Table 3. TPS6109x 5 V Output Design Parameters

10.2.1.2.1 Programming the Output Voltage

The output voltage of the TPS61090 DC-DC converter section can be adjusted with an external resistor divider. The typical value of the voltage on the FB pin is 500 mV. The maximum allowed value for the output voltage is 5.5 V. The current through the resistive divider should be about 100 times greater than the current into the FB pin. The typical current into the FB pin is 0.01 µA, and the voltage across R4 is typically 500 mV. Based on those two values, the recommended value for R4 should be lower than 500 kΩ, in order to set the divider current at 1 µA or higher. Because of internal compensation circuitry the value for this resistor should be in the range of 200 kΩ. From that, the value of resistor R3, depending on the needed output voltage (V_O), can be calculated using Equation 1:

Equation 1.

If as an example, an output voltage of 5.0 V is needed, a 1.8-MΩ resistor should be chosen for R3. If for any reason the value for R4 is chosen significantly lower than 200 kΩ additional capacitance in parallel to R3 is recommended. The required capacitance value can be easily calculated using Equation 2

Equation 2.

10.2.1.2.2 Programming the LBI/LBO Threshold Voltage

The current through the resistive divider should be about 100 times greater than the current into the LBI pin. The typical current into the LBI pin is 0.01 µA, and the voltage across R2 is equal to the LBI voltage threshold that is generated on-chip, which has a value of 500 mV. The recommended value for R2is therefore in the range of 500 kΩ. From that, the value of resistor R1, depending on the desired minimum battery voltage V_BAT, can be calculated using Equation 3.

Equation 3.

The output of the low battery supervisor is a simple open-drain output that goes active low if the dedicated battery voltage drops below the programmed threshold voltage on LBI. The output requires a pullup resistor with a recommended value of 1 MΩ. The maximum voltage which is used to pull up the LBO outputs should not exceed the output voltage of the DC-DC converter. If not used, the LBO pin can be left floating or tied to GND.

10.2.1.2.3 Inductor Selection

A boost converter normally requires two main passive components for storing energy during the conversion. A boost inductor and a storage capacitor at the output are required. To select the boost inductor, it is recommended to keep the possible peak inductor current below the current limit threshold of the power switch in the chosen configuration. For example, the current limit threshold of the TPS6109x's switch is 2500 mA at an output voltage of 5 V. The highest peak current through the inductor and the switch depends on the output load, the input (V_BAT), and the output voltage (V_OUT). Estimation of the maximum average inductor current can be done using Equation 4:

Equation 4.

For example, for an output current of 500 mA at 5 V, at least 1750 mA of average current flows through the inductor at a minimum input voltage of 1.8 V.

The second parameter for choosing the inductor is the desired current ripple in the inductor. Normally, it is advisable to work with a ripple of less than 20% of the average inductor current. A smaller ripple reduces the magnetic hysteresis losses in the inductor, as well as output voltage ripple and EMI. But in the same way, regulation time at load changes rises. In addition, a larger inductor increases the total system costs. With those parameters, it is possible to calculate the value for the inductor by using Equation 5:

Equation 5.

Parameter f is the switching frequency and ΔI_L is the ripple current in the inductor, i.e., 20% × I_L. In this example, the desired inductor has the value of 5.5 µH. With this calculated value and the calculated currents, it is possible to choose a suitable inductor. Care has to be taken that load transients and losses in the circuit can lead to higher currents as estimated in equation 4. Also, the losses in the inductor caused by magnetic hysteresis losses and copper losses are a major parameter for total circuit efficiency.

The following inductor series from different suppliers have been used with the TPS6109x converters:

10.2.1.2.4 Capacitor Selection

10.2.1.2.4.2 Output Capacitor DC-DC Converter

The major parameter necessary to define the minimum value of the output capacitor is the maximum allowed output voltage ripple in steady state operation of the converter. This ripple is determined by two parameters of the capacitor, the capacitance and the ESR. It is possible to calculate the minimum capacitance needed for the defined ripple, supposing that the ESR is zero, by using equation Equation 6:

Equation 6.

Parameter f is the switching frequency and ΔV is the maximum allowed ripple.

With a chosen ripple voltage of 10 mV, a minimum capacitance of 53 µF is needed. The total ripple is larger due to the ESR of the output capacitor. This additional component of the ripple can be calculated using Equation 7:

Equation 7.

An additional ripple of 40 mV is the result of using a tantalum capacitor with a low ESR of 80 mΩ. The total ripple is the sum of the ripple caused by the capacitance and the ripple caused by the ESR of the capacitor. In this example, the total ripple is 50 mV. Additional ripple is caused by load transients. This means that the output capacitance needs to be larger than calculated above to meet the total ripple requirements. The output capacitor has to completely supply the load during the charging phase of the inductor. A reasonable value of the output capacitance depends on the speed of the load transients and the load current during the load change. With the calculated minimum value of 53 µF and load transient considerations, a reasonable output capacitance value is in a 100 µF range. For economical reasons this usually is a tantalum capacitor. Because of this the control loop has been optimized for using output capacitors with an ESR of above 30 mΩ.

10.2.1.2.4.3 Small Signal Stability

When using output capacitors with lower ESR, like ceramics, it is recommended to use the adjustable voltage version. The missing ESR can be easily compensated there in the feedback divider. Typically a capacitor in the range of 10 pF in parallel to R3 helps to obtain small signal stability with lowest ESR output capacitors. For more detailed analysis the small signal transfer function of the error amplifier and regulator, which is given is Equation 8, can be used.

Equation 8.