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

Small Signal Model
The boost regulator has two disadvantages when compared to the buck regulator for small signal modeling of the power stage. First, it has a right-half plane zero that depends on the duty cycle and the load, and complicates the derivation of that model. Second, the boost regulator is not used as often as the buck, and less effort has been spent to derive accurate small signal models. We will now present a simplified model for the current-mode boost converter as a voltage regulator side by side with the modifications necessary to predict the behavior of a boost current regulator.

Peak current-mode control (which in boost regulators controls the inductor/switch current, not the output current) is ubiquitous in low-side controllers and monolithic ICs where the control switch emitter/source connects to the system ground. All of the common switching regulators that can be built with a low-side controller, such as boost, flyback, SEPIC, and Cuk converters have right-half plane zeroes. Current-mode control simplifies their control-to-output transfer functions by moving one of the output L-C poles to high frequency, above the control-loop bandwidth. Both the voltage regulator and current regulator performance can be predicted with the following power-stage transfer equation:

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The differences in this function between voltage regulators and current regulators are contrasted below, referencing the schematics of Figure 6a and Figure 6b:

Figure 6a: Voltage regulator circuit
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Figure 6b: Current regulator circuit
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DC gain
(Voltage regulator on the left; current regulator on the right)

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where G_i is a parameter of the controller IC, R_OP = V_O / _IF

System pole
(Voltage regulator on the left; current regulator on the right)

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Right-hand plane (RHP zero)
(Voltage regulator on the left; current regulator on the right)

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The following quantities are the same for both voltage and current boost regulators:

Duty cycle

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ESR zero

Sampling double-pole quality factor

Natural inductor current slope

S_n = R_CS x V_IN / L

Compensation slope

S_e = V_m x f_SW

(V_m is a parameter of the controller IC, f_SW is the switching frequency)

Sampling double-pole corner frequency

Ω_n = π x f_SW

By far, the greatest change from voltage to current regulation is in the dc gain, stemming from the low value of r_D compared to R_O, and the resistor-divider effect that results from a combined load and feedback path. As an example, consider the case of a voltage regulator delivering an output of 36 V and 1 A from an input of 12 V. Following the calculation for dc gain gives a result of about 30 dB. In contrast, a current regulator driving ten white LEDs (V_O ≈36 V), also at 1 A and also from an input of 12 V, has a dc gain of only 6 dB.

Amplified current sense
Almost any regulator with an adjustable output voltage can be reconfigured as an LED driver. However, simply replacing the top feedback-divider resistor with the LED chain and the bottom feedback resistor with the current-sense resistor will result in wasted power and excess heat. LEDs that run at 1 A would dissipate 1.25 W in their current-sense resistors if the current-sense voltage was not amplified to match the standard bandgap voltage of 1.25V.

Fortunately, the effect on the total control loop is slight. The reduced value of RSNS roughly cancels the added gain. For a gain A_SNS the dc-gain term can be rewritten as follows:

Figure 7 shows a practical implementation of a current-sense amplifier using a low-cost op amp. The 20 Ω injection resistor would be placed between the output of the op-amp and FB pin of the regulator.

Figure 7: Current sense amplifier
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Conclusion
Predicting and measuring the control loop response of LEDs driven with a boost current regulator requires several degrees of change from the standard practice. LED drivers are considered constant-current sources, lacking the load transients that voltage regulators must combat. The temptation exists to ignore the control-to-output response and simply compensate with an integrator.

The reality is that HBLED drivers require careful analysis to provide high dc gain (for accuracy of the output current) and as much bandwidth as possible because of PWM dimming. A fast control loop is required for rapid slewing of the output current in response to this dimming signal, and is as important as the load transient response of a voltage regulator. Careful prediction, design, and measurement is therefore just as important for boost LED drivers as it is for boost voltage regulators.

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.