# Texas Instruments | Extend the Output Voltage Range With a Coupling Inductor | Application notes | Texas Instruments Extend the Output Voltage Range With a Coupling Inductor Application notes

```Application Report
SNVA890 – September 2019
Extend the Boost Converter Output Voltage With a
Coupled Inductor
Jasper Li
ABSTRACT
Maximum output voltage of a boost converter is normally determined by the voltage rating of the
integrated low side MOSFET. This application note introduces a method to extend the maximum output
voltage of a boost converter. The application note firstly analyzes the operating principle. Then it provides
formulas to calculate the voltage and current rating of the power component. Finally, the application note
takes LM27313 as an example to verify the method.
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Contents
Introduction ...................................................................................................................
Operating Principle ..........................................................................................................
Example Using LM27313 ...................................................................................................
Summary ......................................................................................................................
References ...................................................................................................................
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2
4
7
7
List of Figures
1
Simplified Schematic of LM27313 ......................................................................................... 2
2
Power Stage of a Boost Converter with Coupled Inductor ............................................................. 2
3
Operating Waveform at CCM .............................................................................................. 3
4
Operating Waveform at DCM .............................................................................................. 4
5
Schematic of LM27313 with Coupled Inductor
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6
Startup of the LM27313 Circuit
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7
..........................................................................
............................................................................................
Stable Ripple of the LM27313 Circuit .....................................................................................
7
List of Tables
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1
Introduction
A boost converter IC at least integrates a low-side N-type MOSFET and the control circuit to reduce the
cost and total solution size, such as LM27313 in Figure 1. For such a boost converter circuit, the
maximum output voltage must be lower than the voltage rating of the N-MOS which is between SW and
GND pins. This application note utilizes a coupled inductor to increase the output voltage level while
keeping the voltage at SW pin below the absolute maximum ratings.
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Operating Principle
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L1
D1
VIN
VIN
VOUT
SW
C2
LM27313
C1
C3
R1
EN
SHDN
FB
R2
GND
Figure 1. Simplified Schematic of LM27313
2
Operating Principle
The Figure 2 shows the simplified power circuit of a boost converter with coupled inductor. The turns ratio
of the two windings is 1:N. The L1 is the inductance of first winding, and L2 is the inductance of the two
winding in series. The Q1 is the integrated N-MOS. D1 is the rectifier diode, and the C1 and C2 are the
input and output capacitor.
VIN
IL1 1:N
L1
C1
IL2
D1
VOUT
L2
SW
C2
Q1
Figure 2. Power Stage of a Boost Converter with Coupled Inductor
Depending on the current of the coupled inductor at this end of each switching cycle, the circuit could
operate at CCM, DCM, or BCM:
• Continuous conduction mode (CCM), the inductor current is higher than zero at the end of each
switching cycle.
• Discontinuous conduction mode (DCM), the inductor current is zero before the end of each switching
cycle.
• Boundary conduction mode (BCM), the inductor current decreases to zero right at the end of each
switching cycle.
When the converter operates in CCM, the ideal waveforms of the power components voltage and current
are shown in Figure 3, where VD is the reverse voltage of the D1.
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Operating Principle
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VSW
IL1-1
IL1-0
IL1-4
IL1
IL1-2
IL1-3
IL1-2
IL2
IL1-3
VDH
VD
DÂTS
TS
Figure 3. Operating Waveform at CCM
Within one switching period TS, there are two operating status.
• Between zero to D·TS, the low-side MOSFET Q1 is turned on and the D1 is off, so the current through
L1 increases linearly from IL1_0 to IL1_1, as defined by Equation 1.
¿+._1 = +.1_1 F +.1_0 =
8+0
® & ® 65
.1
(1)
The reverse voltage of the diode D1 is defined by Equation 2, where N is the turns ratio of the coupled
inductor.
8&* = 8176 + 0 ® 8+0
•
(2)
Between D·TS and TS, the Q1 turns off and the D1 is on. At the moment that the Q1 turns off, the
current through L1 decreases suddenly as the inductor energy distributes among all turns. The IL1_2 is
defined by Equation 3. Then the inductor current linearly decreases as energy transfers to the output.
At the end of the switching cycle, the current decrease from IL1_2 to IL1_3 as in Equation 4.
+.1_2 =
+.1_1
1+0
¿+._2 = +.1_3 F +.1_2
(3)
8176 F 8+0
8176 F 8+0
=
® :1 F &; ® 65 =
® :1 F &; ® 65
:1 + 0;2 ® .1
.2
(4)
The DC voltage as the SW pin during this period is defined by Equation 5. From the equation, the
voltage at the SW pin is reduced because of the turns ratio, comparing to a normal boost converter.
859 = 8+0 +
•
8176 F 8+0
0+1
(5)
For the next switching cycle, the coupled inductor energy is back to the first winding L1 again. If the
input voltage and output current is stable, the IL1_4 is equal to IL1_0.
At stable condition, each winding of the coupled inductor has voltage-second balance, so:
8+0 ® 65 = 859 ® :1 F &; ® 65 = l8+0 +
8176 F 8+0
p ® :1 F &; ® 65
0+1
(6)
From Equation 6, the duty cycle D at CCM operation is shown in Equation 7. For a conventional boost
converter, the N in the equation is zero.
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Example Using LM27313
&=
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8176 F 8+0
8176 + 0 ® 8+0
(7)
The peak current through the L1 and the internal N-MOS is defined by Equation 8. The saturation current
of the coupled inductor must be higher than this peak current.
+176
¿+._2
+.1_1 = :1 + 0; ® l
F
p + ¿+._1
1F&
2
(8)
If the device is in BCM, the IL1_4 and IL1_0 is zero, then the output current is defined by Equation 9.
+176 =
If
•
•
•
¿+._2
8176 F 8+0
® :1 F &; =
® :1 F &;2 ® 65
2
2 ® :1 + 0;2 ® .1
(9)
the output current is small and the device operates at DCM, the operating waveform is as in Figure 4.
Within D1·TS, the N-MOS is on and the inductor current increases linearly from zero.
Within D2·TS, the N-MOS is off and the current decreases to zero.
In the rest of a switching cycle, both the N-MOS and D1 are off. The VSW are equal to VIN ideally.
VIN
VSW
IL1_1
IL1
IL1_2
IL1_2
IL2
VDH
VD
D1ÂTS
TS
D2ÂTS
Figure 4. Operating Waveform at DCM
The relation of output current and other parameters in DCM is defined by Equation 10.
+176 =
¿+._2 &2 ® 65
8176 F 8+0
®
=
® & 2 ® 65
2
65
2 ® :1 + 0;2 ® .1 2
(10)
For a specific application condition, the method to determine if the device is in CCM or DCM divides into
to three steps.
• Assuming the device is in CCM, the duty cycle can be calculated through Equation 7.
• The output current at the BCM is calculated by Equation 9.
• When the actual output current is lower than the result of the last step, the device is in DCM.
Otherwise, the converter is in CCM.
3
Example Using LM27313
The chapter takes LM27313 as an example to design a DC/DC converter with coupled inductor. The
design target is 5-V input, 100-V output voltage, and 5-mA output current.
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Example Using LM27313
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The most critical external component is the coupled inductor in this power topology. The important
parameter of the coupled inductor are the turns ratio, saturation and temperature current, and voltage
rating. Minimum turns ratio N is limited by voltage rating of the integrated MOSFET and the maximum duty
cycle of the IC.
The maximum SW pin voltage of the LM27313 is 30 V. It is suggested to limit the DC voltage below 25 V,
considering the voltage spike caused by the leakage inductance of the coupling inductor and parasitic
inductor of the PCB. According the Equation 5, the minimum turns ratio can be calculated as Equation 11.
0=
8176 F 8+0
100 F 5
F1=
F 1 = 3.75
859 F 8+0
25 F 5
(11)
One off-the-shelf coupled inductor closed to the requirement from Coilcraft is LPR4012-202LMR, which
has 10-turns ratio and 2-µH L1 inductance with 1.7-A saturation current. The isolation voltage between the
two windings of the coupled inductor is 100 Vac, which is high enough for this application. Using
LPR4012-202LMR, the voltage rating of the low-side MOSFET can be calculated by Equation 12.
859 = 8+0 +
8176 F 8+0
100 F 5
=5+
= 13.6 8
0+1
10 + 1
(12)
The reverse DC voltage of the diode is defined by Equation 13. From the voltage and current requirement,
the BAV3004W-7-F or equivalence can be used as the rectifier diode.
8&* = 0 ® 8+0 + 8176 = 50 + 100 = 150 8
(13)
The output current at BCM can be calculated through Equation 14. As the current at BCM is higher than 5
mA, the device operates at DCM.
+176 =
8176 F 8+0
100 F 5
1
® :1 F &;2 ® 65 =
× :1 F 0.633;2 ×
= 16.5 I#
2
2
2 ® :1 + 0; ® .1
2 × 11 × 2ä
1.6/
(14)
In DCM, D2·TS can be calculated by Equation 15 according to the Equation 10.
2 ® :1 + 0;2 ® .1 ® 65 ® +176
&2 ® 65 = ¨
= 0.126 äO
8176 F 8+0
(15)
Then the inductor peak current is calculated in Equation 16.
+.1_1 =
:8176 F 8+0 ; ® &2 ® 65
= 545 I#
:1 + 0; ® .1
(16)
The output capacitor depends on the output ripple requirement as in Equation 17. For example, the
effective output capacitor must be higher than 83 nF if it require less than 30-mV ripple. If a much smaller
ripple is desired, it is suggested to add RC or LC circuit, instead of pure capacitor, to further filter the
switching frequency.
%176 =
+176
® :65 F &2 ® 65 ;
8176
(17)
Figure 5 shows the schematic of the LM27313 with coupled inductor to support a 5-V input and 100-V, 5mA output. The output capacitor is two GRM31CR72E224KW43 in parallel, the effective capacitance of
which is approximately 0.14 µF with 100-V DC bias voltage. The coupled inductor is LPR4012-202LMR
and the D1 is BAV3004W-7-F.
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Example Using LM27313
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D1
L2
L1
VOUT
VIN
VIN
C2
0.22µF
LM27313
C1
4.7µF
EN
R1
1.5M
SW
SHDN
C4
220pF
C3
0.22µF
R2
1.5M
FB
R3
37.4K
GND
Figure 5. Schematic of LM27313 with Coupled Inductor
Figure 6 shows the start up of the circuit through EN logic. At EN low logic, the output voltage is closed to
input voltage, 5 V. At EN high logic, the output voltage smoothly ramps up to 100 V.
VOUT 20V/div
EN 2V/div
2ms/div
Figure 6. Startup of the LM27313 Circuit
Figure 7 shows the stable operation waveform of the circuit at 5-mA output current. The output voltage
ripple is less than 20 mV. The maximum voltage of the SW is approximately 14 V. The circuit operates at
DCM:
• Within D1·TS, the low-side MOSFET is on, so the SW voltage is closed to zero.
• Within D2·TS, the low-side MOSFET is off and the rectifier diode is on, so the SW voltage is
approximately 14 V.
• In the rest of one switching cycle, Both MOSFET and diode are off. the SW voltage does not drop to
input voltage directly because of the parasitic capacitance of the N-MOS and diode, which causes LC
ringing in SW pin until the next switching cycle.
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Summary
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VOUT(AC) 20mV/div
SW 5V/div
400ns/div
D1ÂTS
D2ÂTS
TS
Figure 7. Stable Ripple of the LM27313 Circuit
4
Summary
The application notes introduces the operating principle of the boost converter with coupled inductor at
DCM, BCM and CCM. Then, the formulas to calculate the voltage and current of the power components
are derived. Finally, the LM27313 is taken as an example to design a 5-V input, 100-V, and 5-mA output
converter. The experiments waveforms show the feasibility of the method.
5
References
•
Texas Instruments, Coupled inductors broaden DC/DC converter usage Technical Brief
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