Engineering Alternative Calculation and Testing Methods for Inductance Value

1 Introduction

In the development of electronic ballasts, electronic energy-saving lamps, inductive ballasts and inductive energy-saving lamps, the calculation problem of ballast inductance and filter inductance values ​​is often encountered.

However, the calculation procedure for inductance value is rather complicated, and in the absence of necessary magnetic material parameter measuring instruments, it is difficult to calculate strictly according to the procedure. Of course, it would be easy if there is design simulation software.

2 Traditional Programming

For example: To design a 40W electronic ballast, the circuit requires an inductor of L=1.6mH. Try to calculate the size of the magnetic core, the number of winding turns, and the length of the magnetic circuit air gap.

First, calculate the core cross-sectional area and determine the core size.

Therefore, the core area product Ap can be calculated by formula (1):

Ap=(392L×Ip×D2)/ΔBm(1)

Where: Ap——Core area product cm4

L——Required inductance value H

Ip——Peak current A passing through the ballast coil

ΔBm——Pulse magnetic induction increment T

D——ballast coil wire diameter mm

According to the calculated value of the core area product Ap, select a standard core in the design manual or design the core size yourself. Here, ΔBm is generally taken as 1/2 to 2/3 of the saturation magnetic induction intensity, that is: ΔBm=（）Bs.

Bs is given in general magnetic material manuals and can be found. Therefore, generally speaking, it is not difficult to calculate the core size by formula (1). The difficulty lies in the dispersion of the parameters of the magnetic material itself. The parameters of the cores of the same furnace may vary greatly. The Bs-H curve and parameters given in the manual are statistical averages. Therefore, the size calculated based on formula (1) must be repeatedly tested and corrected in actual use.

After the core size is determined, the air gap is calculated (for EI cores, it is how thick the spacer is, and for toroidal cores, it is how wide the gap is) according to formula (2): lg=(2)

Where: lg——magnetic core air gap length cm

L——Required inductance value H

Ip——peak current A passing through the coil

ΔBm——Pulse magnetic induction increment T

Sp——core cross-sectional area cm2

Generally speaking, it is not too difficult to calculate the air gap size according to formula (2). The difficulty still lies in the ΔBm value, which is only the statistical average value of the manufacturer. For the same specification of magnetic core, different manufacturers are also different. Therefore, the lg calculated according to formula (2) is only an approximate value, which needs to be repeatedly corrected in practice, that is, trial and error.

Once the core size and air gap length are determined, we can determine how many turns are needed to achieve the required inductance value L.

According to L=4μ·N2×10－9×A(3), we can get N=(4)

Where: N is the required number of winding turns

A——Geometric parameters of the core

To calculate the number of turns according to formula (4), the key is to know the magnetic permeability μ. From the magnetic material manual provided by the manufacturer, the μ value is only a range. For example, the initial magnetic permeability of the R2K core is actually between 1800 and 2600, and the specific value depends on measurement. Generally, factories do not have instruments for measuring magnetic parameters, so it is difficult to calculate the number of turns according to formula (4). Especially under the condition of air gap, it is unknown how much the magnetic permeability decreases compared to the condition without air gap. Therefore, it is more difficult to calculate according to formula (4). Generally, μ is assumed first, and then the number of turns N is calculated. After the trial winding is completed, L is measured to see if it can reach the design value. It is usually difficult to achieve this, so another μ value is set and calculated again. This is repeated until the predetermined L value is approached.

The above is a general method for calculating the core size, air gap and number of winding turns based on the known inductance L.

If you only calculate one inductance value L when designing a ballast, it would be fine to use this trial and error calculation. However, now that we need to face the market, we need ballast inductors of various specifications. If we continue to use this trial and error calculation, it will not only delay the development of new products, but also waste a lot of trial materials. Of course, if there is inductance value calculation simulation software, it will be another matter.

3 Alternative Algorithms

According to the previously calculated core size and air gap length, first wind an inductor with No turns. The actual measured inductance value is Lo, so

Lo = 4μNo2 × 10－9 × A (5)

Divide equation (3) and equation (5) and rearrange them to get: N==No (6)

Where: L——required inductance value

No——The number of turns is known

Lo——Inductance value under known number of turns

In this way, for a magnetic core with the same parameters, the number of turns N can be calculated as long as the three parameters L, No, and Lo are known.

In actual production, we first wind No = 20 turns on the magnetic core (the toroidal core can be wound directly, and the EI type core can be wound on the skeleton), measure Lo on the inductance meter, and substitute this value into formula (6) to calculate the number of turns N that should be wound on the magnetic core. [page]

Determination of gap:

(1) Role of gap

Curve ① in FIG. 1 and FIG. 2 is the magnetization curve of the magnetic core and the curve of magnetic permeability μ and B when there is no gap, and curve ② in FIG. 1 and FIG. 2 is the corresponding curve when there is an air gap.

From the curves of Figures 1 and 2, it can be seen that after the same magnetic core is gapped, the slope of the B-H curve can be reduced, and the saturation point of the magnetic core can be shifted to the right, thereby increasing the ability of the magnetic core to resist DC magnetization. However, the addition of the air gap will reduce the magnetic permeability, so the air gap has an optimal value, that is, when the inductor coil passes the maximum peak current, the magnetic core will not enter saturation, and at the same time, the magnetic permeability will not drop too low, because from formula (3), it can be seen that if the required inductance is constant, if the magnetic permeability is reduced, the number of coil turns must be increased, which is a contradiction.

(2) Determine the optimal air gap

According to the maximum current peak value Ip passing through the ballast inductor, use a DC magnetizing power supply and connect it with an inductance tester. When the DC current reaches Ip, the inductance drops by no more than 10% of the zero current. It is considered that the core has reached the maximum Bm value, and the gap at this time is the optimal air gap length.

If the inductance drops by more than 10% when Ip is applied, it means that the gap is too small and can be increased appropriately. If the inductance does not drop at Ip, it means that the gap is too large and should be reduced appropriately. In this way, the optimal air gap length can be determined in just ten minutes by measuring and modifying, thus avoiding the trouble of repeated trial and error caused by the uncertainty of Bm value when calculating the air gap using formula (2).

Based on the above, we can conclude the three-step method for calculating the inductance value. That is, after the ballast inductance value L is determined according to the circuit requirements or the lamp electrical parameters, the following three steps can be followed:

① Use formula (1) to determine the core size;

② Use a DC magnetizing power supply and an inductance tester to determine the air gap;

③ Use formula (6) to calculate the required number of turns.

Of course, the ballast inductance value determined in this way must be installed in the circuit for experimental confirmation. Generally, a simple correction of the number of turns is sufficient to meet the design requirements. This alternative method of designing the ballast inductance bypasses the accurate understanding of the magnetic performance indicators of the magnetic material, such as μ and Bs, and can smoothly design the required inductance value.

4 Application Effects

(1) We have developed many series of energy-saving lamps

The ballast inductors used in the products are all designed according to the above three-step method, with good results.

(2) Using the alternative calculation method, the inductance value and core value of the known product are

Under the conditions of size and gap thickness, the number of turns of the winding is calculated in reverse.

When the number of turns of some inductor windings cannot be measured with a turn meter, we have to dismantle them one by one and count them. It is easier to dismantle the EI type core, but more difficult to dismantle the toroidal core, especially when the ring is small, the wire is thin, and the number of turns is large. Now, using a workaround, we can just wind 20 to 30 turns of wire on the original inductor, measure the new inductance value Lo, and substitute it into formula (6) to find out the actual number of turns of the inductor.

(3) Using the alternative calculation method to control the consistency of the toroidal core inductance

sex.

When winding the core and processing the gap, due to the problem of operation process, the gap thickness and shape will be inconsistent. In this way, if the winding is carried out according to a fixed number of turns, it is bound to cause a large difference in the inductance value of each ring. If you pay attention to the information from Wall Street, you will find that at the beginning of the new year, the major top investment banks generally lowered the expected economic growth rate indicators of the world and major countries and regions this year. Take the 2001 Global Economic Trends Report released by Merrill Lynch & Co. in December 2000 as an example; the global GDP growth forecast value dropped from 4.2% in 2000 to 3.1% in 2001, among which the United States had the largest decline, from 5.1% in 2000 to 3.3%, the European Union dropped from 3.5% to 2.8%; Japan dropped from 1.8% to 1.4%. A significant feature of the global economic slowdown will be the contraction of demand in major international markets, weakened consumption, and reduced trade volume. For Chinese enterprises that are about to join the WTO this year, especially export enterprises, if they want to achieve good results in the sluggish environment and win the first prize for their official debut in the world economy, adopting Internet-based electronic trading methods will be an indispensable solution.

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Figure 1 Magnetization curve of magnetic material

Figure 2 Relationship between magnetic permeability of magnetic materials and AC magnetic induction intensity

The error is not in accordance with the design requirements.

To solve this problem, it is generally better to wind a few more turns. When measuring the inductance value, the extra turns are removed (of course, removing a few turns is easier than adding a few turns).

When we started producing 250W sodium lamp ballasts, we were afraid that some of the inductances would not be enough after winding, so we would rather wind more than ten turns. As a result, when we tested the inductance one by one, we found that some inductances were basically close to the design value, while some had more than ten turns. We had to remove the extra turns one by one, wasting copper wire and labor time.

To this end, we have specially designed a tool. This tool can be used in conjunction with an LCR tester to directly measure the Lo of each core and affix a label to the core. The tool number is 30 turns. After measuring a batch, the number of turns that should be wound on the core with the same L value can be calculated using formula (6).

For a ballast of a certain power, L is known. For example, the ballast inductance of a 250W sodium lamp, L is generally around 190mH, then: This simplifies a more complex calculation problem and leaves it to the production line workers to operate.