CN113889331B - Integrated inductor design method with high coupling coefficient and low inductance current ripple - Google Patents
Integrated inductor design method with high coupling coefficient and low inductance current ripple Download PDFInfo
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Abstract
The invention relates to an integrated inductor design method with high coupling coefficient and low inductance current ripple, which comprises the following steps: step S1: determining a magnetic circuit model according to the magnetic core structure, and deducing a mutual inductance expression between self inductance of the single-phase inductor and the two-phase inductor; s2, determining the sectional area of the winding post and the thickness of the magnetic yoke on the premise of ensuring that the integrated inductance winding post is unsaturated; s3, determining the sectional area of the non-winding post under the condition that the air gap of the non-winding post is as small as possible according to the relation between the equivalent steady-state inductance and the sectional area of the non-winding post; and S4, further adjusting the air gaps of the winding posts and the non-winding posts according to the equivalent steady-state inductance to obtain the final integrated inductance. The inductor designed by the invention has the characteristics of high coupling degree and small inductance current ripple.
Description
Technical Field
The invention belongs to the field of power electronic magnetic integration, and particularly relates to an integrated inductor design method with high coupling coefficient and low inductance current ripple.
Background
In a DC/DC converter, the weight and volume of the magnetic element is about 20% -30% of the converter, and the loss of the magnetic element is about 30% of the total loss of the converter. The magnetic element is an important component for transmitting and storing electric energy, and the quality of the magnetic element directly influences the volume, efficiency, EMI and other performances of the DC/DC converter. The magnetic element is a customized nonstandard device, is a complex of high-frequency electromagnetic fields, and is designed to be suitable for various factors to be comprehensively considered. The magnetic elements in the DC/DC converter are multiplied due to the progressive widespread use of multiple interleaved parallel circuits. In order to reduce the size and volume of the magnetic elements in the DC/DC converter and further improve the performance of the DC/DC converter, magnetic integration techniques are beginning to be favored. The magnetic integration technology refers to that a plurality of discrete magnetic pieces in the DC/DC converter are replaced by an integrated magnetic piece with a plurality of magnetic circuits, so that the volume of the converter can be effectively reduced, and the power density can be improved. With further research, it is found that the coupling inductance technology is utilized to form coupling between the discrete inductances of the multi-path staggered parallel converter, so that the volume and loss of the converter can be reduced, and the steady-state performance of the converter can be effectively improved.
Disclosure of Invention
Therefore, the invention aims to provide an integrated inductor design method with high coupling coefficient and low inductance current ripple, and the designed inductor has the characteristics of higher coupling degree and smaller inductance current ripple.
In order to achieve the above purpose, the invention adopts the following technical scheme:
an integrated inductance design method with high coupling coefficient and low inductance current ripple comprises the following steps:
step S1: determining a magnetic circuit model according to the magnetic core structure, and deducing a mutual inductance expression between self inductance of the single-phase inductor and the two-phase inductor;
s2, determining the sectional area of the winding post and the thickness of the magnetic yoke on the premise of ensuring that the integrated inductance winding post is unsaturated;
s3, determining the sectional area of the non-winding post under the condition that the air gap of the non-winding post is as small as possible according to the relation between the equivalent steady-state inductance and the sectional area of the non-winding post;
and S4, further adjusting the air gaps of the winding posts and the non-winding posts according to the equivalent steady-state inductance to obtain the final integrated inductance.
Further, the mutual inductance expression between the self inductance of the single-phase inductor and the two-phase inductor is specifically:
the mutual inductance M between the self inductance L of the single-phase inductance and the two-phase inductance is used as the spool magnetic resistance R 1 And non-winding post reluctance R 0 Representation of
Wherein mu 0 Is the magnetic permeability of air, le 0 、Le 1 The size of the non-winding post air gap and the winding post air gap are respectively, N is the number of turns of the inductance winding, S 0 、S 1 The cross-sectional area of the non-winding post and the cross-sectional area of the winding post air gap are respectively.
Further, the thickness of the magnetic yoke is designed as follows: according to the sectional area S of the winding post 1 The minimum cross-sectional area of the yoke is obtained, and the minimum thickness of the yoke is determined.
Further, the step S3 specifically includes:
self-inductance L of integrated inductor is at wrapping post magnetic resistance R 1 And non-winding post air gap Le 0 Cross-sectional area S of non-winding post under definite condition 0 The relation of (3) is as follows:
further deriving the reluctance R of the equivalent steady-state inductor on the winding post 1 And non-winding post air gap Le 0 Cross-sectional area S of non-winding post under definite condition 0 Relation of (2)
Further, the step S4 specifically includes:
step 41, opening the air gap of the non-winding post to the maximum, and firstly, opening the air gap of the winding post to obtain the initial self-inductance and mutual inductance value of the designed integrated inductor;
step S42, the inductance current ripple and inductance current direct current component I of each working mode dc Theoretically calculating a waveform of a whole period, and obtaining single-phase self-inductance L, mutual inductance M, time t and magnetic resistance R 0 、R 1 Is a function of (2);
step S43, non-winding post magnetic resistance R 0 And simulation to obtain initial self-inductance and mutual inductance values to be substituted into the magnetic density B of the middle winding post 1 And non-winding post magnetic density B 0 The expression of (2) is calculated, and the time t with the maximum magnetic density in one working cycle is determined, so that the maximum magnetic density B of each magnetic column can be obtained 1 、B 0 Regarding magnetic resistance R 1 Is a relationship of (2);
step S44, obtaining the design B under the condition of unsaturated winding post 1 The corresponding magnetic resistance R 1 With which the corresponding air gap Le is calculated 1 And using the calculated air gap Le of the winding post 1 Obtaining a new self-inductance value;
step S45, the self-inductance value and R obtained in the step S44 are processed 1 Substituted into non-winding post magnetic density B 0 And R is R 0 In the relation, the design B under the unsaturated condition of the non-winding post is obtained 0 The corresponding magnetic resistance R 0 With which the corresponding air gap Le is calculated 0 Is of a size of (2); with calculated non-winding post air gap Le 0 Obtaining a new self-inductance value, and substituting the new self-inductance value into B 0 And R is R 0 In the relation of (2);
step S46R in step S46 0 The reduction results in less flux cancellation of the winding leg and saturation of the winding leg, so the air gap Le obtained in step S45 1 The need to increase again; similar to step S45, the winding post air gap Le is increased 1 Substituting the obtained self-inductance value into theoretical calculation B 1 Until the winding post is unsaturated, and the design is completed.
Further, the step S42 specifically includes: the circuit has four working modes in one working period, and the inductance current ripple of each mode is as follows:
by inductor current ripple and inductor current direct current component I of each working mode dc Theoretically calculating the waveform of a whole period;
taking the unbalance degree of the two-phase current into consideration, obtaining the winding column magnetic flux phi according to the calculated current waveform 1 And non-winding post magnetic flux phi 2 Waveform:
winding post magnetic density B 1 And non-winding post magnetic density B 0 The calculation is as follows:
further, the step S43 specifically includes:
obtaining the magnetic density B of the winding post according to the step S42 1 Regarding magnetic resistance R 1 Due to the magnetic core material characteristics, find out the design B under the condition of unsaturated winding post 1 The corresponding magnetic resistance R 1 With which the corresponding air gap Le is calculated 1 Is of a size of (2);
with calculated air gap Le of winding post 1 Obtaining a new self-inductance value;
substituting new self-inductance value into B 1 And R is R 1 In the relation of (2), the magnetic density B of the winding post is calculated theoretically 1 Is of a size of (2);
because of errors in theoretical calculation and simulation, the air gap Le of the winding post needs to be continuously adjusted 1 Substituting the newly obtained self-inductance into B 1 And carrying out theoretical calculation on the expression until the winding post is unsaturated.
Further, the step S44 specifically includes:
on the basis of step S43, the non-winding post air gap Le is reduced 0 To reduce R by the size of (2) 0 ；
The self-inductance value and R obtained in the step S43 1 Substituted into non-winding post magnetic density B 0 And R is R 0 In the relation, the design B is designed under the condition of searching unsaturated non-winding posts on the relation diagram 0 The corresponding magnetic resistance R 0 With which the corresponding air gap Le is calculated 0 Is of a size of (2);
with calculated non-winding post air gap Le 0 Obtaining a new self-inductance value, and substituting the new self-inductance value into B 0 And R is R 0 In the relation of (2), calculate the magnetic density B of the non-winding post 0 Up to the size of the non-winding post unsaturation.
Compared with the prior art, the invention has the following beneficial effects:
1. the inductor designed by the invention has the characteristics of higher coupling degree and smaller inductance current ripple;
2. the invention can rapidly acquire the design scheme of the integrated inductor and effectively improve the production efficiency of devices.
Drawings
FIG. 1 is a schematic diagram of an integrated magnetic component of the present invention;
FIG. 2 is a schematic diagram of an integrated inductor structure according to the present invention;
FIG. 3 is a diagram of an integrated magnetic component equivalent magnetic circuit model in an embodiment of the invention;
FIG. 4 shows the self-inductance L and the cross-sectional area S of the non-winding post according to an embodiment of the invention 0 A relationship diagram;
FIG. 5 shows an equivalent steady-state inductance versus non-winding leg cross-sectional area S in an embodiment of the invention 0 A relationship diagram;
FIG. 6 shows the magnetic density B of the winding post according to an embodiment of the present invention 1 And magnetic resistance R 1 Is a schematic of the relationship;
FIG. 7 shows a magnetic density B of non-winding posts according to an embodiment of the invention 0 And magnetic resistance R 0 Is a schematic of the relationship;
in the figure, the winding is 1-winding post, 2-magnetic yoke, 3-non-winding post and 4-inductance winding.
Detailed Description
The invention will be further described with reference to the accompanying drawings and examples.
Referring to fig. 1, the present invention provides a design method of an integrated inductor with high coupling coefficient and low inductance current ripple, in this embodiment, the integrated inductor of a two-phase Buck circuit is taken as an example, and the method specifically includes the following steps:
step S1, obtaining a magnetic circuit model shown in a figure III according to a magnetic core structure, wherein the self inductance L of the single-phase inductor and the mutual inductance M between two-phase inductors can be used as a winding column magnetic resistance R 1 And non-winding post reluctance R 0 Representation (mu) 0 Is the permeability of air).
Cross-sectional area S of winding post for integrated magnetic component 1 Cross-sectional area S of non-winding post 0 And the thickness of the magnetic yoke is designed, since the magnetic core structure adopts ferrite, in order to ensure the magnetic density B of the winding post 1 Unsaturated, the cross-sectional area S of the winding post should be increased as much as the conditions permit 1 . To reduce the adverse effect of magnetic leakage due to open air gap, the non-winding post air gap Le is reduced as much as possible 0 Is of a size of (a) and (b).
Step S2, deriving self-inductance L of the integrated inductor and magnetic resistance R of the winding post 1 And non-winding post air gap Le 0 Cross-sectional area S of non-winding post under definite condition 0 Is to conclude that the self-inductance L follows the sectional area S of the non-winding post 0 As shown in fig. four:
step S3, deducing the magnetic resistance R of the equivalent steady-state inductance on the winding post 1 And non-winding post air gap Le 0 Cross-sectional area S of non-winding post under definite condition 0 As shown in FIG. five, the equivalent steady-state inductance is related to the non-winding post cross-sectional area S 0 Is increased by an increase in (a); the larger the equivalent steady-state inductance is, the smaller the ripple of the inductance current is, so the larger the equivalent steady-state inductance is, the better the non-winding post sectional area S is 0 The larger the condition allows, the better. In addition, S 0 The enlargement also makes the non-winding post less likely to saturate.
By combining the above reasoning, the sectional area S of the winding post 1 And a non-winding post cross-sectional area S 0 It should be as large as possible without increasing the occupation area and the height of the magnetic core.
Preferably, in the present embodiment, the design method of the yoke thickness includes: since the yoke is not saturated in the design process and the magnetic flux flowing through the yoke is basically consistent with the winding post, the sectional area S of the winding post can be determined 1 Obtaining the minimum sectional area of the magnetic yoke, and determining the minimum thickness of the magnetic yoke; meanwhile, the thickness of the magnetic yoke is increased, which means that the height of a magnetic core window is reduced, and the upper limit of the number of turns of the inductance winding which can be wound is also reduced.
After the winding leg cross-sectional area, the non-winding leg cross-sectional area, and the thickness of the yoke are determined, the respective dimensions of the core are determined.
Preliminarily determining the number of turns of the single-phase inductor according to the circuit parameters;
designed to obtain a larger coupling coefficientk, magnetic fluxes generated by two-phase windings of the integrated inductor are offset on the winding posts as much as possible. As can be seen from the expression of the coupling coefficient k, the reluctance R follows the non-winding post 0 The value of k will tend to be-1, at which time the degree of decoupling will be as maximum as possible.
In addition, the equivalent steady-state inductance and the non-winding post cross-sectional area S are derived 0 In relation to the non-winding post air gap Le 0 Under the condition of unchanged state, the equivalent steady-state inductance is along with S 0 Is increased by an increase in (a). Due to non-winding post reluctance R 0 Section S of non-winding post 0 Inversely proportional to the non-winding post air gap Le 0 Proportional, so when S 0 After the determination, the equivalent steady-state inductance is along with the air gap Le of the non-winding post 0 And magnetic resistance R 0 Is decreased by an increase in (c).
To sum up, non-winding post magnetic resistance R 0 The integrated inductor is designed to be a proper value, so that the coupling coefficient is higher while the integrated inductor has a larger equivalent steady-state inductance.
And S4, adjusting the air gaps of the winding posts and the non-winding posts to enable the integrated inductor to have the equivalent steady-state inductance as large as possible on the premise that the magnetic posts are unsaturated.
Step S41, firstly, the air gap of the non-winding post is opened to the maximum (i.e. the non-winding post is all air, at this time R 0 Maximum), the winding post is not opened with an air gap, and initial self inductance and mutual inductance values of the designed integrated inductor are obtained.
The circuit has four working modes in one working period, and the inductance current ripple of each mode is as follows:
inductor current ripple and inductor current direct current component I of each working mode dc The waveform for one entire period is theoretically calculated (as shown below). Due to the designed circuit parameters D, T s 、V H The inductor current is known as a function of the single-phase self-inductance L, the mutual inductance M and the time t.
If the unbalance degree of 5% of the two-phase current is considered, the winding column magnetic flux phi can be obtained according to the calculated current waveform 1 And non-winding post magnetic flux phi 2 Waveform:
winding post magnetic density B 1 And non-winding post magnetic density B 0 The calculation is as follows:
due to the designed circuit parameters D, T s 、V H Known cross-sectional area S 0 、S 1 It has been determined that the above equations are all related to single-phase self-inductance L, mutual inductance M, time t, magnetic resistance R 0 、R 1 Is a function of (2).
Step S42R in step S41 may be performed in order to unsaturated the winding post and the non-winding post 0 Is simulated to obtain initial self inductance and mutual inductance value to be substituted into B 1 、B 0 The expression of (2) is calculated, and the time t with the maximum magnetic density in one working cycle is determined, so that the maximum magnetic density B of each magnetic column can be obtained 1 、B 0 Regarding magnetic resistance R 1 Is a relationship of (3).
Step S43, obtaining the magnetic density B of the winding post from the step S42 1 Regarding magnetic resistance R 1 As shown in FIG. six, since ferrite is used as the core material, the design B under the condition of unsaturated winding post can be found 1 The corresponding magnetic resistance R 1 With which the corresponding air gap Le is calculated 1 Is of a size of (a) and (b).
With calculated air gap Le of winding post 1 Obtaining a new self-inductance value. Substituting new self-inductance value into B 1 And R is R 1 In the relation of (2), the magnetic density B of the winding post is calculated theoretically 1 Is of a size of (a) and (b). Because of errors in theoretical calculation and simulation, the air gap Le of the winding post needs to be continuously adjusted 1 Substituting the newly obtained self-inductance into B 1 And carrying out theoretical calculation on the expression until the winding post is unsaturated.
Step S44, deriving from step S3, reluctance R at winding post 1 And non-winding post air gap Le 0 Under the definite condition, the equivalent steady-state inductance is along with the sectional area S of the non-winding post 0 Is increased by an increase in (a). Due to non-winding post reluctance R 0 And cross-sectional area S 0 Inversely proportional, the equivalent steady-state inductance is inversely proportional to the non-winding post reluctance R 0 Is decreased by an increase in (c).
To obtain larger etcThe effective steady-state inductance is obtained by reducing the air gap Le of the non-winding post based on step S43 0 To reduce R by the size of (2) 0 . The self-inductance value and R obtained in the step S43 1 Substituted into non-winding post magnetic density B 0 And R is R 0 In the relation, B is designed under the condition of searching unsaturated non-winding posts on the relation diagram (shown in the seventh view) 0 The corresponding magnetic resistance R 0 With which the corresponding air gap Le is calculated 0 Is of a size of (a) and (b). With calculated non-winding post air gap Le 0 Obtaining a new self-inductance value, and substituting the new self-inductance value into B 0 And R is R 0 In the relation of (2), the magnetic density B of the non-winding post is calculated theoretically 0 The size of the winding rod is up to the unsaturation of the non-winding rod.
Step S45R in step S44 0 The reduction results in less cancellation of the bobbin magnetic flux, and the bobbin becomes saturated, so the air gap Le obtained by step S43 1 Which needs to be increased again. Similar to step S43, the spool air gap Le is increased 1 Substituting the obtained self-inductance value into theoretical calculation B 1 Until the winding post is unsaturated, and the design is completed.
The foregoing description is only of the preferred embodiments of the invention, and all changes and modifications that come within the meaning and range of equivalency of the claims are therefore intended to be embraced therein.
Claims (4)
1. The integrated inductor design method with high coupling coefficient and low inductance current ripple is characterized by comprising the following steps:
step S1: determining a magnetic circuit model according to the magnetic core structure, and deducing a mutual inductance expression between self inductance of the single-phase inductor and the two-phase inductor;
s2, determining the sectional area of the winding post and the thickness of the magnetic yoke on the premise of ensuring that the integrated inductance winding post is unsaturated;
s3, determining the sectional area of the non-winding post under the condition that the air gap of the non-winding post is as small as possible according to the relation between the equivalent steady-state inductance and the sectional area of the non-winding post;
step S4, according to the equivalent steady-state inductance, further adjusting the air gap between the winding post and the non-winding post to obtain a final integrated inductance;
the step S4 specifically includes:
step 41, opening the air gap of the non-winding post to the maximum, and firstly, opening the air gap of the winding post to obtain the initial self-inductance and mutual inductance value of the designed integrated inductor;
step S42, the inductance current ripple and inductance current direct current component I of each working mode dc Theoretically calculating a waveform of a whole period, and obtaining single-phase self-inductance L, mutual inductance M, time t and non-winding column magnetic resistance R 0 Reluctance R of winding post 1 Is a function of (2);
step S43, non-winding post magnetic resistance R 0 And simulation to obtain initial self-inductance and mutual inductance values to be substituted into the magnetic density B of the middle winding post 1 And non-winding post magnetic density B 0 The expression of (2) is calculated, and the time t with the maximum magnetic density in one working cycle is determined, so that the maximum magnetic density B of each magnetic column can be obtained 1 、B 0 Regarding spool reluctance R 1 Is a relationship of (2);
step S44, obtaining the design B under the condition of unsaturated winding post 1 The corresponding value of the spool magnetic resistance R 1 The corresponding air gap Le is calculated by the magnetic resistance R1 of the winding post 1 And using the calculated air gap Le of the winding post 1 Obtaining a new self-inductance value;
step S45, the self-inductance value and R obtained in the step S44 are processed 1 Substituted into non-winding post magnetic density B 0 Non-winding post reluctance R 0 In the relation, the design B under the unsaturated condition of the non-winding post is obtained 0 Corresponding value of non-winding post magnetic resistance R 0 The corresponding air gap Le is calculated by the magnetic resistance R1 of the winding post 0 Is of a size of (2); with calculated non-winding post air gap Le 0 Obtaining a new self-inductance value, and substituting the new self-inductance value into B 0 Non-winding post reluctance R 0 In the relation of (2);
step S46, non-winding post reluctance R in step S46 0 The reduction results in less flux cancellation of the winding leg and saturation of the winding leg, so the air gap Le obtained in step S45 1 The need to increase again; increasing the air gap Le of the winding post 1 Will obtainSubstituting self-inductance value into theoretical calculation B 1 Until the winding post is unsaturated, and the design is finished;
the step S42 specifically includes: the circuit has four working modes in one working period, and the inductance current ripple of each mode is as follows:
by inductor current ripple and inductor current direct current component I of each working mode dc Theoretically calculating the waveform of a whole period;
taking the unbalance degree of the two-phase current into consideration, obtaining the winding column magnetic flux phi according to the calculated current waveform 1 And non-winding post magnetic flux phi 2 Waveform:
winding post magnetic density B 1 And non-winding post magnetic density B 0 The calculation is as follows:
the step S43 specifically includes:
obtaining the magnetic density B of the winding post according to the step S42 1 Regarding magnetic resistance R 1 Due to the magnetic core material characteristics, find out the design B under the condition of unsaturated winding post 1 The corresponding magnetic resistance R 1 With the magnetic resistance R 1 Calculating the corresponding air gap Le 1 Is of a size of (2);
with calculated air gap Le of winding post 1 Obtaining a new self-inductance value;
substituting new self-inductance value into B 1 And R is R 1 In the relation of (2), the magnetic density B of the winding post is calculated theoretically 1 Is of a size of (2);
because of errors in theoretical calculation and simulation, the air gap Le of the winding post needs to be continuously adjusted 1 Substituting the newly obtained self-inductance into B 1 Carrying out theoretical calculation on the expression until the winding post is unsaturated;
the step S44 specifically includes:
on the basis of step S43, the non-winding post air gap Le is reduced 0 To reduce R by the size of (2) 0 ；
The self-inductance value and R obtained in the step S43 1 Substituted into non-winding post magnetic density B 0 And R is R 0 In the relation, the relation diagram is searched under the condition of unsaturated non-winding postsDesign B 0 The corresponding magnetic resistance R 0 The corresponding air gap Le is calculated by the magnetic resistance R1 of the winding post 0 Is of a size of (2);
with calculated non-winding post air gap Le 0 Obtaining a new self-inductance value, and substituting the new self-inductance value into B 0 And R is R 0 In the relation of (2), calculate the magnetic density B of the non-winding post 0 Up to the size of the non-winding post unsaturation.
2. The method for designing the integrated inductor with high coupling coefficient and low inductance current ripple according to claim 1, wherein the mutual inductance expression between the self inductance of the single-phase inductor and the two-phase inductor is specifically as follows:
the mutual inductance M between the self inductance L of the single-phase inductance and the two-phase inductance is used as the spool magnetic resistance R 1 And non-winding post reluctance R 0 Representation of
Wherein mu 0 Is the magnetic permeability of air, le 0 、Le 1 The size of the non-winding post air gap and the winding post air gap are respectively, N is the number of turns of the inductance winding, S 0 、S 1 The cross-sectional area of the non-winding post and the cross-sectional area of the winding post air gap are respectively.
3. The method for designing the integrated inductor with high coupling coefficient and low inductance current ripple according to claim 1, wherein the thickness of the magnetic yoke is designed as follows: according to the sectional area S of the winding post 1 The minimum cross-sectional area of the yoke is obtained, and the minimum thickness of the yoke is determined.
4. The method for designing the integrated inductor with high coupling coefficient and low inductance current ripple according to claim 1, wherein the step S3 is specifically:
self-inductance L of integrated inductor is at wrapping post magnetic resistance R 1 And non-winding post air gap Le 0 Cross-sectional area S of non-winding post under definite condition 0 The relation of (3) is as follows:
further deriving the reluctance R of the equivalent steady-state inductor on the winding post 1 And non-winding post air gap Le 0 Cross-sectional area S of non-winding post under definite condition 0 Relation of (2)
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| US11094455B2 (en) * | 2018-12-27 | 2021-08-17 | Texas Instruments Incorporated | Module with reversely coupled inductors and magnetic molded compound (MMC) |
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