## 1 Introduction  
As generally recognized, LEDs are getting more attractive in the world due to their small size, light weight, and long life [1, 2]. An LED is driven by the current due to its behavior like a diode [3]. The higher the current in the LED, the higher is the forward-biased voltage across the LED [4]. Furthermore, the higher the temperature in the LED, the lower is the forward-biased voltage across the LED. In general, the arrangement of LEDs is first in series and then in parallel, so as to avoid a high voltage across the output of the LED driver. And hence, the current balance among LED strings is very important so as to avoid uneven currents in the LED strings. These uneven currents will affect the LED luminance and cause the temperature in the LED to be increased and the life of the LED to be reduced. Therefore, many literatures have presented current-sharing methods for LED strings [5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21] so as to make currents distributed among LED strings as identically as possible. The LED current-sharing methods are classified into two types. One is active [5, 6, 7, 8, 9], and the other is passive [10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21]. As for the active current-sharing method, each LED string contains one current regulator and one current sensor to balance currents among LED strings. The main demerit of this method is the high complexity of the circuit. Hence, the passive current sharing method is presented to overcome this disadvantage. This method can be classified into two types. One is based on the differential-mode transformer, and the other is based on the energy-transferring capacitor. For the first type to be considered [10, 11, 12, 13, 14], as the currents in two LED strings are not identical, this transformer will be activated, and hence, the two currents will be forced to be regulated as identically as possible. In [10], an LED driver is constructed of one Zeta converter with several current-balancing transformers such that the magnetizing energy can be recycled. In [11], several daisy-chained transformers are applied to current-balance multiple LED strings. In [12], only for two LED strings to be considered, an LED driver is made of one traditional boost converter with one differential transformer used as a current-sharing device. In [13], the LED driver is the same as that shown in [11], except for isolation capacitors used in the former. In [14], an LED driver is established by one twin-bus converter along with several differential transformers such that the voltage stress on the switch is reduced. However, in practice, the current-sharing error comes from the magnetizing current of the transformer. For the second type to be considered [15; 16; 17; 18; 19; 20; 21], the current balance between the two LED strings is based on the ampere-second balance. In [15], an LED driver constructed of an isolated LCLC resonant circuit along with capacitive current balance. In [16], an LED driver is built from one traditional boost along with one coupled inductor and capacitive current balance such that the output voltage can be upgraded. In [17], an isolated CLL resonant converter with several balance capacitors is applied to driving multiple LED strings. In [18], isolated and non-isolated LED drivers are constructed by the traditional converters with switched capacitors used. In [19], an LED driver is constructed by one voltage-boosting converter with automatic current balance and zero-voltage switching such that the switching loss can be reduced. In [20], an LED driver is built from one traditional boost converter along with capacitive current balance, input ripple cancellation, and passive clamp such that the input current ripple is reduced and the voltage gain improved. In [21], a two-channel LED driver is established by one coupled-inductor converter along with capacitive current balance and one passive regenerative snubber such that the voltage gain is upgraded and the leakage energy can be recycled.