Switching Power Supply Principle and Design (Serial 41) Calculation of Transformer Parameters of Half-bridge Switching Power Supply

1-8-2-5. Calculation of transformer parameters for half-bridge switching power supply

The working principle of the half-bridge transformer switching power supply is very similar to that of the push-pull transformer switching power supply, except that the transformer excitation method and the working power supply access method are a little different; therefore, the mathematical expression used to calculate the number of turns of the primary coil N1 winding of the push-pull transformer switching power supply can be used to calculate the number of turns of the primary coil N1 winding of the half-bridge transformer switching power supply with only slight modification.

A) Calculation of the number of turns of the primary coil of the half-bridge switching power supply transformer

The half-bridge transformer switching power supply is the same as the push-pull switching power supply, which is also a dual-excitation switching power supply. Therefore, the magnetic induction intensity B of the transformer core used for the half-bridge switching power supply can change from the negative maximum value -Bm to the positive maximum value +Bm, and the transformer core does not need to have an air gap. The calculation method of the half-bridge switching power supply transformer is basically the same as the calculation method of the push-pull switching power supply transformer mentioned above, except that the voltage directly added to both ends of the transformer primary coil is only equal to half of the input voltage Ui. According to the calculation formulas (1-150) and (1-151) for the number of turns of the primary coil of the push-pull switching power supply transformer:

Assume that the voltage directly applied to both ends of the primary coil of the half-bridge switching power supply transformer is Uab, and Uab = Ui/2, then the above (1-150) and (1-151) can be rewritten as:

The above formulas (1-174) and (1-175) are the formulas for calculating the number of turns of the primary coil N1 winding of the half-bridge 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); Uab is the voltage applied to both ends of the primary coil N1 winding of the transformer, Uab = Ui/2, Ui is the operating voltage of the switching power supply, in volts; τ = Ton, is the on-time of the control switch, referred to as the pulse width, or the width of the on-time of the power switch tube (unit: seconds);

F is the operating frequency, in Hertz. Generally, when the dual-excitation switching power supply transformer works in the forward and reverse output, its volt-second capacity must be equal. Therefore, the number of turns of the transformer primary coil N1 winding can be directly calculated using the operating frequency; the values ​​of F and τ should reserve a margin of about 20%. The exponents in the formula are used in unified units. If different units are selected, the value of the exponent will be different. 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).

B) Calculation of the primary and secondary turns ratio of the AC output half-bridge switching power supply transformer

If the half-bridge transformer switching power supply is used for DC/AC or AC/AC inverter power supply, that is, converting DC into AC, or rectifying AC into DC and then converting it into AC, this inverter power supply generally does not need to adjust the output voltage, so the circuit is relatively simple and the working efficiency is very high. Please refer to Figure 1-36, Figure 1-38, and Figure 1-39.

The output voltage uo of the half-bridge transformer switching power supply used for inversion is generally a square wave with a duty cycle of 0.5. Since the waveform factor of the square wave (the ratio of the effective value to the half-wave average value) is equal to 1, the effective value Uo of the square wave is equal to the half-wave average value Upa, and the amplitude Up of the square wave is also equal to the half-wave average value Upa. Therefore, as long as the half-wave average value of the output voltage is known, the effective value can be known, and then based on the half-wave average value, the primary and secondary coil turns ratio of the half-bridge switching power supply transformer can be obtained.

According to the previous analysis, the output voltage uo of the half-bridge transformer switching power supply is mainly determined by the forward voltage output by the secondary coil of the switching power supply transformer. Therefore, according to one of the equations (1-158), (1-159), and (1-161), the half-wave average value of the output voltage of the half-bridge transformer switching power supply can be obtained. Thus, the primary and secondary coil turns ratio of the half-bridge inverter switching power supply transformer is obtained:

n = N2/N1 = 2Uo/Ui = 2Upa/Ui —— secondary/primary transformation ratio, when D = 0.5 (1-176)

Formula (1-176) is the formula for calculating the primary-secondary coil turns ratio of the half-bridge inverter switching power supply transformer. In the formula, N1 is the number of turns of the transformer primary coil N1 winding, N2 is the number of turns of the transformer secondary coil, Uo is the effective value of the output voltage, Ui is the DC input voltage, and Upa is the half-wave average value of the output voltage.

Formula (1-176) does not take into account the working efficiency of the transformer. When the working efficiency of the transformer is taken into account, it is best to multiply the right side of Formula (1-176) by a coefficient slightly greater than 1.

C) Calculation of the primary and secondary turns ratio of the DC output voltage non-regulated half-bridge switching power supply transformer

The non-regulated half-bridge switching power supply with DC output voltage is a DC/AC inverter power supply with an additional rectifier filter circuit after the AC output circuit. Please refer to Figure 1-43, Figure 1-44, and Figure 1-45. The duty cycle of the control switches K1 and K2 of this non-regulated half-bridge switching power supply with DC output voltage is the same as that of the DC/AC inverter power supply, which is generally 0.5. Therefore, the primary and secondary coil turns ratio of the non-regulated half-bridge switching power supply transformer with DC output voltage can be directly calculated using formula (1-176). That is:

n = N2/N1 = 2Uo/Ui = 2Upa/Ui —— secondary/primary transformation ratio, when D = 0.5 (1-176)

However, in the case of low voltage and high current output, the voltage drop of the rectifier diode and the working efficiency of the transformer must be considered.

D) Calculation of the primary and secondary turns ratio of the DC output voltage adjustable half-bridge switching power supply transformer

The function of the half-bridge switching power supply with adjustable DC output voltage requires that the output voltage is adjustable. Therefore, the duty cycle of the two control switches K1 and K2 of the half-bridge transformer switching power supply must be less than 0.5; because the half-bridge transformer switching power supply has voltage output in both forward and reverse states, so under the same output voltage (average value), the duty cycle of the two control switches K1 and K2 is equivalent to being half as small. When the adjustable range of the output voltage is required to be the maximum, the duty cycle is preferably 0.25. According to equations (1-140) and (1-145), and replacing the input voltage Ui with Uab, we can obtain:

Formulas (1-177) and (1-178) are the formulas for calculating the ratio of the primary and secondary turns of the half-bridge switching power supply transformer with adjustable DC output voltage. In the formula, N1 is the minimum number of turns of the transformer primary coil N1 winding, N2 is the number of turns of the transformer secondary coil, Uo is the DC output voltage, Uab is the voltage applied to both ends of the transformer primary coil N1 winding, Uab = Ui/2, and Ui is the operating voltage of the switching power supply.

Similarly, in the case of low voltage and high current output, it is important to consider the operating efficiency of the transformer as well as the voltage drop of the rectifier diode and the voltage drop when the switching device is turned on.