As digital still cameras (DSCs) and mobile phone cameras become more popular, users are demanding higher-quality photos under lower-light conditions. The popular Xenon photoflash is excited by high voltage (200 V to 300 V) normally obtained from a circuit powered by a nickel-cadmium, a nickel-metal-hydride or a Li-ion rechargeable battery, or an alkaline nonrechargeable battery.

The input voltage for a DSC can range from 1.8 V when operating by battery to 5 V when operating by ac adapter. Given such low-level input voltages, a flyback converter offers a popular way to derive the required high voltage. Such converters store the energy in a high-voltage capacitor and then transfer it to the Xenon photoflash lamp. Flyback converters are available in several architectures, including peak current limit switching, fixed-frequency switching and constant on-time switching. A brief overview of each architecture will show that constant on time is the optimum method for design flexibility, performance and safety.

### Fixed-frequency switching

Efficiency and performance is poor because the output-voltage range is large and the switching frequency must be adjusted while the output voltage is increasing.

### Constant on-time switching

The on time of the MOSFET is fixed, and the peak transformer current passing through it is determined by the transformer primary inductance. Thus, the primary current can be too low or, if the primary inductance is low, too high, which raises safety issues. This control technique also limits flexibility in choosing the transformer.

### Peak current limit switching

This approach offers high efficiency and safety advantages. Because it limits the peak current, it can be implemented safely with a wide variety of transformers. And because the peak current limit is adjustable, it allows an optimal balance between safety and fast charging.

### Photoflash Charge Circuit

DSC photoflash circuits require small size, a minimum component count, high efficiency and a fast charging time. However, traditional charging circuits include many discrete components. An example of a discrete charging circuit is shown in **Fig. 1**.

In this circuit, Q1 is the main power switch. The circuit is self-oscillating and a PWM control signal applied to the Charge EN terminal controls the charge rate. Zener diode D3 regulates the voltage on capacitor C6 to approximately 300 V. When Flash TRG is enabled, a pulse exceeding 2 kV is applied to the body of the flash tube through T2, causing ignition.

Discrete circuits have low efficiency and occupy considerable pc-board space. As a result, the traditional discrete approach has become less popular. An integrated circuit can simplify photoflash applications by minimizing the external component count and pc-board space (**Fig. 2**). Such circuits exhibit one of the three control techniques described earlier. For example, the MAX8622 IC uses the peak current limit method.

### 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.

Table 1. Comparison of methods simulating the charging time.Input voltage (V) Method 1:Complete charge time (sec) Method 2: Simplifiedcharge time (sec) Difference(%) 2.8 V 5.14262 5.14286 0.0047 3.3 V 4.53385 4.53409 0.0053 3.6 V 4.24976 4.25000 0.0056 4.0 V 3.93726 3.93750 0.0061 4.2 V 3.80333 3.80357 0.0063### Input Voltage Versus Charging Time

Assume that the transformer primary inductance is 5 H, the secondary-to-primary turns ratio is 15 to 1, the peak current limit is 1.6 A and the output voltage ranges from 30 V to 300 V. Ignore power losses. Using Eq. 6, it is possible to simulate the curve for input voltage versus charge time. The simulated ideal (lossless) case is shown on the left side of **Fig. 6.**

This analysis considers the ideal case, which ignores power loss. Actual charging time is longer than the calculated values shown in **Fig. 7**. To simulate power loss, simply add a voltage drop to the input voltage to obtain a calculated charging time that should be close to that actually measured (**Fig. 8**).

Compared with other switching architectures, the MAX8622 peak current limit switching can optimize a design for faster charging time while suppressing the inrush current. The formulas derived for simulation give results very close to the actual measurements.

The MAX8622 also provides input-undervoltage detection, which extends battery life, and a high level of charging accuracy by monitoring the output voltage with an external resistor divider. The analysis and explanation presented in this article help design engineers choose the proper external components, and thereby design a photoflash charger that meets all specified requirements.