A simple and fast way to calculate power supplies. Encyclopedia of radio electronics and electrical engineering

Encyclopedia of radio electronics and electrical engineering / Amateur radio calculations

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The direct calculation method proposed here allows you to quickly and easily determine the parameters of a simple DC power supply and then check the finished circuit with only one oscilloscope. Since the calculation formulas are based on the use of values ​​measured from the output voltage waveform of the circuit during its test, there is no need to perform intermediate calculations.

Testing is even faster because the ripple percentage is determined directly from the maximum DC output voltage level and from the ripple peak-to-peak value of the power supply output voltage.

Fig.1 (click to enlarge)

On fig. 1 shows a circuit of a simple power supply and shows the timing diagram of its output voltage, which in this case is also equal to the voltage across the capacitor. The ripple level in percent and the ripple factor ft can be determined from the output voltage waveform as follows:

In addition, since the change in the output voltage in the time interval between the moments tA and tB depends on the time constant determined by the resistance of the load resistor Rz and the capacitance of the capacitor C, the value of the output voltage at time tB can be written as:

If we divide this equality by Eо(peak), we get

or

which can be rewritten further as

If we reverse this equality and find the natural logarithm of both parts of the latter, we get

The capacitance of the capacitor C can now be calculated by the formula

You can also calculate the capacitance C of the known (or desired) values ​​of such quantities as the output voltage Eo, the load current Iz and the ripple level ft. From the time interval between points A and C, one can determine the pulsation frequency F:

Since the leading edge of the ripple voltage coincides with the sinusoid indicated by the dotted line, the angle O will be equal to

The time interval between points D and B is

Equations 2 and 3 make it possible to calculate the capacitance of the capacitor C according to the given values ​​​​of the quantities included in them

With a half-wave rectifier, the capacitance of the capacitor C is expressed by the following formula

The above formulas allow you to determine the capacitance of additional capacitors, such as capacitors of U-shaped filters, using only capacitive reactances, series active resistances and calculation formulas of the same type as for a voltage divider.

A typical power supply circuit with parallel output voltage stabilization is shown in fig. 2; it uses a zener diode to stabilize the output voltage.

Fig. 2

The graph shows the voltage waveform across the capacitor (Ec). The guard voltage, determined by the series resistor Rs and the zener diode, prevents the voltage across the capacitor from dropping below the output voltage level of the circuit. The value of the guard voltage can be taken equal to approximately Vz / 0,8, where Vz is the stabilization voltage of the zener diode. The maximum value of the voltage across the capacitor can then be written equal to

The output ripple voltage will be

where rz is the internal resistance of the zener diode for AC. The resistance of the series resistor Rs can be calculated from the formula

where Iz (min.) is the minimum value of the current through the zener diode, at which the operating point of the power source lies above the inflection point of the zener diode characteristic; this current value can be taken equal to 0,2 Iz (nom.), where Iz (nom.) is the nominal value of the operating current of the zener diode. From the minimum value of 0,2Iz (nom.) and the maximum value of 0,8Iz (nom.) of the zener diode current, you can determine the requirements for the power dissipated by the zener diode Pz. It is necessary that

Formulas 1-8 allow you to quickly perform a calculation regarding an economical power supply, and the calculation can be quickly and easily verified using a conventional oscilloscope. The selection of all rectifier diodes and the power transformer is carried out in the usual way. This method can be applied in the calculation of more complex power sources.

Author: O.J. Cogburn; Publication: N. Bolshakov, rf.atnn.ru

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