Compensating and measuring the control loop of a high-power LED driver

Power Management
Texas Instruments Incorporated
Compensating and measuring the control
loop of a high-power LED driver
By Jeff Falin
Senior Applications Engineer
A mathematical model is always helpful in determining the
optimal compensation components for a particular design.
However, compensating the loop of a WLED currentregulating boost converter is a bit different than compensating the same converter configured to regulate voltage.
Measuring the control loop with traditional methods is
cumbersome because of low impedance at the feedback
(FB) pin and the lack of a top-side FB resistor. In
Reference 1, Ray Ridley has presented a simplified,
small-signal control-loop model for a boost converter with
current-mode control. The following explains how to modify
Ridley’s model so that it fits a WLED current-regulating
boost converter; it also explains how to measure the boost
converter’s control loop.
Figure 1. Adjustable DC/DC converter used to
regulate voltage
VIN
VIN
VOUT
VOUT
Adjustable
DC/DC
Converter
GND
R OUT
VFB
FB
Loop components
As shown in Figure 1, any adjustable DC/DC converter can
be modified to provide a higher or lower regulated output
voltage from an input voltage. In this configuration, if we
assume ROUT is a purely resistive load, then VOUT = IOUT ×
ROUT. When used to power LEDs, a DC/DC converter actually controls the current through the LEDs by regulating
the voltage across the low-side FB resistor as shown in
Figure 2. Because the load itself (the LEDs) replaces the
upper FB resistor, the traditional small-signal control-loop
equations no longer apply. The DC load resistance is
REQ = VOUT /ILED,
Figure 2. Adjustable DC/DC converter used to
regulate current through LEDs
(1)
VIN
VIN
Adjustable
DC/DC
Converter
GND
with
VOUT
VOUT
FB
VFB
VOUT = n × VFWD + VFB.
(2)
R SENSE
VFWD, taken either from the diodes’ datasheet or from
measurements, is the forward voltage at ILED; and n is the
number of LEDs in the string.
14
High-Performance Analog Products
www.ti.com/aaj
4Q 2008
Analog Applications Journal
Power Management
Texas Instruments Incorporated
ILED for the application and compute the slope. For example, using the dotted tangent line in Figure 3, we get rD =
(3.5 – 2.0 V)/(1.000 – 0.010 A) = 1.51 W at ILED = 350 mA.
Figure 3. I-V curve of OSRAM LW W5SM
OHL02520
Forward Current, ILED (mA)
1000
Small-signal model
TA = 25ºC
As an example of a small-signal model, the TPS61165 peakcurrent-mode converter driving three series OSRAM LW
W5SM parts will be used. Figure 4a shows an equivalent
small-signal model of a current-regulating boost converter,
while Figure 4b shows an even more simplified model.
Equation 3 shows a frequency-based (s-domain) model
for computing DC gain in both the current-regulating and
the voltage-regulating boost converters:
350
100
1 + s  1 − s 
×

ω z   ω RHP 
1
( − D)
GP(s) = K R ×
×
, (3)
Ri
1 + s  
s
s2 
+
× 1+

ω p  
Qpω n ω 2 
n
10
2.0
2.5
3.0
3.5
4.0
Forward Voltage, VFWD (V)
4.5
where the common variables are
ωz =
However, from a small-signal standpoint, the load resist­
ance consists of REQ as well as the dynamic resistances of
the LEDs, rD, at the ILED. While some LED manufacturers
provide typical values of rD at various current levels, the
best way to determine rD is to extract it from the typical
LED I-V curve, which all manufacturers provide. Figure 3
shows an example I-V curve of an OSRAM LW W5SM highpower LED. Being a dynamic (or small-signal) quantity, rD
is defined as the change in voltage divided by the change in
current, or rD = ∆VFWD/∆ILED. To extract rD from Figure 3,
we simply drive a straight tangent line from the VFWD and
Qp =
1
,
ESR × COUT
1


S 
π  1 + e  (1 − D) − 0.5 
S




n
,
ω n = π × fSW ,
and
ω RHP =
R EQ
(1 − D)2 × L
.
Figure 4. Small-signal model of current-regulating boost converter
L
VOUT
VOUT
n
VIN
(1 – D)
Ri
COUT
D
+
+
–
× rD
n
× rD
COUT
REQ
–
–
Ri
ESR
R SENSE
+
Σ
VREF
R SENSE
ESR
–
+
VREF
(a) Complete
(b) Simplified
15
Analog Applications Journal
4Q 2008
www.ti.com/aaj
High-Performance Analog Products
Power Management
Texas Instruments Incorporated
Table 1. Differences in Equation 3 terms for two converter models
TERM
EVALUATION OF
CURRENT-REGULATING
BOOST CONVERTER
EVALUATION OF
VOLTAGE-REGULATING
BOOST CONVERTER
KR
REQ
REQ + n × rD
1+
RSENSE
ROUT
2
1+
wp
n × rD + RSENSE
REQ
2
(ROUT +ESR) × COUT
(n × rD + RSENSE +ESR) × COUT
Measuring the loop
The duty cycle, D, and the modified values for VOUT and
REQ are computed the same way for both circuits. Sn and
Se are the natural inductor and compensation slopes,
respectively, for the boost converter; and fSW is the switching frequency. The only real differences between the smallsignal model for the voltage-regulating boost converter
and the model for a current-regulating boost converter is
the resistance KR—which multiplies by the transconduct­
ance term, (1 – D)/Ri —and the dominant pole, wp. These
differences are summarized in Table 1. See Reference 1
for more information.
Since the value of RSENSE is typically much lower than
that of ROUT in a converter configured to regulate voltage,
the gain for a current-regulating converter, where ROUT =
REQ, will almost always be lower than the gain for a voltageregulating converter.
To measure the control loop gain and phase of a voltageregulating converter, a network or dedicated loop-gain/
phase analyzer typically uses a 1:1 transformer to inject a
small signal into the loop via a small resistance (RINJ). The
analyzer then measures and compares, over frequency, the
injected signal at point A to the returned signal at point R
and reports the ratio in terms of amplitude difference
(gain) and time delay (phase). This resistance can be
inserted anywhere in the loop as long as point A has relatively much lower impedance than point R; otherwise, the
injected signal will be too large and disturb the converter’s
operating point. As shown in Figure 5, the high-impedance
node where the FB resistors sense the output voltage at
the output capacitor (low-impedance node) is the typical
place for such a resistor.
Figure 5. Control-loop measurement for voltageregulating converter
VOUT
VIN
Adjustable
DC/DC
Converter
Configured as
a Voltage
Regulator
GND
Low Z
VOUT
1:1
C OUT
R INJ
k
High Z
FB
A
AC
Source
R
Network or
Loop-Gain
Analyzer
k
16
High-Performance Analog Products
www.ti.com/aaj
4Q 2008
Analog Applications Journal
Power Management
Texas Instruments Incorporated
Figure 6. Control-loop measurement for currentregulating converter
ILED
VIN
VOUT
Adjustable
DC/DC
Converter
Configured
as a Current
Regulator
GND
C OUT
Optional
R INJ
(50 to 100 Ω)
+
FB
–
R SENSE
1:1
A
R
AC Source
Network or LoopGain Analyzer
Figure 7. Measured and simulated loop gain and phase
at VIN = 5 V and ILED = 350 mA
Conclusion
30
Reference
1. Ray Ridley. (2006). Designer’s
Series, Part V: Current-Mode
Control Modeling. Switching Power
Magazine [Online]. Available: http://
www.switchingpowermagazine.com/
downloads/5%20Current%20Mode
%20Control%20Modeling.pdf
Measured
Phase
20
120
60
10
Gain (dB)
While not exact, the mathematical
model gives the designer a good starting point for designing the compensation of a WLED current-regulating
boost converter. In addition, the
designer can measure the control loop
with one of the alternate methods.
180
Simulated
Phase
0
Simulated
Gain
–10
0
Measured
Gain
Phase (°)
In a current-regulating configuration,
with the load itself being the upper FB
resistor, the injection resistor cannot
be inserted in series with the LEDs.
The converter’s operating point must
first be changed so the resistor can be
inserted between the FB pin and the
sense resistor as shown in Figure 6. In
some cases, a non-inverting, unity-gain
buffer amplifier may be necessary to
lower the impedance at the injection
point and reduce measurement noise.
With the measurement setup in
Figure 6 but without the amplifier, and
with RINJ = 51.1 W, a Venable loop analyzer was used to measure the loop.
The model of a current-regulating
converter was constructed in Mathcad ®
using the datasheet design parameters
of the TPS61170, which has the same
core as the TPS61165. With VIN = 5 V
and ILED set to 350 mA, the model gives
the predicted loop response for the
TPS61165EVM as shown in Figure 7,
which provides an easy comparison
with measured data.
We can easily explain the differences
between the measured and simulated
gain by observing variations in the
WLED dynamic resistance and using
the typical LED I-V curve as well as
chip-to-chip variations in the IC’s
amplifier gain.
–60
–120
–20
–30
100
–180
1000
10000
Frequency (Hz)
100000
Related Web sites
power.ti.com
www.ti.com/sc/device/TPS61165
www.ti.com/sc/device/TPS61170
17
Analog Applications Journal
4Q 2008
www.ti.com/aaj
High-Performance Analog Products
IMPORTANT NOTICE
Texas Instruments Incorporated and its subsidiaries (TI) reserve the right to make corrections, modifications, enhancements,
improvements, and other changes to its products and services at any time and to discontinue any product or service without notice.
Customers should obtain the latest relevant information before placing orders and should verify that such information is current and
complete. All products are sold subject to TI’s terms and conditions of sale supplied at the time of order acknowledgment.
TI warrants performance of its hardware products to the specifications applicable at the time of sale in accordance with TI's standard
warranty. Testing and other quality control techniques are used to the extent TI deems necessary to support this warranty. Except
where mandated by government requirements, testing of all parameters of each product is not necessarily performed.
TI assumes no liability for applications assistance or customer product design. Customers are responsible for their products and
applications using TI components. To minimize the risks associated with customer products and applications, customers should
provide adequate design and operating safeguards.
TI does not warrant or represent that any license, either express or implied, is granted under any TI patent right, copyright, mask
work right, or other TI intellectual property right relating to any combination, machine, or process in which TI products or services
are used. Information published by TI regarding third-party products or services does not constitute a license from TI to use such
products or services or a warranty or endorsement thereof. Use of such information may require a license from a third party under
the patents or other intellectual property of the third party, or a license from TI under the patents or other intellectual property of TI.
Reproduction of information in TI data books or data sheets is permissible only if reproduction is without alteration and is accompanied
by all associated warranties, conditions, limitations, and notices. Reproduction of this information with alteration is an unfair and
deceptive business practice. TI is not responsible or liable for such altered documentation. Information of third parties may be subject
to additional restrictions.
Resale of TI products or services with statements different from or beyond the parameters stated by TI for that product or service
voids all express and any implied warranties for the associated TI product or service and is an unfair and deceptive business practice.
TI is not responsible or liable for any such statements.
TI products are not authorized for use in safety-critical applications (such as life support) where a failure of the TI product would
reasonably be expected to cause severe personal injury or death, unless officers of the parties have executed an agreement
specifically governing such use. Buyers represent that they have all necessary expertise in the safety and regulatory ramifications of
their applications, and acknowledge and agree that they are solely responsible for all legal, regulatory and safety-related requirements
concerning their products and any use of TI products in such safety-critical applications, notwithstanding any applications-related
information or support that may be provided by TI. Further, Buyers must fully indemnify TI and its representatives against any
damages arising out of the use of TI products in such safety-critical applications.
TI products are neither designed nor intended for use in military/aerospace applications or environments unless the TI products are
specifically designated by TI as military-grade or “enhanced plastic.” Only products designated by TI as military-grade meet military
specifications. Buyers acknowledge and agree that any such use of TI products which TI has not designated as military-grade is
solely at the Buyer's risk, and that they are solely responsible for compliance with all legal and regulatory requirements in connection
with such use.
TI products are neither designed nor intended for use in automotive applications or environments unless the specific TI products are
designated by TI as compliant with ISO/TS 16949 requirements. Buyers acknowledge and agree that, if they use any non-designated
products in automotive applications, TI will not be responsible for any failure to meet such requirements.
Following are URLs where you can obtain information on other Texas Instruments products and application solutions:
Products
Applications
Amplifiers amplifier.ti.com
Audio www.ti.com/audio
Data Converters dataconverter.ti.com
Automotive www.ti.com/automotive
Clocks and Timers
www.ti.com/clocks
Broadband www.ti.com/broadband
DSP dsp.ti.com
Digital control www.ti.com/digitalcontrol
Interface interface.ti.com
Medical
www.ti.com/medical
Logic logic.ti.com
Military www.ti.com/military
Power Mgmt power.ti.com
Optical Networking www.ti.com/opticalnetwork
Microcontrollers microcontroller.ti.com
Security www.ti.com/security
RFID
www.ti-rfid.com
Telephony www.ti.com/telephony
RF/IF and ZigBee® Solutions
www.ti.com/lprf
Video and Imaging www.ti.com/video
Wireless www.ti.com/wireless
Mailing Address: Texas Instruments
Post Office Box 655303
Dallas, Texas 75265
TI Worldwide Technical Support
Internet
TI Semiconductor Product Information Center Home
Page
support.ti.com
TI Semiconductor KnowledgeBase Home Page
support.ti.com/sc/knowledgebase
Product Information Centers
Americas Phone
+1(972) 644-5580
Asia
Brazil
Phone
0800-891-2616
Mexico
Phone
0800-670-7544
Phone
International
+91-80-41381665
Domestic
Toll-Free Number
Australia
1-800-999-084
China
800-820-8682
Hong Kong
800-96-5941
India
1-800-425-7888
Indonesia
001-803-8861-1006
Korea
080-551-2804
Malaysia
1-800-80-3973
New Zealand
0800-446-934
Philippines
1-800-765-7404
Singapore
800-886-1028
Taiwan
0800-006800
Thailand
001-800-886-0010
Fax
+886-2-2378-6808
Emailtiasia@ti.com or ti-china@ti.com
Internet
support.ti.com/sc/pic/asia.htm
Fax
Internet/Email
+1(972) 927-6377
support.ti.com/sc/pic/americas.htm
Europe, Middle East, and Africa
Phone
European Free Call
International
Russian Support
00800-ASK-TEXAS
(00800 275 83927)
+49 (0) 8161 80 2121
+7 (4) 95 98 10 701
Note: The European Free Call (Toll Free) number is not active in all
countries. If you have technical difficulty calling the free call number,
please use the international number above.
Fax
Internet
+(49) (0) 8161 80 2045
support.ti.com/sc/pic/euro.htm
Japan
Fax
International
Domestic
+81-3-3344-5317
0120-81-0036
Internet/Email International
Domestic
support.ti.com/sc/pic/japan.htm
www.tij.co.jp/pic
Safe Harbor Statement: This publication may contain forward-looking statements that
involve a number of risks and uncertainties. These “forward-looking statements” are
intended to qualify for the safe harbor from liability established by the Private Securities
Litigation Reform Act of 1995. These forward-looking statements generally can be identified
by phrases such as TI or its management “believes,” “expects,” “anticipates,” “foresees,”
“forecasts,” “estimates” or other words or phrases of similar import. Similarly, such
statements herein that describe the company's products, business strategy, outlook,
objectives, plans, intentions or goals also are forward-looking statements. All such forwardlooking statements are subject to certain risks and uncertainties that could cause actual
results to differ materially from those in forward-looking statements. Please refer to TI's
most recent Form 10-K for more information on the risks and uncertainties that could
materially affect future results of operations. We disclaim any intention or obligation to
update any forward-looking statements as a result of developments occurring after the date
of this publication.
E093008
Mathcad is a registered trademark of Parametric Technology Corporation (PTC). ZigBee is a
registered trademark of the ZigBee Alliance. All other trademarks are the property of their
respective owners.
© 2008 Texas Instruments Incorporated
SLYT308