A battery balancing circuit and method based on TL431

Abstract

The present invention relates to the field of battery charging and discharging, and more particularly to a TL431-based battery balancing circuit and method. The circuit comprises battery cells, a voltage sampling circuit, a logic control circuit, a closed-loop balancing circuit based on a TL431 switching power supply, and an isolation circuit. Multiple battery cells are connected in series to form a battery pack, and each battery cell corresponds to a voltage sampling circuit, a closed-loop balancing circuit, an isolation circuit, and a logic control circuit. The voltage sampling circuit and closed-loop balancing circuit are connected in parallel to the battery cell, the isolation circuit is connected to the closed-loop balancing circuit, and the logic control circuit is connected to the isolation circuit and the voltage sampling circuit, respectively. This circuit addresses the issue of uncontrolled switching-controlled balancing circuits by utilizing TL431 closed-loop control to achieve a constant balancing current output within a set operating voltage range.

Description

Technical Field

[0001] The present invention relates to the field of battery charging and discharging, and in particular to a battery balancing circuit based on TL431 and a method thereof. Background Art

[0002] Lithium battery balancing management technology ensures balanced voltage across all cells and reduces differences between cells, thereby meeting the high reliability and long life requirements of space lithium battery packs.

[0003] Currently, balancing control methods can be categorized into passive lossy balancing and active lossless balancing based on the energy consumption requirements of the balancing circuit. Active lossless balancing circuits consume less power than passive lossy balancing circuits, but they suffer from drawbacks such as complex circuit structure and control methods, and difficulty ensuring parameter consistency.

[0004] Passive lossy shunting remains the only method for balancing lithium-ion batteries used in space applications, both domestically and internationally, due to its simple circuitry and high reliability. Passive lossy balancing involves discharging individual cells through shunt resistors. Traditional passive lossy balancing uses a switch to control whether the individual cells are connected to the shunt resistors. Higher cell voltages increase the balancing current, leading to greater heat dissipation in the shunt resistors. This requires consideration of shunt resistor thermal management, which complicates structural design. Summary of the Invention

[0005] The present invention provides a battery balancing circuit and method based on TL431, aiming to achieve constant balancing current output by utilizing TL431 closed-loop control.

[0006] The present invention provides a TL431-based battery balancing circuit, comprising a battery cell, a voltage sampling circuit, a logic control circuit, a closed-loop balancing circuit based on a TL431 switching power supply, and an isolation circuit. A plurality of the battery cells are connected in series to form a battery pack, and each battery cell corresponds to a voltage sampling circuit, a closed-loop balancing circuit, an isolation circuit, and a logic control circuit. The voltage sampling circuit and the closed-loop balancing circuit are both connected in parallel to the battery cell, the isolation circuit is connected to the closed-loop balancing circuit, and the logic control circuit is respectively connected to the isolation circuit and the voltage sampling circuit.

[0007] As a further improvement of the present invention, the logic control circuit includes a switch tube Q2, a resistor R3, and a resistor R4. The isolation circuit includes an optocoupler isolator. The base of the switch tube Q2 is connected to the upper voltage limit of the battery balancing voltage. The collector of the switch tube Q2 is respectively connected to one end of the resistor R3 and the positive electrode of the light-emitting diode in the optocoupler isolator. The other end of the resistor R3 is connected to the VCC terminal. The emitter of the switch tube Q2 is connected to one end of the resistor R4. The other end of the resistor R4 is grounded. The cathode of the light-emitting diode in the optocoupler isolator is connected to the battery cell voltage terminal. The transistor in the optocoupler isolator is connected to the closed-loop balancing circuit.

[0008] As a further improvement of the present invention, the closed-loop balancing circuit includes a TL431 switching power supply, a resistor R1, a resistor R2, a resistor Rs, a capacitor C1, and a switching tube Q1. The collector of the switching tube Q1 is respectively connected to the positive electrode of the battery cell and one end of the resistor R1, and the emitter of the switching tube Q1 is respectively connected to one end of the resistor Rs and the reference electrode of the TL431 switching power supply. The base of the switching tube Q1 is respectively connected to the cathode of the TL431 switching power supply, one end of the capacitor C1, and the emitter of the transistor in the optocoupler isolator. The other end of the resistor R1 is connected to the collector of the transistor in the optocoupler isolator, the other end of the resistor Rs is respectively connected to the negative electrode of the battery cell, the anode of the TL431 switching power supply, and one end of the resistor R2. The other end of the resistor R2 is respectively connected to the reference electrode of the TL431 switching power supply and the other end of the capacitor C1. The anode of the TL431 switching power supply is grounded.

[0009] As a further improvement of the present invention, the switch tubes Q1 and Q2 are triodes or MOSFET tubes.

[0010] As a further improvement of the present invention, the voltage sampling circuit includes an operational amplifier, a resistor R5, a resistor R6, a resistor R7, and a resistor R8. One end of the resistor R5 is connected to the positive electrode of the battery cell, the other end of the resistor R5 is respectively connected to one end of the resistor R6 and the positive input terminal of the operational amplifier, the other end of the resistor R6 is grounded, the two ends of the resistor R7 are respectively connected to the reverse input terminal of the operational amplifier and the output terminal of the operational amplifier, one end of the resistor R8 is connected to the reverse input terminal of the operational amplifier, and the other end of the resistor R8 is grounded. After the operational amplifier output terminals of the battery sampling circuit corresponding to the multiple battery cells are connected in parallel, the voltage upper limit of the battery balancing voltage is output.

[0011] The present invention also provides a battery balancing method based on TL431, comprising the following steps:

[0012] S1. Voltage Sampling Logic Judgment Control: The voltage sampling circuit obtains the battery cell voltage and the upper voltage limit of the cell balancing voltage, inputs the battery cell voltage into the cathode of the light-emitting diode in the optocoupler, and inputs the upper voltage limit of the cell balancing voltage into the base of the switch Q2 in the logic control circuit. The battery cell voltage is compared with the upper voltage limit of the cell balancing voltage to determine the battery cell voltage. If the battery cell voltage is greater than the upper voltage limit of the cell balancing voltage, the optocoupler isolation transistor is turned on, the balancing discharge circuit is activated, and the battery cell continues to discharge until the battery cell voltage equals the upper voltage limit of the cell balancing voltage.

[0013] S2. Balanced discharge control: When the TL431 switching power supply reaches normal working conditions, the balancing circuit works and the battery discharges. A closed-loop integral control loop exists between the anode K of the TL431 switching power supply and the reference electrode ref. The anode voltage V k , reference voltage V ref Remains unchanged, balancing the current I within the battery cell voltage variation range bat Constant.

[0014] As a further improvement of the present invention, in step S1, the upper limit of the battery balancing voltage is the average value of the smallest series-connected battery or battery group, and is divided into the following steps:

[0015] S11. When the battery pack takes the minimum series connection of batteries, the battery cell voltage V bN Greater than the minimum voltage V bmin + V D , the optocoupler isolation transistor is turned on, the balanced discharge circuit works, and the battery cell is discharged until the voltage is equal to the minimum battery cell voltage of the battery pack V bmin + V D ;

[0016] S12. When the battery pack takes the average value of the battery pack, the battery cell voltage V bN Greater than average voltage V bave , the optocoupler isolation transistor is turned on, and the balanced discharge circuit works until the voltages of all battery cells are equal.

[0017] As a further improvement of the present invention, in step S2, when the battery cell voltage is constant, the resistance value of resistor R1 is selected and the regional adjustment boundary line is set. V set , the TL431 switching power supply balanced discharge control is divided into the following three cases:

[0018] a1.Battery cell voltage Vset When the voltage is within the range of 4.2V, the optocoupler isolation transistor is turned on, the closed-loop balancing circuit works, and the TL431 switching power supply realizes closed-loop control. The closed-loop balancing current remains unchanged, and the battery cell uses a larger constant balancing current ( V ref / R s ) Rapid discharge;

[0019] a2. The battery cell voltage is discharged to V min ~ V set When the voltage of the parallel battery decreases gradually, the reference electrode balancing current of the TL431 switching power supply decreases gradually.

[0020] a3. When the battery cell voltage is discharged to the minimum voltage setting value V min When the optocoupler isolation transistor is turned off, the battery cell voltage is V min In the range of ~0V, the closed-loop balancing circuit does not work, maintaining the battery cell voltage at the minimum value V min Place.

[0021] As a further improvement of the present invention, the normal operating conditions of the TL431 switching power supply are: V KA > V ref =2.5V; 1mA< I K <100mA.

[0022] The present invention proposes an active lossy equalization circuit based on TL431, an optocoupler, and an operational amplifier, which has the following beneficial effects:

[0023] (1) Few types of devices and simple circuit structure;

[0024] (2) The TL431 control loop can realize autonomous balancing adjustment in different areas of the lithium battery unit, and has lithium battery current limiting protection and undervoltage protection functions; when the battery voltage is greater than the set value, the TL431 closes the loop, the balancing current is constant, and the current limiting protection function is in effect; when the battery voltage is less than the constant current setting value, the balancing current decreases as the single cell voltage decreases, thereby improving the balancing accuracy; when the lithium battery voltage is lower than the undervoltage setting value, the balancing circuit does not work, and undervoltage protection is provided;

[0025] (3) The circuit can detect the logic of the minimum voltage single-cell imbalance or single-cell imbalance below the average value, and use the optocoupler and transistor conduction characteristics as the isolation and comparison logic judgment link. There is no need for comparators or digital isolators, etc., and the number of control circuits is small and the cost is low. BRIEF DESCRIPTION OF THE DRAWINGS

[0026] Figure 1 This is a block diagram of the battery balancing control circuit of the present invention;

[0027] Figure 2 It is a schematic diagram of the closed-loop balancing circuit and the optical coupler isolation interconnection in the present invention;

[0028] Figure 3 This is a schematic diagram of the voltage sampling circuit in the present invention

[0029] Figure 4 This is a circuit diagram for realizing logic control in the present invention;

[0030] Figure 5 This is a constant current and current sharing circuit diagram with undervoltage protection in the present invention;

[0031] Figure 6 It is a schematic diagram of the working area of ​​the lithium battery balancing circuit of the present invention. DETAILED DESCRIPTION

[0032] In order to make the objectives, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below with reference to the accompanying drawings and embodiments.

[0033] This invention proposes an on-orbit lithium battery pack balancing management technology based on the feedback loop control of the switching power supply TL431. This invention addresses the problem of excessive balancing current in the switching control balancing circuit and utilizes the TL431 closed-loop control to achieve a constant balancing current output.

[0034] The block diagram of the balance control is as follows Figure 1 As shown, it includes voltage sampling, control logic, closed-loop balancing, and optocoupler isolation.

[0035] Specific examples Figure 1 and 2 A battery balancing circuit based on TL431 of the present invention includes a battery cell, a voltage sampling circuit, a logic control circuit, a closed-loop balancing circuit based on a TL431 switching power supply, and an isolation circuit. Multiple battery cells are connected in series to form a battery pack. Each battery cell corresponds to a voltage sampling circuit, a closed-loop balancing circuit, an isolation circuit, and a logic control circuit. The voltage sampling circuit and the closed-loop balancing circuit are both connected in parallel to the battery cell. The isolation circuit is connected to the closed-loop balancing circuit. The logic control circuit is respectively connected to the isolation circuit and the voltage sampling circuit.

[0036] like Figure 2 and Figure 4 As shown, the logic control circuit includes a switch tube Q2, a resistor R3, and a resistor R4. The isolation circuit includes an optocoupler isolator. The base of the switch tube Q2 is connected to the voltage upper limit of the battery balancing voltage. The collector of the switch tube Q2 is respectively connected to one end of the resistor R3 and the positive electrode of the light-emitting diode in the optocoupler isolator. The other end of the resistor R3 is connected to the VCC terminal. The emitter of the switch tube Q2 is connected to one end of the resistor R4. The other end of the resistor R4 is grounded. The cathode of the light-emitting diode in the optocoupler isolator is connected to the battery cell voltage terminal. The transistor in the optocoupler isolator is connected to the closed-loop balancing circuit.

[0037] like Figure 2 and 5 As shown, the closed-loop balancing circuit includes a TL431 switching power supply, resistors R1, R2, Rs, capacitor C1, and a switching transistor Q1. The collector of switching transistor Q1 is connected to the positive electrode of the battery cell and one end of resistor R1, respectively. The emitter of switching transistor Q1 is connected to one end of resistor Rs and the reference electrode of the TL431 switching power supply, respectively. The base of switching transistor Q1 is connected to the cathode of the TL431 switching power supply, one end of capacitor C1, and the emitter of the transistor in the optocoupler isolator, respectively. The other end of resistor R1 is connected to the collector of the transistor in the optocoupler isolator, the other end of resistor Rs is connected to the negative electrode of the battery cell, the anode of the TL431 switching power supply, and one end of resistor R2, respectively. The other end of resistor R2 is connected to the reference electrode of the TL431 switching power supply and the other end of capacitor C1, respectively. The anode of the TL431 switching power supply is grounded. Switching transistors Q1 and Q2 are transistors or MOSFETs.

[0038] like Figure 3 As shown, the voltage sampling circuit includes an operational amplifier, a resistor R5, a resistor R6, a resistor R7, and a resistor R8. One end of the resistor R5 is connected to the positive electrode of the battery cell, and the other end of the resistor R5 is respectively connected to one end of the resistor R6 and the positive input terminal of the operational amplifier. The other end of the resistor R6 is grounded. The two ends of the resistor R7 are respectively connected to the reverse input terminal of the operational amplifier and the output terminal of the operational amplifier. One end of the resistor R8 is connected to the reverse input terminal of the operational amplifier, and the other end of the resistor R8 is grounded, forming a differential sampling circuit. The output terminals of the operational amplifiers corresponding to the battery sampling circuits of the multiple battery cells are connected in parallel to output the voltage upper limit of the battery balancing voltage.

[0039] According to the above-mentioned battery balancing circuit, the present invention mainly innovates the battery balancing method in terms of logic judgment + isolation circuit and closed-loop balancing circuit.

[0040] (1) Logic control + isolation link

[0041] The upper limit of the lithium battery balancing voltage can be the minimum series lithium battery value or the average value of the lithium battery group. The single lithium battery uses a simple resistor voltage divider to perform voltage sampling. Figure 3 (a) is the minimum value simulation circuit for lithium battery pack, Figure 3 (b) The simulation circuit for taking the average value of the lithium battery pack. Figure 4 To correspond to the voltage sampling hardware logic judgment circuit, the host computer software can also be used for judgment. Figure 4 (a) In the minimum unequal current circuit, the lithium battery cell voltage V bN Greater than the minimum voltage V bmin + V D ,in V D Indicates the diode voltage drop, the optocoupler isolation transistor is turned on, the balanced discharge circuit works, and the lithium battery cell is discharged until the voltage is equal to the minimum lithium battery cell voltage of the lithium battery pack V bmin + V D Similarly, Figure 4 (b) In the current-sharing circuit, the lithium battery cell voltage is greater than the average value. V bN Greater than average voltage V bave , the optocoupler isolation transistor is turned on, and the balanced discharge circuit works until the voltages of all lithium battery cells are equal.

[0042] (2) Closed-loop balancing circuit

[0043] The switching power supply TL431 is less affected by temperature. In high or low temperature environments, it can output a stable reference voltage through the feedback control loop, that is, the voltage drop across the shunt resistor remains unchanged, ensuring that the balancing current does not change with the charge and discharge voltage of the lithium battery. Because the semiconductor device Q1 operates in the variable resistance area, the semiconductor device can be a transistor or a MOSFET. Figure 5 As shown, Figure 5 (a) is a constant current equalizing circuit based on TL431. Figure 5 (b) is the TL431 equivalent compensator structure.

[0044] The structure of the TL431 feedback loop of the balanced control discharge circuit is as follows: Figure 5 As shown in (a), each balancing circuit operates independently on its associated battery cell, taking the first lithium battery pack as an example. The normal working conditions of the TL431 circuit are: (1) V KA > V ref =2.5V; (2) 1mA< I K <100mA. When the balancing circuit is working and the lithium battery is discharging, a closed-loop integral control loop exists between the anode K of the TL431 switching power supply and the reference terminal ref.V k 、 V ref The voltage remains constant. At this time, the switch tube operates in the linear region, and the voltage across the shunt resistor V ref Remain unchanged, that is, ensure balanced current within the range of lithium battery voltage change I bat Constant.

[0045] The closed-loop control of the balancing circuit must ensure that the TL431 can work properly, but the resistance of R1 affects the operating current of TL431. When the lithium battery voltage is constant and the resistance of R1 is too large, the TL431 supply current I K If the current is less than the normal working current, TL431 cannot work normally, the closed-loop control loop will be in an open-loop state, and as the lithium battery voltage gradually decreases, V ref The voltage is also decreasing, and the corresponding shunt resistor balancing current is gradually reduced, slowing down the discharge rate of the lithium battery. Therefore, by changing the resistance value of R1, the lithium battery voltage in different areas can be automatically balanced and current limited.

[0046] Select the appropriate resistance value of resistor R1 and set the area adjustment boundary line V set TL431 in region I: the optocoupler transistor of the logic circuit is turned on and the balanced discharge circuit is working. V set Closed-loop control is achieved within the range of ~4.2V, and the battery cells are balanced with a large constant current (V ref / R s ) Rapid discharge. The resistance of resistor R1 is to ensure that the current flowing through it is within the IK range given in the TL431 manual; the voltage range of the lithium-ion battery is 3.0 to 4.2V, and the nominal voltage is 3.7V, so the battery voltage V set Closed-loop control is achieved within the ~4.2V range.

[0047] Lithium battery voltage discharged to region II: V min ~ V set , the logic circuit is still turned on, and TL431 cannot achieve closed-loop control. As the voltage of the parallel lithium battery gradually decreases, the balancing current at the reference end of TL431 gradually decreases.

[0048] When the lithium battery voltage is discharged to the minimum voltage setting value V min When the optocoupler transistor of the logic circuit is cut off, the battery voltage is V minIn the range of ~0V (region III), the parallel balancing control circuit of the lithium battery cells does not work, maintaining the lithium battery voltage at the minimum value V min It can prevent the lithium battery from over-discharging and effectively increase the service life of the lithium battery.

[0049] In the balancing control circuit, V set 、 V min The set values ​​can be set according to actual conditions to meet the requirements of lithium battery cell balancing control in different ranges, with a certain degree of flexibility.

[0050] The above is a further detailed description of the present invention in conjunction with specific preferred embodiments, and the specific implementation of the present invention should not be considered to be limited to these descriptions. For those skilled in the art of the present invention, without departing from the concept of the present invention, several simple deductions or substitutions can be made, which should be considered to fall within the scope of protection of the present invention.

Claims

1. A battery balancing circuit based on TL431, characterized in that: It includes a battery cell, a voltage sampling circuit, a logic control circuit, a closed-loop balancing circuit based on a TL431 switching power supply, and an isolation circuit. Multiple battery cells are connected in series to form a battery pack. Each battery cell corresponds to a voltage sampling circuit, a closed-loop balancing circuit, an isolation circuit, and a logic control circuit. The voltage sampling circuit and the closed-loop balancing circuit are both connected in parallel to the battery cell. The isolation circuit is connected to the closed-loop balancing circuit. The logic control circuit is respectively connected to the isolation circuit and the voltage sampling circuit. The logic control circuit includes a switch tube Q2, a resistor R3, and a resistor R4. The isolation circuit includes an optocoupler isolator. The base of the switch tube Q2 is connected to the upper voltage limit of the battery balancing voltage. The collector of the switch tube Q2 is respectively connected to one end of the resistor R3 and the positive electrode of the light-emitting diode in the optocoupler isolator. The other end of the resistor R3 is connected to the VCC terminal. The emitter of the switch tube Q2 is connected to one end of the resistor R4. The other end of the resistor R4 is grounded. The cathode of the light-emitting diode in the optocoupler isolator is connected to the battery cell voltage terminal. The transistor in the optocoupler isolator is connected to the closed-loop balancing circuit. The closed-loop balancing circuit includes a TL431 switching power supply, a resistor R1, a resistor R2, a resistor Rs, a capacitor C1, and a switching tube Q1. The collector of the switching tube Q1 is respectively connected to the positive electrode of the battery cell and one end of the resistor R1, the emitter of the switching tube Q1 is respectively connected to one end of the resistor Rs and the reference electrode of the TL431 switching power supply, the base of the switching tube Q1 is respectively connected to the cathode of the TL431 switching power supply, one end of the capacitor C1, and the emitter of the transistor in the optocoupler isolator, the other end of the resistor R1 is connected to the collector of the transistor in the optocoupler isolator, the other end of the resistor Rs is respectively connected to the negative electrode of the battery cell, the anode of the TL431 switching power supply, and one end of the resistor R2, the other end of the resistor R2 is respectively connected to the reference electrode of the TL431 switching power supply and the other end of the capacitor C1, and the anode of the TL431 switching power supply is grounded.

2. The battery balancing circuit based on TL431 according to claim 1, characterized in that: The switch tubes Q1 and Q2 are triodes or MOSFET tubes.

3. The battery balancing circuit based on TL431 according to claim 1, characterized in that: The voltage sampling circuit includes an operational amplifier, resistors R5, R6, R7, and R8. One end of the resistor R5 is connected to the positive electrode of the battery cell, the other end of the resistor R5 is respectively connected to one end of the resistor R6 and the positive input terminal of the operational amplifier, the other end of the resistor R6 is grounded, the two ends of the resistor R7 are respectively connected to the negative input terminal of the operational amplifier and the output terminal of the operational amplifier, one end of the resistor R8 is connected to the negative input terminal of the operational amplifier, and the other end of the resistor R8 is grounded. The operational amplifier output terminals of the battery sampling circuit corresponding to the multiple battery cells are connected in parallel to output the voltage upper limit of the battery balancing voltage.

4. A battery balancing method based on the TL431 battery balancing circuit according to any one of claims 1 to 3, characterized in that: The following steps are involved: S1. Voltage Sampling Logic Judgment Control: The voltage sampling circuit obtains the battery cell voltage and the upper voltage limit of the cell balancing voltage, inputs the battery cell voltage into the cathode of the light-emitting diode in the optocoupler, and inputs the upper voltage limit of the cell balancing voltage into the base of the switch Q2 in the logic control circuit. The battery cell voltage is compared with the upper voltage limit of the cell balancing voltage to determine the battery cell voltage. If the battery cell voltage is greater than the upper voltage limit of the cell balancing voltage, the optocoupler isolation transistor is turned on, the balancing discharge circuit is activated, and the battery cell continues to discharge until the battery cell voltage equals the upper voltage limit of the cell balancing voltage. S2. Balanced discharge control: When the TL431 switching power supply reaches normal working conditions, the balancing circuit works and the battery discharges. A closed-loop integral control loop exists between the anode K of the TL431 switching power supply and the reference electrode ref. The anode voltage V k , reference voltage V ref Remains unchanged, balancing the current I within the battery cell voltage variation range bat Constant.

5. The battery balancing method based on TL431 according to claim 4, characterized in that: In step S1, the upper limit of the battery balancing voltage is the average value of the smallest series-connected battery or battery group, and is divided into the following steps: S11. When the battery pack takes the minimum series connection of batteries, the battery cell voltage V bN Greater than the minimum voltage V bmin + V D , the optocoupler isolation transistor is turned on, the balanced discharge circuit works, and the battery cell is discharged until the voltage is equal to the minimum battery cell voltage of the battery pack V bmin + V D ; S12. When the battery pack takes the average value of the battery pack, the battery cell voltage V bN Greater than average voltage V bave , the optocoupler isolation transistor is turned on, and the balanced discharge circuit works until the voltages of all battery cells are equal.

6. The battery balancing method based on TL431 according to claim 4, characterized in that: In step S2, when the battery cell voltage is constant, the resistance value of resistor R1 is selected to set the area adjustment boundary line. V set , the TL431 switching power supply balanced discharge control is divided into the following three cases: a1.Battery cell voltage V set When the voltage is within the range of 4.2V, the optocoupler isolation transistor is turned on, the closed-loop balancing circuit works, and the TL431 switching power supply realizes closed-loop control. The closed-loop balancing current remains unchanged, and the battery cell uses a larger constant balancing current ( V ref / R s ) Rapid discharge; a2. The battery cell voltage is discharged to V min ~ V set When the voltage of the parallel battery decreases gradually, the reference electrode balancing current of the TL431 switching power supply decreases gradually. a3. When the battery cell voltage is discharged to the minimum voltage setting value V min When the optocoupler isolation transistor is turned off, the battery cell voltage is V min In the range of ~0V, the closed-loop balancing circuit does not work, maintaining the battery cell voltage at the minimum value V min Place.

7. The battery balancing method based on TL431 according to claim 4, characterized in that: The normal operating conditions of the TL431 switching power supply are V KA > V ref = 2.5V; 1mA< I K <100mA.

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