Texas Instruments | AN-1696 Designing a Boost LED Driver Using the LM5022 (Rev. B) | Application notes | Texas Instruments AN-1696 Designing a Boost LED Driver Using the LM5022 (Rev. B) Application notes

Texas Instruments AN-1696 Designing a Boost LED Driver Using the LM5022 (Rev. B) Application notes
Application Report
SNVA282B – October 2007 – Revised May 2013
AN-1696 Designing a Boost LED Driver Using the LM5022
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ABSTRACT
This application report provides a component-by-component design guide for a boost converter-based
LED driver using the LM5022.
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Contents
Introduction .................................................................................................................. 2
Output Voltage .............................................................................................................. 2
Duty Cycle ................................................................................................................... 2
LED Current Sensing Resistor ............................................................................................ 3
High-Side Current Sense .................................................................................................. 3
Switching Frequency ....................................................................................................... 4
MOSFET ..................................................................................................................... 4
Output Diode ................................................................................................................. 5
Boost Inductor ............................................................................................................... 5
9.1
Inductance for Minimum Input Voltage .......................................................................... 5
9.2
Inductance for Maximum Input Voltage ......................................................................... 6
Output Capacitor ............................................................................................................ 6
Input Capacitor .............................................................................................................. 7
Open Circuit Zener Diode .................................................................................................. 8
VIN and VO Decoupling Capacitors ........................................................................................ 8
VCC Decoupling Capacitor ................................................................................................ 8
Current Sense Filter ........................................................................................................ 8
RCS, RS2 and Current Limit ................................................................................................. 9
Under-Voltage Lock-Out (UVLO) Threshold ........................................................................... 10
Soft-Start Capacitor ....................................................................................................... 10
Control Loop Compensation ............................................................................................. 10
Control Loop Measurement .............................................................................................. 14
Bill of Materials (BOM) .................................................................................................... 16
References ................................................................................................................. 16
List of Figures
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PNP Current Mirror for High-side Current Sensing .....................................................................
VF vs. IF for Ten White LEDs ..............................................................................................
Power Stage and Error Amp .............................................................................................
Power Stage Gain .........................................................................................................
Power Stage Phase .......................................................................................................
Total Loop Gain ............................................................................................................
Total Loop Phase ..........................................................................................................
Network Analyzer With Op-Amp Buffer .................................................................................
Circuit Schematic
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1
Introduction
1
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Introduction
The converter operates from a 12V ±10% input and drives ten series connected white LEDs with a
controlled current of 1.0A ±10% and an output ripple current of 200 mAP-P or less. The circuit schematic is
shown in Figure 1. For details of the PCB and performance characteristics of this converter, see AN-1605
LM5022 Boost LED Driver Evaluation Board User's Guide (SNVA229).
VIN = 10V to 14V
L1
22 PH
CIN1
CIN2
CINX
6.8 PF
6.8 PF
0.1 PF
0.2:
RG
Q1
RUV2
61.9 k:
1
CSYC
OUT
RT
100 pF
7
RT
56.2 k:
RUV1
10 k:
10
OFF
3
UVLO
SS
LM5022
9
SYNC
VIN
COMP
RS2
8
200:
RS1
6
6.34 k:
VCC
FB
4
2
CF
100:
CCS
1 nF
0.1 PF
CSS
RCS
50 m:
R1
C1
U2
1
3
C2
6.04 k:
D2
R2
20 k:
2.2 nF
Q2
CO
4.7 PF
CS
GND
COX
0.1 PF
RFB2
0:
5
Vo/LED+
RSNS
D1
RB
32.4 k:
2
RFB1
1.24 k:
RZ
1.8 nF
:
GND/LED-
180 pF
DIM
Q3
RPD
10 k:
Figure 1. Circuit Schematic
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Output Voltage
The forward voltage, VF, of each LED varies by manufacturer, by process and with temperature, so to
simplify the design the maximum VF of 4.0V at 1.0A has been selected. Using VF-MAX ensures that the
inductor and power MOSFET will meet the worst-case power dissipation requirements of the system.
Some calculations use the typical forward voltage of the LED array, which is 3.3V per LED.
The total output voltage, VO, is equal to the number of series connected LEDs, n, multiplied by VF plus the
voltage dropped across the current sensing resistor (RSNS) placed in series with the LED chain, VSNS. For
this example VSNS will be 200 mV, a compromise between the power dissipated in RSNS and the signal-tonoise ratio (SNR) of the current sensing circuit.
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VO = n x VF + VSNS
(1)
VO-MAX = 10 x 4.0 + 0.2 = 40.2V (maximum)
(2)
VO = 10 x 3.3 + 0.2 = 33.2V (typical)
(3)
Duty Cycle
All boost regulators (voltage or current) step up the input voltage to produce a higher output voltage, and
have a duty ratio D of:
D=
2
VO - VIN + VD
VO + VD
(VD is the forward voltage drop of the output diode)
AN-1696 Designing a Boost LED Driver Using the LM5022
(4)
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LED Current Sensing Resistor
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4
LED Current Sensing Resistor
RSNS should be 0.2Ω to set an LED current of 1.0A with a sensing voltage of 200 mV. The power
dissipated in RSNS is 1.02 x 0.2 = 200 mW. A 0.33W, 1% resistor in 1206 will be used.
5
High-Side Current Sense
The LM5022 boost LED evaluation boards employ a level shift using a matched pair of PNP transistors.
Matching of the base-to-emitter voltages helps ensure that the output current will meet the ±10%
specification, as unmatched transistors can lead to output current errors greater than ±20%. This circuit,
detailed in Figure 2, serves two purposes. First, it senses the LED current differentially across RSNS and
level-shifts the signal to interface with the FB pin of the LM5022. Second, the transistors amplify the
current sense voltage, VSNS, reducing the power dissipated in RSNS and allowing the user to select the
amplitude of VSNS. A high-side current sense is helpful for applications where the cathode of the last LED
connects to system ground.
RSNS
IF
VO
COMPLETE
LM5022
BOOST
CONVERTER
RFB2
Q2
FB
RFB1
RB
Figure 2. PNP Current Mirror for High-side Current Sensing
Resistor RB sets a bias current through the right-hand transistor. The suggested bias current for the PNP
transistors is 1 mA. RB is selected by dividing the typical output voltage minus one diode drop by 1 mA.
RB = (VO – 0.6) / 0.001 = 32.6 kΩ
RB = 32.4 kΩ 1%
(5)
(6)
RFB1 is set to bias the left-hand PNP at 1 mA, using the following expression.
RFB1 = 1.25 / 0.001 = 1.25 kΩ
RFB1 = 1.24 kΩ 1%
(7)
(8)
RFB2 is set to amplify the current sense signal to equal the feedback voltage:
RFB2 = (IF x RSNS x RFB1) / 1.25
RFB2 = (1.0 x 0.2 x 1240) / 1.25 = 198Ω
RFB2 is 200Ω 1%
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(9)
(10)
(11)
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3
Switching Frequency
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Switching Frequency
The selection of switching frequency is based on the tradeoffs between size, cost, and efficiency. In
general, a lower frequency means larger, more expensive inductors and capacitors will be needed. A
higher switching frequency generally results in a smaller but less efficient solution because switching and
gate charging losses increase with fSW. 300 kHz will be used for this circuit, a good compromise between
inductor size and system efficiency.
-8
RT =
1 - 8 x 10 x fSW
fSW x 5.77 x 10
-11
(fSW in Hz, RT in :)
7
RT = 56.2 kΩ 1%
(12)
MOSFET
Selection of the power MOSFET is also governed by tradeoffs between cost, size, and efficiency.
Breaking down the losses in the MOSFET is one way to determine relative efficiencies between different
devices. For this example, the SO-8 package provides the balance of a small footprint with the ability to
dissipate at least 1W in steady state. Losses in the MOSFET can be broken down into conduction loss,
gate charging loss, and switching loss.
Conduction, or I2R, loss, PC, is approximately:
PC = D x
IO
1-D
2
x RDSON x 1.3
(13)
The factor 1.3 accounts for the increase in MOSFET on resistance due to heating. Alternatively, the factor
of 1.3 can be ignored and the maximum high temperature on-resistance of the MOSFET can be used.
Gate charging loss, PG, results from the current required to charge and discharge the gate capacitance of
the power MOSFET and is approximated as:
PG = VCC x QG x fSW
(14)
QG is the total gate charge of the MOSFET. Gate charge loss differs from conduction and switching losses
because the actual dissipation occurs in the LM5022 and not in the MOSFET itself. If no external bias is
applied to the VCC pin, additional loss in the LM5022 IC occurs as the MOSFET driver supply current
flows through the VCC regulator. The loss term PG for this case becomes:
PG = VIN x QG x fSW
(15)
Switching loss, PSW, occurs during the brief transition period as the MOSFET turns on and off. During the
transition period both current and voltage are present in the channel of the MOSFET. The loss can be
approximated as:
PSW = 0.5 x VIN x [IF / (1 – D)] x (tR + tF) x fSW (tR and tF are the rise and fall times of the MOSFET)
(16)
For this example, the maximum drain-to-source voltage applied across the MOSFET is 40.2V plus the
ringing due to parasitic inductance and capacitance. The maximum drive voltage at the gate of the high
side MOSFET is VCC, or 7V typical. The MOSFET selected must be able to withstand 40.2V plus any
ringing from drain to source, and be able to handle at least 7V plus ringing from gate to source. A
minimum voltage rating of 50VDS and 10VGS MOSFET will be used. Comparing the losses in a
spreadsheet leads to a 60VDS rated MOSFET in SO-8 with a maximum RDSON of 31 mΩ, a gate charge of
27 nC, and rise and falls times of 10 ns and 12 ns, respectively.
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8
Output Diode
The boost regulator requires an output diode D1 (see Figure 1) to carry the inductor current during the
MOSFET off-time. The most efficient choice for D1 is a Schottky diode due to low forward drop and zero
reverse recovery time. D1 must be rated to handle the maximum output voltage plus any switch-node
ringing when the MOSFET is on. In practice, all switching converters have some ringing at the switchnode due to the diode parasitic capacitance and the lead inductance.
D1 must also be rated to handle the average output current, IF. The power dissipation can be calculated
by checking the typical diode forward voltage, VD, from the I-V curve on the diode's data sheet and then
multiplying it by IF. The diode device-specific data sheet will also provide a typical junction-to-ambient
thermal resistance, θJA, that can be used to estimate the operating die temperature of the Schottky.
Multiplying the power dissipation (PD = IF x VD) by θJA gives the temperature rise. The diode case size can
then be selected to maintain the Schottky diode temperature below the operational maximum.
In this example a Schottky diode rated to 60V and 2A will be suitable, as the maximum LED current will be
1A. A small case such as SMA can be used if a small footprint is critical. Larger case sizes generally have
lower θJA and lower forward voltage drop, so for better efficiency the larger SMB case size will be used.
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Boost Inductor
The first criterion for selecting an inductor is the inductance itself. In fixed-frequency boost converters this
value is based on the desired peak-to-peak ripple current, ΔiL, which flows in the inductor along with the
average inductor current, IL. For a boost converter in continuous conduction mode (CCM) IL is greater than
the LED current, IF. The two currents are related by the following expression:
IL = IF / (1 – D)
(17)
As with switching frequency, the inductance used is a tradeoff between size and cost. Larger inductance
means lower input ripple current, however because the inductor is connected to the output during the offtime only there is a limit to the reduction in output ripple voltage. Lower inductance results in smaller, less
expensive magnetics. An inductance that gives a ripple current of 30% to 50% of IL is a good starting point
for a CCM boost converter. Minimum inductance should be calculated at the extremes of input voltage to
find the operating condition with the highest requirement:
L1 =
VIN x D
fSW x 'iL
(18)
By calculating in terms of amperes, volts, and megahertz, the inductance value will come out in
microhenrys. In order to ensure that the boost regulator operates in CCM a second equation is needed,
and must also be evaluated at the corners of input voltage to find the minimum inductance required:
L2 =
D(1-D) x VIN
IO x fSW
(19)
By calculating in terms of volts, amps and megahertz the inductance value will come out in microhenrys.
For this design ΔiL will be set to 40% of IL. First, duty cycle is evaluated at both VIN-MIN and at VIN-MAX.
Second, the average inductor current is evaluated at the two input voltages. Third, the inductor ripple
current is determined. Finally, the inductance can be calculated and a standard inductor value selected
that meets all the criteria.
9.1
Inductance for Minimum Input Voltage
D = (40.2 – 10.8 + 0.5) / (40.2 + 0.5) = 73% IL = 1.0 / (1 – 0.73) = 3.7A ΔiL = 0.4 x 3.7 = 1.5A
L1 = (10.8 x 0.73) / (0.3 x 1.5) = 17.5 µH
L2 = (0.73 x 0.27 x 10.8) / (1.0 x 0.3) = 7.1 µH
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(20)
(21)
(22)
5
Output Capacitor
9.2
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Inductance for Maximum Input Voltage
D = (40.2 – 13.2 + 0.5) / (40.2 + 0.5) = 67% IL = 1.0 / (1 – 0.67) = 3.0A ΔiL = 0.4 x 3.0 = 1.2A
L1 = (13.2 x 0.67) / (0.3 x 1.2) = 24.6 µH
L2 = (0.67 x 0.33 x 13.2) / (1.0 x 0.3) = 9.7 µH
(23)
(24)
(25)
Maximum average inductor current occurs at VIN-MIN, and the corresponding inductor ripple current is 1.5APP. Selecting an inductance that exceeds the ripple current requirement at VIN-MIN and the requirement to
stay in CCM for VIN-MAX provides a tradeoff that allows smaller magnetics at the cost of higher ripple current
at maximum input voltage. For this example, a 22 µH inductor will satisfy these requirements.
The second criterion for selecting an inductor is the peak current carrying capability. This is the level
above which the inductor will saturate. In saturation the inductance can drop off severely, resulting in
higher peak current that may overheat the inductor or push the converter into current limit. In a boost
converter, peak inductor/switch current, IPK, is equal to the maximum average inductor current plus one
half of the ripple current. First, the ripple current must be determined under the conditions that give
maximum average inductor current:
'iL =
VIN x D
fSW x L
(26)
Maximum average inductor current occurs at VIN-MIN. Using the selected inductance of 22 µH yields the
following:
ΔiL = (10.8 x 0.73) / (0.3 x 22) = 1.2AP-P
(27)
The highest peak inductor current is:
IPK = IL + ΔiL / 2 = 3.7 + 0.6 = 4.3A
(28)
Therefore, an inductor must be selected that has a peak current rating greater than 4.3A and an average
current rating greater than 3.7A. One possibility is an off-the-shelf 22 µH ±20% inductor that can handle a
peak current of 4.8A and an average current of 4.6A. Finally, the inductor current ripple is recalculated at
the maximum input voltage. This value will be used later to select the input capacitors.
ΔiL = (13.2 x 0.67) / (0.3 x 22) = 1.3AP-P
10
(29)
Output Capacitor
The output capacitor in a current regulator is selected to control the output ripple current, ΔiF, as opposed
to a voltage regulator, where ΔvO is controlled. As a constant current source, this application does not
need bulk capacitance to supply the load during load transients. LED drivers rarely require more than 10
µF of output capacitance, making multi-layer ceramic capacitors (MLCCs) an attractive choice. For the
output capacitor of a switching regulator the minimum quality dielectric that should be used is X5R, and
X7R or better is preferred.
One simple method to determine the required output capacitance is to first determine the desired output
ripple current and then multiply by the load impedance, ZO. The result is the output ripple voltage, which
can then be used to select CO. For an LED driver ZO is equal to:
ZO = n x rD + RSNS
(30)
In this expression n is the number of LEDs in series, rD is the dynamic resistance of each individual LED in
the chain and RSNS is the LED current sense resistor. Some LED manufacturers provide typical values for
rD, however in most cases it must be determined by taking the inverse of the slope IF vs. VF curve at the
desired value of IF. In practice rD can differ from the stated value by 50% to 200%, and the best method to
determine rD is to measure the I-V characteristic of the entire array. A curve of VF vs. IF for the ten-LED
chain is shown in Figure 3.
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Input Capacitor
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Figure 3. VF vs. IF for Ten White LEDs
The slope of the curve at 1.0A is approximately 3.2Ω.
The recommended range of ΔiF is from 10% to 40% of the average current. For this example the ripple
current will be set to 20% of IF, or 200 mAP-P. Output impedance is therefore equal to 3.4Ω. Minimum
output capacitance should be calculated using the maximum duty cycle (at minimum input voltage).
Calculating in terms of amperes, megahertz and ohms will lead to results in microfarads.
CO-MIN =
IF x D
fSW x 'iF x ZO
(31)
(32)
CO-MIN = (1.0 x 0.73) / (0.3 x 0.2 x 3.4) = 3.6 µF
MLCCs have low ESR, small size, and high ripple current capability, but they suffer a loss in capacitance
when a DC bias is placed across them. For this example, the closest standard voltage rating above 40.2V
is 50V. Consultation of several MLCC data sheets reveals that a 50V, 4.7 µF capacitor in an 1812 case
size loses about 25% of its rated capacitance at 40V, yielding about 3.5 µF. That is close enough for this
application. This device has an ESR, RC, of 3 mΩ.
Output capacitors in boost regulators endure a large AC RMS current due to the discontinuous current
from the inductor. The RMS value for the output capacitor AC current should be calculated at minimum
input voltage using the following:
IO-RMS = 1.13 x IL x D x (1 - D)
(33)
IO-RMS = 1.13 x 3.6 x Sqrt(0.73 x 0.27) = 1.8A
(34)
The 4.7 µF, 50V capacitor in a 2220 case has a ripple current rating of over 3A.
11
Input Capacitor
The input capacitors in a boost regulator control the input voltage ripple, ΔvIN, and prevent impedance
mismatch (also called power supply interaction) between the LM5022 and the inductance of the input
leads. Selection of input capacitors is based on their capacitance, ESR, and RMS current rating.
The minimum input capacitance is based on ΔvIN or prevention of power supply interaction. In general, the
requirement for greatest capacitance comes from the power supply interaction. The inductance, LS, and
resistance, RS, of the input source must be estimated, and if this information is not available, they can be
assumed to be 1 µH and 0.1Ω, respectively. Minimum capacitance is then estimated as:
2 x LS x VO x IF
CMIN =
2
VIN x RS
(35)
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Open Circuit Zener Diode
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Calculation in microhenrys, volts, amperes and ohms will give a result in microfarads. The worst-case
minimum capacitance calculation comes at the minimum input voltage. Using the default estimates for LS
and RS, minimum capacitance is:
CMIN = (2 x 1 x 40.2 x 1.0) / (10.82 x 0.1) = 6.9 µF
(36)
The next closest standard 20% capacitor value is 6.8 µF. The final calculation is for the input RMS current.
For boost converters operating in CCM this can be estimated as:
IIN-RMS = 0.29 x ΔiL
(37)
Maximum inductor ripple current is 1.3A, hence the input capacitor must be rated to handle 0.29 x 1.3 =
0.38ARMS.
For this example, the input capacitor will be two 6.8 µF MLCCs rated to 25V, in the 1210 case size. The
RMS current rating of these capacitors is over 2A each, more than enough for this application, and the
25V rating ensures that enough capacitance remains when the DC bias is applied.
12
Open Circuit Zener Diode
The broken/open LED protection zener diode D2 is selected to close the control loop at a voltage just
above the steady state output voltage in the event the LEDs are disconnected or fail open circuit. For this
example the maximum VO in steady state is 40.2V, hence a zener diode with a minimum breakdown
voltage VZ of 44.65V will be used. The total output voltage when D2 breaks down will be VZ plus 1.25V, or
46.0V, see Figure 1. RFB1 limits the zener current to 1 mA, hence the approximate power dissipation in D2
will be 47 x 0.001 = 47 mW. A 0.25W device in the SOD-323 package will be used.
13
VIN and VO Decoupling Capacitors
All switching regulators benefit from low value MLCCs placed in parallel to their main input and output
capacitors. For the LM5022, 100 nF, X7R, 100V rated capacitors in 0805 should be placed at both the
input and output. The input capacitor, CINX, should be placed closest to the VIN and GND pins of the
LM5022. The output capacitor, COX, should be placed closest to the LEDs or the connector in applications
where the LEDs are mounted on a separate PCB.
14
VCC Decoupling Capacitor
The VCC pin should be decoupled with a ceramic capacitor placed as close as possible to the VCC and
GND pins of the LM5022. The decoupling capacitor should have a minimum X5R or X7R type dielectric to
ensure that the capacitance remains stable over voltage and temperature, and be rated to a minimum of
470 nF. One good choice is a 1.0 µF device with X7R dielectric and 1206 case size rated to 25V.
15
Current Sense Filter
Parasitic circuit capacitance, inductance and gate drive current create a spike in the current sense voltage
at the point where Q1 turns on. In order to prevent this spike from terminating the on-time prematurely,
every circuit should have a low-pass filter that consists of CCS and RS1, shown in Figure 1. The time
constant of this filter should be long enough to reduce the parasitic spike without significantly affecting the
shape of the actual current sense voltage. The recommended range for RS1 is between 10Ω and 1 kΩ,
and the recommended range for CCS is between 100 pF and 2.2 nF. For this example, the values of RS1
and CCS will be 100Ω and 1 nF, respectively.
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16
RCS, RS2 and Current Limit
The current sensing resistor RCS is used for steady state regulation of the peak inductor current and to
sense over-current conditions. The slope compensation resistor RS2 is used to ensure control loop stability,
and both resistors affect the current limit threshold. RCS must be low enough to keep the power dissipation
to a minimum, yet high enough to provide good signal-to-noise ratio for the current sensing circuitry. RCS
and RS2 should be set so that the current limit comparator trips before the sensed current exceeds the
peak current rating of the inductor, without limiting the output power in steady state.
For this example the peak current, at VIN-MIN, is 4.3A, while the inductor peak current rating is 4.8A. The
threshold for current limit, ILIM, is set between these two values to account for tolerance of the circuit
components, at a level of 4.5A. The required resistor calculation must take into account both the switch
current through RCS and the compensation ramp current flowing through RS1, RS2 and an internal 2 kΩ
resistor. For more details, see the LM5022 60V Low Side Controller for Boost and SEPIC Data Sheet
(SNVS480). RCS is selected first because it is a power resistor with higher cost and limited selection. The
following equation should be evaluated at VIN-MIN:
RCS =
L x fSW x VCL
(VO ± VIN) x 3 x D + L x fSW x ILIM
(38)
In this expression, VCL is the threshold of the current limit comparator, equal to 0.5V. Calculating with
microhenrys, megahertz, volts and amperes will give the result in ohms.
RCS =
22 x 0.3 x 0.5
(40.2 ± 10.8) x 3 x 0.73 + 22 x 0.3 x 4.5
= 0.035:
(39)
The limited selection of power resistors leads to a 50 mΩ device. Power dissipation in RCS can be
estimated by calculating the average current. The worst-case average current occurs at minimum input
voltage/maximum duty cycle and can be calculated as:
PCS =
IF 2
x RCS x D
1-D
PCS = [(1.0 / 0.27)2 x 0.05] x 0.73 = 0.5W
(40)
For this example, a 50 mΩ 1%, thick-film chip resistor in a 1210 case size rated to 0.5W will be used.
With RCS selected, RS2 can be determined using the following expression:
RS2 =
VCL - ILIM x RCS
45P x D
- 2000 - RS1
RS2 = (0.5 – 4.5 x 0.05) / (45µ x 0.73) – 2100 RS2 = 6270Ω
(41)
The closest 1% tolerance value is 6.34 kΩ.
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Under-Voltage Lock-Out (UVLO) Threshold
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Under-Voltage Lock-Out (UVLO) Threshold
In this example, the regulator begins to operate after the input voltage has risen above 9.0V. In the case
of a brown-out or droop at the input, the UVLO function prevents the LM5022 from drawing high currents
that could overheat the inductor or the MOSFET. The UVLO threshold is set with a standard resistor
divider equation. With RUV1 set to 10 kΩ 1%, RUV2 is calculated as follows:
RUV2 = [(VIN – 1.25) x RUV1] / 1.25
RUV2 = [(9.0 – 1.25) x 10000] / 1.25 = 62 kΩ
(42)
(43)
The closest 1% tolerance value is 61.9 kΩ.
18
Soft-Start Capacitor
The possibility of PWM dimming puts greater importance on the soft-start circuitry than in a standard
voltage regulator. Dimming is done by enabling and disabling the converter, and to achieve the highest
possible dimming ratio, the soft-start time should be as short as possible. A good starting value is 2.2 nF,
and laboratory testing is recommended to determine if this value can be reduced without causing too great
of an overshoot in the LED current upon startup.
19
Control Loop Compensation
The LM5022 uses peak current-mode PWM control to correct changes in output current due to transients.
Peak current-mode provides inherent cycle-by-cycle current limiting, improved line transient response, and
easier control loop compensation than voltage-mode control. Although there are no load transients, PWM
dimming requires a fast control loop so that the output can turn on and off quickly.
The control loop is comprised of two parts. The first is the power stage, which consists of the pulse width
modulator, output filter, current sense circuitry, and the LEDs. The second part is the error amplifier, which
is an op-amp configured as an inverting amplifier.
L
High Side
Sense
CO
D
VIN
+
-
RC
RCS
ZO
+
R2
R1
C2
C1
+
VREF
+
-
Figure 4. Power Stage and Error Amp
One popular method for selecting the compensation components is to create Bode plots of gain and
phase for the power stage and error amplifier. Combined, they make the overall bandwidth and phase
margin of the regulator easy to determine. Software tools such as Excel, MathCAD, and Matlab are useful
for observing how changes in compensation or the power stage affect system gain and phase.
10
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Control Loop Compensation
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The power stage in a CCM peak current mode boost converter consists of the DC gain, APS, a load pole,
fP, the ESR zero, fZ, a right-half plane zero, fRHP, and a double pole resulting from the sampling of the peak
inductor current. The high-side current sense circuitry is treated as a DC gain and included in the
expression for APS. The power stage transfer function (also called the control-to-output transfer function)
can be written:
1+
GPS = APS x
s
1+Z
P
s
ZZ
1+
1-
s
ZRHP
s
s2
Qn x Zn + Zn
(44)
The DC gain term is:
(1 - D) x RSNS
APS =
Gi x RCS 1+
ZO + RSNS
x ASNS
ROP
(45)
The operating point resistance is:
ROP = VO / IF
(46)
The current sense gain is:
ASNS = RFB1 / RRFB2 = 6.25
(47)
The current sense gain is:
Gi = 3
(48)
The ESR zero is:
ZZ =
1
RC x C O
(49)
RC for this example is 3 mΩ.
The load pole is:
1+
ZP =
ZO + RSNS
ROP
(ZO + RSNS + RC) x CO
(50)
The right-half plane zero is:
VIN
VO
ROP x
ZRHP =
2
L
(51)
The sampling double pole quality factor is:
1
Qn =
S -D + 0.5 + (1 - D)
Se
Sn
(52)
The sampling corner frequency is:
ωn = π x fSW
(53)
The inductor current slope is:
Sn = RCS x VIN / L
(54)
The compensation ramp slope is:
Se = 45µ x (2000 + RS1 + RS2) x fSW
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11
Control Loop Compensation
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In the equation for APS, DC gain is highest when input voltage is at the maximum and output voltage at the
minimum, therefore this worst-case analysis done for VIN = 13.2V and VO = 33.4V. DC gain is 9.2 dB. The
load frequency pole fP = ωP / 2π is at 14 kHz (calculated with CO = 3.5 µF), the ESR zero fZ = ωZ / 2π is at
22 MHz, and the right-half plane zero fRHP = ωRHP / 2π is at 38 kHz. The sampling double-pole occurs at
one-half of the switching frequency. Proper selection of slope compensation (via RS2) is most evident in
the sampling double pole. A well-selected RS2 value eliminates peaking in the gain and reduces the rate of
change of the phase lag. Gain and phase plots for the power stage are shown in Figure 5 and Figure 6.
POWER STAGE GAIN (dB)
10
0
-10
-20
-30
-40
-50
100
1k
10k
100k
1M
FREQUENCY (Hz)
Figure 5. Power Stage Gain
POWER STAGE PHASE (°)
180
120
60
0
-60
-120
-180
100
1k
10k
100k
1M
FREQUENCY (Hz)
Figure 6. Power Stage Phase
The load pole causes a roll-off in the gain of -20 dB/decade at lower frequencies. The combination of the
RHP zero and sampling double pole maintain the slope out to beyond the switching frequency. The phase
tends towards -90° at lower frequency but then increases to -180° and beyond from the RHP zero and the
sampling double pole. The effect of the ESR zero is not seen because its frequency is several decades
above the switching frequency. The combination of increasing gain and decreasing phase makes
converters with RHP zeroes difficult to compensate. Setting the overall control loop bandwidth to 1/3 to
1/10 of the RHP zero frequency minimizes these negative effects, but requires a compromise in the
control loop bandwidth.
12
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Compensation is done with the error amplifier, and provides high DC gain (for output accuracy) and high
phase margin (for control loop stability). The transfer function of the compensation block, GEA, can be
derived by treating the error amplifier as an inverting op-amp with input impedance ZI and feedback
impedance ZF. The majority of applications will require a Type II, or two-pole one-zero amplifier, shown in
Figure 4. The LaPlace domain transfer function for this Type II network is given by the following:
GEA =
ZF
ZI
=
1
R2 (C1 + C2)
X
s x R1 x C1 +1
s x R1 x C1 x C2
s
+1
C1 + C2
(56)
Control loop compensation is often set by fixing the mid-band gain of the error amplifier transfer function
first and then positioning the compensation zero and pole. A stable control loop should have at least 45°
of phase margin and 8 dB of gain margin.
1. Fix the compensation zero frequency, fZ1: The suggested placement for this zero is at the load pole
of the power stage, fP = ωP / 2π. For this example, fZ1 = fP = 14 kHz
2. Fix the compensation pole frequency, fP1: The suggested placement for this pole is at half of the
switching frequency, fP1 = 150 kHz
3. Determine the desired control loop bandwidth, f0dB: For this example, f0dB is set at approximately ¼
of the RHP zero frequency, 10 kHz
4. Determine the gain of the power stage at f0dB: This value, A, can be read graphically from the gain
plot of GPS or calculated by replacing the ‘s’ terms in GPS with 2πf0dB. For this example the gain at 10
kHz is approximately 7.5 dB.
5. Calculate the negative of A, subtract 3 dB and convert it to a linear gain: Subtracting 3 dB
accounts for the difference between the error amplifier gain at fZ1 and the actual mid-band gain. For
this example, -7.5 -3 = -10.5 dB = 0.3V/V
6. Select the resistance of R2: This value is arbitrary, however selecting a resistance between 10 kΩ and
100 kΩ will lead to practical values of R1, C1 and C2. For this example, R2 = 20 kΩ 1%.
7. Set R1 = A x R2: For this example: R1 = 0.3 x 20000 = 6 kΩ
8. Set C2 = 1 / (2π x R1 x fZ1): For this example, C2 = 1.81 nF
C1 =
C2
2S x C2 x R1 x fP1 - 1
9. Set:
For this example, C1 = 196 pF
10. Substitute the closest 1% resistor values for R1 and R2, and the closest 10% capacitor values
for C1 and C2: For this example:R1 = 20 kΩ 1%, R2 = 6.04 kΩ 1%, C1 = 180 pF 10%, C2 = 1.8 nF
10%
11. Use the values of C1, C2, R1 and R2 to model the error amp: The open-loop gain and bandwidth
of the LM5022’s internal error amplifier are 75 dB and 4 MHz, respectively. Their effect on GEA can be
2S x GBW
OPG =
2S x GBW
s+
ADC
modeled using the following expression:
The error amplifier transfer
IF x RSNS x RFB1
RFB2 =
1.25
function is:
ADC is a linear gain, and the linear equivalent of 75 dB is
approximately 5600V/V.
12. Plot or evaluate the complete control loop transfer function: The complete control loop transfer
function is obtained by multiplying the power stage and error amplifier transfer functions together. The
bandwidth and phase margin can then be read graphically or evaluated numerically.
SNVA282B – October 2007 – Revised May 2013
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13
Control Loop Measurement
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60
OVERALL LOOP GAIN (dB)
40
20
0
-20
-40
-60
100
1k
10k
100k
1M
FREQUENCY (Hz)
Figure 7. Total Loop Gain
OVERALL LOOP PHASE (°)
180
120
60
0
-60
-120
-180
100
1k
10k
100k
1M
FREQUENCY (Hz)
Figure 8. Total Loop Phase
13. Evaluate the bandwidth, phase margin, and gain margin: For this example the bandwidth is 12.6
kHz, the phase margin is 48°, and the gain margin is 8.3 dB. All the conditions for stability have been met.
20
Control Loop Measurement
Control loop measurements like those shown in Figure 5 through Figure 8 are taken using a network
analyzer that requires a point to inject an AC signal. A small resistor, typically 20Ω to 50Ω, is placed in
series with the control loop, and the AC source is injected across it. The injection node must be low
impedance at one side and high impedance at the other to prevent measurement error. In voltage
regulators the most common point is between the regulator output (low impedance) and the top feedback
divider resistor (high impedance). For the LM5022 boost LED driver, however, the injection node should
be between resistor R2 and the output of the PNP current mirror (shown as the ‘High Side Sense’ block in
Figure 4). R2 provides the high impedance on one side, but the PNP current mirror has a high impedance
as well. One solution to this problem is shown in Figure 9. A high-bandwidth op-amp can be used as a
buffer. This technique should also be used in circuit simulators.
To measure the complete control loop, the network analyzer inputs A and R should be placed at the AC
signal injection points, as shown in Figure 9. To measure the power stage only, input R should be moved
to the COMP pin. The error amplifier can be measured by moving input A to the comp pin.
14
AN-1696 Designing a Boost LED Driver Using the LM5022
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High Side
Sense
VIN
VIN
NGATE
LM5022
LMH6642
20:
R2
+
-
FB
GND
NETWORK
ANALYZER
R
A
Figure 9. Network Analyzer With Op-Amp Buffer
SNVA282B – October 2007 – Revised May 2013
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15
Bill of Materials (BOM)
21
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Bill of Materials (BOM)
Table 1. Bill of Materials (BOM)
Qty
ID
Part Number
Type
Size
1
U1
LM5022
Low-Side Controller
MSOP-10
1
Q1
Si4850EY
N-MOSFET
1
Q2
DMMT5401
1
Q3
TN0200K
1
D1
CMSH2-60
Schottky Diode
1
D2
CMDZ47L
Zener
1
L1
PF0552.223NL
Inductor
2
Cin1 Cin2
C3225X7R1E685M
Capacitor
1
Co
C4532X7R1H475M
22
Vendor
SO-8
60V, 31 mΩ, 27nC
Vishay
Dual PNP
SOT-26
150V, 300 mW
Diodes, Inc
N-MOSFET
SOT-23
20V, 0.7A
Vishay
SMB
60V, 2A
Central Semi
SOD-323
47V, 50 µA
Central Semi
12.5 x12.5 x 6.0mm
22 µH, 4.8A, 35 mΩ
Pulse
1210
6.8 µF, 25V
TDK
Capacitor
1812
4.7 µF, 50V, 3 mΩ
TDK
TDK
TI
1
Cf
C3216X7R1E105K
Capacitor
1206
1 µF, 25V
2
Cinx Cox
C2012X7R2A104M
Capacitor
0805
100 nF, 100V
TDK
1
C1
VJ0805Y181KXXAT
Capacitor
0805
180 pF 10%
Vishay
1
C2
VJ0805Y182KXXAT
Capacitor
0805
1.8 nF 10%
Vishay
1
Css
VJ0805Y222KXXAT
Capacitor
0805
2.2 nF 10%
Vishay
1
Ccs
VJ0805Y102KXXAT
Capacitor
0805
1 nF 10%
Vishay
1
Csyc
VJ0805A101KXXAT
Capacitor
0805
100 pF 10%
Vishay
1
R1
CRCW08056041F
Resistor
0805
6.04 kΩ 1%
Vishay
1
R2
CRCW08052002F
Resistor
0805
20 kΩ 1%
Vishay
1
Rb
CRCW08053242F
Resistor
0805
32.4 kΩ 1%
Vishay
1
Rfb1
CRCW08051241F
Resistor
0805
1.24 kΩ 1%
Vishay
1
Rfb2
CRCW08052000F
Resistor
0805
200Ω 1%
Vishay
2
Ruv1 Rpd
CRCW08051002F
Resistor
0805
10 kΩ 1%
Vishay
2
Rg,Rz
CRCW08050RJ
Resistor
0805
0Ω
Vishay
1
Rs1
CRCW0805101J
Resistor
0805
100Ω 5%
Vishay
1
Rs2
CRCW08056341F
Resistor
0805
6.34 kΩ 1%
Vishay
1
Rcs
ERJL14KF50M
Resistor
1210
50 mΩ, 0.5W 1%
Panasonic
1
Rsns
ERJ8BQFR20V
Resistor
1206
0.2Ω, 1%, 0.33W
Panasonic
1
Rt
CRCW08055622F
Resistor
0805
56.2 kΩ 1%
Vishay
1
Ruv2
CRCW08056192F
Resistor
0805
61.9 kΩ 1%
Vishay
References
•
•
16
Parameters
AN-1605 LM5022 Boost LED Driver Evaluation Board User's Guide (SNVA229)
LM5022 60V Low Side Controller for Boost and SEPIC Data Sheet (SNVS480)
AN-1696 Designing a Boost LED Driver Using the LM5022
SNVA282B – October 2007 – Revised May 2013
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