TPS54478RTET [TI]

2.95-V to 6-V Input, 4-A Output, 2-MHz, Synchronous Step-Down; 2.95 V至6 V的输入, 4 A输出, 2 - MHz的同步降压型
TPS54478RTET
型号: TPS54478RTET
厂家: TEXAS INSTRUMENTS    TEXAS INSTRUMENTS
描述:

2.95-V to 6-V Input, 4-A Output, 2-MHz, Synchronous Step-Down
2.95 V至6 V的输入, 4 A输出, 2 - MHz的同步降压型

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中文:  中文翻译
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TPS54478  
www.ti.com  
SLVSAS2 JUNE 2011  
2.95-V to 6-V Input, 4-A Output, 2-MHz, Synchronous Step-Down  
Switcher With Integrated FETs ( SWIFT)  
Check for Samples: TPS54478  
1
FEATURES  
DESCRIPTION  
The TPS54478 device is a full featured 6 V, 4 A,  
synchronous step down current mode converter with  
two integrated MOSFETs.  
2
Two 30-m(typical) MOSFETs for High  
Efficiency at 4 A Loads  
200kHz to 2MHz Switching Frequency  
0.6 V ± 1% Voltage Reference Over  
Temperature (40°C to 150°C)  
Start up with Pre-Biased Voltage  
Synchronizes to External Clock  
Adjustable Slow Start / Sequencing  
UV and OV Power Good Output  
Cycle by Cycle Current Limit and Hiccup  
Current Protection  
The TPS54478 enables small designs by integrating  
the MOSFETs, implementing current mode control to  
reduce external component count, reducing inductor  
size by enabling up to 2 MHz switching frequency,  
and minimizing the IC footprint with a small 3mm x  
3mm thermally enhanced QFN package.  
The TPS54478 provides accurate regulation for a  
variety of loads with an accurate ±1% Voltage  
Reference (VREF) over temperature.  
Thermally Enhanced 3mm × 3mm 16-pin QFN  
(RTE)  
Pin Compatible to TPS54418  
Efficiency is maximized through the integrated 30mΩ  
MOSFETs and 525μA typical supply current. Using  
the enable pin, shutdown supply current is reduced to  
2.5µA by entering a shutdown mode.  
APPLICATIONS  
Under voltage lockout is internally set at 2.6 V, but  
can be increased by programming the threshold with  
a resistor network on the enable pin. The output  
voltage startup ramp is controlled by the slow start  
pin. An open drain power good signal indicates the  
output is within 93% to 107% of its nominal voltage.  
Low-Voltage, High-Density Power Systems  
Point of Load Regulation for High Performance  
DSPs, FPGAs, ASICs and Microprocessors  
Broadband, Networking and Optical  
Communications Infrastructure  
Cycle-by-cycle current limit, hiccup overcuurent  
protection and thermal shutdown protect the device  
during an overcurrent condition.  
SIMPLIFIED SCHEMATIC  
vertical spacer  
The TPS54478 is supported in the SwitcherPro™  
Software Tool at www.ti.com/switcherpro.  
For more SWIFTTM documentation, see the TI  
website at www.ti.com/swift.  
vertical spacer  
VIN  
C
BOOT  
VIN  
BOOT  
TPS54478  
C
I
R
R
4
5
L
O
VOUT  
EN  
95  
PH  
C
O
90  
R
1
2
PWRGD  
V
= 5 V  
85  
80  
75  
70  
65  
60  
IN  
VSENSE  
V
= 3.3 V  
IN  
R
SS/TR  
RT /CLK  
COMP  
GND  
AGND  
C
POWERPAD  
ss  
R
R
T
3
C
F
= 1 MHz,  
1
S
DCR = 6.8 mW,  
= 1.8 V  
55  
50  
V
O
0
0.5  
1
1.5  
2
2.5  
3
3.5  
4
I
- Output Current - A  
O
1
Please be aware that an important notice concerning availability, standard warranty, and use in critical applications of Texas  
Instruments semiconductor products and disclaimers thereto appears at the end of this data sheet.  
2
SWIFT, SwitcherPro are trademarks of Texas Instruments.  
PRODUCTION DATA information is current as of publication date.  
Products conform to specifications per the terms of the Texas  
Instruments standard warranty. Production processing does not  
necessarily include testing of all parameters.  
Copyright © 2011, Texas Instruments Incorporated  
TPS54478  
SLVSAS2 JUNE 2011  
www.ti.com  
These devices have limited built-in ESD protection. The leads should be shorted together or the device placed in conductive foam  
during storage or handling to prevent electrostatic damage to the MOS gates.  
ORDERING INFORMATION(1)  
TJ  
PACKAGE  
PART NUMBER  
40°C to 150°C  
3 × 3 mm QFN  
TPS54478RTE  
(1) For the most current package and ordering information, see the Package Option Addendum at the end  
of this document, or see the TI website at www.ti.com  
ABSOLUTE MAXIMUM RATINGS(1)  
UNIT  
VIN  
0.3 to 7  
0.3 to 7  
PH + 7  
0.3 to 3  
0.3 to 3  
0.3 to 7  
0.3 to 3  
0.3 to 3.3  
7
EN  
BOOT  
VSENSE  
COMP  
Input voltage  
V
PWRGD  
SS/TR  
RT/CLK  
BOOT-PH  
PH  
Output voltage  
Source current  
Sink current  
0.6 to 7  
2 to 10  
100  
V
PH 10 ns Transient  
EN  
µA  
RT/CLK  
COMP  
100  
100  
µA  
mA  
µA  
kV  
V
PWRGD  
SS/TR  
10  
100  
Electrostatic discharge (Human Body Model) QSS 009-105 (JESD22-A114A)(2)  
2
Electrostatic discharge (Charged Devic Model) QSS 009-147 (JESD22-C101B.01)  
500  
Tj  
Temperature  
Tstg  
40 to 150  
65 to 150  
°C  
°C  
(1) 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 under ELECTRICAL  
SPECIFICATIONS is not implied. Exposure to absolute-maximum-rated conditions for extended periods may affect device reliability.  
(2) The human body model is a 100-pF capacitor discharged through a 1.5-kresistor into each pin. The machine model is a 200-pF  
capacitor discharged directly into each pin.  
2
Copyright © 2011, Texas Instruments Incorporated  
TPS54478  
www.ti.com  
SLVSAS2 JUNE 2011  
THERMAL INFORMATION  
TPS54478  
(RTE)  
THERMAL METRIC(1)(2)(3)  
UNITS  
(QFN-16) PINS  
θJA  
Junction-to-ambient thermal resistance  
49.1  
0.7  
ψJT  
Junction-to-top characterization parameter  
Junction-to-board characterization parameter  
Junction-to-case(top) thermal resistance  
Junction-to-case(bottom) thermal resistance  
Junction-to-board thermal resistance  
ψJB  
21.8  
50.7  
7.5  
°C/W  
θJC(top)  
θJC(bottom)  
θJB  
21.8  
(1) For more information about traditional and new thermal metrics, see the IC Package Thermal Metrics application report, SPRA953.  
(2) Maximum power dissipation may be limited by overcurrent protection  
(3) Power rating at a specific ambient temperature TA should be determined with a junction temperature of 150°C. This is the point where  
distortion starts to substantially increase. Thermal management of the PCB should strive to keep the junction temperature at or below  
150°C for best performance and long-term reliability. See power dissipation estimate in application section of this data sheet for more  
information.  
ELECTRICAL CHARACTERISTICS  
TJ = 40°C to 150°C, VIN = 2.95 to 6 V (unless otherwise noted)  
DESCRIPTION  
SUPPLY VOLTAGE (VIN PIN)  
Operating input voltage  
CONDITIONS  
MIN  
TYP  
MAX  
UNIT  
2.95  
6.0  
V
V
Input under voltage lockout threshold  
Shutdown supply current  
No voltage hysteresis  
2.6  
0.7  
EN = 0 V, 25°C, 2.95 V VIN 6 V  
2.5  
μA  
μA  
Quiescent Current - Iq  
VSENSE = 0.7 V, VIN = 5 V, 25°C, RT = 78.7 kΩ  
525  
700  
ENABLE AND UVLO (EN PIN)  
Rising  
1.30  
1.21  
Enable threshold  
Input current  
V
Falling  
Enable threshold + 50 mV  
Enable threshold 50 mV  
3.4  
μA  
0.64  
VOLTAGE REFERENCE (VSENSE PIN)  
Voltage Reference  
2.95 V VIN 6 V, 40°C <TJ < 150°C  
0.594 0.600 0.606  
V
MOSFET  
BOOT-PH = 5 V  
BOOT-PH = 3.3 V  
VIN = 5 V  
30  
37  
30  
37  
60  
70  
60  
70  
High side switch resistance  
Low side switch resistance  
mΩ  
mΩ  
VIN = 3.3 V  
ERROR AMPLIFIER  
Input current  
7
nA  
Error amplifier transconductance (gm)  
2 μA < I(COMP) < 2 μA, V(COMP) = 1 V  
225  
μmhos  
Error amplifier transconductance (gm) during 2 μA < I(COMP) < 2 μA, V(COMP) = 1 V,  
77  
μmhos  
slow start  
Vsense = 0.4 V  
Error amplifier source/sink  
COMP to Iswitch gm  
V(COMP) = 1 V, 100 mV overdrive  
±20  
μA  
14  
A/V  
Copyright © 2011, Texas Instruments Incorporated  
3
TPS54478  
SLVSAS2 JUNE 2011  
www.ti.com  
ELECTRICAL CHARACTERISTICS (continued)  
TJ = 40°C to 150°C, VIN = 2.95 to 6 V (unless otherwise noted)  
DESCRIPTION  
CURRENT LIMIT  
CONDITIONS  
MIN  
TYP  
MAX  
UNIT  
Current limit threshold  
VIN = 6V, Fs = 500 KHz  
5.2  
6.5  
512  
8.2  
A
Cycles before entering hiccup  
Cycles of converter in off state during hiccup  
Low side Fet reverse current limit  
THERMAL SHUTDOWN  
Thermal shutdown  
Cycles  
Cycles  
A
16384  
3.1  
165  
15  
°C  
°C  
Hysteresis  
TIMING RESISTOR AND EXTERNAL CLOCK (RT/CLK PIN)  
Switching frequency range using RT mode  
200  
400  
300  
75  
2000  
600  
kHz  
kHz  
kHz  
ns  
V
Switching frequency  
R(RT/CLK) = 78.7 kΩ  
500  
Switching frequency range using CLK mode  
Minimum CLK pulse width  
RT/CLK voltage  
2000  
R(RT/CLK) = 78.7 kΩ  
0.5  
1.6  
0.6  
75  
RT/CLK high threshold  
RT/CLK low threshold  
2.2  
V
0.4  
V
RT/CLK falling edge to PH rising edge delay  
PLL lock in time  
Measure at 500 kHz with RT resistor in series  
Measure at 500 kHz  
ns  
μs  
14  
PH (PH PIN)  
Measured at 50% points on PH, VIN = 5 V, IOUT = 2 A  
100  
120  
Minimum On time  
ns  
Measured at 50% points on PH, VIN = 5 V,  
IOUT = 0 A  
Prior to skipping off pulses, VIN = 5 V,  
IOUT = 2 A  
Minimum Off time  
110  
ns  
Rise Time  
1.5  
1.5  
VIN = 5 V, 4 A  
V/ns  
Fall Time  
BOOT (BOOT PIN)  
BOOT Charge Resistance  
BOOT-PH UVLO  
VIN = 5 V  
15  
VIN = 2.95 V  
2.2  
V
SLOW START AND TRACKING (SS/TR PIN)  
SS voltage threshold (VSSTHR  
)
0.15  
45  
V
Charge Current  
V
(SS/TR) < VSSTHR  
(SS/TR) > VSSTHR  
μA  
V
2.2  
65  
SS/TR to VSENSE matching  
V(SS/TR) = 0.3 V  
mV  
V
SS/TR to reference crossover  
98% normal  
0.86  
2.5  
900  
SS/TR discharge voltage (Overload)  
SS/TR discharge current (Overload)  
VSENSE = 0 V  
mV  
µA  
VSENSE = 0 V, V(SS/TR) = 0.4 V  
SS discharge current (UVLO, EN, Thermal  
fault)  
VIN = 5 V, V(SS) = 0.5 V  
1.16  
mA  
POWER GOOD (PWRGD PIN)  
VSENSE falling (Fault)  
VSENSE rising (Good)  
VSENSE rising (Fault)  
VSENSE falling (Good)  
VSENSE falling  
93  
95  
107  
105  
2
VSENSE threshold  
% Vref  
Hysteresis  
% Vref  
nA  
Output high leakage  
On resistance  
VSENSE = VREF, V(PWRGD) = 5.5 V  
VIN = 2.95 V  
7
56  
120  
4
Copyright © 2011, Texas Instruments Incorporated  
TPS54478  
www.ti.com  
SLVSAS2 JUNE 2011  
ELECTRICAL CHARACTERISTICS (continued)  
TJ = 40°C to 150°C, VIN = 2.95 to 6 V (unless otherwise noted)  
DESCRIPTION  
CONDITIONS  
MIN  
TYP  
0.2  
MAX  
0.3  
UNIT  
V
Output low  
I(PWRGD) = 3 mA  
Minimum VIN for valid output  
V(PWRGD) < 0.5 V at 100 μA  
1.2  
1.6  
V
DEVICE INFORMATION  
PIN CONFIGURATION  
QFN16  
RTE PACKAGE  
(TOP VIEW)  
16  
15  
14  
13  
1
12  
11  
10  
9
VIN  
VIN  
PH  
2
3
PH  
PH  
PowerPAD  
(17)  
GND  
4
SS/TR  
GND  
5
6
7
8
PIN FUNCTIONS  
PIN  
DESCRIPTION  
NAME  
AGND  
BOOT  
NO.  
5
Analog Ground should be electrically connected to GND close to the device.  
13  
A bootstrap capacitor is required between BOOT and PH. If the voltage on this capacitor is below the minimum  
required by the BOOT UVLO, the output is forced to switch off until the capacitor is refreshed.  
COMP  
EN  
7
Error amplifier output, and input to the output switch current comparator. Connect frequency compensation  
components to this pin.  
15  
Enable pin, internal pull-up current source. Pull below 1.21 V to disable. Float to enable. Can be used to set the  
on/off threshold (adjust UVLO) with two additional resistors.  
GND  
PH  
3, 4  
Power Ground. This pin should be electrically connected directly to the power pad under the IC.  
10, 11, The source of the internal high side power MOSFET, and drain of the internal low side (synchronous) rectifier  
12  
MOSFET.  
PowerPAD  
PWRGD  
17  
GND pin should be connected to the exposed power pad for proper operation. This power pad should be  
connected to any internal PCB ground plane using multiple vias for good thermal performance.  
14  
An open drain output; asserts low if output voltage is low due to thermal shutdown, overcurrent,  
over/under-voltage or EN shut down.  
RT/CLK  
SS/TR  
8
9
Resistor Timing or External Clock input pin.  
Slow start and tracking. An external capacitor connected to this pin sets the output voltage rise time. The SS  
provides higer charge current when SS is below 0.15V, resulting in two slopes of the SS voltage.  
This pin can also be used for tracking.  
VIN  
1, 2, 16 Input supply voltage, 2.95 V to 6 V.  
Copyright © 2011, Texas Instruments Incorporated  
5
TPS54478  
SLVSAS2 JUNE 2011  
www.ti.com  
PIN FUNCTIONS (continued)  
PIN  
DESCRIPTION  
NAME  
NO.  
VSENSE  
6
Inverting node of the transconductance (gm) error amplifier.  
FUNCTIONAL BLOCK DIAGRAM  
VIN  
Shutdown  
Thermal  
Shutdown  
Enable  
Comparator  
93%  
Logic  
Shutdown  
Shutdown  
Logic  
107%  
Enable  
Threshold  
Boot  
Charge  
Voltage  
Reference  
Boot  
UVLO  
Minimum  
COMP Clamp  
Current  
Sense  
ERROR  
AMPLIFIER  
PWM  
Comparator  
VSENSE  
SS/TR  
BOOT  
PWM  
Latch  
R
Q
Logic  
Logic  
S
Shutdown  
Logic  
Slope  
Compensation  
PH  
COMP  
Maximum  
Clamp  
Overload  
Recovery  
Oscillator  
with PLL  
PGND  
TPS54478RTE Block Diagram  
GND  
RT/CLK  
POWERPAD  
6
Copyright © 2011, Texas Instruments Incorporated  
TPS54478  
www.ti.com  
SLVSAS2 JUNE 2011  
TYPICAL CHARACTERISTICS CURVES  
SHUTDOWN SUPPLY CURRENT vs TEMPERATURE  
VIN SUPPLY CURRENT vs TEMPERATURE  
580  
570  
560  
550  
540  
530  
520  
510  
500  
3
2.5  
2
V
= 5 V  
IN  
V
= 5 V  
IN  
1.5  
1
V
= 3.3 V  
IN  
V
= 3.3 V  
IN  
0.5  
0
490  
480  
-50  
-25  
0
25  
50  
75  
100  
125  
150  
-50  
-25  
0
25  
50  
75  
100  
125  
150  
T
- Junction Temperature - °C  
T
- Junction Temperature - °C  
J
J
Figure 1.  
Figure 2.  
EN PIN VOLTAGE vs TEMPERATURE  
EN PIN CURRENT vs TEMPERATURE  
1.32  
1.31  
1.3  
0
-0.5  
-1  
EN Rising, Vin = 3.3 V  
EN Pin Current @ Vin = 5 V, VEN = Threshold - 50 mV  
1.29  
1.28  
1.27  
1.26  
1.25  
1.24  
1.23  
1.22  
1.21  
1.2  
EN Pin Current @ Vin = 3.3 V, VEN = Threshold - 50 mV  
EN Rising, Vin = 5 V  
-1.5  
-2  
-2.5  
-3  
EN Falling, Vin = 3.3 V  
EN Pin Current @ Vin = 5 V, VEN = Threshold + 50 mV  
EN Pin Current @ Vin = 3.3 V, VEN = Threshold + 50 mV  
-3.5  
-4  
EN Falling, Vin = 5 V  
1.19  
1.18  
-50  
-25  
0
25  
50  
75  
100  
125  
150  
-50  
-25  
0
25  
50  
75  
100  
125  
150  
T
- Junction Temperature - °C  
T
- Junction Temperature - °C  
J
J
Figure 3.  
Figure 4.  
VOLTAGE REFERENCE vs  
TEMPERATURE  
MOSFET Rdson vs TEMPERATURE  
60  
55  
50  
45  
40  
35  
30  
25  
20  
0.606  
0.605  
0.604  
0.603  
0.602  
0.601  
0.6  
High Side Rdson Vin = 3.3 V  
Low Side Rdson Vin = 3.3 V  
V
= 5 V  
IN  
0.599  
0.598  
0.597  
0.596  
V
= 3.3 V  
IN  
Low Side Rdson Vin = 5 V  
0.595  
0.594  
High Side Rdson Vin = 5 V  
25 50  
-50  
-25  
0
25  
50  
75  
100  
125  
150  
-50  
-25  
0
75  
100  
125  
150  
T
- Junction Temperature - °C  
T
- Junction Temperature - °C  
J
J
Figure 5.  
Figure 6.  
Copyright © 2011, Texas Instruments Incorporated  
7
 
TPS54478  
SLVSAS2 JUNE 2011  
www.ti.com  
TYPICAL CHARACTERISTICS CURVES (continued)  
HIGH SIDE FET CURRENT LIMIT vs  
TEMPERATURE  
TRANSCONDUCTANCE vs TEMPERATURE  
7
6.5  
6
310  
290  
270  
250  
230  
210  
V
= 5 V  
IN  
V
= 3.3 V  
IN  
V
= 3.3 V  
IN  
V
= 5 V  
IN  
5.5  
190  
170  
5
-50  
-50  
-25  
0
25  
50  
75  
100  
125  
150  
-25  
0
25  
50  
75  
100  
125  
150  
150  
150  
T
- Junction Temperature - °C  
T
- Junction Temperature - °C  
J
J
Figure 7.  
Figure 8.  
SWITCHING FREQUENCY vs RT RESISTANCE  
SWITCHING FREQUENCY vs TEMPERATURE  
2000  
1800  
1600  
1400  
1200  
1000  
800  
500  
495  
490  
485  
480  
475  
RT = 84 kW,  
Vin = 5 V  
600  
400  
200  
0
10  
30  
50  
70  
90  
110  
130  
150  
-50  
-25  
0
25  
50  
75  
100  
125  
RT - Resistance - kW  
T
- Junction Temperature - °C  
J
Figure 9.  
Figure 10.  
VSS VOLTAGE THRESHOLD VSSTHR vs TEMPERATURE  
SS CHARGE CURRENT vs TEMPERATURE  
0.16  
-40  
-41  
-42  
-43  
-44  
-45  
-46  
-47  
-48  
0.159  
0.158  
V
= 3.3 V  
IN  
0.157  
0.156  
0.155  
0.154  
0.153  
0.152  
Vin = 5 V, Vss < 0.15 V  
V
= 5 V  
IN  
Vin = 3.3 V, Vss < 0.15 V  
0.151  
0.15  
-49  
-50  
-50  
-25  
0
25  
50  
75  
100  
125  
150  
-50  
-25  
0
25  
50  
75  
100  
125  
T
- Junction Temperature - °C  
T
- Junction Temperature - °C  
J
J
Figure 11.  
Figure 12.  
8
Copyright © 2011, Texas Instruments Incorporated  
TPS54478  
www.ti.com  
SLVSAS2 JUNE 2011  
TYPICAL CHARACTERISTICS CURVES (continued)  
SS CHARGE CURRENT vs TEMPERATURE  
PWRGD Rdson vs TEMPERATURE  
100  
-2  
-2.1  
-2.2  
-2.3  
-2.4  
-2.5  
-2.6  
-2.7  
-2.8  
-2.9  
-3  
Vin = 5 V; Vss = 0.4 V  
90  
80  
Vin = 3.3 V; Vss = 0.4 V  
70  
V
= 5 V  
IN  
60  
50  
40  
-50  
-25  
0
25  
50  
75  
100  
125  
150  
-50  
-25  
0
25  
50  
75  
100  
125  
150  
T
- Junction Temperature - °C  
T
- Junction Temperature - °C  
J
J
Figure 13.  
Figure 14.  
PWRGD THRESHOLD vs TEMPERATURE  
PWRGD LEAKAGE CURRENT vs TEMPERATURE  
110  
108  
106  
104  
102  
100  
98  
20  
18  
16  
14  
12  
10  
8
Vsense (Fault) Rising  
Vsense (Good) Falling  
Vsense (Good) Falling  
V
= 5.5 V  
IN  
96  
6
94  
4
92  
Vsense (Fault) Falling  
2
90  
0
88  
-50  
-25  
0
25  
50  
75  
100  
125  
150  
-50  
-25  
0
25  
50  
75  
100  
125  
150  
T
- Junction Temperature - °C  
T
- Junction Temperature - °C  
J
J
Figure 15.  
Figure 16.  
EFFICIENCY vs LOAD CURRENT  
EFFICIENCY vs LOAD CURRENT  
100  
95  
90  
85  
80  
75  
70  
65  
60  
100  
95  
90  
85  
80  
75  
70  
65  
60  
55  
50  
V
= 2.5 V  
O
V
= 3.3 V  
O
V
= 1.8 V  
O
V
= 2.5 V  
O
V
= 1.8 V  
V
= 1.2 V  
O
O
V
= 1.2 V  
O
V
= 1 V  
O
V
= 1 V  
O
Vin = 5 V,  
Vin = 3.3 V,  
DCR = 6.8 mW,  
Fs = 1 MHz,  
Tj = 25°C  
DCR = 6.8 mW,  
Fs = 1 MHz,  
Tj = 25°C  
55  
50  
0
0.5  
1
1.5  
2
2.5  
- Output Current - A  
3
3.5  
4
0
0.5  
1
1.5  
2
2.5  
- Output Current - A  
3
3.5  
4
I
I
O
O
Figure 17.  
Figure 18.  
Copyright © 2011, Texas Instruments Incorporated  
9
TPS54478  
SLVSAS2 JUNE 2011  
www.ti.com  
TYPICAL CHARACTERISTICS CURVES (continued)  
EFFICIENCY vs LOAD CURRENT  
EFFICIENCY vs LOAD CURRENT  
100  
95  
90  
85  
80  
75  
70  
65  
60  
55  
50  
100  
95  
90  
V
= 3.3 V  
V
O
V
= 2.5 V  
V
O
85  
80  
75  
70  
65  
60  
= 2.5 V  
O
= 1.8 V  
V
O
V
= 1.8 V  
O
= 1.2 V  
V
O
V
= 1.2 V  
O
= 1 V  
O
V
= 1 V  
O
Vin = 3.3 V,  
DCR = 18 mW,  
Fs = 500 kHz,  
Tj = 25°C  
Vin = 5 V,  
DCR = 18 mW,  
Fs = 500 kHz,  
Tj = 25°C  
55  
50  
0
0.5  
1
1.5  
2
2.5  
- Output Current - A  
3
3.5  
4
0
0.5  
1
1.5  
2
2.5  
- Output Current - A  
3
3.5  
4
I
I
O
O
Figure 19.  
Figure 20.  
OVERVIEW  
The TPS54478 is a 6-V, 4-A, synchronous step-down (buck) converter with two integrated n-channel MOSFETs.  
To improve performance during line and load transients the device implements a constant frequency, peak  
current mode control which reduces output capacitance and simplifies external frequency compensation design.  
The wide switching frequency of 200 kHz to 2000 kHz allows for efficiency and size optimization when selecting  
the output filter components. The switching frequency is adjusted using a resistor to ground on the RT/CLK pin.  
The device has an internal phase lock loop (PLL) on the RT/CLK pin that is used to synchronize the power  
switch turn on to a falling edge of an external system clock.  
The TPS54478 has a typical default start up voltage of 2.6 V. The EN pin has an internal pull-up current source  
that can be used to adjust the input voltage under voltage lockout (UVLO) with two external resistors. In addition,  
the pull up current provides a default condition when the EN pin is floating for the device to operate. The total  
operating current for the TPS54478 is typically 525 μA when not switching and under no load. When the device  
is disabled, the supply current is less than 2.5 μA.  
The integrated 30 mMOSFETs allow for high efficiency power supply designs with continuous output currents  
up to 4 amperes.  
The TPS54478 reduces the external component count by integrating the boot recharge diode. The bias voltage  
for the integrated high side MOSFET is supplied by a capacitor between the BOOT and PH pins. The boot  
capacitor voltage is monitored by an UVLO circuit and turns off the high side MOSFET when the voltage falls  
below a preset threshold. This BOOT circuit allows the TPS54478 to operate approaching 100%. The output  
voltage can be stepped down to as low as the 0.600 V reference.  
TPS54478 features monotonic starup under pre-bias conditions. The low side Fet turns on for a very short time  
period every cycle before the output voltage reaches the pre-biased voltage. This ensures the boot cap has  
enough charge to turn on the top Fet when the output voltage reaches the pre-biased voltage.  
The TPS54478 has a power good comparator (PWRGD) with 2% hysteresis.  
The TPS54478 minimizes excessive output overvoltage transients by taking advantage of the overvoltage power  
good comparator. When the regulated output voltage is greater than 107% of the nominal voltage, the  
overvoltage comparator is activated, and the high side MOSFET is turned off and masked from turning on until  
the output voltage is lower than 105%.  
The SS/TR (slow start/tracking) pin is used to minimize inrush currents or provide power supply sequencing  
during power up. A small value capacitor should be coupled to the pin for slow start. The SS/TR pin is  
discharged before the output power up to ensure a repeatable restart after an overtemperature fault, UVLO fault  
or disabled condition. To optimize the output startup waveform, two levels of SS current are implemented. The  
first slope has more current so that the converter can get out of the region requiring small minimum ON time.  
10  
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To reduce the power dissipation of TPS54478 during overcurrent event, the hiccup protection is implemented  
beyond the cycle-by-cycle protection. Thermal shutdown prevents the overheat damage of the device.  
DETAILED DESCRIPTION  
FIXED FREQUENCY PWM CONTROL  
The TPS54478 uses an adjustable fixed frequency, peak current mode control. The output voltage is compared  
through external resistors on the VSENSE pin to an internal voltage reference by an error amplifier which drives  
the COMP pin. An internal oscillator initiates the turn on of the high side power switch. The error amplifier output  
is compared to the high side power switch current. When the power switch current reaches the COMP voltage  
level the high side power switch is turned off and the low side power switch is turned on. The COMP pin voltage  
increases and decreases as the output current increases and decreases. The device implements a current limit  
by clamping the COMP pin voltage to a maximum level and also implements a minimum clamp for improved  
transient response performance.  
SLOPE COMPENSATION AND OUTPUT CURRENT  
The TPS54478 adds a compensating ramp to the switch current signal. This slope compensation prevents  
sub-harmonic oscillations as duty cycle increases. The available peak inductor current remains constant over the  
full duty cycle range.  
BOOTSTRAP VOLTAGE (BOOT) AND LOW DROPOUT OPERATION  
The TPS54478 has an integrated boot regulator and requires a small ceramic capacitor between the BOOT and  
PH pin to provide the gate drive voltage for the high side MOSFET. The value of the ceramic capacitor should be  
0.1 μF. A ceramic capacitor with an X7R or X5R grade dielectric with a voltage rating of 10 V or higher is  
recommended because of the stable characteristics over temperature and voltage.  
To improve drop out, the TPS54478 is designed to operate at 100% duty cycle as long as the BOOT to PH pin  
voltage is greater than 2.2 V. The high side MOSFET is turned off using an UVLO circuit, allowing for the low  
side MOSFET to conduct when the voltage from BOOT to PH drops below 2.2 V. Since the supply current  
sourced from the BOOT pin is very low, the high side MOSFET can remain on for more switching cycles than are  
required to refresh the capacitor, thus the effective duty cycle of the switching regulator is very high.  
ERROR AMPLIFIER  
The TPS54478 has a transconductance amplifier. The error amplifier compares the VSENSE voltage to the lower  
of the SS/TR pin voltage or the internal 0.600 V voltage reference. The transconductance of the error amplifier is  
225μA/V during normal operation. When the voltage of VSENSE pin is below 0.600 V and the device is  
regulating using the SS/TR voltage, the gm is typically greater than 77 μA/V, but less than 225 μA/V. The  
frequency compensation components are placed between the COMP pin and ground.  
VOLTAGE REFERENCE  
The voltage reference system produces a precise ±1% voltage reference over temperature by scaling the output  
of a temperature-stable bandgap circuit. The bandgap and scaling circuits produce 0.600 V at the non-inverting  
input of the error amplifier.  
ADJUSTING THE OUTPUT VOLTAGE  
The output voltage is set with a resistor divider from the output node to the VSENSE pin. It is recommended to  
use divider resistors with 1% tolerance or better. Start with a 20 kfor the R1 resistor and use the Equation 1 to  
calculate R2. To improve efficiency at very light loads consider using larger value resistors. If the values are too  
high the regulator is more susceptible to noise and voltage errors from the VSENSE input current are noticeable.  
vertical spacer  
vertical spacer  
æ
ç
è
ö
÷
ø
0.6 V  
R2 = R1 ´  
VO - 0.6 V  
(1)  
11  
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TPS54478  
V
O
R1  
R2  
VSENSE  
+
0.6 V  
Figure 21. Voltage Divider Circuit  
ENABLE AND ADJUSTING UNDER-VOLTAGE LOCKOUT  
The TPS54478 is disabled when the VIN pin voltage falls below 2.6 V. If an application requires a higher  
under-voltage lockout (UVLO), use the EN pin as shown in Figure 22 to adjust the input voltage UVLO by using  
two external resistors. It is recommended to use the EN resistors to set the UVLO falling threshold (VSTOP) above  
2.6V. The rising threshold (VSTART) should be set to provide enough hysteresis to allow for any input supply  
variations. The EN pin has an internal pull-up current source that provides the default condition of the TPS54478  
operating when the EN pin floats. Once the EN pin voltage exceeds 1.30 V, an additional 2.76 μA of hysteresis is  
added. When the EN pin is pulled below 1.21 V, the 2.76 μA is removed. This additional current facilitates input  
voltage hysteresis.  
TPS54478  
i
hys  
VIN  
2.76 mA  
i
p
R1  
R2  
0.64 mA  
+
EN  
Vena  
Figure 22. Adjustable Under Voltage Lock Out  
æ
ç
è
ö
VENFALLING  
VSTART  
- VSTOP  
÷
VENRISING  
ø
R1 =  
æ
ö
÷
ø
VENFALLING  
I
1-  
+I  
p ç  
h
VENRISING  
è
(2)  
(3)  
vertical spacer  
R1´ VENFALLING  
R2 =  
VSTOP - VENFALLING + R1(Ip + Ih )  
Where Ih = 2.76uA, Ip = 0.64uA, VENRISING = 1.30V, VENFALLING = 1.21V  
12  
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SLOW START / TRACKING PIN  
The TPS54478 regulates to the lower of the SS/TR pin and the internal reference voltage. A capacitor on the  
SS/TR pin to ground implements a slow start time. Before the SS pin reaches the voltage threshold VSSTHR, the  
charge current is about 45 μA. The TPS54478 internal pull-up current source of 2.2 μA charges the external slow  
start capacitor after the SS pin voltage exceeds VSSTHR. Equation 4 calculates the required slow start capacitor  
value where Tss is the desired slow start time in ms and Css is the required capacitance in nF.  
vertical spacer  
Css(nF) = 3 ´ Tss(mS)  
(4)  
If during normal operation, the VIN goes below the UVLO, EN pin pulled below 1.21 V, or a thermal shutdown  
event occurs, the TPS54478 stops switching. When the VIN goes above UVLO, EN is released or pulled high, or  
a thermal shutdown is exited, then SS/TR is discharged to below 65 mV before reinitiating a powering up  
sequence. The VSENSE voltage will follow the SS/TR pin voltage with a 65mV offset up to 90% of the internal  
voltage reference. When the SS/TR voltage is greater than 90% of the internal reference voltage the offset  
increases as the effective system reference transitions from the SS/TR voltage to the internal voltage reference.  
SEQUENCING  
Many of the common power supply sequencing methods can be implemented using the SS/TR, EN and PWRGD  
pins. The sequential method can be implemented using an open drain or collector output of a power on reset pin  
of another device. Figure 23 shows the sequential method. The PWRGD is coupled to the EN pin on the  
TPS54478 which enables the second power supply once the primary supply reaches regulation.  
Ratio-metric start up can be accomplished by connecting the SS/TR pins together. The regulator outputs ramp  
up and reach regulation at the same time. When calculating the slow start time the pull up current source must  
be doubled in Equation 4. The ratio metric method is illustrated in Figure 25.  
TPS54478  
PWRGD1  
EN1  
EN1  
EN2  
SS1  
SS2  
VO1  
PWRGD2  
PWRGD1  
VO2  
t - Time=1 ms/div
Figure 23. Sequential Start-Up Sequence  
Figure 24. Sequential Startup using EN and  
PWRGD  
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TPS54478  
EN1  
EN1  
SS/TR1  
Io  
Vo1  
Vo2  
PWRGD1  
TPS54478  
EN2  
t - Time = 1 ms/div  
SS/TR2  
PWRGD2  
Figure 25. Schematic for Ratio-metric Start-Up  
Figure 26. Ratio-metric Startup  
Sequence  
vertical spacer  
Simultaneous power supply sequencing can be implemented by connecting the resistor network of R1 and R2  
shown in Figure 27 to the output of the power supply that needs to be tracked or another voltage reference  
source. Using Equation 5 and Equation 6, the tracking resistors can be calculated. To minimize the effect of the  
inherent SS/TR to VSENSE offset (Vssoffset) in the slow start circuit and the offset created by the pullup current  
source (Iss) and tracking resistors, the Vssoffset and Iss are included as variables in the equations. As the  
SS/TR voltage becomes more than 85% of the nominal reference voltage the Vssoffset becomes larger as the  
slow start circuits gradually handoff the regulation reference to the internal voltage reference. The SS/TR pin  
voltage needs to be greater than 0.86 V for a complete handoff to the internal voltage reference as shown in  
Figure 28.  
vertical spacer  
Vout2  
Vssoffset  
Iss  
R1 =  
´
Vref  
(5)  
(6)  
vertical spacer  
Vref ´ R1  
R2 =  
Vout2 - Vref  
vertical spacer  
vertical spacer  
vertical spacer  
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TPS54478  
EN1  
VOUT1  
SS/TR1  
PWRGD1  
TPS54478  
VOUT2  
EN2  
EN1 = 5 / div  
SS2 = 500 mV / div  
Vo1 = 500 mV / div  
Vo2 = 500 mV / div  
R1  
R2  
SS/TR2  
PWRGD2  
Time = 1 msec / div  
Figure 27. Simultaneous Startup Sequence  
Figure 28. Simultaneous Start-Up using Coupled  
SS/TR Pins  
CONSTANT SWITCHING FREQUENCY and TIMING RESISTOR (RT/CLK Pin)  
The switching frequency of the TPS54478 is adjustable over a wide range from 200 kHz to 2000 kHz by placing  
a maximum of 150 kand minimum of 16 k, respectively, on the RT/CLK pin. An internal amplifier holds this  
pin at a fixed voltage when using an external resistor to ground to set the switching frequency. The RT/CLK is  
typically 0.5 V. To determine the timing resistance for a given switching frequency, use the curve in Figure 5 or  
Equation 7.  
90066  
Fs(kHz)1.135  
RT (kW) =  
(7)  
vertical spacer  
23439  
RT(kW)0.8813  
Fs(kHz) =  
(8)  
To reduce the solution size one would typically set the switching frequency as high as possible, but tradeoffs of  
the efficiency, maximum input voltage and minimum controllable on time should be considered.  
The minimum controllable on time is typically 100 ns at full current load and 120 ns at no load, and limits the  
maximum operating input voltage or output voltage.  
OVERCURRENT PROTECTION  
The TPS54478 implements current mode control which uses the COMP pin voltage to turn off the high side  
MOSFET and turn on the low side MOSFET on a cycle by cycle basis. Each cycle the switch current and the  
COMP pin voltage are compared, when the peak switch current intersects the COMP voltage the high side  
switch is turned off. During overcurrent conditions that pull the output voltage low, the error amplifier will respond  
by driving the COMP pin high, increasing the switch current. The error amplifier output is clamped internally.  
This clamp functions as a switch current limit. When the OCP reaches 512 cycles, the converter enters hiccup  
mode in which no switching action happens for about 16000 cycles. This helps the reduction of the power  
consumption during the over current event.  
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START-UP into Pre-Biased Output  
The TPS54478 features monotonic startup into pre-biased output. The low side Fet turns on for a very short time  
period every cycle before the output voltage reaches the pre-biased voltage. This ensures the boot cap has  
enough charge to turn on the top Fet when the output voltage reaches the pre-biased voltage. The TPS54478  
also implements low side current protection by detecting the voltage over the low side MOSFET. When the  
converter sinks current through its low side FET is more than 3.1A, the control circuit will turn the low side Fet  
off. Due to the implemented prebias function, the low side Fet reverse current protection should not be reached,  
but it provides another layer of protection in the undesired events such as oscillation induced by load.  
SYNCHRONIZE USING THE RT/CLK PIN  
The RT/CLK pin is used to synchronize the converter to an external system clock. See Figure 29. To implement  
the synchronization feature in a system, connect a square wave to the RT/CLK pin with an on time of at least  
75ns. If the pin is pulled above the PLL upper threshold, a mode change occurs and the pin becomes a  
synchronization input. The internal amplifier is disabled and the pin is a high impedance clock input to the  
internal PLL. If clocking edges stop, the internal amplifier is re-enabled and the mode returns to the frequency set  
by the resistor. The square wave amplitude at this pin must transition lower than 0.6 V and higher than 1.6 V  
typically. The synchronization frequency range is 300 kHz to 2000 kHz. The rising edge of the PH is  
synchronized to the falling edge of RT/CLK pin.  
TPS54478  
EXT_CLK  
PLL  
RT/CLK  
Clock  
RT  
Source  
PH  
t - Time = 1 ms/div  
Figure 29. Synchronizing to a System Clock  
Figure 30. Plot of Synchronizing to System Clock  
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POWER GOOD (PWRGD PIN)  
The PWRGD pin output is an open drain MOSFET. The output is pulled low when the VSENSE voltage enters  
the fault condition by falling below 93% or rising above 107% of the nominal internal reference voltage. There is  
a 2% hysteresis on the threshold voltage, so when the VSENSE voltage rises to the good condition above 95%  
or falls below 105% of the internal voltage reference the PWRGD output MOSFET is turned off. It is  
recommended to use a pull-up resistor between the values of 1kand 100kto a voltage source that is 6 V or  
less. The PWRGD is in a valid state once the VIN input voltage is greater than 1.6 V.  
OVERVOLTAGE TRANSIENT PROTECTION  
The TPS54478 incorporates an overvoltage transient protection (OVTP) circuit to minimize voltage overshoot  
when recovering from output fault conditions or strong unload transients. The OVTP feature minimizes the output  
overshoot by implementing a circuit to compare the VSENSE pin voltage to the OVTP threshold which is 107%  
of the internal voltage reference. If the VSENSE pin voltage is greater than the OVTP threshold, the high side  
MOSFET is disabled preventing current from flowing to the output and minimizing output overshoot. When the  
VSENSE voltage drops lower than the OVTP threshold the high side MOSFET is allowed to turn on the next  
clock cycle.  
THERMAL SHUTDOWN  
The device implements an internal thermal shutdown to protect itself if the junction temperature exceeds 165°C.  
The thermal shutdown forces the device to stop switching when the junction temperature exceeds the thermal  
trip threshold. Once the die temperature decreases below 150°C, the device reinitiates the power up sequence  
by discharging the SS pin to below 65 mV. The thermal shutdown hysteresis is 15°C.  
SMALL SIGNAL MODEL FOR LOOP RESPONSE  
Figure 31 shows an equivalent model for the TPS54478 control loop which can be modeled in a circuit simulation  
program to check frequency response and dynamic load response without slope compensation effect. The error  
amplifier is a transconductance amplifier with a gm of 225 μA/V. The error amplifier can be modeled using an  
ideal voltage controlled current source. The resistor R0 and capacitor Co model the open loop gain and  
frequency response of the amplifier. The 1-mV AC voltage source between the nodes a and b effectively breaks  
the control loop for the frequency response measurements. Plotting a/c shows the small signal response of the  
frequency compensation. Plotting a/b shows the small signal response of the overall loop. The dynamic loop  
response can be checked by replacing the RL with a current source with the appropriate load step amplitude and  
step rate in a time domain analysis.  
PH  
VO  
Power Stage  
14 A/V  
a
b
R1  
RESR  
RL  
COMP  
c
COUT  
VSENSE  
R2  
0.6 V  
CO RO  
R3  
C1  
gm  
225 µA/V  
C2  
Figure 31. Small Signal Model for Loop Response without Slope Comp Effect  
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SIMPLE SMALL SIGNAL MODEL FOR PEAK CURRENT MODE CONTROL  
Figure 31 is a simple small signal model that can be used to understand how to design the frequency  
compensation without slope compensation effect. The TPS54478 power stage can be approximated to a voltage  
controlled current source (duty cycle modulator) supplying current to the output capacitor and load resistor. The  
control to output transfer function is shown in Equation 9 and consists of a dc gain, one dominant pole and one  
ESR zero. The quotient of the change in switch current and the change in COMP pin voltage (node c in  
Figure 31) is the power stage transconductance. The gm for the TPS54478 is 14 A/V. The low frequency gain of  
the power stage frequency response is the product of the transconductance and the load resistance as shown in  
Equation 10. As the load current increases and decreases, the low frequency gain decreases and increases,  
respectively. This variation with load may seem problematic at first glance, but the dominant pole moves with  
load current [see Equation 11]. The combined effect is highlighted by the dashed line in the right half of  
Figure 32. As the load current decreases, the gain increases and the pole frequency lowers, keeping the 0-dB  
crossover frequency the same for the varying load conditions which makes it easier to design the frequency  
compensation.  
vertical spacer  
vertical spacer  
VO  
Adc  
VC  
R
ESR  
fp  
R
L
gm  
ps  
C
OUT  
fz  
Figure 32. Simple Small Signal Model and Frequency Response for Peak Current Mode Control without  
Slope Comp Effect  
æ
ç
è
æ
ç
è
s
ö
÷
ø
ö
÷
ø
1+  
1+  
2p × ¦z  
vo  
vc  
= Adc ´  
s
2p × ¦p  
(9)  
Adc = gmps ´ RL  
(10)  
1
¦p =  
COUT ´ RL ´ 2p  
(11)  
(12)  
vertical spacer  
¦z =  
1
COUT ´ RESR ´ 2p  
SMALL SIGNAL MODEL FOR FREQUENCY COMPENSATION  
The TPS54478 uses a transconductance amplifier for the error amplifier and readily supports two of the  
commonly used frequency compensation circuits. The compensation circuits are shown in Figure 33. The Type 2  
circuits are most likely implemented in high bandwidth power supply designs using low ESR output capacitors. In  
Type 2A, one additional high frequency pole is added to attenuate high frequency noise.  
18  
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VO  
R1  
VSENSE  
Vref  
Type 2A  
Type 2B  
COMP  
gm  
ea  
CO  
R3  
C1  
C2  
R3  
RO  
R2  
5pF  
C1  
Figure 33. Type-II of Frequency Compensation  
The design guidelines for TPS54478 loop compensation will be addressed in the APPLICATION INFORMATION  
section with more details. The approach is to run the Pspice model first to find the accurate response of the  
power stage with slope compensation effect. The compensation network is then designed based on the desired  
crossover frequency. The crossover frequency and phase margin are more closer to the measured results when  
the slope compensation effect is included.  
For type-II compensation, the modulator pole, fpmod, and the esr zero, fz1 can be calculated using Equation 13  
and Equation 14. Derating the output capacitor (COUT) is needed if the output voltage is a high percentage of the  
capacitor rating. Use the capacitor manufacturer information to derate the capacitor value. Use Equation 15 and  
Equation 16 to estimate a starting point for the crossover frequency, fc. Equation 15 is the geometric mean of the  
modulator pole and the esr zero and Equation 16 is the mean of modulator pole and the switching frequency.  
Use the lower value of Equation 15 or Equation 16 as the maximum crossover frequency.  
Ioutmax  
¦p mod =  
2p ´ Vout ´ Cout  
(13)  
vertical spacer  
1
¦z mod =  
2p ´ Resr ´ Cout  
(14)  
vertical spacer  
¦
=
¦p mod´ ¦z mod  
vertical spacer  
¦p mod´  
C
(15)  
(16)  
¦sw  
¦
=
C
2
vertical spacer  
The type-III compensation is recommended to achieve higher crossover frequency by introducing extra phase lift.  
By adding a small capacitor C3 in parallel with R1, one-pair of zero and pole is generated as given by  
Equation 17 and Equation 18. The following APPLICATION INFORMATION section provides step-by-step design  
guideline for the type-III compensation wih the effect of slope compensation included.  
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Vo  
R1  
VSENSE  
Vref  
C3  
gm  
ea  
Type 3A  
Type 3B  
COMP  
R3  
C1  
RO  
R2  
C2  
R3  
CO  
5 pF  
C1  
Figure 34. Type-III of Frequency Compensation  
1
¦z =  
¦p =  
2p´R1´ C3  
(17)  
(18)  
1
2p´(R1/ /R2)´ C3  
20  
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APPLICATION INFORMATION  
DESIGN GUIDE STEP-BY-STEP DESIGN PROCEDURE  
This example details the design of a high frequency switching regulator design using ceramic output capacitors.  
This design is available as the TPS54478EVM-037 (PWR037) evaluation module (EVM). A few parameters must  
be known in order to start the design process. These parameters are typically determined on the system level.  
For this example, we start with the following known parameters:  
Output Voltage  
1.8 V  
Transient Response 1 A to 3.0 A load step  
Maximum Output Current  
Input Voltage  
ΔVout = 3%  
4 A  
3 V to 6V, 5 V nominal  
< 30 mV p-p  
1000 kHz  
Output Voltage Ripple  
Switching Frequency (Fsw)  
The schematic diagram for this design example is shown in Figure 35. The component reference designators of  
this schematic are used for the equations in APPLICATION INFORMATION.  
SELECTING THE SWITCHING FREQUENCY  
The first step is to decide on a switching frequency for the regulator. Typically, you want to choose the highest  
switching frequency possible since this produces the smallest solution size. The high switching frequency allows  
for lower valued inductors and smaller output capacitors compared to a power supply that switches at a lower  
frequency. However, the highest switching frequency causes extra switching losses, which hurt the converters  
performance. The converter is capable of running from 300 kHz to 2 MHz. Unless a small solution size is an  
ultimate goal, a moderate switching frequency of 1MHz is selected to achieve both a small solution size and a  
high efficiency operation. Using Equation 7, R4 is calculated to be 35.4 k. A standard 1% 35.7 kvalue was  
chosen in the design.  
Copyright © 2011, Texas Instruments Incorporated  
21  
 
TPS54478  
SLVSAS2 JUNE 2011  
www.ti.com  
Figure 35. High Frequency, 1.8 V Output Power Supply Design with Adjusted UVLO  
22  
Copyright © 2011, Texas Instruments Incorporated  
TPS54478  
www.ti.com  
SLVSAS2 JUNE 2011  
OUTPUT INDUCTOR SELECTION  
The inductor selected works for the entire TPS54478 input voltage range. To calculate the value of the output  
inductor, use Equation 19. KIND is a coefficient that represents the amount of inductor ripple current relative to the  
maximum output current. The inductor ripple current is filtered by the output capacitor. Therefore, choosing high  
inductor ripple currents impacts the selection of the output capacitor since the output capacitor must have a  
ripple current rating equal to or greater than the inductor ripple current. In general, the inductor ripple value is at  
the discretion of the designer; however, KIND is normally from 0.1 to 0.3 for the majority of applications.  
For this design example, use KIND = 0.3 and the inductor value is calculated to be 1.05 μH. For this design, a  
nearest standard value was chosen: 1.2 μH. For the output filter inductor, it is important that the RMS current  
and saturation current ratings not be exceeded. The RMS and peak inductor current can be found from  
Equation 21 and Equation 22.  
For this design, the RMS inductor current is 4.01 A and the peak inductor current is 4.53 A. The chosen inductor  
is a Coilcraft XAL5030-122ME. It has a saturation current rating 0f 11.8 A (20% inductance loss) and a RMS  
current rating of 8.7 A (20 °C. temperature rise). The series resistance is 6.78 mΩ typical.  
The current flowing through the inductor is the inductor ripple current plus the output current. During power up,  
faults or transient load conditions, the inductor current can increase above the calculated peak inductor current  
level calculated above. In transient conditions, the inductor current can increase up to the switch current limit of  
the device. For this reason, the most conservative approach is to specify an inductor with a saturation current  
rating equal to or greater than the switch current limit rather than the peak inductor current.  
Vinmax - Vout  
Vout  
L1 =  
´
Io ´ Kind  
Vinmax ´ ¦sw  
(19)  
vertical spacer  
Vinmax - Vout  
Vout  
Iripple =  
´
L1  
Vinmax ´ ¦sw  
(20)  
vertical spacer  
æ
ö2  
÷
1
Vo ´ (Vinmax - Vo)  
Vinmax ´ L1 ´ ¦sw  
ILrms = Io2  
+
´
ç
12  
è
ø
(21)  
(22)  
vertical spacer  
ILpeak = Iout +  
Iripple  
2
OUTPUT CAPACITOR  
There are three primary considerations for selecting the value of the output capacitor. The output capacitor  
determines the modulator pole, the output voltage ripple, and how the regulator responds to a large change in  
load current. The output capacitance needs to be selected based on the more stringent of these three criteria.  
The desired response to a large change in the load current is the first criteria. The output capacitor needs to  
supply the load with current when the regulator can not. This situation would occur if there are desired hold-up  
times for the regulator where the output capacitor must hold the output voltage above a certain level for a  
specified amount of time after the input power is removed. The regulator is temporarily not able to supply  
sufficient output current if there is a large, fast increase in the current needs of the load such as transitioning  
from no load to a full load. The regulator usually needs two or more clock cycles for the control loop to see the  
change in load current and output voltage and adjust the duty cycle to react to the change. The output capacitor  
must be sized to supply the extra current to the load until the control loop responds to the load change. The  
output capacitance must be large enough to supply the difference in current for 2 clock cycles while only allowing  
a tolerable amount of droop in the output voltage. Equation 23 shows the minimum output capacitance necessary  
to accomplish this.  
Copyright © 2011, Texas Instruments Incorporated  
23  
 
 
 
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For this example, the transient load response is specified as a 3% change in Vout for a load step from 1 A (25%  
load) to 3 A (75% load). For this example, ΔIout = 3 - 1 = 2.0A and ΔVout= 0.03 × 1.8 = 0.054 V. Using these  
numbers gives a minimum capacitance of 74.1 μF. This value does not take the ESR of the output capacitor into  
account in the output voltage change. For ceramic capacitors, the ESR is usually small enough to ignore in this  
calculation.  
Equation 24 calculates the minimum output capacitance needed to meet the output voltage ripple specification.  
Where fsw is the switching frequency, Vripple is the maximum allowable output voltage ripple, and Iripple is the  
inductor ripple current. In this case, the maximum output voltage ripple is 30 mV. Under this requirement,  
Equation 24 yields 4.4 uF.  
vertical spacer  
2 ´ DIout  
Co >  
¦sw ´ DVout  
(23)  
vertical spacer  
1
1
Co >  
´
Voripple  
8 ´ ¦sw  
Iripple  
Where ΔIout is the change in output current, fsw is the regulators switching frequency and ΔVout is the  
allowable change in the output voltage.  
(24)  
vertical spacer  
Equation 25 calculates the maximum ESR an output capacitor can have to meet the output voltage ripple  
specification. Equation 25 indicates the ESR should be less than 28.6 m. In this case, the ESR of the ceramic  
capacitor is much less than 28.6 m.  
Additional capacitance de-ratings for aging, temperature and DC bias should be factored in which increases this  
minimum value. For this example, two 47 μF 10 V X5R ceramic capacitors with 3 mof ESR are used. The  
estimated capacitance after derating is 2 x 45 µF = 90 µF.  
Capacitors generally have limits to the amount of ripple current they can handle without failing or producing  
excess heat. An output capacitor that can support the inductor ripple current must be specified. Some capacitor  
data sheets specify the RMS (Root Mean Square) value of the maximum ripple current. Equation 26 can be used  
to calculate the RMS ripple current the output capacitor needs to support. For this application, Equation 26 yields  
303 mA.  
Voripple  
Resr <  
Iripple  
(25)  
vertical spacer  
Vout ´ (Vinmax - Vout)  
Icorms =  
12 ´ Vinmax ´ L1 ´ ¦sw  
(26)  
INPUT CAPACITOR  
The TPS54478 requires a high quality ceramic, type X5R or X7R, input decoupling capacitor of at least 10 μF of  
effective capacitance and in some applications a bulk capacitance. The effective capacitance includes any DC  
bias effects. The voltage rating of the input capacitor must be greater than the maximum input voltage. The  
capacitor must also have a ripple current rating greater than the maximum input current ripple of the TPS54478.  
The input ripple current can be calculated using Equation 27.  
The value of a ceramic capacitor varies significantly over temperature and the amount of DC bias applied to the  
capacitor. The capacitance variations due to temperature can be minimized by selecting a dielectric material that  
is stable over temperature. X5R and X7R ceramic dielectrics are usually selected for power regulator capacitors  
because they have a high capacitance to volume ratio and are fairly stable over temperature. The output  
capacitor must also be selected with the DC bias taken into account. The capacitance value of a capacitor  
decreases as the DC bias across a capacitor increases.  
24  
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TPS54478  
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For this example design, a ceramic capacitor with at least a 10 V voltage rating is required to support the  
maximum input voltage. For this example, one 10 μF and one 0.1 μF 10 V capacitors in parallel have been  
selected. The input capacitance value determines the input ripple voltage of the regulator. The input voltage  
ripple can be calculated using Equation 28. Using the design example values, Ioutmax=4 A, Cin=10 μF, Fsw=1  
MHz, yields an input voltage ripple of 99 mV and a rms input ripple current of 1.95 A.  
Vinmin - Vout  
(
)
Vout  
Icirms = Iout ´  
´
Vinmin  
Vinmin  
(27)  
(28)  
vertical spacer  
Ioutmax ´ 0.25  
Cin ´ ¦sw  
DVin =  
SLOW START CAPACITOR  
The slow start capacitor determines the minimum amount of time it takes for the output voltage to reach its  
nominal programmed value during power up. This is useful if a load requires a controlled voltage slew rate. This  
is also used if the output capacitance is very large and would require large amounts of current to quickly charge  
the capacitor to the output voltage level. The large currents necessary to charge the capacitor may make the  
TPS54478 reach the current limit or excessive current draw from the input power supply may cause the input  
voltage rail to sag. Limiting the output voltage slew rate solves both of these problems.  
The slow start capacitor value can be calculated using Equation 29. For the example circuit, the slow start time is  
not too critical since the output capacitor value is 2 x 47 μF which does not require much current to charge to 1.8  
V. The example circuit has the slow start time set to an arbitrary value of 3.33 ms which requires a 10 nF  
capacitor.  
C6(nF) = 3 × Tss(mS)  
(29)  
BOOTSTRAP CAPACITOR SELECTION  
A 0.1 μF ceramic capacitor must be connected between the BOOT to PH pin for proper operation. It is  
recommended to use a ceramic capacitor with X5R or better grade dielectric. The capacitor should have 10 V or  
higher voltage rating.  
OUTPUT VOLTAGE AND FEEDBACK RESISTORS SELECTION  
For the example design, 10.0 kwas selected for R7. Using Equation 30, R6 is calculated as 20.0 k. The  
nearest standard 1% resistor is 20.0 k.  
æ
ç
è
ö
VOUT  
R6 = R7 ×  
-1  
÷
VREF  
ø
(30)  
Due to the internal design of the TPS54478, there is a minimum output voltage limit for any given input voltage.  
The output voltage can never be lower than the internal voltage reference of 0.6 V. Above 0.6 V, the output  
voltage may be limited by the minimum controllable on time. The minimum output voltage in this case is given by  
Equation 31  
Voutmin = Ontimemin´Fsmax ´ Vinmax - loutmin´RDSmin -Ioutmin´ RL + RDSmin  
(
(
)
)
Where:  
Voutmin = minimum achievable output voltage  
Ontimemin = minimum controllable on-time (100 ns typical. 120 ns no load)  
Fsmax = maximum switching frequency including tolerance  
Vinmax = maximum input voltage  
Ioutmin = minimum load current  
RDSmin = minimum high-side MOSFET on resistance (See Electrical Characteristics)  
RL = series resistance of output inductor  
(31)  
There is also a maximum achievable output voltage which is limited by the minimum off time. The maximum  
output voltage is given by Equation 32  
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Offtimemax  
ts  
tdead  
ts  
æ
ö
æ
ö
Voutmax = Vin´ 1-  
-Ioutmax ´ RDSmax + RI - 0.7 -Ioutmax ´RDSmax ´  
(
) (  
)
ç
÷
ç
÷
è
ø
è
ø
Where:  
Voutmax = maximum achievable output voltage  
Vin = minimum input voltage  
Offtimemax = maximum off time (180 ns typical for adequate margin)  
ts = 1/Fs  
Ioutmax = maximum current  
RDSmax = maximum high-side MOSFET on resistance (See Electrical Characteristics)  
RI = DCR of the inductor  
tdead = dead time (40 ns)  
(32)  
COMPENSATION  
There are several possible methods to design closed loop compensation for dc/dc converters. For the ideal  
current mode control, the design equations can be easily simplified. The power stage gain is constant at low  
frequencies, and rolls off at -20 dB/decade above the modulator pole frequency. The power stage phase is 0  
degrees at low frequencies and starts to fall one decade above the modulator pole frequency reaching a  
minimum of -90 degrees one decade above the modulator pole frequency. The modulator pole is a simple pole  
shown in Equation 33.  
1
F
=
PMOD  
2× p ×COUT ×ROUT  
(33)  
For the TPS54478 most circuits will have relatively high amounts of slope compensation. As more slope  
compensation is applied, the power stage characteristics will deviate from the ideal approximations. The phase  
loss of the power stage will now approach -180 degrees, making compensation more difficult. The power stage  
transfer function can be solved but it is a tedious hand calculation that does not lend itself to simple  
approximations. It is best to use Pspice or TINA-TI to accurately model the power stage gain and phase so that a  
reliable compensation circuit can be designed. That is the technique used in this design procedure. Using the  
pspice model of SLVM279 apply the values calculated previously to the output filter components of L1, C9 and  
C10. Set Rload to the appropriate value. For this design, L1 = 1.2 µH. C8 and C9 use the derated capacitance  
value of 45 µF, and the ESR is set to 3 mohm. The Rload resistor is 1.8 / 4 = 450 mΩ. Now the power stage  
characteristic can be plotted as shown in Figure 36.  
60  
180  
120  
60  
40  
Gain  
20  
-0  
0
-12.03 dB  
-20  
-40  
-60  
-60  
-120  
-180  
Phase  
>>  
0.1  
1
10  
100  
1000  
Frequency - kHz  
Figure 36. Power Stage Gain and Phase Characteristics  
For this design, the intended crossover frequency is 70 kHz. From the power stage gain and phase plots, the  
gain at 70 kHz is -12.03 dB and the phase is -131.86 degrees. For 60 degrees of phase margin, additional phase  
boost from a feed forward capacitor in parallel with the upper resistor of the voltage set point divider will be  
required. R3 sets the gain of the compensated error amplifier to be equal and opposite the power stage gain at  
crossover. The required value of R3 can be calculated from Equation 34.  
26  
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TPS54478  
www.ti.com  
-GPWRSTG  
SLVSAS2 JUNE 2011  
20  
Vout  
10  
R3 =  
×
gmEA  
VREF  
(34)  
To maximize phase gain, the compensator zero is placed one decade below the crossover frequency of 70 kHz.  
The required value for C5 is given by Equation 35.  
1
C5 =  
FCO  
2× p ×R3 ×  
10  
(35)  
To maximize phase gain the high frequency pole is not implemented and C4 is not populated. The pole can be  
useful to offset the ESR of aluminum electrolytic output capacitors. If desired the value for C4 can be calculated  
from Equation 36.  
1
C4 =  
2× p ×R3 ×F  
P
(36)  
For maximum phase boost, the pole frequency FP will typically be one decade above the intended crossover  
frequency FCO  
.
The feed forward capacitor C10, is used to increase the phase boost at crossover above what is normally  
available from Type II compensation. It places an additional zero/pole pair located at Equation 37 and  
Equation 38.  
1
FZ =  
2× p ×C10 ×R6  
(37)  
1
F =  
P
2× p ×C10 ×R6 P R7  
(38)  
This zero and pole pair is not independent. Once the zero location is chosen, the pole is fixed as well. For  
optimum performance, the zero and pole should be located symmetrically about the intended crossover  
frequency. The required value for C10 can calculated from Equation 39.  
1
C10 =  
VREF  
2× p ×R6 ×FCO  
×
VOUT  
(39)  
For this design the calculated values for the compensation components are R3 = 30.6 kΩ ,C5 = 736 pF and C10  
= 197 pF. Using standard values, the compensation components are R3 = 30.9 kΩ ,C5 = 820 pF and C10 = 220  
pF.  
APPLICATION CURVES  
100  
90  
80  
70  
60  
50  
40  
30  
20  
100  
90  
80  
70  
60  
50  
40  
30  
20  
10  
0
V
= 3.3 V  
V
= 3.3 V  
IN  
IN  
V
= 5 V  
IN  
V
= 5 V  
IN  
10  
0
0
0.5  
1
1.5  
2
2.5  
3
3.5  
4
0.001  
0.01  
0.1  
Output Current - A  
1
10  
Output Current - A  
Figure 37. EFFICIENCY vs LOAD CURRENT  
Figure 38. EFFICIENCY vs LOAD CURRENT  
Copyright © 2011, Texas Instruments Incorporated  
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TPS54478  
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V
= 5 V/div  
IN  
V
= 50 mV / div (ac coupled)  
OUT  
EN = 5 V/div  
V
= 2 V/div  
I
= 1 A / div  
OUT  
OUT  
Load step = 1 - 3 A, slew rate = 0.167 A / ms  
PWRGD = 5 V/div  
Time = 100 ms/div  
Time = 2 ms/div  
Figure 39. TRANSIENT RESPONSE, 2 A STEP  
Figure 40. POWER UP VOUT, VIN  
V
= 5 V/div  
IN  
EN = 5 V/div  
EN = 5 V/div  
V
= 2 V/div  
OUT  
V
= 500 mV/div  
OUT  
PWRGD = 5 V/div  
Pre-bias voltage = 500 mV  
Time = 2 ms/div  
Time = 2 msec / div  
Figure 41. POWER UP VOUT, EN  
Figure 42. POWER UP INTO PRE-BIAS VOLTAGE  
V
= 5 V/div  
V
= 5 V/div  
IN  
IN  
EN = 5 V/div  
EN = 5 V/div  
V
= 2 V/div  
VOUT = 2 V/div  
OUT  
PWRGD = 5 V/div  
PWRGD = 5 V/div  
Time = 2 ms/div  
Time = 2 ms/div  
Figure 43. POWER DOWN VOUT, VIN  
Figure 44. PWER DOWN VOUT, EN  
28  
Copyright © 2011, Texas Instruments Incorporated  
TPS54478  
www.ti.com  
SLVSAS2 JUNE 2011  
V
= 100 mV/div (ac coupled)  
IN  
V
= 20 mV/div (ac coupled)  
OUT  
PH = 2 V/div  
PH = 2 V/div  
Time = 500 ns/div  
Time = 500 ns/div  
Figure 45. OUTPUT RIPPLE, IOUT = 4 A  
Figure 46. INPUT RIPPLE, IOUT = 4 A  
0.2  
0.15  
0.1  
180  
150  
120  
90  
60  
50  
40  
V
= 5 V  
IN  
Phase  
30  
60  
20  
Gain  
0.05  
0
V
= 3.3 V  
30  
10  
IN  
0
0
-30  
-60  
-90  
-120  
-150  
-180  
-10  
-20  
-30  
-40  
-50  
-60  
-0.05  
-0.1  
-0.15  
-0.2  
0
0.5  
1
1.5  
2
2.5  
3
3.5  
4
10  
100  
1k  
10k  
100k  
1M  
Output Current - A  
f - Frequency - Hz  
Figure 47. CLOSED LOOP RESPONSE, VIN = 5 V,  
IOUT = 4 A  
Figure 48. OUTPUT VOLTAGE REGULATION vs  
LOAD CURRENT  
0.1  
I
= 2 A  
OUT  
0.08  
0.06  
0.04  
0.02  
0
V
= 1 V/div  
OUT  
-0.02  
-0.04  
-0.06  
-0.08  
-0.1  
I
= 5 A/div  
OUT  
Time = 1 ms/div  
3
3.5  
4
4.5  
5
5.5  
6
Input Voltage - V  
Figure 49. OUTPUT VOLTAGE REGULATION vs  
INPUT VOLTAGE  
Figure 50. HICCUP MODE CURRENT LIMIT  
Copyright © 2011, Texas Instruments Incorporated  
29  
TPS54478  
SLVSAS2 JUNE 2011  
www.ti.com  
V
= 1 V/div  
OUT  
V = 500 mV/div  
OUT  
I
= 5 A/div  
OUT  
Time = 500 ms/div  
Time = 5 ms/div  
Figure 51. HICCUP MODE CURRENT LIMIT  
Figure 52. START UP CHARACTERISTIC  
POWER DISSIPATION ESTIMATE  
The following formulas show how to estimate the IC power dissipation under continuous conduction mode (CCM)  
operation. The power dissipation of the IC (Ptot) includes conduction loss (Pcon), dead time loss (Pd), switching  
loss (Psw), gate drive loss (Pgd) and supply current loss (Pq).  
Pcon = Io2 × RDS_on_Temp  
Pd = ƒsw × Io × 0.7 × 40 × 109  
Psw = 1/2 × Vin × Io × ƒsw× 7 × 109  
Pgd = 2 × Vin × ƒsw× 6 × 109  
Pq = Vin × 525 × 106  
Where:  
IO is the output current (A).  
RDS_on_Temp is the on-resistance of the high-side MOSFET with given temperature ().  
Vin is the input voltage (V).  
ƒsw is the switching frequency (Hz).  
30  
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TPS54478  
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SLVSAS2 JUNE 2011  
So  
Ptot = Pcon + Pd + Psw + Pgd + Pq  
For given TA,  
TJ = TA + Rth × Ptot  
For given TJMAX = 150°C  
TAmax = TJ max Rth × Ptot  
Where:  
Ptot is the total device power dissipation (W).  
TA is the ambient temperature (°C).  
TJ is the junction temperature (°C).  
Rth is the thermal resistance of the package (°C/W).  
TJMAX is maximum junction temperature (°C).  
TAMAX is maximum ambient temperature (°C).  
There are additional power losses in the regulator circuit due to the inductor AC and DC losses and trace  
resistance that impact the overall efficiency of the regulator.  
LAYOUT  
Layout is a critical portion of good power supply design. There are several signal paths that conduct fast  
changing currents or voltages that can interact with stray inductance or parasitic capacitance to generate noise  
or degrade the power supplies performance. Care should be taken to minimize the loop area formed by the  
bypass capacitor connections and the VIN pins. See Figure 53 for a PCB layout example. The GND pins and  
AGND pin should be tied directly to the power pad under the IC. The power pad should be connected to any  
internal PCB ground planes using multiple vias directly under the IC. Additional vias can be used to connect the  
top side ground area to the internal planes near the input and output capacitors. For operation at full rated load,  
the top side ground area along with any additional internal ground planes must provide adequate heat dissipating  
area.  
Locate the input bypass capacitor as close to the IC as possible. The PH pin should be routed to the output  
inductor. Since the PH connection is the switching node, the output inductor should be located very close to the  
PH pins, and the area of the PCB conductor minimized to prevent excessive capacitive coupling. The boot  
capacitor must also be located close to the device. The sensitive analog ground connections for the feedback  
voltage divider, compensation components, slow start capacitor and frequency set resistor should be connected  
to a separate analog ground trace as shown. The RT/CLK pin is particularly sensitive to noise so the RT resistor  
should be located as close as possible to the IC and routed with minimal lengths of trace. The additional external  
components can be placed approximately as shown. It may be possible to obtain acceptable performance with  
alternate PCB layouts, however this layout has been shown to produce good results and is meant as a guideline.  
Copyright © 2011, Texas Instruments Incorporated  
31  
TPS54478  
SLVSAS2 JUNE 2011  
www.ti.com  
VIA to  
Ground  
Plane  
UVLO SET  
RESISTORS  
VIN  
BOOT  
CAPACITOR  
VIN  
INPUT  
OUTPUT  
INDUCTOR  
VIN  
VIN  
PH  
PH  
PH  
SS  
VOUT  
BYPASS  
CAPACITOR  
OUTPUT  
FILTER  
EXPOSED  
POWERPAD  
AREA  
CAPACITOR  
GND  
GND  
PH  
SLOW START  
CAPACITOR  
FEEDBACK  
RESISTORS  
ANALOG  
GROUND  
TRACE  
FREQUENCY  
SET  
RESISTOR  
COMPENSATION  
NETWORK  
TOPSIDE  
GROUND  
AREA  
VIA to Ground Plane  
Figure 53. PCB Layout Example  
32  
Copyright © 2011, Texas Instruments Incorporated  
PACKAGE OPTION ADDENDUM  
www.ti.com  
30-Jun-2011  
PACKAGING INFORMATION  
Status (1)  
Eco Plan (2)  
MSL Peak Temp (3)  
Samples  
Orderable Device  
Package Type Package  
Drawing  
Pins  
Package Qty  
Lead/  
Ball Finish  
(Requires Login)  
TPS54478RTER  
TPS54478RTET  
ACTIVE  
ACTIVE  
WQFN  
WQFN  
RTE  
RTE  
16  
16  
3000  
250  
Green (RoHS  
& no Sb/Br)  
CU NIPDAU Level-2-260C-1 YEAR  
Green (RoHS  
& no Sb/Br)  
CU NIPDAU Level-2-260C-1 YEAR  
(1) The marketing status values are defined as follows:  
ACTIVE: Product device recommended for new designs.  
LIFEBUY: TI has announced that the device will be discontinued, and a lifetime-buy period is in effect.  
NRND: Not recommended for new designs. Device is in production to support existing customers, but TI does not recommend using this part in a new design.  
PREVIEW: Device has been announced but is not in production. Samples may or may not be available.  
OBSOLETE: TI has discontinued the production of the device.  
(2) Eco Plan - The planned eco-friendly classification: Pb-Free (RoHS), Pb-Free (RoHS Exempt), or Green (RoHS & no Sb/Br) - please check http://www.ti.com/productcontent for the latest availability  
information and additional product content details.  
TBD: The Pb-Free/Green conversion plan has not been defined.  
Pb-Free (RoHS): TI's terms "Lead-Free" or "Pb-Free" mean semiconductor products that are compatible with the current RoHS requirements for all 6 substances, including the requirement that  
lead not exceed 0.1% by weight in homogeneous materials. Where designed to be soldered at high temperatures, TI Pb-Free products are suitable for use in specified lead-free processes.  
Pb-Free (RoHS Exempt): This component has a RoHS exemption for either 1) lead-based flip-chip solder bumps used between the die and package, or 2) lead-based die adhesive used between  
the die and leadframe. The component is otherwise considered Pb-Free (RoHS compatible) as defined above.  
Green (RoHS & no Sb/Br): TI defines "Green" to mean Pb-Free (RoHS compatible), and free of Bromine (Br) and Antimony (Sb) based flame retardants (Br or Sb do not exceed 0.1% by weight  
in homogeneous material)  
(3) MSL, Peak Temp. -- The Moisture Sensitivity Level rating according to the JEDEC industry standard classifications, and peak solder temperature.  
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Addendum-Page 1  
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