SBAA885 October   2026 BQ76907-Q1

 

  1.   1
  2.   Abstract
  3.   Trademarks
  4. 1Introduction
  5. 2Passive Balancing Mechanism of BQ76907
    1. 2.1 Balancing Current Path
    2. 2.2 Balancing Current
    3. 2.3 Balancing Time Estimation
  6. 3Particularity of Supercapacitor Systems
    1. 3.1 ESR and Voltage Recovery Effect
    2. 3.2 Impact on Balancing Strategy
  7. 4Balancing Scheme Design
  8. 5Reference Algorithm Implementation and Example
    1. 5.1 Algorithm Flow and Pseudocode
    2. 5.2 Design Example
  9. 6Conclusion
  10. 7References

2.3 Balancing Time Estimation

For supercapacitors:

Equation 3. I = C ∙ d V d t

Substituting gives:

Equation 4. C n ∙ d V n d t = - η C B ∙ V n R b a l , n

Arranged as:

Equation 5. d V n d t = - η C B R b a l , n C n V n

Solving this first-order differential equation yields:

Equation 6. V n t = V n 0 ∙ e - t / τ n

Where the time constant is:

Equation 7. τ n = R b a l , n C n η C B

This indicates that:

The faster the balancing target, the smaller Rbal or the higher the effective duty cycle ηCB is required. Supercapacitor capacitance is proportional to the balancing time constant.

The engineering approximation formula can be obtained based on the above formula:

In a small voltage difference and short time interval, it can also be approximately considered that the current does not change significantly with voltage, at this time:

Equation 8. t b a l ≈ C ∙ ∆ V I b a l , a v g

Further substituting the average balancing current:

Equation 9. t b a l ≈ C ∙ ∆ V ∙ R b a l η C B ∙ V c e l l

This formula is suitable for estimating how long it takes for a certain string to converge when it is higher than the lowest string by ΔV; and what balancing resistor should be selected to achieve the target balancing time. This formula is only applicable in the range of ΔV<100mV, Vcell>1V.