Calculating Essential Charge-Pump Parameters

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

Applying the Results

So far, we've analyzed the operation of the charge-pump model presented at the beginning of this article. We obtained a number of equations that express circuit parameters in steady-state mode as a function of the capacitors used in the model, the series resistor with the flying capacitor, switching frequency, duty cycle, input voltage and load. These expressions were obtained by evaluating the circuit in each interval separately, and then forcing the initial-condition values in each interval to support steady-state operation in the circuit.

Many of the equations are complex, which hampers our intuitive understanding of how the circuit works. However, you can compensate for this drawback with mathematical software such as Matlab or Excel. With the expressions derived in this article, we can accurately simulate numerous scenarios by varying the circuit parameters, and thereby reveal a much more comprehensive picture of the circuit operation. You can add refinements to the simplified model presented previously, such as series inductances for the traces and series resistors for the capacitors. However, the subsequent analysis is fundamentally the same.

We can now plug the expressions obtained previously into our numerical-computation software and run some simulations to see how the circuit works. More importantly, we can discover whether our model predicts the operation of a real circuit with accuracy. A calculation spreadsheet in Excel allows you to input all circuit parameters discussed in this article, and obtain numerical values for the model's average output voltage and efficiency using the equations derived in this article.

To test the validity of our model, a bench test was performed using a switched-capacitor voltage inverter from Maxim (MAX870). The internal structure of this device (an unregulated inverting charge pump) is close to that of the model, except the output voltage is inverted (i.e., the output ground connection is flipped during interval two). That action has no effect on the validity of the equations, but to compare with results from the model, we must ignore the output sign and consider only the absolute value of the output voltage.

A series of tests was performed in which the MAX870's load resistor (R2), flying capacitance (C1) and output capacitance (C2) were varied while measuring the absolute value of the output voltage. The results were then compared with those predicted by the calculation spreadsheet (Fig. 4, Fig. 5, and Fig. 6).

Other parameters for the circuit were measured experimentally: f = 134 kHz, D = 50% and R1 = 5 ¦¸. As can be seen, the experimental results agree very closely with results obtained using the MAX870, thereby validating the model as a convenient tool for quick calculations and first-order approximations when designing simple charge pumps.

Note that the charge pump's average output voltage is strongly influenced by the value of R1 (Fig. 7). Higher values of R1 cause the output voltage to drop in magnitude, and a proper choice of switching frequency, load and flying capacitor make the relationship nearly linear. This is important because it allows us to understand how to regulate the output voltage. The mechanism for regulation is almost analogous to that of a linear regulator.

For regulated charge pumps, R1 is a MOSFET whose resistance is regulated according to a feedback signal that senses the output voltage. You should obtain the range of values that R1 can assume from the data sheet for that particular charge pump. When working with unregulated charge pumps, on the other hand, R1 represents the sum of switch resistances seen by the flying capacitor.

That parameter, usually called internal switch resistance, should be specified in the data sheet for the charge-pump IC. Note that the capacitor may see more than one switch, in which case the resistance of individual switches should be added. If you include a flying capacitor with substantial series resistance, you should also account for that value in the parameter R1.

Finally, charge-pump efficiency is an important consideration. An increase of R1 causes efficiency to go down almost the same way as the output voltage. For relatively high switching frequencies, it can be shown that charge-pump efficiency is identical to that of an LDO (i.e., it equals the ratio of output voltage to input voltage).

Many other conclusions can be drawn from the model. To examine a parameter of interest while varying the input variables, be sure to use the calculation spreadsheet, appendix and derivations.

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