Taming the Boost: Predicting and measuring feedback loops in current-mode boost high-brightness LED drivers, Part 1 of 2

Boost regulators have been used to drive low-power LEDs (50 mA or less) in portable equipment for years; however, these regulators are often switched-capacitor type, use pulse frequency modulation (PFM), or use PWM with fixed compensation and a preset list of conditions (input voltage, output current, output capacitor, inductor, etc.) to guarantee a stable control loop. High power LEDs (100 mA or more) must operate over a much wider range of input voltage, output voltage, and output current. Higher output power makes both switched-capacitor and PFM regulators impractical, leaving fixed-frequency PWM as the control method of choice. A controller with an external power MOSFET and adjustable compensation is the only viable option.

Such controllers almost invariably use current-mode PWM control (not to be confused with being current regulators) and they require the user to calculate the control loop compensation. As the following shows, current regulators differ so greatly in the small-signal domain from voltage regulators that an IC with a compensation fixed for voltage regulation will not be suitable for current regulation.

Load position
Figure 1a shows a basic schematic of a boost voltage regulator, and Figure 1b shows the equivalent boost current regulator. A fundamental difference exists even if the two circuits deliver similar output voltages and output currents: the position of the load. This basic difference is not exclusive to boost regulators; it occurs in any voltage regulator that has been changed into a current regulator.

Figure 1a: Voltage regulator
(Click on image to enlarge)

Figure 1b: Current regulator
(Click on image to enlarge)

In voltage regulators, the load connects from the converter output to ground. A separate resistor divider forms the feedback path, and the impedance of these resistors is much greater than that of the load, allowing them to be ignored in the small signal analysis. By contras, the load itself (the LEDs) form the feedback path in a current regulator, connecting from the output to the feedback pin. This leads to a significant reduction in gain for current regulators, as the feedback signal is divided by the LEDs and the current sensing circuitry.

Output resistance
In current-mode converters, output resistance contributes heavily to both the dc gain and the system pole. For voltage regulators, the load is mainly resistive, and the calculation of output resistance is straightforward:
R_O = V_O / I_O.
Current regulators driving LEDs are more complicated because the load consists of the dynamic resistance of the diodes, r_D, and the operating point resistance, R_OP = V_O / I_F. Output voltage for a current regulator is the sum of the forward voltages of each LED in series, plus the voltage drop across the current sensing resistor:

V_O = n x V_F + V_SNS

Typical values for r_D are provided by some LED manufacturers, and for those that do not it must be determined by examining the slope of the I-V curve that is provided in all LED datasheets. Figure 2 shows an example curve where current has been plotted as the independent variable; however, different manufacturers may plot V_F versus I_F or I_F versus V_F. This plot, from a 5 W white (InGaN) LED, demonstrates how much r_D can shift from 10 mA up to 1.5 A.

Figure 2: V_F Vs. I_F and r_D Vs. I_F curves
(Click on image to enlarge)

To determine r_D at a specific operating point, a line tangent to the I-V curve is drawn and extended to the edges of the plot (dashed line on the left-hand plot of Figure 2). The change in forward voltage, ΔV_F, is divided by the change in forward current, ΔI_F. For example, in Figure 2 the tangent line is drawn for 1000 mA, giving the following values:

ΔV_F = 4.0 V " 3.45 V

ΔI_F = 1.35 A " 0 A

r_D = ΔV_F / ΔI_F = 0.55 / 1.35 = 0.4 Ω

Once r_D has been calculated the current regulator output resistance can be estimated as:

R_O = n x r_D + R_SNS
('n' is the number of LEDs in series)

An alternative method to determine the total dynamic resistance of a string of LEDs is to use a curve tracer to plot the total I-V characteristic, and then use the tangent line method described above. Not all curve tracers have the power to drive a long string of high current LEDs. In this case, or if no curve tracer is available, a benchtop power supply in controlled-current mode can be used to create a table of I_F versus V_F points which can then be plotted to form a less-accurate I-V curve. When using either method, it is important to test the LED(s) with a heatsink equivalent to the final design heatsink. This minimizes the change in V_F due to differing LED die temperature between the test case and the final case.

Measurement techniques
Control loop gain and phase are measured in working regulators using network analyzers. The network analyzer provides an ac signal that is injected via a 1:1 transformer across a small resistance (typically 20 to 50 Ω) placed between a low impedance node and a high impedance node of the control loop. (Figure 3)

Figure 3: Using a network analyzer with a voltage regulator
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The injection point must be high impedance at point 'R' and low impedance at point 'A' to minimize disturbance of the circuit's operating point The most common injection point in a voltage regulator is between the output and the top feedback divider resistor.

The frequency of the ac source is swept over the desired frequency band, and the voltage measured by two probes, A and R. The results are processed to produce plots of gain and phase. Placing A and R on either side of the signal injection resistor will measure the complete control loop. Moving A or R to the output of the regulator's error amplifier (EAO pin) as shown in Figure 4a and Figure 4b will measure the power stage (control to output) or compensation (feedback) individually.

Figure 4a: Control to output (voltage).
(Click on image to enlarge)

Figure 4b: Feedback (voltage)
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Current regulators, such as HBLED drivers, cannot tolerate a resistor in series with the LED chain. Even 20 Ω would increase the output voltage by 20 V in a 1 A regulator. The ac source injection must move to a different point, such as the input to the error amplifier.

This change in measurement technique highlights the load-position difference between current and voltage regulators described above. Where the control to output gain of a voltage regulator is measured from EAO to V_O, in a current regulator it is measured from EAO to FB (Figure 5a) Likewise, the current regulator feedback transfer function is measured from FB to EAO (Figure 5b) .

Figure 5a: Control to output (current)
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Figure 5b: Feedback (current)
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The figures show an op-amp used as a unity-gain buffer to ensure a low impedance for probe A. This buffer is needed only for taking small signal measurements; however the op-amp could also be used as non-inverting amplifier to reduce the voltage across the current sense resistor as discussed in the 'Amplified Current Sense' section. In such a case the op-amp serves both as a buffer and an amplifier.

(Part 2 of this article will present the small-signal model, amplified current-sense mode, and relevant equations. It is available at: www.planetanalog.com/features/showArticle.jhtml?articleID=202602680)

About the Author
Chris Richardson is an Applications Engineer in the Power Management Products group, Medium and High Voltage Division, at National Semiconductor Corp. His responsibilities are divided between lab work, bench evaluation of new ICs, written work such as datasheets and applications notes, and training for field engineers and seminars. Since joining National Semiconductor in 2001, Chris has worked mainly on synchronous buck controllers and regulators. In the last three years he has focused on products for the emerging high brightness LED market in the automotive and industrial areas. Chris holds a BSEE from the Virginia Polytechnic Institute and State University.