How to Calculate Inductance of a Transformer in One Article

[Introduction] For example, Zhang San, a novice engineer with little understanding of power supply pulse transformer design, asked Li Xi and Wang Wu for advice. Give Zhang San a set of calculation formulas. Zhang San then enthusiastically calculated from formulas given by two people. After calculations, he found that inductance values ​​calculated from two formulas were completely different, and there were many differences. Is this a Li Xi pair or a Wang Wu pair?

I've been designing switching power supplies for a few years now, and there are a lot of newbies who come into contact with switching power supplies. there is aforementioned problem of different sensitivity in transformer calculation. I can say this, since you are a power engineer who has this question, then you are a beginner and you have not mastered transformer design method. In fact, it is normal that inductance calculated by two engineers is different, I can even say that if same project is given to two different and experienced engineers to calculate a transformer, inductance calculated by two engineers should be different. Same.

Why? There are many reasons for this. Let's take reverse as an example. There are no absolutely right or wrong calculations of transformer inductance. As long as your transformer is running at its lowest input voltage and maximum output power, transformer core does not saturate and temperatures can be passed. , it cannot be said that his method of calculation is wrong.

For seasoned engineers who have calculated transformers for so many years, why do they have to recalculate every new design? Why not just use an equivalent power transformer directly? In fact, it is necessary to theoretically ensure non-saturation of magnetic circuit (of course, there are other points that need to be guaranteed, but it is enough for beginners to understand this, please be patient with veterans).

Let me take a set of calculation methods to explain inductance calculation! Let's take DCM backswing calculation as an example. First, according to law of conservation of energy, we can get:

Among them, Lp is primary side inductance of transformer, Ip is peak current of primary side inductance, P is input power of switching power supply, and T is switching period of switching power supply.

Then by definition, if a constant voltage is applied to inductor, current through inductor increases linearly with time, which can be obtained:

When calculating flyback DCM, if we ensure that DCM operates at minimum input and maximum output power, we can ensure that entire input voltage range and entire power range are in DCM.

Let's look at formula 1. Formula 1 is only valid for DCM and BCM (critical) because in continuous mode, initial current energy must be subtracted to get P*T value. See picture below. .

Then let's look at formula 2, formula 2 is only valid in DCM, naturally BCM is also valid), in CCM mode, Ip should be changed to △Ip, (CCM only contains this formula, where △Ip = Ip-I1).

Since two formulas are only valid in DCM, of course BCM is also valid, so if two formulas are solved, resulting inductance can ensure that transformer is in entire input voltage range and in entire output power range. DCM. To solve a system of equations from two formulas, there must be less than two unknowns.

Let's look at parameters in formulas 1 and 2:

In Formula 1, Lp and Ip are unknown, P is known power, and T is a fixed switching period (T=1/f).

In formula 2, Ip and Ip are unknown, Vin is known (calculated at lowest input voltage as above), and D can be set. We usually calculate duty cycle at lowest input voltage and maximum power. For example. , here you can use 0.45, if above Vin is higher than minimum input voltage, then you need to make it less than D. If you are interested, you can calculate it yourself, f is fixed.

Two formulas in a system of equations have only two unknowns, so they can definitely be solved. Formula 1 and formula 2 can be solved by solving equations:

Now we can calculate inductance. Next, we get the balance of volt-seconds:

It's worth noting that Formula 4 is only valid in CCM or BCM (BCM is a critical condition and is also currently valid), and it's not valid in DCM. See description in picture below. :

Formula 3 is installed in BCM and DCM and Formula 4 is installed in BCM and CCM.

If we combine formula 3 and formula 4 to solve a system of equations, we take intersection of establishment conditions of two formulas, and intersection of establishment conditions is BCM criticality. That is, parameters of transformer after solving equations are at minimum input voltage Vin of full load, because formula 3 is calculated at minimum input and full load, and transformer is just in BCM state.

Currently, we can calculate Vor (reflected voltage) by combining formula 3 and formula 4.

Everyone knows that after calculating reflected voltage, you can calculate number of turns. This time we only need to calculate number of turns, and basic parameters of transformer are almost same. The calculation of number of turns is to ensure that transformer does not saturate.

At this stage, you can calculate number of turns. Now let's look at four formulas:

Using a specific Vin, minimum input voltage we used above, and then using these four formulas to calculate transformer, meaning transformer is in critical condition when Vin is input. Then in actual full load test, when input voltage is adjusted to be above this Vin (Vin used in calculations), transformer should go into discontinuous state, and when input voltage is adjusted to be below this Vin (Vin is used in calculations). calculations), then transformer will necessarily go into a continuous state. This is a transformer method for calculating critical point.

Then, if we deliberately overestimate Vin for calculation, for example, if we use Vin=176 for calculation, and now we use Vin=264 for calculation, then calculated inductance at this point in time should be higher than initial Inductance, of course with increased Vin D must be reduced. This should be taken into account. If you are interested, you can calculate by yourself. At this time, as long as transformer does not saturate over entire range, calculated inductance is also correct, and different. Moreover, critical point has been raised.

So size of inductor is only height of critical point of reaction, this is not right or wrong, you can set critical point to 85V so whole range is discontinuous, of course if you want it to be more discontinuous you can keep setting Vin lower one point, you can also set critical point to 264V, whole range is continuous, of course, if you want to be more continuous, you can keep setting Vin a little higher, or you can set critical point to 220V (above 220 is intermittent, below 220 continuously) it is up to you until it is saturated your transformer is good.

Remember: inductance basically reflects level of critical point, higher critical point, more continuous transformer, and lower critical point, more intermittent transformer.

Although until transformer saturates, it doesn't, but you have to evaluate how it fits better. For example, when power is small, it is generally more suitable for discontinuous operation: power is small, switching loss is main loss, and conduction loss is second. As for loss, small discontinuous loss can reduce switching loss when power is relatively large, generally , it is more appropriate to be continuous: power is high, switching loss constitutes secondary loss, and conduction loss constitutes main loss, and continuous point can reduce conduction loss.

I hope all aspiring engineers will be inspired after reading this article. Do not immediately ask why inductance is small according to Li Xi's calculation, but inductance is high according to Wang Wu's calculation. who is right and who is to blame. Just your understanding is not enough.