CN115347781A - Design method of intrinsically safe single-inductor multi-output switch converter - Google Patents

Design method of intrinsically safe single-inductor multi-output switch converter Download PDF

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CN115347781A
CN115347781A CN202211060764.0A CN202211060764A CN115347781A CN 115347781 A CN115347781 A CN 115347781A CN 202211060764 A CN202211060764 A CN 202211060764A CN 115347781 A CN115347781 A CN 115347781A
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converter
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CN115347781B (en
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皇金锋
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Pingyuan Power Supply Co Of State Grid Shandong Electric Power Co
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Shaanxi University of Technology
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    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02M—APPARATUS FOR CONVERSION BETWEEN AC AND AC, BETWEEN AC AND DC, OR BETWEEN DC AND DC, AND FOR USE WITH MAINS OR SIMILAR POWER SUPPLY SYSTEMS; CONVERSION OF DC OR AC INPUT POWER INTO SURGE OUTPUT POWER; CONTROL OR REGULATION THEREOF
    • H02M1/00—Details of apparatus for conversion
    • H02M1/0083—Converters characterised by their input or output configuration
    • H02M1/009—Converters characterised by their input or output configuration having two or more independently controlled outputs
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02M—APPARATUS FOR CONVERSION BETWEEN AC AND AC, BETWEEN AC AND DC, OR BETWEEN DC AND DC, AND FOR USE WITH MAINS OR SIMILAR POWER SUPPLY SYSTEMS; CONVERSION OF DC OR AC INPUT POWER INTO SURGE OUTPUT POWER; CONTROL OR REGULATION THEREOF
    • H02M3/00—Conversion of dc power input into dc power output
    • H02M3/02—Conversion of dc power input into dc power output without intermediate conversion into ac
    • H02M3/04—Conversion of dc power input into dc power output without intermediate conversion into ac by static converters
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02M—APPARATUS FOR CONVERSION BETWEEN AC AND AC, BETWEEN AC AND DC, OR BETWEEN DC AND DC, AND FOR USE WITH MAINS OR SIMILAR POWER SUPPLY SYSTEMS; CONVERSION OF DC OR AC INPUT POWER INTO SURGE OUTPUT POWER; CONTROL OR REGULATION THEREOF
    • H02M3/00—Conversion of dc power input into dc power output
    • H02M3/02—Conversion of dc power input into dc power output without intermediate conversion into ac
    • H02M3/04—Conversion of dc power input into dc power output without intermediate conversion into ac by static converters
    • H02M3/10—Conversion of dc power input into dc power output without intermediate conversion into ac by static converters using discharge tubes with control electrode or semiconductor devices with control electrode
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02B—CLIMATE CHANGE MITIGATION TECHNOLOGIES RELATED TO BUILDINGS, e.g. HOUSING, HOUSE APPLIANCES OR RELATED END-USER APPLICATIONS
    • Y02B70/00—Technologies for an efficient end-user side electric power management and consumption
    • Y02B70/10—Technologies improving the efficiency by using switched-mode power supplies [SMPS], i.e. efficient power electronics conversion e.g. power factor correction or reduction of losses in power supplies or efficient standby modes

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Abstract

The invention discloses a design method of an intrinsically safe single-inductor multi-output switching converter, which comprises the following steps: step 1: determining basic characteristics of the SIDO Buck converter; step 2: analyzing output short-circuit energy of the SIDO Buck converter, and determining an output intrinsic safety criterion of the converter; and 3, step 3: designing an intrinsic safety inductor of the SIDOBuck converter; and 4, step 4: an intrinsically safe capacitive design for the SIDO Buck converter. The SIDO Buck converter designed by the invention is suitable for dangerous environments such as mines and the like, can provide theoretical guidance for the research of intrinsically safe SIDO Buck converters, and can also provide ideas for the research of other intrinsically safe SIMO DC-DC converters.

Description

Design method of intrinsically safe single-inductor multi-output switch converter
Technical Field
The invention belongs to the technical field of converters, and particularly relates to a design method of an intrinsically safe single-inductor multi-output switch converter.
Background
Nowadays, the coal mine industry pays more and more attention to production safety, the underground environment is very complex and is often accompanied by inflammable and explosive gases such as gas and the like, so that various electronic equipment is needed to monitor underground conditions in real time, the power supply of the electronic equipment needs to meet the explosion-proof requirement, the intrinsic safety is the best explosion-proof form at present, and therefore, the research on the intrinsically safe power supply applicable to the underground has important significance.
The linear power supply has the advantages of stability and low noise, most of the current intrinsically safe power supplies adopt the form, but the linear power supply is large in volume and high in cost, in recent years, more and more experts and scholars are dedicated to researching explosion-proof intrinsically safe switching power supplies applied underground, the switching power supply has the advantages of wide input, wide output, small volume, low cost and the like, the research on an intrinsically safe switching converter is the basis of researching the intrinsically safe switching power supply, in recent years, researchers in the field of intrinsically safe switching converters, particularly the research on a Single-output intrinsically safe switching converter has more achievements, but because the output form of the traditional Single-output switching converter is Single, the practical application of the traditional Single-output switching converter is greatly limited, a Single-Inductor Multiple-output (Single-Inductor Multiple-output) converter only needs one Inductor to realize Multiple outputs in recent years, the Single-Inductor Multiple-output converter has wide attention, as shown in figure 1, if the Single-Inductor Multiple-output intrinsically safe switching power supply can be applied to the intrinsically safe power supply, the Single-Inductor Multiple-output converter not only has the advantage compared with the realization of Multiple outputs, and the Single-Inductor Multiple-output energy-output converter can release the maximum energy storage limit when the energy is released. Due to the existence of the branch switching tube, if a short circuit occurs in the output of a certain branch of the converter, the system can turn off the switching tube of the branch in time without affecting the normal work of other branches, and the short circuit releases energy which is only the energy released by a single capacitor. Even in the worst case (all outputs are short-circuited at the same time), the short-circuit release energy is only the sum of the energy released by all capacitors and the energy released by one inductor, which is much smaller than the energy released by the parallel converters due to the short-circuit at the same time, so that the single-inductor multi-output converter is easier to effectively realize explosion prevention.
Disclosure of Invention
The invention aims to provide a design method of an intrinsically safe single-inductor multi-output switch converter, and the designed SIDO Buck converter can be used for meeting the explosion-proof requirement of an intrinsically safe power supply source under a mine.
The invention adopts the technical scheme that a design method of an intrinsically safe single-inductor multi-output switching converter is implemented according to the following steps:
step 1: determining basic characteristics of the SIDO Buck converter;
step 1.1: calculating the output voltage of the SIDO Buck converter;
step 1.2: calculating the output ripple voltage of the SIDO Buck converter;
step 1.3: determining the working area of the SIDO Buck converter;
step 2: analyzing the output short-circuit energy of the SIDO Buck converter and determining the output intrinsic safety criterion of the converter;
and 3, step 3: designing an intrinsic safety inductor of the SIDO Buck converter;
and 4, step 4: an intrinsically safe capacitive design for the SIDO Buck converter.
The present invention is also characterized in that,
the step 1.1 specifically comprises the following steps:
the SIDO Buck converter comprises a switching tube S i 、S a 、S b Diode VD, inductor L, capacitor C a 、C b And a load resistor R a 、R b ，D i 、D a 、D b Is a switch tube S i 、S a 、S b And satisfies: d i <D b ，D a +D b ＝1；
When the converter works in a continuous conduction mode CCM, the load resistance R in the converter is obtained according to a time-averaged equivalent circuit method a 、R b The output voltages of the two branches are respectively as follows:
Figure BDA0003825702320000031
in the formula (1), V i Representing the converter input voltage; v oa Represents the output voltage of branch a; v ob Representing the branch b output voltage.
The step 1.2 specifically comprises the following steps:
peak inductor current I when SIDO Buck converter is operated in CCM LP Turning over the inductive current I LT Valley inductive current I LV The calculation is as follows:
Figure BDA0003825702320000032
in the formula (2), I o Means for indicating flatnessAll induce current, an
Figure BDA0003825702320000033
T represents a switching period;
when the converter is operating in the critical state of CCM and DCM, I LV At a certain moment exactly zero, and D is eliminated by formula (1) i Critical inductance L can be obtained C Comprises the following steps:
Figure BDA0003825702320000034
therefore, when L is>L C When the converter is in CCM; when L is<L C When the converter is operating in DCM.
Critical inductance L C Are respectively to R a And R b The partial derivatives are obtained:
Figure BDA0003825702320000041
therefore, if the critical load R of the converter is C >R min ，R aC >R amin ，R bC >R bmin ，R min 、R aC 、R amin 、R bmin Respectively representing minimum load, critical load of branch a, minimum load of branch a and minimum load of branch b, when the load of the converter takes R a,min 、R b,min When the converter is in CCM;
load resistor R when SIDO Buck converter works in CCM a 、R b The output ripple voltage of the two branches is respectively as follows:
Figure BDA0003825702320000042
in the formula (5), f represents a switching frequency;
thus, a converter load resistance R is obtained a 、R b The maximum output voltage is:
Figure BDA0003825702320000043
the step 1.3 is specifically as follows:
let the input voltage range of the SIDO Buck converter be V i,min ～V i,max The load ranges of the two branches are respectively: r is a,min ～R a,max And R b,min ～R b,max With V i 、R a 、R b Establishing O-V for coordinate axes i R a R b The working area of the SIDO Buck converter in the space rectangular coordinate system is a cube, and the vertex and the coordinate of the cube are respectively A (R) b,min ，R a,max ，V i,min )、B(R b,max ，R a,max ，V i,min )、C(R b,max ，R a,min ，V i,min )、D(R b,min ，R a,min ，V i,min )、E(R b,min ，R a,max ，V i,max )、F(R b,max ，R a,max ，V i,max )、G(R b,max ，R a,min ，V i,max )、H(R b,min ，R a,min ，V i,max ) Different L can be drawn according to the formulas (3) and (4) C Curve, critical inductance L corresponding to points D and F CD 、L CF Respectively as follows:
Figure BDA0003825702320000044
Figure BDA0003825702320000051
when inductance L = L CD In time, the converter operates in DCM in the full dynamic range; when inductance L = L CF The converter operates in CCM over its full dynamic range.
The step 2 specifically comprises the following steps:
step 2.1: peak inductor current analysis for a converter
From formula (1) to obtain D i And substituting the peak value of the peak inductance current I of the SIDO Buck converter into the formula (2) to obtain the CCM LP Comprises the following steps:
Figure BDA0003825702320000052
in the formula (9), the reaction mixture is,
Figure BDA0003825702320000053
Figure BDA0003825702320000054
will I LP Are respectively paired with V i 、R a And R b Obtaining a partial derivative:
Figure BDA0003825702320000055
in order to meet the requirements of both output ripple voltage and intrinsically safe output, the inductor is designed to be L CD <L<L CF In this range, when the converter operates partially in CCM and partially in DCM, the peak inductor current of the converter takes a maximum value when the input voltage is maximum and the load resistance is minimum, as can be seen from equation (10), and therefore the maximum value of the peak inductor current of the SIDO Buck converter is the following value in the entire operating region:
Figure BDA0003825702320000056
step 2.2: output short circuit energy analysis of converter
Assuming the circuit is faulty, the load resistance R a 、R b One branch of the two branches is short-circuited, the other branch of the two branches works normally, the circuit turns off a switching tube of the fault branch in time, the connection between the fault branch and the circuit is cut off, and a short-circuit discharge model of the converterFor single capacitor discharge, the maximum short-circuit energy released by the converter at this time is:
Figure BDA0003825702320000061
in this case, the short-circuit energy released by the converter is only the energy released by the fault branch capacitor;
assuming the circuit is faulty, the load resistance R a 、R b When two branches are short-circuited simultaneously, the short-circuit discharge model of the converter is single-inductor double-capacitor discharge if the main switch tube S i And timely turning off, and cutting off the connection with the power supply, wherein the sum of short-circuit energy released by the inductor and the capacitor is as follows:
Figure BDA0003825702320000062
therefore, the maximum short-circuit energy released by the short-circuit of the converter output is as follows:
W max ＝W max2 (14)
substituting equation (6) and equation (11) into equation (13) yields the maximum output short-circuit energy of the converter:
Figure BDA0003825702320000063
in the formula (15), the reaction mixture is,
Figure BDA0003825702320000064
in general, the high-frequency output ripple voltage of the switching power supply is small, so equation (15) is approximated as:
Figure BDA0003825702320000065
when V is expressed by the formulas (11) and (16) i ＝V i,max ，R a ＝R a,min ，R b ＝R b,min When the current is measured, the output short-circuit energy of the converter is the maximum, and the output short-circuit energy is increased along with the increase of values of the inductor and the capacitor;
step 2.3: determining an intrinsically safe criterion for the output of a converter
The output of the SIDO Buck converter can be equivalent to a capacitive circuit, so when the output voltages of the converter are V respectively oa 、V ob The corresponding filter capacitors are respectively C aB 、C bB The minimum energy for the circuit to ignite the gas is:
Figure BDA0003825702320000071
if the maximum output short-circuit energy of the converter in the full dynamic working range is less than W B Then the converter is intrinsically safe, so the criterion for determining the intrinsic safety of the converter output is:
W max ＜W B (18)
since the transmission energy of the circuit in DCM is smaller than that in CCM, if the converter in CCM meets the intrinsic safety requirement, the DCM must also meet the intrinsic safety requirement.
The step 3 specifically comprises the following steps:
when R is a ＝R a,min ，R b ＝R b,min In order to maximize the peak inductor current, the input voltage must be V i ＝V i,max The minimum inductance to meet intrinsic safety conditions is therefore:
Figure BDA0003825702320000072
the maximum inductance is determined by intrinsic safety conditions when the capacitance C a And C b After selection, the value of the inductance must meet the requirements of intrinsic safety:
Figure BDA0003825702320000073
therefore, the inductance L of the formula (20) is satisfied max Is the maximum inductance that meets the intrinsic safety conditions,
to sum up, the value range of the inductance L of the intrinsically safe SIDO Buck converter is as follows:
L∈[L min ，L max ] (21)。
the step 4 specifically comprises the following steps:
from the equation (5), the capacitor C satisfying the ripple voltage output from the converter a 、C b The minimum capacitance values are respectively:
Figure BDA0003825702320000074
considering the influence of circuit parasitic parameters on the output ripple voltage of the converter, when the capacitance is actually selected, a margin lambda is required, lambda = 1-2, so that the capacitance C a 、C b Minimum value C of actually selected capacitance min Respectively as follows:
Figure BDA0003825702320000081
when the output of the converter is short-circuited, that is, two branches are short-circuited at the same time, it is assumed that the maximum energy released by the converter is exactly equal to the ignition energy, that is, in a critical ignition state, so that:
W max ＝W B (24)
namely:
Figure BDA0003825702320000082
thus satisfying C of formula (25) a,max And C b,max Is the maximum capacitance that meets the intrinsic safety requirements,
the value range of the capacitor meeting the intrinsic safety requirement of the SIDO Buck converter is as follows:
Figure BDA0003825702320000083
the beneficial effects of the invention are:
the invention relates to a design method of an intrinsically safe single-inductor multi-output switch converter, which determines a working area of the converter, a short-circuit condition and maximum output short-circuit energy which may occur in the working area of the converter under the full-dynamic input voltage-load working condition, obtains an output intrinsic safety criterion of the converter, and obtains an inductor and capacitor design range of the converter meeting intrinsic safety requirements on the basis of meeting basic output indexes of the converter; the designed SIDO Buck converter is suitable for dangerous environments such as mines and the like, can provide theoretical guidance for the research of intrinsically safe type SIDO Buck converters, and can also provide ideas for the research of other intrinsically safe type SIMO DC-DC converters.
Drawings
FIG. 1 is a diagram of a single-inductor multiple-output intrinsically safe power supply;
FIG. 2 is a circuit topology diagram of an SIDO Buck converter;
FIG. 3 is a waveform diagram of each branch of the SIDO Buck converter operating in CCM;
FIG. 4 is a diagram of the operating area of an SIDO Buck converter;
FIG. 5 shows the load resistance R of the SIDO Buck converter a 、R b A circuit state diagram when one branch of the two branches is short-circuited and the other branch of the two branches works normally;
FIG. 6 shows the load resistance R of the SIDO Buck converter a 、R b A circuit state diagram of the two branches in which the two branches are short-circuited at the same time;
FIG. 7 is an experimental waveform diagram of an example;
FIG. 8 is a graph of output short circuit energy distribution for different operating conditions of the example.
Detailed Description
The present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.
The invention relates to a design method of an intrinsically safe single-inductor multi-output switch converter, which is implemented according to the following steps:
step 1: determining basic characteristics of the SIDO Buck converter;
step 1.1: calculating the output voltage of the SIDO Buck converter;
as shown in FIG. 2, the SIDO Buck converter comprises a switch tube S i 、S a 、S b Diode VD, inductor L, capacitor C a 、C b And a load resistor R a 、R b ，D i 、D a 、D b Is a switch tube S i 、S a 、S b And satisfies: d i <D b ，D a +D b ＝1；
When the converter works in a continuous conduction mode CCM, the load resistance R in the converter is obtained according to a time-averaged equivalent circuit method a 、R b The output voltages of the two branches are respectively as follows:
Figure BDA0003825702320000091
in the formula (1), V i Representing the converter input voltage; v oa Represents the branch a output voltage; v ob Representing the branch b output voltage.
Step 1.2: calculating the output ripple voltage of the SIDO Buck converter;
the waveforms of the branches of the SIDO Buck converter are shown in FIG. 3 when the converter operates in CCM, and the peak value of the inductor current I when the converter operates in CCM LP A turning inductance current I LT Valley inductive current I LV The calculation is as follows:
Figure BDA0003825702320000101
in the formula (2), I o Represents the average inductor current, an
Figure BDA0003825702320000102
T represents a switching period;
when the converterAt the critical state of CCM and DCM, I LV At t 3 At exactly zero time, using formula (1) to eliminate D i Obtaining the critical inductance L C Comprises the following steps:
Figure BDA0003825702320000103
therefore, when L is>L C When the converter is operating in CCM; when L is<L C The converter operates in DCM.
Critical inductance L C Are respectively to R a And R b The partial derivatives are obtained:
Figure BDA0003825702320000104
therefore, if the critical load R of the converter is C >R min ，R aC >R amin ，R bC >R bmin ，R min 、R aC 、R amin 、R bmin Respectively representing minimum load, critical load of branch a, minimum load of branch a and minimum load of branch b, when the load of the converter takes R a,min 、R b,min The converter must operate in CCM;
load resistor R when SIDO Buck converter works in CCM a 、R b The output ripple voltage of the two branches is respectively as follows:
Figure BDA0003825702320000111
in the formula (5), f represents a switching frequency;
thus, converter load resistance R is obtained a 、R b The maximum output voltage is:
Figure BDA0003825702320000112
step 1.3: determining the working area of the SIDO Buck converter;
let the input voltage range of the SIDO Buck converter be V i,min ～V i,max The load ranges of the two branches are respectively: r is a,min ～R a,max And R b,min ～R b,max As shown in FIG. 4, with V i 、R a 、R b Establishing O-V for coordinate axes i R a R b The working area of the SIDO Buck converter in the space rectangular coordinate system is a cube, and the vertex and the coordinates of the cube are A (R) b,min ，R a,max ，V i,min )、B(R b,max ，R a,max ，V i,min )、C(R b,max ，R a,min ，V i,min )、D(R b,min ，R a,min ，V i,min )、E(R b,min ，R a,max ，V i,max )、F(R b,max ，R a,max ，V i,max )、G(R b,max ，R a,min ，V i,max )、H(R b,min ，R a,min ，V i,max ) Different L can be drawn according to the formulas (3) and (4) C Curve, critical inductance L corresponding to points D and F CD 、L CF Respectively as follows:
Figure BDA0003825702320000113
Figure BDA0003825702320000114
when inductance L = L CD When the converter works in DCM in the full dynamic range; when inductance L = L CF The converter operates in CCM over its full dynamic range.
Step 2: analyzing output short-circuit energy of the SIDO Buck converter, and determining an output intrinsic safety criterion of the converter;
step 2.1: peak inductor current analysis for a converter
From formula (1) to obtain D i And substituting the peak value of the inductance current I of the SIDO Buck converter into the formula (2) to obtain CCM LP Comprises the following steps:
Figure BDA0003825702320000121
in the formula (9), the reaction mixture is,
Figure BDA0003825702320000122
Figure BDA0003825702320000123
will I LP Are respectively paired with V i 、R a And R b Obtaining a deviation derivative:
Figure BDA0003825702320000124
in order to meet the requirements of both output ripple voltage and intrinsically safe output, the inductor is designed to be L CD <L<L CF In this range, when the converter operates partly in CCM and partly in DCM, the peak inductor current of the converter takes a maximum value when the input voltage is maximum and the load resistance is minimum, as can be seen from equation (10), and therefore the maximum value of the peak inductor current of the SIDO Buck converter is:
Figure BDA0003825702320000125
step 2.2: output short circuit energy analysis of converter
Assuming that the circuit is malfunctioning, the load resistance R is shown in FIG. 5 a 、R b One branch of the two branches is in short circuit, the other branch of the two branches works normally, the circuit turns off a switching tube of a fault branch in time, the connection between the fault branch and the circuit is cut off, a short-circuit discharge model of the converter is single-capacitor discharge, and the maximum short-circuit energy released by the converter at the moment is as follows:
Figure BDA0003825702320000126
in this case, the short-circuit energy released by the converter is only the energy released by the fault branch capacitor;
assuming that the circuit is malfunctioning, as shown in FIG. 6, the load resistance R a 、R b When two branches are short-circuited simultaneously, the short-circuit discharge model of the converter is single-inductor double-capacitor discharge, if the main switch tube S i And timely turning off, and cutting off the connection with the power supply, wherein the sum of short-circuit energy released by the inductor and the capacitor is as follows:
Figure BDA0003825702320000131
therefore, the maximum short-circuit energy released by the converter output short-circuit is as follows:
W max ＝W max2 (14)
substituting equation (6) and equation (11) into equation (13) yields the maximum output short-circuit energy of the converter as:
Figure BDA0003825702320000132
in the formula (15), the reaction mixture is,
Figure BDA0003825702320000133
in general, the high-frequency output ripple voltage of the switching power supply is small, so equation (15) is approximated as:
Figure BDA0003825702320000134
when V is expressed by the formulas (11) and (16) i ＝V i,max ，R a ＝R a,min ，R b ＝R b,min When the output short-circuit energy of the converter is maximum, anThe output short-circuit energy is increased along with the increase of the values of the inductor and the capacitor;
step 2.3: determining an intrinsically safe criterion for the output of a converter
The output of the SIDO Buck converter can be equivalent to a capacitive circuit, so when the output voltages of the converter are V respectively oa 、V ob The corresponding filter capacitors are respectively C aB 、C bB The minimum energy for the circuit to ignite the gas is:
Figure BDA0003825702320000135
if the maximum output short-circuit energy of the converter in the full dynamic working range is less than W B Then the converter is intrinsically safe, so the criterion for determining the intrinsic safety of the converter output is:
W max ＜W B (18)
since the transmission energy of the circuit is smaller than that of CCM in DCM, if the converter in CCM meets the intrinsic safety requirement, the DCM must also meet the intrinsic safety requirement.
And 3, step 3: designing an intrinsic safety inductor of the SIDO Buck converter;
when R is a ＝R a,min ，R b ＝R b,min In order to maximize the peak inductor current, the input voltage must be V i ＝V i,max The minimum inductance to meet intrinsic safety conditions is therefore:
Figure BDA0003825702320000141
the maximum inductance is determined by intrinsic safety conditions when the capacitance C a And C b After selection, according to the intrinsic safety requirement, the value of the inductance must satisfy:
Figure BDA0003825702320000142
therefore, the inductance L of the formula (20) is satisfied max Is the maximum inductance that meets the intrinsic safety conditions,
to sum up, the value range of the inductance L of the intrinsically safe SIDO Buck converter is as follows:
L∈[L min ，L max ] (21)。
and 4, step 4: designing an intrinsic safety capacitor of the SIDO Buck converter;
from the equation (5), the capacitor C satisfying the ripple voltage output from the converter a 、C b The minimum capacitance values are respectively:
Figure BDA0003825702320000143
considering the influence of circuit parasitic parameters on the output ripple voltage of the converter, when the capacitance is actually selected, a margin lambda is required, lambda = 1-2, so that the capacitance C a 、C b Actually selecting the minimum value C of the capacitance min Respectively as follows:
Figure BDA0003825702320000144
when the output of the converter is short-circuited, that is, two branches are short-circuited at the same time, it is assumed that the maximum energy released by the converter is exactly equal to the ignition energy, that is, in a critical ignition state, so that:
W max ＝W B (24)
namely:
Figure BDA0003825702320000151
thus satisfying C of formula (25) a,max And C b,max Is the maximum capacitance that meets the intrinsic safety requirements,
the value range of the capacitor meeting the intrinsic safety requirement of the SIDO Buck converter is as follows:
Figure BDA0003825702320000152
example verification
In order to verify the correctness of theoretical analysis, an intrinsic safety type SIDO Buck converter is designed, and the main parameters of a circuit of the intrinsic safety type SIDO Buck converter are shown in table 1.
TABLE 1 converter circuit parameters
Figure BDA0003825702320000153
Selection of V i ＝20V，R a ＝R b =10 Ω (the short-circuit energy is maximum at this time), and the duty ratio D can be obtained by substituting equation (1) i And D b Respectively as follows: d i ＝0.42，D b =0.67. By substituting the parameters into equation (19), the minimum inductance obtained is: l is min =70 μ H, so inductance L =500 μ H can be taken. The parameters are substituted into formula (22), and the values of capacitance are obtained by taking lambda = 1.2: c a ＝81μF，C b ＝107μF。
Substituting the calculated inductance and capacitance values into an equation (16) to obtain the maximum output short-circuit energy W max =7.092mJ, less than a given minimum ignition energy, thus meeting set intrinsic safety requirements.
In the experimental circuit, the inductance is 500 muH, and the value of the capacitance is as follows: c a ＝81μF，C b =107 μ F, and the experimental waveform is shown in fig. 7.
Analyzing FIG. 7, it can be seen that the output voltage V of the branch a oa =5V, output ripple voltage V PP-oa =168mV; output voltage V of branch b ob =10V, output ripple voltage V PP-ob =182mV; therefore, the output voltage and the output ripple voltage of the converter both meet the design requirements. It can be seen from the figure that the peak inductor current I LP W is calculated by substituting 1.8A into the formula (16) max =7.173mJ, less than a given minimum ignition energy, so the converter meets the intrinsically safe design requirements, verifying the correctness of the theoretical analysis.
Further onExperiments were conducted under different input voltage, load conditions, where the input voltage was taken as V i =15V and V i =20V, and the load ranges of the branch a and the branch b are 10-50 Ω, so that the distribution of the short circuit release energy under the most dangerous working condition is shown in fig. 8.
It can be seen from fig. 8 that the output short-circuit energy follows the input voltage V i Increases with decreasing load resistance, and when the input voltage assumes 20V, the load assumes R a ＝10Ω、R b When the voltage is not less than 10 omega, the short circuit of the converter releases the maximum energy, the experimental result is consistent with the theoretical analysis, and the correctness of the theoretical analysis is verified.

Claims (7)

1. A design method of an intrinsically safe single-inductor multi-output switching converter is characterized by comprising the following steps:
step 1: determining basic characteristics of the SIDO Buck converter;
step 1.1: calculating the output voltage of the SIDO Buck converter;
step 1.2: calculating the output ripple voltage of the SIDO Buck converter;
step 1.3: determining the working area of the SIDO Buck converter;
and 2, step: analyzing output short-circuit energy of the SIDO Buck converter, and determining an output intrinsic safety criterion of the converter;
and 3, step 3: designing an intrinsic safety inductor of the SIDO Buck converter;
and 4, step 4: an intrinsically safe capacitive design for the SIDO Buck converter.
2. The design method of the intrinsically safe single-inductor multi-output switching converter according to claim 1, wherein the step 1.1 is specifically:
the SIDO Buck converter comprises a switching tube S i 、S a 、S b Diode VD, inductor L, capacitor C a 、C b And a load resistor R a 、R b ，D i 、D a 、D b Is a switching tube S i 、S a 、S b And satisfies: d i <D b ，D a +D b ＝1；
When the converter works in a continuous conduction mode CCM, the load resistance R in the converter is obtained according to a time-averaged equivalent circuit method a 、R b The output voltages of the two branches are respectively as follows:
Figure FDA0003825702310000011
in the formula (1), V i Representing the converter input voltage; v oa Represents the output voltage of branch a; v ob Representing the branch b output voltage.
3. The design method of the intrinsically safe single-inductor multi-output switching converter according to claim 2, characterized in that the step 1.2 is specifically:
peak inductor current I when SIDO Buck converter is operated in CCM LP A turning inductance current I LT Valley inductive current I LV The calculation is as follows:
Figure FDA0003825702310000021
in the formula (2), I o Represents the average inductor current, and
Figure FDA0003825702310000022
t represents a switching period;
when the converter is operating in the critical state of CCM and DCM, I LV At a certain moment exactly zero, and D is eliminated by formula (1) i Critical inductance L can be obtained C Comprises the following steps:
Figure FDA0003825702310000023
therefore, when L is>L C When the converter is operating in CCM; when L is<L C When the converter works in DCM;
critical inductance L C Are respectively to R a And R b The partial derivatives are obtained:
Figure FDA0003825702310000024
therefore, if the critical load R of the converter C >R min ，R aC >R amin ，R bC >R bmin ，R min 、R aC 、R amin 、R bmin Respectively representing minimum load, critical load of branch a, minimum load of branch a and minimum load of branch b, when the load of the converter takes R a,min 、R b,min The converter must operate in CCM;
load resistor R when SIDO Buck converter works in CCM a 、R b The output ripple voltage of the two branches is respectively as follows:
Figure FDA0003825702310000025
in formula (5), f represents a switching frequency;
thus, converter load resistance R is obtained a 、R b The maximum output voltage is:
Figure FDA0003825702310000031
4. the design method of the intrinsically safe single-inductor multi-output switching converter according to claim 3, characterized in that the step 1.3 is specifically as follows:
let the input voltage range of the SIDO Buck converter be V i,min ～V i,max The load ranges of the two branches are respectively: r a,min ～R a,max And R b,min ～R b,max In the order of V i 、R a 、R b Establishing O-V for coordinate axes i R a R b The working area of the SIDO Buck converter in the space rectangular coordinate system is a cube, and the vertex and the coordinate of the cube are respectively A (R) b,min ，R a,max ，V i,min )、B(R b,max ，R a,max ，V i,min )、C(R b,max ，R a,min ，V i,min )、D(R b,min ，R a,min ，V i,min )、E(R b,min ，R a,max ，V i,max )、F(R b,max ，R a,max ，V i,max )、G(R b,max ，R a,min ，V i,max )、H(R b,min ，R a,min ，V i,max ) Different L is drawn according to the formulas (3) and (4) C Curve, critical inductance L corresponding to points D and F CD 、L CF Respectively as follows:
Figure FDA0003825702310000032
Figure FDA0003825702310000033
when inductance L = L CD In time, the converter operates in DCM in the full dynamic range; when inductance L = L CF The converter operates in CCM over its full dynamic range.
5. The design method of the intrinsically safe single-inductor multi-output switching converter according to claim 4, wherein the step 2 is specifically:
step 2.1: peak inductor current analysis for a converter
From formula (1) to obtain D i And substituting the peak value of the peak inductance current I of the SIDO Buck converter into the formula (2) to obtain the CCM LP Comprises the following steps:
Figure FDA0003825702310000041
in the formula (9), the reaction mixture is,
Figure FDA0003825702310000042
Figure FDA0003825702310000043
will I LP Are respectively paired with V i 、R a And R b Obtaining a partial derivative:
Figure FDA0003825702310000044
in order to meet the requirements of both output ripple voltage and intrinsically safe output, the inductor is designed to be L CD <L<L CF In this range, when the converter operates partly in CCM and partly in DCM, the peak inductor current of the converter takes a maximum value when the input voltage is maximum and the load resistance is minimum, as can be seen from equation (10), and therefore the maximum value of the peak inductor current of the SIDO Buck converter is:
Figure FDA0003825702310000045
step 2.2: output short circuit energy analysis of converter
Assuming that the circuit is faulty, the load resistance R a 、R b One branch of the two branches is in short circuit, the other branch works normally, the circuit turns off a switching tube of a fault branch in time, the connection between the fault branch and the circuit is cut off, a short-circuit discharge model of the converter is single-capacitor discharge, and the maximum short-circuit energy released by the converter at the moment is as follows:
Figure FDA0003825702310000046
in this case, the short-circuit energy released by the converter is only the energy released by the fault branch capacitor;
assuming that the circuit is faulty, the load resistance R a 、R b When two branches are short-circuited simultaneously, the short-circuit discharge model of the converter is single-inductor double-capacitor discharge, if the main switch tube S i And timely turning off, and cutting off the connection with the power supply, wherein the sum of short-circuit energy released by the inductor and the capacitor is as follows:
Figure FDA0003825702310000051
therefore, the maximum short-circuit energy released by the converter output short-circuit is as follows:
W max ＝W max2 (14)
substituting equation (6) and equation (11) into equation (13) yields the maximum output short-circuit energy of the converter as:
Figure FDA0003825702310000052
in the formula (15), the reaction mixture is,
Figure FDA0003825702310000053
in general, the high-frequency output ripple voltage of the switching power supply is small, so equation (15) is approximated as:
Figure FDA0003825702310000054
when V is expressed by the formulas (11) and (16) i ＝V i,max ，R a ＝R a,min ，R b ＝R b,min The output short-circuit energy of the converter is maximum, and the output short-circuit energy is valued along with the inductance and the capacitanceIncreased by an increase;
step 2.3: determining an intrinsically safe criterion for the output of a converter
The output of the SIDO Buck converter is equivalent to a capacitive circuit, so when the output voltages of the converter are V respectively oa 、V ob The corresponding filter capacitors are respectively C aB 、C bB The minimum energy for the circuit to ignite the gas is:
Figure FDA0003825702310000055
if the maximum output short-circuit energy of the converter in the full dynamic working range is less than W B The converter is intrinsically safe, so the criterion for determining the intrinsic safety of the converter output is:
W max ＜W B (18)
since the transmission energy of the circuit in DCM is smaller than that in CCM, if the converter in CCM meets the intrinsic safety requirement, the DCM must also meet the intrinsic safety requirement.
6. The design method of the intrinsically safe single-inductor multi-output switching converter according to claim 2, wherein the step 3 is specifically as follows:
when R is a ＝R a,min ，R b ＝R b,min The converter must operate in CCM, and in order to maximize the peak inductor current, the input voltage is V i ＝V i,max The minimum inductance to meet intrinsic safety conditions is therefore:
Figure FDA0003825702310000061
the maximum inductance is determined by intrinsic safety conditions when the capacitance C a And C b After selection, the value of the inductance must meet the requirements of intrinsic safety:
Figure FDA0003825702310000062
therefore, the inductance L of the formula (20) is satisfied max Is the maximum inductance that meets the intrinsic safety conditions,
to sum up, the value range of the inductance L of the intrinsically safe SIDO Buck converter is as follows:
L∈[L min ，L max ] (21)。
7. the design method of the intrinsically safe single-inductor multiple-output switching converter according to claim 6, wherein the step 4 is specifically as follows:
from the equation (5), the capacitor C satisfying the ripple voltage output from the converter a 、C b The minimum capacitance values are respectively:
Figure FDA0003825702310000063
considering the influence of circuit parasitic parameters on the output ripple voltage of the converter, when the capacitor is actually selected, a margin lambda is required, lambda = 1-2, so that the capacitor C a 、C b Minimum value C of actually selected capacitance min Respectively as follows:
Figure FDA0003825702310000064
when the output of the converter is short-circuited, that is, two branches are short-circuited at the same time, it is assumed that the maximum energy released by the converter is exactly equal to the ignition energy, that is, the converter is in a critical ignition state, so that:
W max ＝W B (24)
namely:
Figure FDA0003825702310000071
thus satisfying C of formula (25) a,max And C b,max Is the maximum capacitance that meets the intrinsic safety requirements,
the value range of the capacitor meeting the intrinsic safety requirement of the SIDO Buck converter is as follows:
Figure FDA0003825702310000072
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