance of Lin, LIS primary and secondary windings

LM1 primary winding inductance, also known as excitation inductance

n turns ratio of ideal transformer, N = N1/N2

the equivalent circuit of the pulse transformer in Figure 2

convert the secondary circuit of the circuit shown in Figure 2 into one, do approximate processing, and combine some parameters to obtain the circuit shown in Figure 3. The leakage inductance Li includes Lin and LIS, and the total distributed capacitance C includes C1 and C2; The total resistance Rs includes RSI, RP and RSO; LM1 is the excitation inductance, which is the same as LM1 above; RL is the resistance value equivalent to RL on the primary side, RL =rl/n2, and the converted output voltage U o=uo/n

after this treatment, there are only five elements in the equivalent circuit, but each element does not play a major role at the same time during each period of pulse action. We know that any pulse waveform can be decomposed into the superposition of fundamental wave and many harmonics. The rising and falling edges of the pulse contain various high-frequency components, while the flat top part of the pulse contains various low-frequency components. Therefore, in the process of rising, falling and flattening, the impedance of each element (L, C, etc.) is also different. Therefore, we divide this process into several stages to analyze, and find out the elements that play a major role in each stage, ignoring the secondary factors. For example, when the input signal is a rectangular pulse, it can be analyzed in three stages, namely, the rising stage, the flat top stage and the falling stage

(1) rising phase

for normal positive pulses, the rising phase is the pulse front, and the signal contains rich high-frequency components. When the high-frequency components pass through the pulse transformer, in the equivalent circuit shown in Figure 3, the capacitive reactance 1/C of C is very small, while the inductive reactance LM1 of LM1 is very large. Compared, the role of LM1 can be ignored, while the role of Li is more significant in the branches in series. Therefore, the equivalent circuit shown in Fig. 3 can be simplified into the equivalent circuit shown in Fig. 4

equivalent circuit diagram of Figure 3 and Figure 2 4 simplified circuit of Figure 3

in this circuit, the higher the frequency, the greater the Li, and the smaller the 1/C, so most of the high-frequency signals fall on Li, and the output high-frequency components are reduced. It can be seen that the high-frequency components contained in the front of the input signal USM cannot be completely transmitted to the output end, and the higher the frequency components reach the output end, the smaller the result is that the front of the waveform at the output end is different from the input waveform, That is, distortion occurs

to reduce this waveform distortion, it is necessary to minimize the distributed capacitance C (the number of turns of the primary winding of the transformer should be reduced). However, it is necessary to obtain a certain amount of winding inductance, so a magnetic core with high permeability is required. In winding, some measures can also be taken to reduce the distributed capacitance, such as subsection winding; In order to reduce the leakage inductance L1, the overlapping winding method of primary and secondary windings can be used

(2) in the flat top stage, the flat top of the

pulse contains various low-frequency components. In the case of low frequency, among the three elements connected in parallel at the output end, the capacitance reactance 1/C of capacitor C is very large, so capacitor C can be ignored. At the same time, in the series branch, the inductive reactance li of Li is very small, which can also be omitted. Therefore, the circuit in Figure 3 can be simplified to the low-frequency equivalent circuit shown in Figure 5. The signal source can also be equivalent to a DC power supply with electromotive force of USM

here, the following formula can be used to express

u o= (usmrl) e-t//(RS + RL)

=lm1 (RS + RL) rsrl

it can be seen that u o is a decreasing exponential waveform, and its decreasing speed depends on the time constant. The larger the decreasing speed is, the slower the decreasing speed is, that is, the smaller the waveform distortion is. Therefore, LM1 should be increased and RS and RL should be reduced as much as possible, but this is limited. If LM1 is too large, the number of turns of the winding is bound to be large, which will increase the distributed capacitance of the winding and deteriorate the rising edge of the pulse

the low-frequency equivalent circuit of Figure 5 and figure 3

the equivalent circuit of Figure 6 in the pulse descent phase

(3) the signal source of the descent phase

the descent phase is equivalent to the phase from closing to opening of the switch s in series with the DC power USM. Although it is a relative process with the rise phase, it has two differences; First, there is excitation current in inductance LM1 and it begins to release, so LM1 cannot be omitted; Second, after the switch S is disconnected, RS will not work, so the equivalent circuit in the descent phase is obtained, as shown in Figure 6

generally speaking, after the flat top stage of the pulse transformer, LM1 stores relatively large magnetic energy, so after the switch is disconnected, there will be violent oscillation and large undershoot. Damping measures are often used to eliminate undershoot

2 parameters and formula of power transformer

2.1 basic parameters of transformer

in the magnetic circuit, the degree of magnetic flux concentration is called magnetic flux density or magnetic induction intensity, which is expressed in B, and the unit is Tesla (T), usually still in Gauss (GS) unit, 1t=104gs. On the other hand, the magnetic force that produces magnetic flux is called the magnetic field intensity, which is represented by the symbol h, and the unit is a/m

h=0.4 Ni/Li

where: the number of turns of N winding

I current intensity

Li magnetic circuit length

the hysteresis loop of magnetic material indicates the change of magnetic characteristics in the process of complete magnetization and complete demagnetization of magnetic material. Figure 7 shows a typical magnetization curve

the curve from coordinate 0 to point a is called the initial magnetization curve

Some key points in the curve are very important. BS: saturated flux density, Br: remanence, HC: coercive forcewhen BR is closer to the BS value, the shape of the hysteresis curve is closer to a rectangle, as shown in Figure 8 (a). At the same time, when the coercive force HC is larger, the hysteresis curve is wider, which indicates that the magnetization characteristics of this magnetic material are harder, indicating that this material is a hard magnetic material. The larger the difference between BR and BS, the smaller the coercive force HC, that is, the thinner the hysteresis curve, indicating that this material is soft magnetic material. The magnetic core material of pulse transformer should be soft magnetic material, as shown in Figure 8 (b)

Figure 7 hysteresis loop without air gap

figure 8 hard/soft magnetic materials and hysteresis loop

(a) hard magnetic materials (b) soft magnetic materials

If an air gap is opened in the magnetic core, a magnetic circuit with air gap will be established, which will change the effective length of the magnetic circuit. Because the permeability of the air gap is 1, the effective magnetic circuit length Le is

le=li + ILG

where: Li magnetic circuit length in magnetic material

LG magnetic circuit length in air gap

I permeability of magnetic material

for a given ampere turn, the magnetic flux density of the magnetic core with air gap is smaller than that without air gap

2.2 basic formula for designing transformer

in order to ensure that the transformer works in the linear area of the magnetization curve, the following formula can be used to calculate the maximum magnetic flux density (unit: T)

bm= (up 104)/kfnpsc

where: the voltage applied on the primary winding of up transformer (V)

f pulse transformer working frequency (Hz)

np transformer primary winding turns (turns)

sc effective cross-sectional area (cm2)

k coefficient, It is 4.44 for sine wave and 4.0

for rectangular wave. Generally, the BM value of switching power transformer should be lower than the saturated flux density BS

the output power of the transformer can be calculated by the following formula (unit: W)

po=1.16bmfjscso 10-5

where: J wire current density (a/mm2)

effective cross-sectional area of SC core (cm2)

window area of so core (cm2)

3 requirements for power transformer

(1) leakage inductance should be small

Figure 9 shows the typical voltage of bipolar circuit (half bridge, full bridge, push-pull, etc.).Current waveform, Voltage spikes caused by transformer leakage inductance energy storage are one of the reasons for the damage of power switches

Figure 9 waveform of bipolar power converter

the size of voltage spike when the power switch is turned off is related to factors such as collector circuit configuration, circuit turning off conditions and leakage inductance. As far as the transformer is concerned, reducing leakage inductance is very important

(2) avoid transient saturation

the working magnetic flux density of general power frequency power transformer is designed at the B-H curve close to the inflection point, so at the moment of power on, great surge current is generated due to the serious saturation of transformer core. It decays quickly, and its duration is generally only a few cycles. For pulse transformer, if the working magnetic flux density is larger, magnetic saturation will occur at the moment of power on. Because the pulse transformer is directly connected with the power switch tube and applied with a high voltage, the saturation of the pulse transformer, even a few short cycles, will lead to the damage of the power switch tube, which is not allowed. Therefore, there is usually a soft start circuit in the control circuit to solve this problem

(3) consider the influence of temperature

the switching power supply has a high working frequency. It is required that the power loss of the magnetic core material at the working frequency should be as small as possible. With the increase of the working temperature, the reduction of the saturated magnetic flux density should be as small as possible. In the design and selection of core materials, in addition to the conventional parameters such as saturated magnetic flux density and loss, special attention should be paid to its temperature characteristics. Generally, the magnetic flux density should be selected according to the actual working temperature. Generally, the BM value of ferrite core is easily affected by temperature. Considering that the working environment temperature of switching power supply is 40 ℃, the core temperature can reach 60 ~ 80 ℃, and generally, bm=0.2 ~ 0.4t, that is, 2000 ~ 4000gs

(4) reasonable structural design

from the perspective of structure, the following factors should be considered:

magnetic leakage should be small to reduce the leakage inductance of the winding

it is easy to wind, and the outgoing line and transformer should be installed conveniently for production and maintenance

convenient for heat dissipation

4 choice of magnetic core material

soft magnetic ferrite is widely used in switching power supply because of its low price, good adaptability and high frequency performance

soft ferrite is commonly divided into manganese zinc ferrite and nickel zinc ferrite

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