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Li-Ion battery charger design for laptop computer applications Song Qu Applications Engineer Cherry Semiconductor Corporation Abstract The paper discusses the practical design issues of Li-Ion battery chargers using Cherry Semiconductor CS5361/2 battery charger controller. The controller provides all functions necessary for charging Li-Ion battery packs. The theory of operation and design guideline is described and a reference design is presented. Battery Current I. Introduction In recent years, Li-Ion rechargeable batteries are becoming more and more popular in portable applications, due to their size, weight and energy storage advantages. The growth in the LiIon battery market has drastically boosted the demand for high performance battery chargers. Cherry Semiconductor CS5361/ 2 battery charger controller is designed for charging Li-Ion battery packs. It can regulate both output current and output voltage with high accuracy and can provide smooth transition between current and voltage regulation. This paper will discuss topology selection, control methods for current and voltage regulation, and compensation design. Because of its unique characteristics, the charging requirement for Li-Ion battery will be introduced first. II. Li-Ion Battery Charge Requirement The differences in chemistry among various battery types result in different charge requirements. Li-Ion batteries are charged with a constant-voltage, constant-current supply. Fig. 1 illustrates the charging voltage and current profiles of a Li-Ion battery. When the battery voltage is low, the charger operates in constant current mode. The charger regulates the output current to a preset value. The battery voltage increases when it is being charged. When it reaches the end-of-charge voltage (4.1 or 4.2V), the current will start to taper off. The charger enters into constant voltage mode and regulates the output voltage to the end-of-charge voltage. The current will continue to taper off until it almost reaches zero. Charging can be terminated after the current falls below a preset threshold. The charge current is usually expressed as C-rate. The Crate describes the battery capacity in Ampere-Hours. It measures how much current is required to fully charge the battery within one hour, assuming no losses. For a 1600 mAh battery, Battery Voltage Time Figur e 1: Lithium-Ion Battery Charging Profile 1C charge current means charging the battery with 1.6A. Ideally, it will take one hour to fully charge the battery at 1C rate. But because batteries are not 100% efficient in converting charge current into stored charge, it takes longer than one hour to fully charge the battery at 1C rate. III. Selection of Charger Topology There are two categories of battery chargers: linear chargers and switching-regulator-based chargers. Most portable applications, such as laptop computers and cellular phones, require high efficiency, smaller size and lighter weight. Therefore, switching-regulator-based chargers are preferred in those applications. For battery charger applications, Buck regulator is the most suitable one in different switching regulator topologies, because the output voltage is lower than the input voltage. Fig. 2 shows the power stage of a typical Synchronous Buck regulator. In Synchronous Buck topology, MOSFET Q2 replaces the low side diode in a conventional Buck converter. This eliminates the power loss associated with diode forward voltage and increases system efficiency. The PWM control circuitry modulates the duty cycle of the high side MOSFET Q1 to regulate the output voltage. The switching actions of Q1 and Q2 are International IC – China • Conference Proceedings 37 where ∆VO is the peak-to-peak output voltage ripple given by the design specs. If the ESR value obtained from the above equation is smaller than ESR specified in the capacitor manufacturer’s data sheet, several capacitors should be paralleled to get the right value. IV. Current Regulation Figur e 2: Power Stage of Synchronous Buck Regulator complementary. At the beginning of each switching cycle, the gate signal turns on the Q1 and turns off the Q2. Therefore, the difference between input and output voltage (Vin-Vo) is applied across the inductor. The inductor current increases linearly. The energy is transferred from the input source to the inductor. When Q1 turns off and Q2 turns on, the voltage across the inductor becomes negative Vo and the inductor current linearly decreases. The energy stored in the inductor is transferred to the load. A non-overlapping time is always inserted between the turn-on signal of the Q1 and Q2 to prevent the cross conduction. The body diode of the Q2 will temporarily conduct when both switches are turned off. The value of the output inductor can be calculated based on the inductor current ripple requirement: The control method used in CS5361/2 for current regulation is called Current-Mode Constant-Current control, also known as I2 control for the purpose of brevity. A block diagram of I2 control for a Buck regulator is shown in Fig. 3. A constantfrequency clock signal initiates the on time of the high side switch. There are two feedback loops. The feedback signal ISENSE is the voltage across the sense resistor and is proportional to the inductor current. The DC portion is used by the outer loop and is fed to Average Current Error Amplifier. The Error Amplifier compares the feedback signal ISENSE to an externally set reference voltage IAVG to generate a control voltage ICOMP. In CS5361/2, the ICOMP pin is open to users for compensation design. The ripple portion of the feedback signal is used as the ramp signal of the PWM comparator. When the ramp signal intersects with the voltage of ICOMP pin, the output latch will be set. The controller turns off the high side switch and turns off the low side switch. The duty cycle of the high side switch is adjusted so that the output current (inductor current) can be regulated. (1) where Vo is the output voltage; is the period of one switching cycle; ∆ IL is the peak-to-peak inductor current ripple given by the design specifications; and D is the duty cycle of the high side switch. Because both duty cycle and the output voltage are changing during charge operation, the designer should determine the maximum possible product (I-D) of and Vo to calculate the inductance. The peak inductor current is given by: (2) where IL, peak is the peak inductor current and IO is the average output current. The peak current should not saturate the core of the inductor. The output capacitor is used to filter out the inductor ripple current. If the capacitance is large enough, most of the ripple current will flow through the output capacitor. Under this circumstance, the inductor current ripple value and Equivalent Series Resistance (ESR) of the output capacitor will determine the output voltage ripple. The maximum allowable ESR is given by: (3) 38 International IC – China • Conference Proceedings Figur e 3: Block Diagram of I2 Control Method I2 control method has inherent compensation for duty cycle in response to line voltage change. When there is a line voltage variation, the inductor current ripple will change instantaneously, so will the ramp signal. Therefore, the duty cycle can be adjusted on a pulse-by-pulse basis even before the Error Amplifier responds to the line variation. While the inner control loop handles the transient response, the outer loop tightly regulates the output current and provides easy loop compensation. A high gain, low bandwidth error amplifier can be used to improve DC accuracy, loop stability and noise immunity. The I2 compensation network design is based on a smaller signal model proposed in [1]. Fig. 4 is the block diagram of the model. The model is accurate up to half of the switching frequency and can predict the small signal characteristics of I2 control including sub-harmonic oscillation. Fm is the gain of PWM comparator, which is: (8) where Sn is the on-time slope of the current sense waveform. The closed current-loop control-to-inductor-current transfer function can be obtained from the block diagram. (9) The system is third order. The transfer function possesses three poles and one zero. Since the denominator is very complicated, an approximate transfer function can be obtained by ignoring some minor terms in the expression. (10) Figur e 4: Small Signal Model of I2 Control Method The open loop duty-cycle-to-inductor-current transfer function of the Buck regulator can be derived using a standard PWM switch model developed in [2]. When the Buck regulator is operating in continuous conduction mode, the transfer function has the following form: (4) Where RC is the Equivalent Series Resistance (ESR) of the output capacitor. In the block diagram, Ri is the gain of the current sense network. He (s) represents the sampling action of current-mode control. The sampling gain is invariant for all converters and has infinite number of poles and zeros. Actually, a complex pair of RHP zeros provides a simplified representation of this transfer function, which is accurate up to half of the switching frequency [3]. The transfer function is given by: (5) where In Equation (10), the low frequency pole and the zero can be cancelled out. The system becomes second order. It has only a pair of complex poles at half of the switching frequency. (11) Notice that the complex pole pair is at very high frequency (half of the switching frequency) and there is no zero in the system, the compensation design becomes very simple. Only one integration pole is required for the compensation network. The pole gives the system high DC gain and makes it cross over 0dB with a slope of -20dB/dec. After the 0dB crossover, the system will come across the complex pole pair, which causes the amplitude to decrease rapidly and increase the stability margin. If a transconductrance amplifier is used as the error amplifier, the pole can be implemented by grounding the amplifier output through a capacitor. The compensation gain is given by: (12) where G is the transconductance, RO is the output impedance of the error amplifier and Ccomp is the compensation capacitor. Fig. 5 illustrates the effect of the compensation capacitor on (6) and (7) International IC – China • Conference Proceedings 39 frequency should be chosen well below the switching frequency. (14) V. Voltage Regulation Current-mode voltage control method is used to regulate the output voltage. The VFB pin of CS5361/2 monitors the battery voltage. A resistor divider is used to scale down the voltage to the reference level set at the VREF pin. CS5361/2 provides a 4.2V reference voltage, which can obviate the need for a resistor divider network if charging a single 4.2V cell. The Voltage Error Amplifier compares VFB and VREF. The output of the Error Amplifier VCOMP is then compared with ramp signal, which is generated from the inductor current ripple, to adjust the duty cycle of the high side switch. The small signal model of current-mode control is given in [3]. The control-to-output transfer function with closed current loop is given by: Figur e 5: Bode Plot of Closed Current-Loop Control-to-Output Transfer Function ––––––– With Compensation –– –– –– Without Compensation (15) the system. The total loop gain is (13) The value of the compensation capacitor can be calculated if the crossover frequency is known. Generally, the crossover Figur e 6: 18V/16.8V Four-Cell Battery Charger Design 40 International IC – China • Conference Proceedings Compare the above expression with equation (11), we can find the transfer function of current mode voltage control has the same poles as I2 control. The difference is the zero. For I2 control, both ESR of the output capacitor and the load resistor determine the zero. And it can be cancelled out with the low frequency pole. But for current-mode voltage control, It is a high frequency ESR zero. The low frequency pole cannot be cancelled. So the system is third order. The Bode plot of the closed loop control-to-output transfer function is illustrated in Fig. 8. For a transconductance error amplifier, a possible compensation network is shown in Fig. 9. The compensation network has two poles and one zero. The compensation gain is given by: (16) VII. Conclusion Cherry Semiconductor’s CS5361/2 battery charger controller was introduced. The design issues, such as topology selection, current regulation, voltage regulation and compensation design, for Lithium-Ion battery charger for laptop computers were discussed. A reference design and experimental waveforms were given. Reference: The integrator pole will give the system high DC gain. Use the zero to compensate the excessive phase delay caused by the low frequency pole of the control-to-output transfer function. The other pole should be placed around the ESR zero to assure the amplitude decrease fast after the 0dB crossover. VI. Reference Design A 4-cell Lithium-Ion battery charger was built utilizing Cherry Semiconductor’s CS5361. The schematic is illustrated in Figure 6 with all the component specifications. The input voltage is 18V, the target charge current is 2A. The end-of-charge voltage is 16.8V. A Schottky diode is added at the input to block the possible reverse current flowing from the battery to the input power supply when the supply is shut off. The high side Pchannel MOSFET allows high input voltage and requires no charge pump. Besides I≤ control, the part also features another operation mode, which is bias mode. In the bias mode, the part is shut off and the high side MOSFET is turned on so that the battery can discharge to the load. (a) (a) Line Regulation of I2 Control CH1: Inductor Current CH2: Input Voltage CH4: Switching Node Voltage [1] S. Qu, D, Goder, “A Novel Battery Charger Solution Using I2 Control Method” Proceedings of High Frequency Power Conversion Conference, November 9-11, 1999, Chicago, Illinois. [2] V. Vorperian, “Simplified Analysis of PWM Converters Using the Model of PWM Switch: Part I and II” IEEE Transactions on Aerospace and Electronic System, March 1990, Vol.26, No.2. [3] R. Ridley, “A New Continuous-Time Model for CurrentMode Control” Proceedings of Power Conversion and Intelligent Motion Conference, October 16-19, 1989, Long Beach, CA. Author’s contact details: Song Qu Cherry Semiconductor Corporation 2000 South County Trail, East Greenwich, RI 02818 USA Phone: 1 401 886 3850 Fax: 1 401 886 3336 E-mail: [email protected] (b) (b) Current Regulation of I2 Control CH1: Switching Node Voltage CH3: Output Voltage CH4: Inductor Current Figur e 7: Experimental Waveforms International IC – China • Conference Proceedings 41 Presentation Materials Presentation Overview CS5361/2 Battery Charger Controller Li-Ion Battery Charge Requirement 42 International IC – China • Conference Proceedings Selection of Charger Topology Select Output Innductor Select Output Capacitor International IC – China • Conference Proceedings 43 Current Regulation Method I2 Control Method Small Signal Model of I2 Control 44 International IC – China • Conference Proceedings Small Signal Model of I2 Control Small Signal Model of I2 Control Design Compensation International IC – China • Conference Proceedings 45 Simulation Results Design of Current Compensation Small Signal Model of Current Control 46 International IC – China • Conference Proceedings Design of Voltage Compensation Reference Design Key Operation Waveforms International IC – China • Conference Proceedings 47 Experimental Results Conclusion 48 International IC – China • Conference Proceedings