19-1679; Rev 2; 12/07 12V, Ultra-Low-IQ, Low-Dropout Linear Regulators with POK The MAX8880/MAX8881 are ultra-low supply current, low-dropout linear regulators, capable of delivering up to 200mA. They are designed for battery-powered applications where reverse battery protection and long battery life are critical. These regulators’ low 3.5µA supply current extends battery life in applications with long standby periods. Unlike PNP-based designs, a 2Ω PMOS device maintains ultralow supply current throughout the entire operating range and in dropout. The parts are internally protected from output short circuits, reverse battery connection, and thermal overload. An internal power-OK (POK) comparator indicates when the output is out of regulation. The MAX8880 output is adjustable from 1.25V to 5V using an external resistor-divider. The MAX8881 provides only factory-preset output voltages of 1.8V, 2.5V, 3.3V, or 5V (see Ordering Information). The devices are available in 6-pin SOT23 and 6-pin TDFN packages. Features ♦ 3.5µA Supply Current at 12V ♦ Reverse Battery Protection ♦ 2.5V to 12V Input Voltage Range ♦ ±1.5% Output Voltage Accuracy ♦ 200mA max Output Current ♦ 2Ω PMOS Output Device ♦ Short-Circuit and Thermal Overload Protection ♦ POK Output for Out-of-Regulation Indicator ♦ Fixed 1.8V, 2.5V, 3.3V, and 5V (MAX8881) Adjustable from 1.25V to 5V (MAX8880) ♦ Tiny 6-Pin SOT23 Package ♦ Thin 6-Pin TDFN Package ________________________Applications Smoke Detectors Battery-Powered Alarms Remote Transmitters Smart Battery Packs PDAs Handy Terminals CMOS Backup Power Real-Time Clocks Pin Configurations TOP VIEW POK SHDN 6 IN 1 6 5 Typical Operating Circuit IN 4 POK VIN 2.5V TO 12V IN OUT FB 1μF GND 2 MAX8880 MAX8881 OUT 3 5 SHDN 4 FB MAX8881 MAX8880 ON 1 SOT23-6 2 VOUT 1.25V TO 5V UP TO 200mA 4.7μF OFF 3 REGULATION OK SHDN POK GND FB GND OUT TDFN 3mm x 3mm Ordering Information OUTPUT TEMP RANGE PIN-PACKAGE TOP MARK MAX8880EUT-T PART Adjustable -40°C to +85°C 6 SOT23-6 AAHR MAX8880ETT-T Adjustable -40°C to +85°C 6 TDFN AGS AAHS MAX8881EUT18-T 1.8V -40°C to +85°C 6 SOT23-6 MAX8881EUT25-T 2.5V -40°C to +85°C 6 SOT23-6 AAHT MAX8881EUT33-T 3.3V -40°C to +85°C 6 SOT23-6 AAHU MAX8881EUT50-T 5.0V -40°C to +85°C 6 SOT23-6 AAHV ________________________________________________________________ Maxim Integrated Products For pricing, delivery, and ordering information, please contact Maxim Direct at 1-888-629-4642, or visit Maxim's website at www.maxim-ic.com. 1 MAX8880/MAX8881 General Description MAX8880/MAX8881 12V, Ultra-Low-IQ, Low-Dropout Linear Regulators with POK ABSOLUTE MAXIMUM RATINGS OUT Continuous Current...................................................200mA OUT Short Circuit...........................................................Indefinite Continuous Power Dissipation (TA = +70°C) 6-Pin SOT23 (derate 8.7mW/°C above +70°C)...........696mW 6-Pin TDFN (derate 24.4mW/°C above +70°C) ........1951mW Operating Temperature Range ...........................-40°C to +85°C Junction Temperature ......................................................+150°C Storage Temperature.........................................-65°C to +165°C Lead Temperature (soldering, 10s) .................................+300°C IN to GND ................................................................-14V to +14V SHDN to GND .............................................-0.3V to (VIN + 0.3V), -0.3V to +0.3V when VIN < 0V OUT, FB to GND...............................-0.3V to +6V when VIN > 5.7V, -0.3V to (VIN + 0.3V) when 0V ≤ VIN ≤ 5.7V, -0.3V to +0.3V when VIN < 0V POK to GND ...........................................................-0.3V to +14V Stresses beyond those listed under “Absolute Maximum Ratings” may cause permanent damage to the device. These are stress ratings only, and functional operation of the device at these or any other conditions beyond those indicated in the operational sections of the specifications is not implied. Exposure to absolute maximum rating conditions for extended periods may affect device reliability. ELECTRICAL CHARACTERISTICS (VIN = VOUT + 1V, SHDN = IN, COUT = 4.7µF, TA = -40°C to +85°C, unless otherwise noted. Typical values are at TA = +25°C.) (Note 1) PARAMETER Input Voltage Range Supply Current Shutdown Supply Current Input Undervoltage Lockout FB Voltage, Adjustable Mode SYMBOL CONDITIONS VIN IIN IIN(SHDN) VFB MAX UNITS 12 V VIN = 12V 3.5 10 μA V SHDN = 0, VIN = 12V, VOUT = 0, TA = +25°C 1.5 3 μA 2.1 2.4 V 1.257 1.276 MAX8880, IOUT = 20mA MAX8881, IOUT = 20mA TA = +25°C 1.238 TA = 0°C to +85°C 1.232 1.282 TA = -40°C to +85°C 1.219 1.295 -1.5 1.5 -2 2 TA = +25°C TA = 0°C to +85°C TA = -40°C to +85°C VOUT TYP 2.5 VUVLO OUT Voltage Accuracy (Note 2) OUT Voltage Range MIN MAX8880 -3 3 1.25 5.5 V % V OUT Line Regulation VIN = VOUT + 1V to 12V 0.01 0.05 %/V OUT Load Regulation (Note 3) IOUT = 10μA to 100mA 0.006 0.015 %/mA Current Limit (Note 3) IOUT 200 Dropout Voltage (Notes 3, 4) ΔVDO IN Reverse Leakage Current IIN(REV) VIN = -12V, V SHDN = 0 Foldback Current Limit IOUT(SC) VIN = 5V, VOUT = 0 SHDN Input Threshold VIH VIL SHDN Input Bias Current FB Input Bias Current IFB IOUT = 50mA 100 200 250 0.5 V SHDN = 0 to 12V, TA = +25°C -100 FB = 1.25V, TA = +25°C, MAX8880 only Falling TA = +25°C 0 87.5 TA = -40°C to +85°C Hysteresis IPOK VPOK = 12V, TA = +25°C POK Low Voltage VPOK IPOK = 1mA 2 90.5 86 V nA 20 93.5 nA 1.5 _______________________________________________________________________________________ mA 100 95 50 mV mA 2 POK Off-Current 2 mA 1 VIN = 2.5V to 12V POK Trip Threshold 400 % of VOUT 100 nA 200 mV 12V, Ultra-Low-IQ, Low-Dropout Linear Regulators with POK (VIN = VOUT + 1V, SHDN = IN, COUT = 4.7µF, TA = -40°C to +85°C, unless otherwise noted. Typical values are at TA = +25°C.) (Note 1) PARAMETER SYMBOL Thermal Shutdown Threshold TTSD OUT Noise Note 1: Note 2: Note 3: Note 4: CONDITIONS MIN TYP (Hysteresis = 15°C) VOUT(NOISE) f = 10Hz to 100kHz, IOUT = 1mA MAX UNITS 160 °C 300 μVRMS All devices are 100% production tested at TA = +25°C. All temperature limits are guaranteed by design. Output accuracy with respect to nominal preset voltages. FB = OUT. This specification is valid for VIN > 3V. The dropout voltage is defined as VIN - VOUT , when VOUT is 100mV below the value of VOUT for VIN = VOUT + 1V. Typical Operating Characteristics (VIN = 5V, VOUT = 3.3V, IOUT = 30mA, COUT = 4.7µF, TA = +25°C, unless otherwise noted. See Figure 1.) NO LOAD 2.5 2.0 1.5 3.5 3.0 2.5 2.0 1.5 300 250 200 0.5 0.5 50 0 0 0 6 8 10 -40 12 -15 10 35 60 TA = +25°C 150 100 4 TA = +85°C 350 1.0 2 MAX8880/1-03 400 1.0 TA = -40°C 0 85 50 100 150 INPUT VOLTAGE (V) TEMPERATURE (°C) LOAD CURRENT (mA) POWER-SUPPLY REJECTION RATIO vs. FREQUENCY OUTPUT NOISE SPECTRAL DENSITY vs. FREQUENCY OUTPUT NOISE vs. LOAD CURRENT NOISE (µV/√Hz) 50 40 30 20 1 0.10 10 COUT = 1.0μF 350 OUTPUT NOISE (μVRMS) 60 400 200 MAX8880/1-06 10 MAX8880/1-04 70 MAX186-14A 0 PSRR (dB) 450 DROPOUT VOLTAGE (mV) 4.0 SUPPLY CURRENT (µA) SUPPLY CURRENT (µA) 3.5 VOUT = 1.8V 4.5 500 MAX8880/1-02 IOUT = 30 mA 3.0 5.0 MAX8880/1-01 4.5 4.0 DROPOUT VOLTAGE vs. LOAD CURRENT SUPPLY CURRENT vs. TEMPERATURE SUPPLY CURRENT vs. INPUT VOLTAGE 300 250 COUT = 4.7μF 200 150 100 50 0 0.01 0.1 1 10 100 FREQUENCY (Hz) 1k 10k VOUT = 1.8V 0 10 100 1k FREQUENCY (Hz) 10k 100k 0 20 40 60 80 100 LOAD CURRENT (mA) _______________________________________________________________________________________ 3 MAX8880/MAX8881 ELECTRICAL CHARACTERISTICS (continued) Typical Operating Characteristics (continued) (VIN = 5V, VOUT = 3.3V, IOUT = 30mA, COUT = 4.7µF, TA = +25°C, unless otherwise noted. See Figure 1.) SUPPLY CURRENT OUTPUT VOLTAGE ERROR OUTPUT VOLTAGE vs. LOAD CURRENT vs. LOAD CURRENT vs. INPUT VOLTAGE -0.1 -0.2 -0.3 -0.4 MAX8880/1-09 3.00 OUTPUT VOTLAGE (V) 3.7 SUPPLY CURRENT (μA) 0 3.50 MAX8880/1-08 0.1 OUTPUT VOLTAGE ERROR (%) 3.8 MAX8880/1-07 0.2 3.6 3.5 2.50 2.00 1.50 1.00 3.4 0.50 -0.5 3.3 -0.6 0 50 100 150 0 0 200 50 100 150 200 0 2 4 6 8 10 12 LOAD CURRENT (mA) LOAD CURRENT (mA) INPUT VOLTAGE (V) CHANGE FROM NOMINAL OUTPUT VOLTAGE vs. TEMPERATURE REGION OF STABLE COUT ESR vs. OUTPUT CURRENT LINE-TRANSIENT RESPONSE MAX8880/1-11 0.15 14 MAX8880/1-12 100 MAX8880/1-10 0.20 0.10 COUT ESR (Ω) CHANGE FROM NOMINALOUTPUT VOLTAGE (%) MAX8880/MAX8881 12V, Ultra-Low-IQ, Low-Dropout Linear Regulators with POK 0.05 0 -0.05 10 9.75V COUT = 10µF 9V 1 COUT = 4.7µF -0.10 -0.15 STABLE REGION 0.1 -0.20 -40 -15 10 35 60 0 85 50 100 200 150 TEMPERATURE (°C) OUTPUT CURRENT (mA) LOAD-TRANSIENT RESPONSE LOAD-TRANSIENT RESPONSE NEAR DROPOUT 200µs/div CH1 = VIN, 500mV/div, AC COUPLED CH2 = VOUT, 20mV/div, AC COUPLED VOUT = 5V, IOUT = 5mA TURN-ON RESPONSE MAX8880/1-14 MAX8880/1-13 MAX8880/1-15 32.5mA 32.5mA 4V 1.25mA 1.25mA 400µs/div CH1 = IOUT, 12.5mA/div CH2 = VOUT, 100mV/div, AC COUPLED VOUT(NOMINAL) = 5V, VIN = 9V 4 1.8V 400µs/div CH1 = IOUT, 12.5mA/div CH2 = VOUT, 100mV/div, AC COUPLED VIN = 5.2V, VOUT(NOMINAL) = 5V 100µs/div CH1 = SHDN, 2V/div CH2 = VOUT, 1V/div VIN = 4.0V _______________________________________________________________________________________ 12V, Ultra-Low-IQ, Low-Dropout Linear Regulators with POK PIN MAX888_ (SOT) NAME FUNCTION 1 MAX888_ (TDFN) 4 IN 2 2 GND Ground 3 3 OUT Output Voltage. Bypass with a 4.7µF capacitor (<0.5Ω ESR) to GND for load currents up to 200mA. For load currents up to 40mA, 1µF is acceptable. 4 1 FB Feedback Set Point, 1.25V (MAX8880 only). Output sense, connect to OUT externally (MAX8881 only). 5 5 SHDN ON/OFF Control. Regulator is ON when V SHDN > 2V. If unused, connect to IN. If reverse battery protection of the SHDN input is desired, connect a 100kΩ resistor in series with SHDN. 6 6 POK — — EP Input Voltage. Bypass with a 1µF capacitor to GND. POK Output, Open Drain. Low when OUT is out of regulation or in shutdown. Connect POK to OUT through a high-value resistor for a simple error Exposed paddle (TDFN only). Connect to the circuit ground plane. Detailed Description The MAX8880/MAX8881 are low-dropout, low-quiescent current linear regulators designed primarily for battery-powered applications (Figure 1). The MAX8880 provides an adjustable output voltage from 1.25V to 5V using an external resistor-divider. The MAX8881 is available in factory preset output voltages of 1.8V, 2.5V, 3.3V, and 5V. Both devices have a +1.25V reference, error amplifier, MOSFET driver, and P-channel pass transistor (Figure 2). Low-Dropout Regulator The 1.25V reference is connected to the error amplifier’s inverting input. The error amplifier compares this reference with the selected feedback voltage and amplifies the difference. The MOSFET driver reads the error signal and applies the appropriate drive to the Pchannel pass transistor. If the feedback voltage is lower than the reference voltage, the pass-transistor gate is VIN 2.5V TO 12V C1 1μF VOUT IN OUT FB R2* 100k C2 4.7μF MAX8881 POK GND *OPTIONAL Figure 1. Standard Application Circuit Internal P-Channel Pass Transistor The MAX8880/MAX8881 feature a 2Ω P-channel MOSFET pass transistor. This provides advantages over similar designs using PNP pass transistors, including longer battery life. The P-channel MOSFET requires no base drive, which reduces quiescent current considerably. PNP-based regulators waste considerable current in dropout when the pass transistor saturates. They also use high base-drive currents under large loads. The MAX8880/MAX8881 do not suffer from these problems and consume only 3.5µA of supply current (see Typical Operating Characteristics). Dropout Voltage REGULATION OK SHDN pulled lower, allowing more current to pass, increasing the output voltage. If the feedback voltage is higher than the reference voltage, the pass-transistor gate is driven higher, allowing less current to pass to the output. The output voltage is fed back through either an internal resistor voltage divider by externally connecting FB to OUT (MAX8881), or an external resistor network connected to FB (MAX8880). Additional blocks include an output current limiter, reverse battery protection, a thermal sensor, shutdown logic, and a POK comparator to indicate when the output is out of regulation (Figure 2). A regulator’s minimum input-output differential (or dropout voltage) determines the lowest usable supply voltage. In battery-powered systems, this determines the useful end-of-life battery voltage. Because the MAX8880/MAX8881 use a P-channel MOSFET pass transistor, their dropout voltage is RDS(ON) (2Ω) multiplied by the load current (see Electrical Characteristics). _______________________________________________________________________________________ 5 MAX8880/MAX8881 Pin Description MAX8880/MAX8881 12V, Ultra-Low-IQ, Low-Dropout Linear Regulators with POK IN SHDN REVERSE BATTERY PROTECTION MOS DRIVER WITH ILIMIT ERROR AMP P OUT FB SHUTDOWN LOGIC MAX8881 POK 1.25V REF THERMAL SENSOR POK 91% REF GND Figure 2. Functional Diagram Current Limiting VIN 2.5V TO 12V IN VOUT 1.25V TO 5.5V UP TO 200mA OUT C1 1μF C2 4.7μF R3 Thermal Overload Protection MAX8880 FB SHDN GND POK REGULATION OK R4 Figure 3. Adjustable Output Using External Feedback Resistors Reverse Battery Protection The MAX8880/MAX8881 have a unique protection scheme that limits the reverse supply current to less than 1mA when VIN is forced below ground. The circuit monitors the polarity of IN, disconnecting the internal circuitry and parasitic diodes when the battery is reversed. This feature prevents the device from electrical stress and damage when the battery is connected backwards. If reverse battery protection is needed, drive SHDN through a 100kΩ resistor. 6 The MAX8880/MAX8881 include a current limiter. When the output is shorted to ground, drive to the output PMOS is limited. The output can be shorted to ground without damage to the part. Thermal overload protection limits total power dissipation in the MAX8880/MAX8881. When the internal junction temperature exceeds TJ = +160°C, the thermal sensor signals the shutdown logic, turning off the pass transistor and allowing the IC to cool. The thermal sensor turns the pass transistor on again after the IC’s junction temperature cools by 15°C, resulting in a pulsed output during continuous thermal-overload conditions. Thermal-overload protection is designed to protect the MAX8880/MAX8881 in the event of fault conditions. For continuous operation, do not exceed the absolute maximum junction temperature rating of TJ(MAX) = +150°C. Operating Region and Power Dissipation The MAX8880/MAX8881’s maximum power dissipation depends on the thermal resistance of the case and circuit board, the temperature difference between the die junction and ambient air, and the rate of airflow. The power dissipation in the device is P = I OUT (V IN VOUT). The maximum power dissipation allowed is: _______________________________________________________________________________________ 12V, Ultra-Low-IQ, Low-Dropout Linear Regulators with POK (MAX ) where TJ(MAX) = +150°C, TA is the ambient temperature, θJC is the thermal resistance from the junction to the case, and θCA is the thermal resistance from the case through the PC board, copper traces, and other materials to the surrounding air. POK Output The open-drain POK output is useful as a simple error flag, as well as a delayed reset output. POK sinks current when the output voltage is 10% below the regulation point. Connect POK to OUT through a high-value resistor for a simple error flag indicator. Connect a capacitor in parallel with the resistor to produce a delayed POK signal (delay set by the RC time constant). POK is low during out of regulation or in shutdown and is high impedance during normal operation. Applications Information Capacitor Selection and Regulator Stability The MAX8880/MAX8881 are designed to be stable with an output filter capacitor as low as 1µF and an ESR as high as 1Ω. For general purposes, use a 1µF capacitor on the device’s input and a 4.7µF capacitor on the output. Larger input capacitor values and lower ESR provide better supply-noise rejection and transient response. Use a higher value input capacitor (10µF may be necessary) if large, fast transients are anticipated and the device is located several inches from the power source. Use large output capacitors to improve loadtransient response, stability, and power-supply rejection. Note that some ceramic dielectric materials (e.g., Z5U and Y5V) exhibit a large temperature coefficient for both capacitance and ESR, and a larger output capacitance may be needed to ensure stability at low temperatures. A 4.7µF output capacitor with X7R or X5R dielectrics should be sufficient for stable operation over the full temperature range, with load currents up to 200mA. For load currents up to 40mA, 1µF is acceptable. A graph of the Region of Stable Cout ESR vs. Output Current is shown in the Typical Operating Characteristics. output to 5V. Connect the MAX8881’s FB to OUT for proper operation. The MAX8880 features an adjustable output voltage from 1.25V to 5.5V, using two external resistors connected as a voltage-divider to FB (Figure 3). The output voltage is set by the following equation: R3 ⎞ ⎛ VOUT = VFB ⎜1 + ⎟ ⎝ R4 ⎠ where typically VFB = 1.257V. Choose R4 = 1.2MΩ to optimize quiescent current, accuracy, and high-frequency power-supply rejection. To simplify resistor selection: ⎛V ⎞ R3 = R4 ⎜ OUT − 1⎟ ⎝ VFB ⎠ The total current through the external resistive feedback and load resistors should be greater than 1µA. Since the VFB tolerance is typically less than ±1.5%, the output can be set using fixed resistors instead of trim pots. Power-Supply Rejection and Operation from Sources Other than Batteries The MAX8880/MAX8881 are designed to deliver lowdropout voltages and low quiescent currents in batterypowered systems. Power-supply rejection is -66dB at low frequencies and rolls off with frequencies above 100Hz. At high frequencies, the output capacitor is the major contributor to the rejection of power-supply noise (see Power-Supply Rejection Ratio vs. Frequency in the Typical Operating Characteristics). When operating from sources other than batteries, improve supply-noise rejection and transient response by increasing the value of the input and output capacitors and by using passive filtering techniques. The MAX8880/MAX8881 load-transient response graphs (see Typical Operating Characteristics) show the output response due to changing load current. Reduce overshoot by increasing the output capacitor’s value up to 10µF and by reducing its ESR. Chip Information TRANSISTOR COUNT: 134 Output Voltage Selection The MAX8881 features a preset output voltage. Internal precision feedback resistors set the MAX8881EUT18 output to 1.8V, the MAX8881EUT25 output to 2.5V, the MAX8881EUT33 output to 3.3V, and the MAX8881EUT50 _______________________________________________________________________________________ 7 MAX8880/MAX8881 PMAX = (TJ − TA ) (θJC + θCA ) Package Information (The package drawing(s) in this data sheet may not reflect the most current specifications. For the latest package outline information go to www.maxim-ic.com/packages.) 6LSOT.EPS MAX8880/MAX8881 12V, Ultra-Low-IQ, Low-Dropout Linear Regulators with POK PACKAGE OUTLINE, SOT 6L BODY 21-0058 8 _______________________________________________________________________________________ I 1 2 12V, Ultra-Low-IQ, Low-Dropout Linear Regulators with POK PACKAGE OUTLINE, SOT 6L BODY 21-0058 I 2 2 _______________________________________________________________________________________ 9 MAX8880/MAX8881 Package Information (continued) (The package drawing(s) in this data sheet may not reflect the most current specifications. For the latest package outline information go to www.maxim-ic.com/packages.) Package Information (continued) (The package drawing(s) in this data sheet may not reflect the most current specifications. For the latest package outline information go to www.maxim-ic.com/packages.) 6, 8, &10L, DFN THIN.EPS MAX8880/MAX8881 12V, Ultra-Low-IQ, Low-Dropout Linear Regulators with POK 10 ______________________________________________________________________________________ 12V, Ultra-Low-IQ, Low-Dropout Linear Regulators with POK COMMON DIMENSIONS PACKAGE VARIATIONS SYMBOL MIN. MAX. PKG. CODE N D2 E2 e JEDEC SPEC b [(N/2)-1] x e A 0.70 0.80 T633-2 6 1.50±0.10 2.30±0.10 0.95 BSC MO229 / WEEA 0.40±0.05 1.90 REF D 2.90 3.10 T833-2 8 1.50±0.10 2.30±0.10 0.65 BSC MO229 / WEEC 0.30±0.05 1.95 REF E 2.90 3.10 T833-3 8 1.50±0.10 2.30±0.10 0.65 BSC MO229 / WEEC 0.30±0.05 1.95 REF A1 0.00 0.05 T1033-1 10 1.50±0.10 2.30±0.10 0.50 BSC MO229 / WEED-3 0.25±0.05 2.00 REF L 0.20 0.40 T1033-2 10 1.50±0.10 2.30±0.10 0.50 BSC MO229 / WEED-3 0.25±0.05 2.00 REF k 0.25 MIN. T1433-1 14 1.70±0.10 2.30±0.10 0.40 BSC ---- 0.20±0.05 2.40 REF A2 0.20 REF. T1433-2 14 1.70±0.10 2.30±0.10 0.40 BSC ---- 0.20±0.05 2.40 REF ______________________________________________________________________________________ 11 MAX8880/MAX8881 Package Information (continued) (The package drawing(s) in this data sheet may not reflect the most current specifications. For the latest package outline information go to www.maxim-ic.com/packages.) MAX8880/MAX8881 12V, Ultra-Low-IQ, Low-Dropout Linear Regulators with POK Revision History REVISION NUMBER REVISION DATE 2 12/07 DESCRIPTION Correction to Pin Description, updated Package Information, incorporated style changes PAGES CHANGED 1, 5, 8–11 Maxim cannot assume responsibility for use of any circuitry other than circuitry entirely embodied in a Maxim product. No circuit patent licenses are implied. Maxim reserves the right to change the circuitry and specifications without notice at any time. 12 ____________________Maxim Integrated Products, 120 San Gabriel Drive, Sunnyvale, CA 94086 408-737-7600 © 2007 Maxim Integrated Products is a registered trademark of Maxim Integrated Products, Inc.
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