Table 3. Design Parameters

8.2.1.2.1 Maximum Output Current

The overcurrent limit in a boost converter limits the maximum input current and thus maximum input power for a given input voltage. Maximum output power is less than maximum input power due to power conversion losses. Therefore, the current limit setting, input voltage, output voltage and efficiency can all change maximum current output. The current limit clamps the peak inductor current; therefore, the ripple has to be subtracted to derive maximum DC current. The ripple current is a function of switching frequency, inductor value and duty cycle. Equation 3 and Equation 4 take into account of all the above factors for maximum output current calculation.

Equation 3.

where

• I_p = inductor peak-to-peak ripple
• L = inductor value
• V_f = Schottky diode forward voltage
• Fs = switching frequency
• V_out = output voltage of the boost converter. It is equal to the sum of VFB and the voltage drop across LEDs.

Equation 4.

where

• I_{out_max} = maximum output current of the boost converter
• I_lim = overcurrent limit
• η = efficiency

For instance, when V_IN is 3 V, 8 LEDs output equivalent to V_OUT of 26 V, the inductor is 22 μH, the Schottky forward voltage is 0.2 V; and then the maximum output current is 65 mA in typical condition. When V_IN is 5 V, 10 LEDs output equivalent to V_OUT of 32 V, the inductor is 22 μH, the Schottky forward voltage is 0.2 V; and then the maximum output current is 85 mA in typical condition.

8.2.1.2.2 Inductor Selection

The selection of the inductor affects steady state operation as well as transient behavior and loop stability. These factors make it the most important component in power regulator design. There are three important inductor specifications, inductor value, DC resistance and saturation current. Considering inductor value alone is not enough.

The inductor value determines the inductor ripple current. Choose an inductor that can handle the necessary peak current without saturating, according to half of the peak-to-peak ripple current given by Equation 3, pause the inductor DC current given by:

Equation 5.

Inductor values can have ±20% tolerance with no current bias. When the inductor current approaches saturation level, its inductance can decrease 20% to 35% from the 0A value depending on how the inductor vendor defines saturation current. Using an inductor with a smaller inductance value forces discontinuous PWM when the inductor current ramps down to zero before the end of each switching cycle. This reduces the boost converter’s maximum output current, causes large input voltage ripple and reduces efficiency. Large inductance value provides much more output current and higher conversion efficiency. For these reasons, a 10-μH to 22-μH inductor value range is recommended. A 22-μH inductor optimized the efficiency for most application while maintaining low inductor peak-to-peak ripple. Table 4 lists the recommended inductor for the TPS61160 or TPS61161. When recommending inductor value, the factory has considered –40% and 20% tolerance from its nominal value.

The TPS61160 and TPS61161 have built-in slope compensation to avoid sub-harmonic oscillation associated with current mode control. If the inductor value is lower than 10 μH, the slope compensation may not be adequate, and the loop can be unstable. Therefore, customers need to verify the inductor in their application if it is different from the recommended values.

8.2.1.2.3 Schottky Diode Selection

The high switching frequency of the TPS61160, TPS61161 demands a high-speed rectification for optimum efficiency. Ensure that the diode average and peak current rating exceeds the average output current and peak inductor current. In addition, the diode’s reverse breakdown voltage must exceed the open LED protection voltage. The ONSemi MBR0540 and the ZETEX ZHCS400 are recommended for TPS61160 and TPS61161.

8.2.1.2.4 Compensation Capacitor Selection

The compensation capacitor C3 (see the Functional Block Diagram), connected from COMP pin to GND, is used to stabilize the feedback loop of the TPS61160, TPS61161. A 220-nF ceramic capacitor for C3 is suitable for most applications.

8.2.1.2.5 Input and Output Capacitor Selection

The output capacitor is mainly selected to meet the requirements for the output ripple and loop stability. This ripple voltage is related to the capacitor’s capacitance and its equivalent series resistance (ESR). Assuming a capacitor with zero ESR, the minimum capacitance needed for a given ripple can be calculated by:

Equation 6.

where

• V_ripple = peak-to-peak output ripple

The additional output ripple component caused by ESR is calculated using:

Equation 7.

Due to its low ESR, V_{ripple_ESR} can be neglected for ceramic capacitors, but must be considered if tantalum or electrolytic capacitors are used.

Care must be taken when evaluating a ceramic capacitor’s derating under DC bias, aging and AC signal. For example, larger form factor capacitors (in 1206 size) have a resonant frequencies in the range of the switching frequency. So the effective capacitance is significantly lower. The DC bias can also significantly reduce capacitance. Ceramic capacitors can loss as much as 50% of its capacitance at its rated voltage. Therefore, leave the margin on the voltage rating to ensure adequate capacitance at the required output voltage.

The capacitor in the range of 1 μF to 4.7 μF is recommended for input side. The output requires a capacitor in the range of 0.47 μF to 10 μF. The output capacitor affects the loop stability of the boost regulator. If the output capacitor is below the range, the boost regulator can potentially become unstable. For example, when using an output capacitor of 0.1 μF, a 470-nF compensation capacitor has to be used for the loop stable.

The popular vendors for high value ceramic capacitors are:

TDK (http://www.component.tdk.com/components.php)

Murata (http://www.murata.com/cap/index.html)

Table 5. Design Parameters for White LEDs with External PWM Dimming

8.2.2.2.1 Choosing Component Values

As per SLVA471, the values of R_FLTR, C_FLTR, R₁, R₂, and R_SET are determined by the system parameters and error tolerance. The main source of LED current error is leakage current from the FB pin. The error gets worse as the LED current decreases. The error due to leakage current is given by Functional Block Diagram, where the impedance seen by the FB pin has a major impact. To reduce error due to the leakage current, the impedance seen by the FB pin needs to be small. Because R₂ is much smaller than R₁ + R_FLTR, R₂ must be chosen to be small to minimize the impedance seen by the FB pin. In general, R₂ must be chosen to be 1 kΩ or less. If greater accuracy at smaller currents is needed, then R₂ must be chosen to be even smaller.

Equation 8.

Once R₂ has been chosen, the value of R_SET and R₁ + R_FLTR can be calculated using Equation 9, Equation 10, Equation 11, and Equation 12. The individual values of R₁ and R_FLTR can be any combination that sums up to R₁ + R_FLTR . In general, choosing R₁ and R_FLTR to be the same value gives a minimum requirement for C_FLTR.

Equation 9.

Equation 10.

Equation 11.

Equation 12.

Finally, C_FLTR can be chosen based on the amount of filtering desired or to provide a gradual dimming effect that is popular in many lighting products. At a minimum, C_FLTR must be chosen to provide at least 20 dB of attenuation at the PWM frequency. Equation 13 can be used to calculate the minimum capacitor value to provide this attenuation.

Equation 13.

To provide gradual dimming, a large capacitor must be chosen to provide a long transient time when changing the PWM duty cycle. Equation 14 shows how to calculate the recommended corner frequency of the RC filter based on the 10% to 90% rise time. Once the corner frequency is known, it can be used to calculate the required capacitor using Equation 15.

Equation 14.

Equation 15.

For example, a design with R_FLTR and R₁ equal to 10 kΩ and a desired rise time of 500 ms requires a corner frequency of 0.7 Hz and a capacitor of 47 μF.

Table 6. Design Parameters for Li-Ion Driver with 6 White LEDs

Table 7. Design Parameters for Li-Ion Driver with 8 White LEDs