11.2.2.1 Programming the Output Voltage

The output voltage of the TPS6107x dc/dc converter can be adjusted with an external resistor divider. The typical value of the voltage at the FB pin is 500 mV. The maximum recommended 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 R2 is typically 500 mV. Based on those two values, the recommended value for R2 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 R1, depending on the needed output voltage (V_O), is calculated using Equation 1:

Equation 1.

For example, if an output voltage of 3.3 V is needed, a 1 MΩ resistor should be chosen for R1. If for any reason the value chosen for R2 is significantly lower than 200 kΩ, additional capacitance in parallel to R1 is recommended, if the device shows instable regulation of the output voltage. The required capacitance value is calculated using Equation 2:

Equation 2.

11.2.2.2 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 TPS6107x's switch is 600 mA. 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 is done using Equation 3:

Equation 3.

For example, for an output current of 75 mA at 3.3 V, at least 340 mA of average current flows through the inductor at a minimum input voltage of 0.9 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 rises at load changes. In addition, a larger inductor increases the total system costs. With these parameters, it is possible to calculate the value for the inductor by using Equation 4:

Equation 4.

Parameter f is the switching frequency and ΔI_L is the ripple current in the inductor, i.e., 40% ΔI_L. In this example, the desired inductor has the value of 4 µH. With this calculated value and the calculated currents, it is possible to choose a suitable inductor. In typical applications, a 4.7-µH inductance is recommended. The device has been optimized to operate with inductance values between 2.2 µH and 10 µH. Nevertheless, operation with higher inductance values may be possible in some applications. Detailed stability analysis is then recommended. Care must be taken because 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 TPS6107x converters:

11.2.2.3 Capacitor Selection

11.2.2.3.2 Output Capacitor

The major parameter necessary to define the output capacitor is the maximum allowed output voltage ripple 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 5:

Equation 5.

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 4.5 µF is needed. In this value range, ceramic capacitors are a good choice. The ESR and the additional ripple created are negligible. It is calculated using Equation 6:

Equation 6.

The total ripple is the sum of the ripple caused by the capacitance and the ripple caused by the ESR of the capacitor. Additional ripple is caused by load transients. This means that the output capacitor has to completely supply the load during the charging phase of the inductor. The 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 4.5 µF and load transient considerations, the recommended output capacitance value is in a 10 µF range.

Care must be taken on capacitance loss caused by derating due to the applied dc voltage and the frequency characteristic of the capacitor. For example, larger form factor capacitors (in 1206 size) have their self resonant frequencies in the same frequency range as the TPS6107x operating frequency. So the effective capacitance of the capacitors used may be significantly lower. Therefore, the recommendation is to use smaller capacitors in parallel instead of one larger capacitor.

11.2.2.4 Small Signal Stability

To analyze small signal stability in more detail, the small signal transfer function of the error amplifier and the regulator, which is given in Equation 7, can be used:

Equation 7.