Calculation of Transformer Parameters of Forward Switching Power Supply

Calculation of Transformer Parameters for Forward Switching Power Supply

The calculation of the parameters of the forward switching power supply transformer is mainly considered from the following aspects. One is the number of turns and volt-second capacity of the primary coil of the transformer. 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 winding of the transformer . The working principle and parameter design of the switching power supply transformer will be analyzed in more detail later, so here we will only give a relatively simple introduction.

Calculation of the number of turns of the primary coil of the forward switching power supply transformer

In Figure 1, when the input voltage Ui is applied to both 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, and the magnetic flux in the transformer core is all generated by the excitation current. When the control switch is turned on, the excitation current will increase with time, and the magnetic flux in the transformer core will also increase with time. According to the electromagnetic induction theorem:

e1 = L1di/dt = N1dф/dt = Ui —— K on-time (1-92)

Where E1 is the electromotive force generated by the primary coil of the transformer, L1 is the inductance of the primary coil of the transformer, ф is the magnetic flux in the iron core of the transformer, and Ui is the input voltage of the primary coil of the transformer. The magnetic flux ф can also be expressed as:

ф= S×B (1-93)

In the above formula, S is the magnetic conductive area of ​​the transformer core (unit: square centimeters), and B is the magnetic induction intensity, also known as the magnetic induction density (unit: Gauss), that is, the magnetic flux per unit area.

Substitute (1-93) into (1-92) and integrate:

Formula (1-95) is the formula for calculating the number of turns of the primary coil N1 winding of the single-excitation switching power supply transformer. In the formula, N1 is the minimum number of turns of the primary coil N1 winding of the transformer, S is the magnetic conductive area of ​​the transformer core (unit: square centimeters), Bm is the maximum magnetic induction intensity of the transformer core (unit: Gauss), Br is the residual magnetic induction intensity of the transformer core (unit: Gauss), Br is generally referred to as residual magnetism, τ= Ton, is the on-time of the control switch, referred to as the pulse width, or the width of the power switch tube conduction time (unit: second), generally τ value should reserve more than 20% margin, Ui is the working voltage, unit is volt. The exponent in the formula is used for unified units, and the value of the exponent is different when different units are selected. Here, the CGS unit system is selected, that is, the length is centimeters (cm), the magnetic induction intensity is Gauss (Gs), and the magnetic flux unit is Maxwell (Mx).

(1-95) In the formula, Ui×τ is the volt-second capacity of the transformer , that is, the volt-second capacity is equal to the product of the input pulse voltage amplitude and the pulse width. Here, we use US to represent the volt-second capacity. The volt-second capacity US indicates how high the input voltage and how long the impact can be withstood by a transformer. Under certain transformer volt-second capacity conditions, the higher the input voltage, the shorter the time the transformer can withstand the impact. Conversely, the lower the input voltage, the longer the transformer can withstand the impact. Under certain working voltage conditions, the larger the transformer volt-second capacity, the lower the magnetic induction intensity in the transformer core, and the transformer core is less likely to saturate. The volt-second capacity of the transformer has nothing to do with the volume and power of the transformer, but only with the change in magnetic flux.

It must be pointed out that neither Bm nor Br is a constant. When the current flowing through the primary coil of the transformer is very small, Bm increases as the current increases, but when the current continues to increase, Bm will not continue to increase. This phenomenon is called magnetic saturation. The transformer should avoid working in a magnetic saturation state. In order to prevent the pulse transformer from saturating, a certain air gap is generally left in the magnetic circuit of the switching transformer. Since the magnetic permeability of air differs from that of the iron core by thousands of times, as long as one percent or several hundredths of the air gap length is left in the magnetic circuit, most of its magnetic resistance or magnetomotive force will fall on the air gap, so it is difficult for the magnetic core to saturate.

In the transformer core without air gap, the values ​​of Bm and Br are generally high, but the difference between them is small; in the transformer core with air gap, the values ​​of Bm and Br are generally reduced, but the difference between them can be increased. The larger the air gap, the greater the difference between them. Generally, Bm can be 1000~4000 Gauss, and Br can be 500~1000. By the way, if the air gap of the transformer core is too large, the coupling coefficient between the primary and secondary coils of the transformer will be reduced, thereby increasing the leakage inductance of the primary and secondary coils of the transformer, reducing the working efficiency, and easily generating back electromotive force to break down the power switch tube.

There are also some high permeability, high flux density magnetic materials (such as Permalloy). The permeability and Bm value of this transformer core can reach more than 10,000 Gauss, but these high permeability, high flux density magnetic materials are generally only used in dual-excitation switching power supply transformers.

Although the variable of transformer primary coil inductance is not seen in formula (1-95) , it can be obtained from formula (1-92):

L1 = N1dф/dt (1-96)

The above formula indicates that the inductance of the transformer primary coil is equal to the ratio of the total magnetic flux passing through the transformer primary coil to the excitation current flowing through the transformer primary coil. In addition, due to the mutual inductance between the coils, that is, the excitation current is affected by the input voltage as well as the inductance of the coil. Therefore, the inductance of the transformer coil is proportional to the square of the number of turns of the transformer coil. It can be seen from formulas (1-95) and (1-96) that the more turns the transformer primary coil has, the greater the volt-second capacity and the inductance of the primary coil. Therefore, for the forward switching power supply transformer, if the resistance loss of the transformer primary coil itself is not considered, the more turns the transformer primary coil has, the better, and the greater the inductance, the better. However, when designing a transformer, factors such as cost and copper resistance loss must also be considered.