The BQ25970 device adopts charge pump topology with a 2-phase interleaving fixed 50% duty-cycle, this structure can get higher efficiency because the 2-phase power stage can balance power dissipation between them.

Figure 1-1 Ideal Charge Pump Working Process

Based on the ideal (ignore all of the impendence on power stage and power trace) working process of a charge pump as Figure 1-1 shows, the equation between V_IN and V_BAT can be expressed as,

Equation 1.

Equation 1 shows V_O is always following V_IN, in other words, the BQ25970 device behaves just like a kind of 2:1 voltage follower, when V_IN changes, V_O is changed accordingly.

Figure 1-2 Actual Charge Pump Working Process

In an actual system, the impedance on the power stage and power trace cannot be ignored, as Figure 1-2 shows. The internal resistance of the BQ25970 device can be described as R1 –R4 or R_DS(on) for Q1–Q4, R_ESR means CFLY capacitor ESR, so change Equation 1 as in Equation 2:

Equation 2.

Some definitions can be made in the whole working cycle of the charge pump, charging and discharging as done in Equation 3, and Equation 4.

Equation 3.

Equation 4.

Then, substitute ΔV_{BQ25970_SYS} into the original formula:

Equation 5.

This reforms Equation 5 into Equation 6,

Equation 6.

Since the BQ25970 device is a 2:1 charge pump, V_O will be expressed as Equation 7.

Equation 7.

To create a charger using a Programmable Power Supply (PPS) protocol, such as the Power Delivery (PD) protocol, use an output voltage set slightly higher (such as ΔV) than 2 times the calculated voltage, as in Equation 7, (V_BAT + 0.5 × ΔV_{BQ25970_SYS}). To the BQ25970 device, it does not have a feedback loop for V_O, therefore, it is a kind of open loop power source, meaning that the BQ25970 device should be looked upon as a power source with non-zero internal resistance because its output voltage cannot be kept to a fixed value (for a power converter with feedback control loop, because the control loop can always keep the output as a fixed value whatever load current changes or not, meaning its internal resistance can be looked as 0, or an ideal power source). As Figure 1-3 shows, it is equivalent V_{O_PPS} circuitry for BQ25970 output, it can be viewed as an ideal power source with internal resistance: the internal resistance is R_{BQ25970_SYS}, the voltage of V_{O_PPS_Ideal} equals to V_{O_PPS} from the PPS pre-set according to PPS protocol and all of impendence on the BQ25970 and PCB trace is ignored.

Figure 1-3 V_{O_PPS} Equivalent Circuitry

Equation 8.

Equation 9.

Equation 8 and Equation 9 assumes the total resistance of power trace between BQ25970 output and battery is R_{Power_Trace}, the charging current is calculated using Equation 10:

Equation 10.

In Equation 10, either ΔV or R is changed and the charging current will be changed accordingly. If the designer can keep R or ΔV on power trace at a lower level, they will get higher efficiency at the same charging current condition.