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# Tank inductance calculation

2023-09-15【Archive】

The buck converter, also called buck converter, is a series switching power supply.

The function is to convert input high voltage into low voltage that people need. Do not use AC 220V power, and DC 310V after rectification and filtering. Most electronic products are low voltage circuits, generally 5V, 12V, 24V, 36V, 48V, etc. .These low-voltage electronic devices cannot directly supply DC voltage after AC input is rectified.A converter must be used to convert to applicable low voltage. Of course, there are many converters capable of converting high voltage to low voltage, and Buck is just one of them, advantages of which are high efficiency, small size, and good voltage stabilization effect under various loads.

The main power device of circuit consists of a switching tube Q1, a diode D1, an inductor L1 and an output filter capacitor C1.

The following is parsed at steady state.

When Q1 is on, current flows from positive input through Q1→L1→load and then back to negative input, forming loop 1. According to KVL in loop 1, voltage across inductor L1 while Vin-Vo -Rds* I, without taking into account voltage drop across mos tube, voltage across inductor is VL=Vin-Vo, conduction time is Ton, inductor current increases linearly (before inductor reaches saturation), and inductor current is turned off when Q1 is turned off. Reach maximum lLmax.

When Q1 is turned off, since inductor current cannot suddenly change, in order to maintain main current, D1 turns on, and current flows from L1→load→D1→L1, forming a loop 2. According to COL, in loop, voltage is 0. At this time voltage across inductor is VL=Vo+Vd. If we neglect voltage drop across diode, then voltage across inductor is Vo, and turn-off time is Toff.

Inductor discharge time Tm,

When Tm Toff, inductor current is continuous, and this continuous inductor current is called continuous mode (CCM). When Tm=Toff, inductor current has just been released and this is called critical mode (BCM) between continuous and intermittent mode.

We look at entire circuit 1 and circuit 2, L1 choke and load are always there, and load output current is constant Io. The input current of inductor varied throughout cycle, but average current is same as output current, which is Io. And since inductor current increases linearly and then decreases linearly (the inductor does not saturate), we can judge whether inductor is operating continuously or intermittently by maximum current on inductor.

At maximum inductor current ILmax = 2Io, inductor current is critical. At maximum inductor current ILmax>2Io, inductor current works intermittently. row.

The following are continuous and intermittent inductor current waveforms.

It can be seen from above figure that if output current is used as a reference, when △I=2Io, set switching frequency fs, at that time it can be calculated according to U=L di/ dt, and output process is in following way.

When Q1 is on, voltage across inductor is U=Uin-Uo,

dt — conduction time, Tone,

Formula for calculating inductance

Assuming that input voltage is 12 V, output voltage is 5 V, output current is 2 A, and switching frequency is 100 kHz, it is necessary to calculate inductance L of inductor in lower critical mode.

Critical mode, then change in current on inductor △I=2 Io=4A

Ts=1/fs=1/100 kHz=10 µs

Because this is a critical mode, first input voltage range Uin_min-Uin_max, output voltage Uo, output current Io, when calculating inductance here, we need to know if we design minimum critical voltage of input voltage is greater than minimum voltage of entire inductance It is discontinuous.If we will design highest critical voltage, entire input range will be continuous under full load.

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