Principle and Design of switching power supply the calculation of transformer parameters of excited switch power supply (16)

-6-3-2. Calculation of parameters of the transformer of the excited switch power supply
The parameters of the transformer of the excited switch power supply are mainly calculated from these aspects. One is the turns of the primary coils of the transformer and the volt second capacity. The larger the volt second capacity, the smaller the excitation current of the transformer. The other is the turns ratio of the Primary and Secondary Coils of the transformer, and the rated input or output current or power of each transformer winding. The working principle and parameter design of the switching power supply transformer will be analyzed in detail later. Here is a brief introduction.
1-6-3-2-1. Calculation of the number of turns of the primary coils of the excited switch power supply transformer

In Figure 1-17, when the input voltage UI is added to the two ends of the primary coil of the switching power supply transformer and all the secondary Coils of the transformer are open, the current flowing through the transformer is only the excitation current, the magnetic flux in the Transformer Core is all produced by the excitation current. When the control switch is switched on, the excitation current increases with time, and the magnetic flux in the Transformer Core increases with time. According to the electromagnetic induction theorem:
E1 = l1di/dt = n1d restart/dt = UI -- k During connection (1-92)
Type E1 is the EMR generated by the primary coil of the transformer, L1 is the inductance of the primary coil of the transformer, fill is the magnetic flux of the transformer core, and UI is the input voltage of the primary coil of the transformer. The magnetic fl can also be expressed:
Bytes = s × B (1-93)
In the above formula, S is the magnetic conductivity area of the transformer core (unit: square centimeter), B is the magnetic induction intensity, also known as the magnetic induction density (unit: Gauss), that is, the magnetic flux per unit area.
Place the (1-93) type into the (1-92) type and perform points:
 

The (1-95) formula is used to calculate the number of turns in the N1 winding of the primary coil of the single-excited switch power supply transformer. In the formula, N1 is the least turns of the N1 winding of the primary coil of the transformer, S is the magnetic conducting area of the transformer core (unit: square centimeter), and BM is the maximum magnetic induction intensity of the transformer core (unit: gaussian), BR is the residual magnetic induction strength of the transformer core (unit: Gaussian), BR is generally referred to as residual magnetic, Tau = ton, is the control switch on time, short for pulse width, or the width of the power switch's turn-on time (unit: seconds). Generally, a margin of more than 20% must be reserved for the value of Tau. The UI is the working voltage, unit: v. In the formula, the index is used in a unified unit. Different units are used, and the index values are different. Here, the cgs unit system is used, that is, the length is cm ), the magnetic induction intensity is Gaussian (GS), and the unit of magnetic flux is Maxwell (MX ).
In the (1-95) formula, the ui x-Tau is the transformer's volatile second capacity, that is, the volatile second capacity equals the product of the input pulse voltage amplitude and the pulse width, here we use us to represent the capacity of the Volt-second. A transformer can withstand high input voltage and long-time impact, says the Volt-second capacity us.
The higher the input voltage, the shorter the impact on the transformer. The lower the input voltage, the longer the transformer will be able to withstand the impact. Under certain operating voltage conditions, the larger the transformer's volatile capacity, the lower the magnetic induction intensity of the transformer core, transformer cores are less saturated. The transformer's volt-second capacity is independent of the transformer's volume and power, but only related to the variation of the magnetic flux.
It must be pointed out that both BM and BR are not constants. When the current flowing through the primary coil of the transformer is very small, BM increases with the current increasing, but when the current continues to increase, BM cannot continue to increase. This phenomenon is called magnetic saturation. The transformer should not work in the magnetic saturation state. To prevent saturation of the pulse transformer, the switch transformer usually leaves a certain air gap in the magnetic circuit. Because the air permeability differs from the core permeability by thousands of times, as long as the air gap length of 1% or several 1% is left in the magnetic circuit, the reluctance or magnetic momentum of the air will mostly fall into the air gap, therefore, the magnetic core is hard to be saturated.
The BM and BR values in the Transformer Core without air gap are generally high, but the difference between the two is very small; the Transformer Core with air gap is left, the value of BM and BR is generally reduced, but the difference between the two can be increased. The larger the air gap is, the greater the difference between the two. Generally, BM can be 1000 ~ 4000 Gauss, BR 500 ~ 1000. By the way, it is pointed out that the air gap of the transformer core is too large, and the coupling coefficient between the first and second coils of the transformer will be reduced, so that the leakage of the first and second coils of the transformer will increase and the work efficiency will be reduced, in addition, it is easy to generate a back-voltage force to break down the power switch.
There are also some high magnetic conductivity, high magnetic flux density magnetic materials (such as Permo alloy), the core of this transformer magnetic conductivity and BM value can be more than 10000 Gauss, however, these magnetic materials are generally used only in dual-Excited Switching Power Transformers.
Although the variable of the inductance of the primary coil of the transformer is not found in the (1-95) formula, it can be obtained from the (1-92) formula:
L1 = n1d incubator/dt (1-96)
The above expression indicates that the electric inductance of the primary coil of the transformer is equal to the total magnetic flux passing through the primary coil of the transformer, and the ratio of the excitation current flowing through the primary coil of the transformer. In addition, because of mutual inductance between the coils, that is, the excitation voltage outflow is affected by the input voltage and the Coil Inductance. Therefore, the inductance of the transformer coil is proportional to the square of the turns of the transformer coil. As can be seen from the (1-95) and (1-96) types, the more turns the primary coils of the transformer have, the larger the Voltage Capacity and the electric inductance of the primary coils. Therefore, if the resistance loss of the transformer's primary coil is not considered, the more turns the primary coil, the better the inductance. However, when designing a transformer, we need to consider costs, copper resistance loss, and other factors.