Calculating Essential Charge-Pump Parameters

Jul 1, 2006 12:00 PM
By Vladimir Vitchev, Customer Service Engineer, Maxim Integrated Products, Sunnyvale, Calif.

Average Output Voltage

We find the average output voltage by integrating the output capacitor waveform over one period and dividing the result by the period interval T. Since this waveform consists of two separate waveforms for each interval, we can split the integral into two separate integrals as follows:

Evaluating the integrals, we obtain (see derivation 6):

Similarly, we obtain the average flying-capacitor voltage as follows:

Evaluating the integrals in Eq. 23, we obtain (see derivation 7):

Finally, we calculate the charge-pump circuit's efficiency. By definition, efficiency equals power delivered to the output divided by power consumed at the input. Since we have a device that is switching and whose voltage waveforms vary with time, we are interested in the ratio of the average power at input and output, as opposed to the ratio of instantaneous powers. We define the average power per period as the integral of instantaneous power divided by the period interval:

Evaluating the integrals in Eq. 26, we obtain (see derivation 8):

Next, we evaluate input power ¡ª the power that is delivered from the source V_G to the charge pump. Note that input power is consumed only during the first interval, when the flying capacitor is connected. Because no constant load is connected to the input (or to the output), we can find the instantaneous input power by multiplying the input voltage V_G by the input current. Thus, it can be shown that the instantaneous input power is:

Having obtained the average input power and average output power, we can now calculate the charge-pump efficiency as: