Three-stage single-cell lithium battery linear charging circuit with current comparison switching mode

Abstract

The present invention discloses a three-stage single-cell lithium battery charging circuit with a current comparison switching mode, comprising a self-reference LDO module, a reference circuit, a voltage comparison circuit, an external resistor and a charging loop. The present invention sets a current comparison control circuit in the self-reference LDO module, and its output voltage is used as the power supply of the low-voltage module. A current comparison switching circuit is set in the charging loop, and a current mirror structure is adopted, which overcomes the shortcomings of the prior art circuits that have unnecessary zeros and poles and cause safety hazards to users. The present invention has the advantages of reduced chip area, reduced circuit complexity, reduced cost, improved charging current accuracy, low-voltage device circuits are not easy to break down, low technical implementation difficulty, and high chip success rate.

Description

Technical Field

[0001] The present invention belongs to the field of microelectronics technology, and further relates to a three-stage single-cell lithium battery charging circuit with a current comparison switching mode in the field of integrated circuit technology. The present invention can linearly charge small and medium-sized electronic devices when the voltage of the power supply device is too high. Background Art

[0002] In recent years, linear charging has become a more competitive charging method for small and medium-sized electronic devices due to its advantages of simple circuits, low cost and small area. With the diversification of charging scenarios, the power supply may be far higher than the circuit's withstand voltage, destroying the charging circuit, affecting battery life, and posing safety risks to users.

[0003] Nanjing Ruihe Electronics Co., Ltd. disclosed a linear charging circuit with switchable power supply in its patent document "A Highly Integrated Linear Charging Voltage Stabilizing Circuit and Its Application" (application publication number CN 110224497 A). The charging circuit includes voltage detection and protection, power supply detection and automatic switching, output current detection circuit and voltage comparison loop control circuit. The charging circuit uses the power supply when the power supply is within the required range, and switches to the second power supply when it is not within the required range, so that the charging circuit can work normally. However, the shortcomings of the charging circuit are still there: the circuit is complex to implement, and when switching the power supply, it will generate impact current disturbance, which affects the accuracy of the charging current, causing the battery to be overcharged and affecting the battery life.

[0004] Pang-Jung Liu and Lin-Hao Chien proposed a high-efficiency multi-cell lithium battery linear charging circuit based on the traditional three-stage circuit in their published paper "A High-Effificiency Integrated Multimode Battery Charger With an Adaptive Supply Voltage Control Scheme" (IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 33, NO. 8, AUGUST 2018). The charging circuit includes a charging tube, a sampling tube, a full protection circuit, a zero current detection circuit and a dcdc converter. The charging circuit changes the input voltage through a dcdc converter to achieve normal charging under high input voltage conditions. However, the shortcomings of the charging circuit are: due to the presence of inductance in the dcdc converter, unnecessary zeros and poles are generated, which affects the stability of the charging current and makes the charging circuit tape-out yield low. Summary of the invention

[0005] The purpose of the present invention is to address the problems existing in the above-mentioned prior art and to propose a three-stage single-cell lithium battery charging circuit with a current comparison switching mode, so as to solve the problems of unstable power supply, high cost and insufficient charging current accuracy of the three-stage single-cell lithium battery charging circuit in the prior art.

[0006] In order to achieve the above purpose, a current comparison control circuit is set in the self-reference LDO module. When the power supply is within the required range, the power supply is used to power the charging loop. When it is not within the required range, the output of the self-reference LDO module is switched as the power supply, which can solve the problem of unstable power supply of the circuit. A current comparison switching circuit is set in the charging loop, and the output control current is generated by using the principle of virtual short and virtual break of the operational amplifier. The output current signal of the operational amplifier is amplified by a current mirror composed of high-voltage devices, and then compared with the input current IBIAS to improve the judgment accuracy of the charging current size.

[0007] The three-stage single-cell lithium battery charging circuit of the current comparison switching mode of the present invention comprises a self-reference LDO module, a reference circuit, a voltage comparison circuit, an external resistor and a charging loop.

[0008] The fourth MOS tube M4 and the fifth MOS tube M5 in the current comparison control circuit form a current mirror, the gate of the fourth MOS tube M4 is connected to its drain, and the sources of the fourth MOS tube M4 and the fifth MOS tube M5 are connected to the input voltage VIN; the gates of the sixth MOS tube M6 and the seventh MOS tube M7 are connected to the input clamping voltage Vclamp, the drain of the sixth MOS tube M6 is connected to the drain of the fourth MOS tube M4, the drain of the seventh MOS tube M7 is connected to the drain of the fifth MOS tube M5 and the output voltage Vp, and the source of the seventh MOS tube M7 is connected to the drain of the eighth MOS tube M8; the gate of the eighth MOS tube M8 is grounded, and its source is also grounded; the gate of the third MOS tube M3 is connected to the input voltage Vback, its source is grounded, and its drain is connected to the source of the sixth MOS tube M6.

[0009] The twelfth MOS tube M12 and the thirteenth MOS tube M13 in the current comparison switching circuit form a current mirror form, the gate of the twelfth MOS tube M12 is connected to its drain, and the sources of the twelfth MOS tube M12 and the thirteenth MOS tube M13 are connected to the input voltage VIN; the gates of the fourteenth MOS tube M14 and the fifteenth MOS tube M15 are connected to the input clamping voltage Vclamp, the drain of the fourteenth MOS tube M14 is connected to the drain of the twelfth MOS tube M12, the drain of the thirteenth MOS tube M13 is connected to the drain of the fifteenth MOS tube M15 and to the voltage Vx, the source of the fifteenth MOS tube M15 is connected to the input current IBIAS and to ground, and the source of the fourteenth MOS tube M14 is connected to the outputs of the first operational amplifier CC, the second operational amplifier CV and the third operational amplifier OTP and to ground.

[0010] Compared with the prior art, the present invention has the following advantages:

[0011] First, the present invention sets a current comparison control circuit in the self-reference ldo module, uses the first Zener diode D1 to generate a clamping voltage, and adjusts the output voltage Vpre by adjusting the voltage of the gate of the eighth MOS tube M8, which is used as a reference voltage and a power supply for other low-voltage modules, thereby overcoming the shortcomings of the prior art, such as complex circuit implementation, impact current disturbance, and low charging current accuracy, so that the present invention has the advantages of reduced chip area, reduced circuit complexity, and reduced cost.

[0012] Second, the present invention sets a current comparison switching circuit in the charging loop, uses only six high-voltage tubes (M10, M12, M13, M14, M15, M16), and switches the charging mode by changing the gate voltage of the sixteenth MOS tube M16 through current comparison, thereby overcoming the shortcomings of the prior art of large chip area and many high-voltage devices, so that the present invention has the advantages of low cost, greatly saving circuit area, and reducing circuit complexity.

[0013] Thirdly, the present invention adopts a current mirror structure in the current comparison switching circuit, which overcomes the shortcomings of the prior art circuits that have unnecessary zeros and poles and pose a potential safety hazard to users, so that the present invention has the advantages of low-voltage device circuits that are not easy to break down, improved charging current accuracy, low technical implementation difficulty, and a high success rate of wafer production. BRIEF DESCRIPTION OF THE DRAWINGS

[0014] Figure 1 is a block diagram of the present invention;

[0015] Figure 2 It is an electrical schematic diagram of the self-referenced LDO circuit of the present invention;

[0016] Figure 3 It is the electrical schematic diagram of the charging loop of a single lithium battery of the present invention;

[0017] Figure 4 It is the electrical schematic diagram of the voltage comparison circuit of the present invention. DETAILED DESCRIPTION

[0018] The present invention is further described in detail below in conjunction with the accompanying drawings and embodiments.

[0019] Reference Figure 1 , the overall circuit of the present invention is further described in detail.

[0020] The positive electrode of the external lithium battery in the three-stage single-cell lithium battery charging circuit of the current comparison switching mode is connected to the pin VBAT, and the negative electrode thereof is grounded. In the embodiment of the present invention, it is an ordinary single-cell lithium battery.

[0021] The power supply of the self-referenced LDO module is the input voltage VIN, which can be any voltage value between 0 and 36V. The output clamping voltage Vclamp of the self-referenced LDO module may be 6 or 7V, and the Vclamp voltage is connected to the charging loop. The output voltage Vpre of the self-referenced LDO module is the power supply of the reference circuit. When the input voltage VIN is less than 5V, Vpre is equal to the VIN voltage. When the input voltage VIN is greater than 5V, the Vpre voltage is always 5V. The voltage comparison circuit has two inputs, one of which is the voltage Vpre and the other is the pin VBAT. The value of the output voltage VH is the larger of the two inputs. The reference circuit has four output voltages, of which VBG1 is always 1.05V, VBG2 is always 0.1V, VBG3 is always 0.6V, and VBG4 is always 1V. These four output voltages are respectively connected to the four input voltages of the same name of the charging loop. The power supply of the charging loop is the input voltage VIN, and its external pin VSECE is connected to the external resistor RSET, and the other pin of the external resistor is grounded. The value of the external resistor is generally 1KΩ.

[0022] Reference Figure 2 , the self-reference LDO circuit of the present invention is further described in detail.

[0023] The first MOS tube M1, the second MOS tube M2, the fourth MOS tube M4, the fifth MOS tube M5 and the ninth MOS tube M9 in the self-reference ldo circuit all adopt high-voltage resistant P-type metal-oxide-semiconductor tubes. The sixth MOS tube M6 and the seventh MOS tube M7 both adopt high-voltage resistant N-type metal-oxide-semiconductor tubes. The third MOS tube M3 adopts an N-type metal-oxide-semiconductor tube, and the eighth MOS tube M8 adopts an N-type depletion-oxide-semiconductor tube. The first resistor R1 and the second resistor R2 are ordinary integrated resistors, and the ratio of the resistance values ​​of R1 and R2 is 1:3. In the embodiment of the present invention, the resistance value of R1 is 10kΩ, and the resistance value of R2 is 30kΩ. The first Zener diode D1 is a common integrated Zener diode. The gate voltage Vbias1 of the eighth MOS tube M8 voltage is always 0v. The first MOS tube M1 and the second MOS tube M2 form a current mirror, the gate of the second MOS tube M2 is connected to its drain and to the voltage Vclamp, the sources of the first MOS tube M1 and the second MOS tube M2 are connected to the input voltage VIN, and the drain of the first MOS tube M1 is grounded. The negative end of the first Zener diode D1 is connected to the drain of the second MOS tube M2, and the positive end thereof is grounded. The fourth MOS tube M4 and the fifth MOS tube M5 form a current mirror, the gate of the fourth MOS tube M4 is connected to its drain, and the sources of the fourth MOS tube M4 and the fifth MOS tube M5 are connected to the input voltage VIN. The gates of the sixth MOS tube M6 and the seventh MOS tube M7 are connected to the voltage Vclamp, the drain of the sixth MOS tube M6 is connected to the drain of the fourth MOS tube M4, the drain of the seventh MOS tube M7 is connected to the drain of the fifth MOS tube M5 and to the gate of the ninth MOS tube M9, and the source of the seventh MOS tube M7 is connected to the drain of the eighth MOS tube M8. The gate of the eighth MOS tube M8 is grounded, and its source is also grounded. The gate of the third MOS transistor M3 is connected to the voltage Vback, the source thereof is grounded, and the drain thereof is connected to the source of the sixth MOS transistor M6. The gate of the ninth MOS transistor M9 is connected to the voltage Vp, the source thereof is connected to the input voltage VIN, the drain thereof is connected to one end of the first resistor R1 and to the output voltage Vpre, the other end thereof is connected to one end of the second resistor R1 and to the voltage Vback, and the other end of the second resistor R2 is grounded.

[0024] Reference Figure 3 , the charging loop of the present invention is further described in detail.

[0025] The tenth MOS tube M10, the twelfth MOS tube M12, the thirteenth MOS tube M13 and the sixteenth MOS tube M16 in the charging loop all adopt high-voltage-resistant P-type metal-oxide-semiconductor tubes. The fourteenth MOS tube M14 and the fifteenth MOS tube M15 all adopt high-voltage-resistant N-type metal-oxide-semiconductor tubes. The eleventh MOS tube M11 adopts a P-type metal-oxide-semiconductor tube. The ratio of the width to length of the tenth MOS tube M10 and the sixteenth MOS tube M16 is 1000:1. The third resistor R3 and the fourth resistor R4 are ordinary integrated resistors, and the ratio of the resistance values ​​of R3 and R4 is 1:3. In the embodiment of the present invention, the resistance value of R3 is 1MΩ, and the resistance value of R2 is 3MΩ. The fifth external resistor RSET is an ordinary resistor, and the resistance value of RSET in the embodiment of the present invention is 1kΩ. The twelfth MOS tube M12 and the thirteenth MOS tube M13 form a current mirror, the gate of the twelfth MOS tube M12 is connected to its drain, and the source of the twelfth MOS tube M12 and the thirteenth MOS tube M13 is connected to the input voltage VIN. The first operational amplifier CC, the second operational amplifier CV, the third operational amplifier OTP and the fourth operational amplifier A1 all use ordinary metal-oxide-semiconductor tubes. The twelfth MOS tube M12 and the thirteenth MOS tube M13 form a current mirror, the gate of the twelfth MOS tube M12 is connected to its drain, and the source of the twelfth MOS tube M12 and the thirteenth MOS tube M13 is connected to the input voltage VIN. The gates of the fourteenth MOS tube M14 and the fifteenth MOS tube M15 are connected to the input clamping voltage Vclamp, the drain of the fourteenth MOS tube M14 is connected to the drain of the twelfth MOS tube M12, the drain of the thirteenth MOS tube M13 is connected to the drain of the fifteenth MOS tube M15 and to the voltage Vx, and the source of the fifteenth MOS tube M15 is connected to the input current IBIAS and grounded. The outputs of the first operational amplifier CC, the second operational amplifier CV and the third operational amplifier OTP are connected to the source of the fourteenth MOS tube M14 and grounded. The positive input terminal of the first operational amplifier CC is connected to VBG1, and its negative input terminal is connected to the voltage V2. The positive input terminal of the second operational amplifier CV is connected to one end of the first switch K1, and its negative input terminal is connected to the pin Vsence, and the other end of the first switch K1 can select the voltage VBG4 or VBG2; the gates of the sixteenth MOS tube M16 and the tenth MOS tube M10 are connected to the voltage Vx, and their sources are connected to the input voltage VH. The negative input terminal of the fourth operational amplifier A1 is connected to the drain of the sixteenth MOS tube M16 and the source of the eleventh MOS tube M11, the positive input terminal thereof is connected to the drain of the tenth MOS tube M10 and the external pin VBAT, and the output thereof is connected to the gate of the eleventh MOS tube M11. One end of the external resistor RSET is connected to the drain of the eleventh MOS tube M11, and the other end thereof is grounded. One end of the third resistor R3 is connected to the drain of the tenth MOS tube M10, and the other end thereof is connected to one end of the fourth resistor R4, and the other end of the fourth resistor R4 is grounded.

[0026] Reference Figure 4 , the schematic diagram of the comparison circuit of the present invention is further described in detail.

[0027] The nineteenth MOS tube M19, the eighteenth MOS tube M18, the twenty-second MOS tube M22 and the seventeenth MOS tube M17 in the voltage comparison circuit all adopt P-type metal-oxide-semiconductor tubes. The twentieth MOS tube M20 and the twenty-first MOS tube M21 all adopt N-type metal-oxide-semiconductor tubes. The first inverter NOR1 adopts a common metal-oxide-semiconductor tube. The nineteenth MOS tube M19 and the eighteenth MOS tube M18 form a current mirror form, and the gate of the nineteenth MOS tube M19 is connected to its drain. The source of the nineteenth MOS tube M19 is connected to the input voltage VBAT, and the source of the eighteenth MOS tube M18 is connected to the input voltage Vpre. The gate of the twentieth MOS tube M20 is connected to the input voltage Vpre, its drain is connected to the drain of the nineteenth MOS tube M19, and its source is grounded; the gate of the twenty-first MOS tube M21 is connected to the input voltage VBAT, its drain is connected to the drain of the eighteenth MOS tube M18 and to the voltage EN, and its source is grounded. The input of the first inverter NOR1 is connected to the voltage EN, and the output thereof is connected to the voltage EN. The gate of the sixteenth MOS transistor M16 is connected to the voltage EN, the drain thereof is connected to the input voltage Vpre, and the source thereof is connected to the output voltage VH. The gate of the seventeenth MOS transistor M17 is not connected to the input voltage EN, the drain thereof is connected to the input voltage VBAT, and the source thereof is connected to the output voltage VH.

[0028] The working principle of the three-stage single-cell lithium battery charging management circuit in the current comparison switching mode of the present invention is described in detail below.

[0029] The function of the self-referenced LDO circuit is to reduce the input voltage, which can be any voltage value between 0 and 36V. When the input voltage VIN is less than 5V, the output voltage Vpre of the self-referenced LDO circuit is equal to the voltage value of VIN. When the input voltage VIN is greater than 5V, the output voltage Vpre is always 5V. Since the first Zener diode D1 cannot pass a large current, the first MOS tube M1 and the second MOS tube M2 form a current mirror structure. The first MOS tube M1 copies the current in the second MOS tube M2 to divert the large current, thereby protecting the first Zener diode D1.

[0030] The comparison circuit module is a commonly used source end comparator, which finds the larger voltage value between Vpre and VBAT and assigns it to the output voltage VH of the comparison circuit.

[0031] The charging loop is the main module for realizing linear charging. In this embodiment, a single lithium battery is fully charged to 4.2V. When the lithium battery voltage is less than 2.8V, it enters the trickle charging mode, and the current for charging the lithium battery is 100mA. When the lithium battery voltage is greater than 2.8V, it enters the constant current charging mode, and the current for charging the lithium battery is 1000mA. The outputs of the first operational amplifier CV, the second operational amplifier CC, and the third operational amplifier OTP are all currents. After being amplified by the current mirror composed of the twelfth MOS tube M12 and the thirteenth MOS tube M13, this current is compared with the input current IBIAS at the Vx point, and the charging state is switched by adjusting the gate voltages of the tenth MOS tube M10 of the charging tube and the sixteenth MOS tube M16 of the sampling tube.

[0032] The magnitude of the lithium battery charging current in constant current and trickle current modes is determined by VSECE / RSET. By utilizing the virtual short and virtual disconnect characteristics of the first op amp CC input, the VSECE voltage in constant current mode is the same as VBG4, and the VSECE voltage in trickle current mode is the same as VBG2. In this embodiment, VBG4 is 1V and VBG4 is 0.1V. The switching of the circuit trickle current and constant current charging modes is achieved by the first switch K1. When the VBAT voltage is less than 2.8V, the switch K1 selects VBG2. When the VBAT voltage is greater than 2.8V, the switch K1 selects VBG4. The ratio of the width to length of the tenth MOS tube M10 of the charging tube and the sixteenth MOS tube M16 of the sampling tube is 1000:1. In the trickle current mode, the current flowing through the sixteenth MOS tube M16 is I M16 =0.1V / 1kΩ, the current copied to the tenth MOS tube M10 is I M10 =I M16 *1000=100mA, the current flowing through the sixteenth MOS tube M16 in constant current mode is I M16 =1V / 1kΩ, the current copied to the tenth MOS tube M10 is I M10 =I M16 *1000=1000mA. The fourth operational amplifier A1 also uses the characteristics of virtual short and virtual open input to make the drain voltages of the tenth MOS tube M10 and the sixteenth MOS tube M16 equal, so as to prevent the channel modulation effect from affecting the accurate copy of the current.

[0033] When the battery voltage reaches 4.2V, it is fully charged, and the first CV op amp starts to work. When the battery voltage is greater than 4.2V, the sampling voltage v2 is greater than VBG1, the output current of the first CV op amp increases, causing the voltage at the Vx point to increase, the charging loop is turned off, and the battery is fully charged.

[0034] When the temperature of the chip is too high during charging, it will cause safety problems. Therefore, a fourth op amp OTP is added. The input of its negative end is the voltage VBE across the source and drain of the triode. The VBE voltage has a negative temperature coefficient. As the temperature rises, the voltage becomes lower. When the temperature is high enough, the VBE voltage is lower than VBG3, and the output current of the fourth op amp OTP becomes larger, causing the voltage at the Vx point to increase, the charging loop is shut down, and the over-temperature protection function is realized.

Claims

1. A three-stage single-cell lithium battery charging circuit in current comparison switching mode, comprising a self-reference LDO module, a reference circuit, a voltage comparison circuit, an external resistor and a charging loop, characterized in that: A current comparison control circuit is provided in the self-reference LDO module, and a current comparison switching circuit is provided in the charging loop: The fourth MOS tube M4 and the fifth MOS tube M5 in the current comparison control circuit form a current mirror, the gate of the fourth MOS tube M4 is connected to its drain, and the sources of the fourth MOS tube M4 and the fifth MOS tube M5 are connected to the input voltage VIN; the gates of the sixth MOS tube M6 and the seventh MOS tube M7 are connected to the input clamping voltage Vclamp, the drain of the sixth MOS tube M6 is connected to the drain of the fourth MOS tube M4, the drain of the seventh MOS tube M7 is connected to the drain of the fifth MOS tube M5 and to the output voltage Vp, and the source of the seventh MOS tube M7 is connected to the drain of the eighth MOS tube M8; the gate of the eighth MOS tube M8 is grounded, and its source is also grounded; the gate of the third MOS tube M3 is connected to the input voltage Vback, its source is grounded, and its drain is connected to the source of the sixth MOS tube M6; The twelfth MOS tube M12 and the thirteenth MOS tube M13 in the current comparison switching circuit form a current mirror form, the gate of the twelfth MOS tube M12 is connected to its drain, and the sources of the twelfth MOS tube M12 and the thirteenth MOS tube M13 are connected to the input voltage VIN; the gates of the fourteenth MOS tube M14 and the fifteenth MOS tube M15 are connected to the input clamping voltage Vclamp, the drain of the fourteenth MOS tube M14 is connected to the drain of the twelfth MOS tube M12, the drain of the thirteenth MOS tube M13 is connected to the drain of the fifteenth MOS tube M15 and to the voltage Vx, the source of the fifteenth MOS tube M15 is connected to the input current IBIAS and to ground, and the source of the fourteenth MOS tube M14 is connected to the outputs of the first operational amplifier CC, the second operational amplifier CV and the third operational amplifier OTP and to ground.

2. The three-stage single-cell lithium battery charging circuit with current comparison switching mode according to claim 1, characterized in that: The nineteenth MOS tube M19 and the eighteenth MOS tube M18 in the voltage comparison circuit form a current mirror form, the gate of the nineteenth MOS tube M19 is connected to its drain; the source of the nineteenth MOS tube M19 is connected to the input voltage VBAT, and the source of the eighteenth MOS tube M18 is connected to the input voltage Vpre; the gate of the twentieth MOS tube M20 is connected to the input voltage Vpre, its drain is connected to the drain of the nineteenth MOS tube M19, and its source is grounded; the gate of the twenty-first MOS tube M21 is connected to the input voltage VBAT, its drain is connected to the drain of the eighteenth MOS tube M18 and to the voltage EN, and its source is grounded; the input of the first inverter NOR1 is connected to the voltage EN, and its output is connected to the voltage EN; the gate of the sixteenth MOS tube M16 is connected to the voltage EN, its drain is connected to the input voltage Vpre, and its source is connected to the output voltage VH; the gate of the seventeenth MOS tube M17 is not connected to the input voltage EN, its drain is connected to the input voltage VBAT, and its source is connected to the output voltage VH.

3. The three-stage single-cell lithium battery charging circuit with current comparison switching mode according to claim 1, characterized in that: The fourth MOS tube M4 and the fifth MOS tube M5 are both high-voltage-resistant P-type metal-oxide-semiconductor tubes.

4. The three-stage single-cell lithium battery charging circuit with current comparison switching mode according to claim 1, characterized in that: The sixth MOS tube M6 and the seventh MOS tube M7 are both high-voltage-resistant N-type metal-oxide-semiconductor tubes.

5. The three-stage single-cell lithium battery charging circuit with current comparison switching mode according to claim 1, characterized in that: The third MOS tube M3 is an N-type metal-oxide-semiconductor tube.

6. The three-stage single-cell lithium battery charging circuit with current comparison switching mode according to claim 1, characterized in that: The eighth MOS tube M8 is a depletion-type oxide-semiconductor tube.

7. The three-stage single-cell lithium battery charging circuit with current comparison switching mode according to claim 1, characterized in that: The twelfth MOS tube M12 and the thirteenth MOS tube M13 are both high-voltage-resistant P-type metal-oxide-semiconductor tubes.

8. The three-stage single-cell lithium battery charging circuit with current comparison switching mode according to claim 1, characterized in that: The fourteenth MOS tube M14 and the fifteenth MOS tube M15 are both high-voltage-resistant N-type metal-oxide-semiconductor tubes.

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