For example, to design a 40W electronic ballast, the circuit needs inductance L =1.6mh. Try to calculate the size of the magnetic core, the number of windings and the air gap length of the magnetic circuit.
Firstly, calculate the cross-sectional area of the magnetic core and determine the size of the magnetic core.
Therefore, the product Ap of the core area can be calculated by the formula (1).
AP =(392 l×IP×D2)/δBm( 1)
Where: AP- magnetic core area product cm4
L- required inductance value h
Ip—— peak current a passing through the ballast coil.
δ δ BM-pulse magnetic induction increment t
D- diameter of ballast coil wire, mm
According to the calculated value of core area product Ap, select the standard core in the design manual or design the core size by yourself.
Here, δ BM is generally 1/2 ~ 2/3 of the saturated magnetic induction, that is, δ BM = (1/2 ~ 2/3) bs.
Bs is given in the handbook of general magnetic materials and can be found out. Therefore, generally speaking, it is not difficult to calculate the size of the magnetic core with the formula (1). What is difficult is the discreteness of the parameters of the magnetic material itself. The parameters of the same furnace core sometimes vary greatly. The BS-H curves and parameters given in the manual are statistical averages, so it is not difficult to calculate the size with formula (1).
After the size of the core is determined, the calculation of the air gap (how thick the gasket of the EI core is and how wide the air gap of the ring core is) is generally calculated according to Formula (2):
LG =(0.4πL I2 }/SpδB2m(2)
Where: LG- air gap length cm of magnetic core
L- required inductance value h
Ip-peak current a through the coil.
δ δ BM-pulse magnetic induction increment t
Sp—— Cross-sectional area of magnetic core cm2
Generally speaking, it is not too difficult to calculate the air gap size according to Formula (2). The difficulty still lies in the δ BM value, which is only the statistical average of manufacturers. Magnetic cores of the same specification are different from different manufacturers. Therefore, lg calculated according to formula (2) is only an approximate value, which needs to be revised repeatedly in practice, that is, try again.
When the size of the magnetic core is determined and the length of the air gap is also determined, it can be determined how many turns are needed to achieve the required inductance L.
According to l = 4 μ N2× 10-9× a (3)
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Where: n is the required number of winding turns.
A—— Geometric parameters of magnetic core.
The key to calculating the number of turns according to formula (4) is to know the magnetic permeability μ, which is only a range according to the magnetic material specification given by the manufacturer. For example, the initial permeability of R2K core is actually between 1800 ~ 2600, which is worth measuring. There is no instrument for measuring magnetic parameters in general factories, so it is difficult to calculate the number of turns according to formula (4). Especially in the case of air gap, it is unknown how much the permeability decreases compared with that without air gap. Therefore, it is difficult to calculate according to Formula (4). Generally assume μ, calculate the number of turns n, and measure whether L can reach the design value after winding. It is usually difficult to achieve, then set another μ value, recalculate, and try again and again until it approaches the predetermined L value.
The above is a general method to find the size of magnetic core, air gap and winding turns according to the known inductance L.
If the ballast is designed to calculate only one inductance value L, this trial and error calculation is unnecessary. Now facing the market, ballast inductors of various specifications are needed. If you try again, it will not only delay the development progress of new products, but also waste a lot of test data. Of course, if there is inductance calculation simulation software, it is another matter.
3 alternative algorithm
According to the magnetic core size and air gap length calculated above, firstly, an inductor with the number of turns of No is wound, and the measured inductance value is Lo, so there is
Lo=4μNo2× 10-9×A (5)
After sorting out Formula (3) and Formula (5) separately, we get:
Where: l is the required inductance value.
No-it's a known number of laps.
Lo- is the inductance value with known turns.
In this way, for a magnetic core with the same parameters, as long as the three parameters of L, No and Lo are known, the number of turns n can be obtained.
In actual production, we first wound the magnetic core (the annular magnetic core can be wound directly, and the EI-type magnetic core can be wound on the skeleton) with No=20 turns, measured the Lo on the inductance meter, and substituted this value into the formula (6), then we can find out the number of turns n that should be wound on the magnetic core.
Determination of clearance rate:
The role of (1) notch
Curve ① in figure 1 and figure 2 is the curve of magnetization and permeability μ, b of the magnetic core without air gap, and figure 1 and curve ② in figure 2 is the corresponding curve with air gap.
From the curves in Figure 1 and Figure 2, it can be seen that the slope of the B-H curve can be reduced and the saturation point of the core can be moved to the right after the air gap is opened in the same core, thus increasing the ability of the core to resist DC magnetization. However, after the air gap is added, the magnetic permeability decreases, so there is an optimal value in the air gap, that is, when the inductance coil passes through the maximum peak current, the magnetic core will not enter saturation, and the magnetic permeability will not decrease too low, because it is a contradiction from Formula (3) that the magnetic permeability decreases if the required inductance is constant.
(2) Determine the best air gap
According to the maximum current peak Ip of ballast inductor, DC magnetizing power supply is connected to the inductor tester, so that when DC current reaches Ip, the inductance drop does not exceed 65,438+00% of zero current, that is, the magnetic core has reached the highest Bm value, and the gap at this time is the optimal air gap length.
If the inductance decreases by more than 10% when Ip is turned on, it means that the gap becomes smaller and can be appropriately increased; If the inductance does not decrease when Ip is turned on, it means that the gap is large and the point should be reduced appropriately. In this way, the optimal air gap length can be determined in more than ten minutes when measuring, and the trouble of repeated trial and error caused by the uncertainty of Bm value when calculating the air gap with formula (2) is avoided.
According to the three-step method of inductance calculation, that is, after determining the ballast inductance value L according to the circuit requirements or the electrical parameters of lamps, it can be divided into the following three steps:
① Determine the size of the magnetic core with formula (1);
② Using DC magnetizing power supply and inductance tester to measure air gap;
③ Calculate the required number of turns by Formula (6).
Of course, the ballast inductance value determined in this way has to be put into the circuit for experimental confirmation. In general, the design requirements can be met only by modifying the number of turns. Using this alternative method to design ballast inductance bypasses the accurate understanding of magnetic properties such as μ and Bs, and the required inductance can be designed smoothly.
4 Application effect
(1) ballast inductors used in many series of energy-saving lamps developed by us are designed according to the above three-step method, and the effect is good.
(2) Using flexible calculation method, under the condition of known product inductance value, magnetic core size and air gap thickness, the number of winding turns is obtained in reverse.
When some inductance windings can't be measured by coil measuring instrument, they should be disassembled one by one, which is good for EI core. For the annular iron core, it is more difficult to disassemble, especially in the case of small ring, thin wire and many turns. Now, by using a flexible algorithm, we can find out the actual number of turns of the inductor as long as we try to wind it for 20 ~ 30 turns on the original inductor, and then measure the new winding inductance value Lo and substitute it into Equation (6).
(3) Flexible calculation method is adopted to control the consistency of the inductance of the annular iron core.
When winding the core and machining the gap, the thickness and shape of the gap will be inconsistent due to problems in the operation process. In this way, if the iron core is wound according to a fixed number of turns, the inductance value of each turn will be very different, which does not meet the design requirements.
In order to solve this problem, the method of winding more turns is generally adopted. When measuring the inductance value, the extra turns are removed (of course, it is easier to remove a few turns than to increase a few turns)
When we started to produce 250W sodium lamp ballast, we would rather wind it more than ten times, for fear that the inductance would not be enough. As a result, when we tested the inductors one by one, we found that some inductors were basically close to the design value, and some inductors were wound with more than ten turns, so we had to remove the extra turns one by one, wasting copper wires and working hours.
Therefore, we specially designed a fixture, which combined with LCR tester can directly measure the Lo of each core, and put a label on the core. The number of turns of the fixture is 30. After measuring a batch, use formula (6) to calculate the number of turns to be wound on the iron core with the same L value.
For a certain power ballast, l is known. For example, the ballast inductance of a 250W sodium lamp is generally about 190mH, then:
This simplifies a complicated calculation problem and leaves it to the production line workers to operate.
The formula is a graph, but it cannot be copied. The website is:
/jszl/zs/2009- 1 1- 19/ 1 1720 . html
I hope it helps you!