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
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
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
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Analog Applications Journal
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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
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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
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
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
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Texas Instruments Incorporated
Figure 6. Control-loop measurement for currentregulating converter
ILED
VIN
VOUT
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/
%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
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
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