Pick the right output capacitors for LED drivers
Keywords:LED? LED array? output capacitor? white LED?
Texas Instruments
Driving an LED or LED array is not without its challenges. The LEDs require a well-designed constant-current source for controlled brightness. More specifically, the output capacitor in the traditional buck converter that serves to drive the LEDs can have a significant effect on control-loop characteristics, and the capacitor type as well as the output circuit configuration is often critical.
Placing the capacitor in parallel with the LEDs, vs. from output to ground, for example, can make the difference between using the simpler type-two compensation circuit and a type-three circuit for reduced parts count, a more linear and stable loop transfer function, and ease in design.
Ultimately, output capacitor sizing and type is determined by what is best for the intended application and there are several options. The output capacitor can be ceramic or aluminum; sometimes the designer may choose to omit the output capacitor entirely. SPICE circuit modeling provides a good way to validate and confirm the design.
LED design
The use of LEDs in automotive and outdoor lighting applications and the like has grown substantially, largely due to the availability of more efficient, white high-power devices. Luminous efficacies of greater than 175 lumens/W in white LEDs are now commercially available. Operational lifetimes of greater than 50,000hrs and compact size are driving their increased usage.
An LED has a forward V-I characteristic curve that is similar to a diode. Below the LED turn-on threshold, which for a white LED is approximately 3.5V, very little current will flow through it. Above that threshold, current flow increases rapidly for incremental increases in forward voltage. The rise in current is exponential. Thus, the LED can be accurately modeled in SPICE, for a given operating current, as a voltage source in series with a resistor. That is, for accurate modeling the resistor's value depends on the amount of current flowing through the LED. Figure 1 shows the measured impedance of a 1W white LED. The slope of the LED's V-I curve essentially represents the LED's dynamic impedance as a function of the load current.
A 1W LED illuminates at currents as low as 1mA, although not very brightly. At large forward currents, the LED operates at a high power level, which in turn begins to heat the die. As a result, the LED's forward drop increases, as does its dynamic impedance. It is critical to consider the thermal environment when the LED's impedance is determined.
Modeling the converter
The LED's driving source must be designed very carefully. Consider, for example, the voltage-mode buck converter in Figure 2 using the TPS40200 controller, with the converter designed to drive three series LEDs at a constant current of 1A. It regulates the voltage across the current sense resistor (R8) at a constant 0.7V. In essence, R8 programs the current regulated in the LED string.
The output from the converter is equal to the voltage across the LED string, plus the reference voltage (0.7V). For three white LEDs, the output is approximately (3.5)(3) + 0.7 = 11.2V. In a typical buck converter, the output capacitor (C8) is connected from the output-to-ground. However, in this circuit the output capacitor is connected across the LEDs. Although this may seem like a minor difference, it greatly simplifies stabilizing the control loop.
Figure 3: SPICE model for LED buck converter. |
Figure 3 shows the SPICE model of the AC control loop. The modulator "gain" block is internally set to a fixed gain of 8V/V (minimum), as programmed by the TPS40200 controller. This gain is constant over input voltage due to the voltage feed-forward feature of the controller, which changes the oscillator ramp amplitude in proportion to any input voltage variations. From Figure 1, the dynamic impedance of a single LED driven with 1A is 0.5?. Three LEDs are modeled as a lump sum of three series 0.5? resistors and three series 3.5V sources. Note that the resultant 10.5V DC source has no effect on the AC control loop model (SPICE shorts out all DC voltage sources in AC loop analyses). To measure the closed loop gain and phase margin, we break the feedback path and insert an AC voltage source (Vac) at the current regulation point (R8).
Simulation with ceramic capacitor across LEDs
Figure 4 shows the results of the AC simulation in terms of total loop gain, phase response, and the power stage's voltage gain (defined as the sum of the modulator's fixed "gain" block of eight (i.e., 18dB) and the output filter response. This control-to-output gain is a measure of the full loop gain minus the error amplifier gain and is equal to Vo/Vea out.
The power stage gain starts out flat at 7.5dB and rolls off with a slope of -1 (i.e., -20dB/decade) at 3.7kHz. At frequencies below the single-order pole at 3.7kHz, the gain is equal to R8/ (R8 + R_{LED} + R_{L1}) multiplied by the "gain" block. The inductor resistance (R_{L1}) is small relative to the other terms, and does not affect the overall transfer function much. The frequency of the pole in the power stage gain is
The actual measured gain and phase plots for the circuit modeled in Figure 2 is shown in Figure 5.
Figure 5: Measured transfer functions, ceramic output capacitor across LED. |
With a loop gain of 26KHz and 77 phase margin, the measured response correlates well with the simulated response.
So why isn't the output capacitor a factor in the above equation? At frequencies above the pole, the impedance of C8 is large relative to the lower impedances of R_{LED} and R8, allowing those two terms to dominate. At these higher frequencies, the impedance of L1 is large and forms a voltage divider with R_{LED} and R8. A zero occurs at
The frequency of the zero is where the impedance of capacitor C8 is equal to the sum of the LED's impedance and the capacitor's ESR. Normally this would cause the power stage gain to flatten out from its slope of -1. This does not happen because C8 is "shorting out" only a portion of the impedance at the output and the increasing impedance of L1 dominates the filter response. C8 essentially has no impact on the filter's response when the value of C8 is small (where the boundary condition for C8 is met). For large values of C8, the zero it introduces becomes noticeable at a frequency lower than the pole of the power stage gain. If the value of C8 is equal to the boundary condition in the first equation, the zero frequency of the first equation and the pole frequency in the second equation are equal.
Simulation with a large aluminum capacitor
Now we replace the output capacitor in the simulation circuit with a large aluminum electrolytic capacitor (Figure 6).
Figure 6: SPICE model, large aluminum capacitor across LED. |
The ESR is significantly larger than that of a ceramic capacitor. The capacitance value is selected to demonstrate the change in the loop transfer functions when the zero from the second equation is placed at a frequency lower than the pole frequency in the first equation.
As seen in Figure 7, a low-frequency zero causes an increase in gain, but ultimately the gain is limited to 18dB by the "gain" block in Figure 3. Above this zero frequency, a low-frequency pole begins to decrease the gain at a frequency determined by
Thus, the pole is shifted slightly lower in frequency than indicated by the first equation. The above equation is an approximation based on a large capacitance, where the ESR dominates C8's capacitive reactance at the pole frequency. Essentially, the ESR is in parallel with the LED impedance. At higher frequencies, the gain rolls off at a slope of -1, similar to the response shown previously for the smaller value of C8.
To compensate the loop gain for this given power stage gain, the zero of the type-two compensation circuit should be located near the pole frequency in the equation above. Once the loop is properly compensated, the size of C8 has little difference in the overall loop gain and phase margin. The choice of capacitor value and type is up to the designer, and the choice impacts the ripple current in the LED.
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