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Mar 1, 2007 12:00 PM
By Rayleigh Lan, Field Applications Engineering Director, and Hunter Chen, Field Applications Engine

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Peak Current Limit Analysis

Operating from two alkaline cells or a single lithium cell, the MAX8622 implements charging with an integrated power MOSFET and a peak current limit control strategy. The architecture of the application circuit (Fig. 3) allows the use of low-cost transformers to charge a 100-µF capacitor to 300 V in 2.8 seconds. It can also charge any other size of photoflash capacitor. Other features include programmable input-current limit up to 1.6 A, input-undervoltage detection and input-voltage monitoring to extend battery life. A charge-done indicator and an automatic-refresh mode are also provided.

The cycle-by-cycle peak current adjustment of this flyback converter suppresses the inrush current while charging the output capacitor rapidly and efficiently. Sensing directly at the transformer secondary prevents discharge of the output capacitor through feedback resistors.

According to the flyback principle, energy is stored in the primary-coil magnetizing inductance of the transformer when the MOSFET is on, and transferred to the secondary's output capacitor when the MOSFET is off. Primary current increases linearly when the MOSFET conducts, because the input voltage is charging the primary inductor. When this current rises to the limit set by ISET (pin 1), the MOSFET turns off. Energy stored in the primary inductance then transfers to the output capacitor until the secondary current reaches its valley limit, which turns the MOSFET on again. The controller follows this sequence until the output-capacitor voltage reaches its set value.

Figs. 4 and 5 show the primary and secondary currents during startup and at a later period. Charging time is an important specification for this kind of application. The following two methods of theoretical analysis derive equations for calculating the output-voltage waveform, the input-current waveform and the charging time.

Method One

Define the transformer turns ratio as N, the primary inductance as LP and the secondary inductance as LS=N2LP. When the MOSFET turns on:

where tON defines the MOSFET's turn-on time during each period.

From Eq. 1, we see that tON for each period is fixed when the quantities IPPK, VIN and LP have fixed values. When the MOSFET turns off, the circuit becomes a series-LC circuit, and we have:

where the initial value of IS is 1/N×IPPK and COUT is the output capacitor, and we define VOUT0 as the initial value of VOUT in each period. The MOSFET turns on and switches to the next cycle when IS equals zero, so we can derive the off time for each period as:

From Eq. 2, we see that tOFF during each period is not fixed, but grows smaller as the output-capacitor voltage increases. We assume the initial value of the output-capacitor voltage is zero (VOUT0 equals zero), so the first cycle's off time is 1/w0 × π/2, which equals, 1\4×f0, the period of 1/4 × LP/N2 × COUT.

The output-capacitor voltage for one specific period, K, is:

and the total charge time is:

where we define VOUTM equals VTARGET. (Eq. 4)

Method Two

From a high-resolution viewpoint (time scale close to the switching period), the output voltage rises only when the MOSFET is off and stays flat when the MOSFET is on. We can express this envelope of output voltage with an analytical equation (Fig. 5). Assuming the variation of output voltage in every switch period is very small (VOUT0 equals VOUT):

(ΔQ charges the output capacitor during the off time.)

Because ΔVOUT, tON and tOFF are very small, ΔVOUT/Δt canbe regarded as the derivative of output voltage VOUT with respect to time:

Therefore,

From Eq. 6, we can easily calculate the no-loss charging time based on a given input voltage, output voltage, output-capacitor value and transformer turns ratio. The charging time is not affected by different values of primary inductance in the transformer. However, larger values of transformer turns ratio provide a faster charging time. From Eq. 7, we can calculate the output-voltage waveform.

Input Current

The input voltage charges the transformer primary when the MOSFET is on. During this on time, the charge stored in the primary inductance is:

The input-current formula is derived as follows:

From Eq. 8, we can calculate the input-current waveform.

LX Node Voltage

When the MOSFET conducts, the LX terminal voltage (Fig. 3) is zero. The LX voltage is a function of the input voltage, output voltage and transformer turns ratio when the MOSFET is off:

Design Example

Consider the following conditions: VIN ranges from 2.5 V to 5.5 V, transformer turns ratio N equals 15 to 1, the primary inductance is 5 μH, the primary peak current limit is 1.2 A, the output capacitance (CO) equals 150 µF and the output voltage (VO) equals 300 V. To calculate charging time over the input-voltage range, the formula based on theoretical analysis can be used by software to analyze the charge circuit and make calculations. For example, the charging time can be observed by considering different value combinations for the transformer turns ratio, primary inductance and primary peak current.

Using Eqs. 7-10, we can simulate waveforms for the output-voltage charge curve, input current and LX voltage. We assume a transformer primary inductance of 5 μH, a secondary-to-primary turns ratio of 15 to 1, a current limit of 1.2 A, an input voltage of 3.5 V and an output-voltage range of 0 V to 300 V. Fig. 6 compares the simulated waveforms with ones based on actual measurements.

Table 1 compares the simulated results obtained by using Method 1 and Method 2.

These simulations show that both methods give similar results. Method 1 is more rigorous, but needs more computation time and does not produce results directly from the equation. Method 2 uses reasonable approximations to obtain an equation for the envelope curve of output voltage, and quickly calculates the charging time.