For white LEDs to maintain constant luminosity, they're typically driven with a constant dc current source. In portable applications with a single-cell lithium-ion (Li-ion) source, the sum of the voltage drop across the white LED and the current source can be lower or higher than the battery voltage. This means that whereas a single-cell Li-ion battery can directly power a red LED, a white LED sometimes requires a boosted battery voltage. The easiest way to boost the voltage is via a step-up dc-dc converter.

The advantage of this method is very high efficiency over all load and input voltage conditions, because the input voltage can be boosted to the sum of the LED forward voltage and current-source headroom voltage. This significantly optimizes efficiency at the expense of cost and pc-board area. As a matter of fact, the inductor footprint can be almost twice as big as the driver IC's footprint. Moreover, the inductor is a source of electromagnetic-interference (EMI) that can affect, in a mobile phone, performance of the display and of the radio.

Basic Principles Of Charge Pumps

An alternative method of boosting the battery voltage is to use a charge pump, also called switched-capacitor converter. Capacitors store electrical charge or energy for release at some predetermined rate and at some predetermined time. If an ideal capacitor is charged with an ideal voltage source, V G *(Fig. 1a), * the charge storage occurs instantaneously, corresponding to a Dirac impulse function for the current *(Fig. 1b). *The total stored charge is :

Q = CV_{G}

Real capacitors have equivalent series resistance (ESR) and equivalent series inductance (ESL), neither of which affects the capacitor's ability to store energy. They do, however, seriously impact the overall efficiency of the switched-capacitor voltage converter. Figure 1c shows an equivalent circuit for the charge of a real capacitor, where R SW is the switch resistance. The charging current path also will have a series inductance that can be reduced with proper component layout.

As soon as the circuit is energized, transient conditions of an exponential nature occur until a steady-state condition is reached. The capacitor parasitics limit the peak charge current and increase the charge transfer time *(Fig. 1d)*. In other words, the capacitor charge buildup can't occur instantaneously, which means that the initial voltage variation across the capacitor equals zero.

Charge pumps use this property of capacitors *(Fig. 2)*. The voltage conversion is achieved in two phases. During the first phase, switches S1, S2, and S3 are closed, whereas switches S4 to S8 are open. Therefore, C1 and C2 are stacked and, assuming C1 = C2, charged to half the input voltage:

V _{C1+} - V _{C1-} = V _{C2+} - V _{C2-} = V_{IN} /2

The output load current is supplied by the output capacitor C_{HOLD} . As this capacitor discharges and the output voltage falls below the desired output voltage, the second phase is activated to boost the output voltage above this value. During the second phase, C1 and C2 are in parallel, tied between V_{IN} and V_{OUT} . Switches S4 to S7 are closed, whereas switches S1 to S3 and S8 are open. Because the voltage drop across the capacitor can't change instantaneously, the output voltage jumps to one-and-a-half times the value of the input voltage:

V_{C1+}- V_{C1-} = V_{C2+}- V_{C2-} = V_{OUT}- V_{IN} = V_{IN} /2 => V_{OUT} = 3V_{IN} /2

This accomplishes voltage-boost operation. The duty cycle of the switching signal is usually 50%, since this value generally yields the optimal charge-transfer efficiency. Closing switch S8 and leaving switches S1 to S7 open achieves a voltage conversion with a gain of 1X.

Constant-Current LED Driver

The device in Figure 3 is based on an adaptive charge pump with gains of 1X and 1.5X. The input to the charge pump is connected to the V_{IN} pin, and the output is connected to the V_{OUT} pin. The charge pump has both open- and closed-loop modes of operation. In open-loop mode, the voltage at V_{OUT} is equal to the gain times the voltage at the input. When the charge pump operates in closed-loop mode, the voltage at V_{OUT} is regulated to a constant voltage (V _{REG}) . Internal current sources control current for each LED, arranged in a common-anode configuration. Peak drive current is programmed through the external resistor (R_{SET} ) .

Low-dropout regulators achieve current regulation *(Fig. 4)*. The error amplifier takes the voltage across R_{2} (V_{2}) and compares it against the reference voltage (V_{REF} ) . It then adjusts the LED current (I_{DX} ) via the series-pass element, an nMOS transistor, to the value required to drive the error signal (V_{ERR} = V_{REF}- V_{2} ) as close as possible to zero. V_{REF} is:

V_{REF} = I_{SET} x R1

where:

I_{SET} = 1.25 V/R_{SET}

Setting V_{REF} = V2, the current through each LED is:

I_{DX} = (R1/R2) x I_{SET}

This holds true only if V_{OUT}- V_{LED} is sufficiently high to keep the pass element from saturating. In fact, the current sources require a minimum voltage, called headroom voltage (V_{HR} ) , across them to supply the desired regulated current through the LEDs. The headroom voltage is modeled with a resistor, R_{HR}*(Fig. 5)*:

V_{HR} = R_{HR} x I_{DX}

The gain transitions are actively selected to maintain current regulation based on the LED forward voltage drop, the voltage across the current sources, and the input voltage *(Fig. 3, again)*. As a result, the devices can stay in the most efficient gain mode of 1X over the widest range of the input voltage, reducing the power consumed from the battery.

An important parameter of the charge pump is called output resistance (R_{OUT}) . This parameter depends on the gain with which the charge pump is operating, and it models the internal losses of the charge pump that result in a voltage droop at the charge-pump output V_{OUT} . Because the magnitude of the voltage droop is proportional to the output current of the charge pump, the loss parameter is modeled as a resistance.

Assume that when operating with a gain of 1X, the voltage supplied at V_{IN} is high enough to power all of the LEDs with the programmed current:

V_{IN} ≥ (4R_{OUTx1} x I_{DX} ) + V_{LED(MAX)} + V_{HR} + V_{HYS}

The quantity V_{HYS} is a voltage that creates a hysteresis between the 1X-to-1.5X and the 1.5X-to-1X gain transitions *(Fig. 6)*. The hysteresis allows for clean gain transitions by preventing the charge pump from switching continuously back and forth from one gain to the other due to small and short variations in the system parameters (V_{IN} , V_{LED} , etc.).

The device will operate in closed-loop mode with a regulated output voltage of V REG , which is set greater than the sum of V_{LED(MAX)}, V_{HYS}, and V_{HR}, if the following condition is verified:

(1 x V_{IN}) - (4R_{OUTx1} x I_{DX} ) > V_{REG}

If the latter condition isn't verified, the devices will operate in open-loop mode, allowing the output voltage to track the input voltage:

V_{OUT} = V_{IN}- (4R_{OUTx1} x I_{DX} ) < V_{REG}

Open-loop mode with a gain of 1X also is called Pass mode. This mode of operation is similar to the behavior of a low-dropout regulator working in the dropout region. Internal circuits monitor all current sources for the onset of dropout—the point at which the current sources no longer supply the programmed current. As the battery voltage decreases, the LED with the largest forward voltage will reach the dropout threshold first:

V_{LED(MAX)} = V_{IN}- (4R_{OUTx1} x I_{DX} ) - V_{HR}

When any of the LEDs reach the dropout threshold, the LED driver will switch to a gain of 1.5X, and the charge pump will operate in closed-loop mode with the output voltage V_{OUT} being regulated to V_{REG} . The devices will operate with a gain of 1.5X as long as:

V_{LED(MAX)}> V_{IN}- (R_{OUTx1} x 4I_{LED} ) - V_{HR}- V_{HYS}

When operating with a gain of 1.5X and the voltage supplied at V_{IN} isn't high enough to maintain the regulated output voltage V_{REG} , the charge pump will operate in open-loop mode:

V_{OUT} = 1.5V_{IN}- (R_{OUTx1.5} x 4I_{LED} ) < V_{REG}

Output voltage regulation is achieved by modulating the supply voltage of the switch drive circuits. This results in the modulation of the losses within the charge pump. Having modeled the losses in a charge pump with a resistor, regulating R_{OUT} will provide the desired output voltage, V_{REG} :

V_{REG} = (Gain x V_{IN} ) - (R_{OUT} x I_{OUT} )

R_{OUTx1.5} and R_{OUTx1} represent the minimum values of the output resistance at the gains of 1.5X and 1X, respectively. Typical values for V_{REG} , R_{HR}, R_{OUTx1} , and R_{OUTx1.5} are 4.5 V, 10 mV/mA, 1 W , and 3 W , respectively.

Input Power And LED Efficiency

The output-power relation to be used in the efficiency calculation, assuming all LEDs are identical, is:

P_{OUT} = 4 x V_{LED} x I_{DX}

The LED drive efficiency is:

η = (4 x V_{LED} x I_{DX} )/(V_{IN} x I_{IN} )

where I_{IN} = Gain x 4 x I_{Q} , and I_{Q} i s the supply current of the LED driver. Figure 7 shows a typical efficiency plot with the step indicating a gain transition.

But for a given LED current, the forward voltage can vary with process and temperature. This means that the efficiency of white LEDs can vary while still maintaining constant brightness, since the latter depends solely on the current.

To make things clear, consider an adaptive charge-pump-based LED driver circuit with the following specifications: V_{LED} = 3.0 V, I_{DX} = 15 mA, and V_{IN} = 3.7 V. Neglecting the quiescent current I_{Q}, the input current, when the charge pump operates with a gain of 1X, is:

I_{IN} = 1 x 4 x I_{DX} = 60 mA

Thus, efficiency and input power are:

η = (4 x V_{LED} x I_{DX} )/(V_{IN} x I_{IN} ) @ 81.1%

P_{IN} = 222 mW

To calculate efficiency and input power for the same circuit, but with LEDs having a 3.3-V forward voltage:

η = (4 x V_{LED} x I_{DX} )/(V_{IN} x I_{IN} ) @ 89.2%

P IN = 222 mW

Efficiency has increased, but input power remains the same. This means that LED efficiency, given by (4 x V_{LED} x I_{DX} ), doesn't affect the power drained from the battery, but rather the amount of power dissipated in the driver circuit. Efficiency is, therefore, not an adequate figure of merit to evaluate power consumption. What must be considered is input power versus LED brightness, i.e., LED current. Input power is the true measure of how many electrons are drained from the battery for a given LED brightness. With a gain of 1.5X, under the previous conditions, the input power is equal to 333 mW regardless of V_{LED}.

Because a charge-pump converter has a finite number of voltage gains, there will always be, based on the application specifications, a certain amount of wasted power in the driver circuit. Therefore, to minimize input power, it's important to operate the charge pump with the smallest possible gain. Low R_{OUT} and V_{HR} values enable the charge pump to operate at a gain of 1X over the widest possible input-voltage range.

When designing the color-display backlight in a portable application, the main constraints that a designer must face are power consumption, space, cost, and brightness quality.

There are certain advantages in using switched-capacitor rather than inductor-based switching techniques. An obvious advantage of switched-capacitor converters is that they eliminate the inductor and the related magnetic design issues. As a result, they usually have relatively low noise and minimal radiated EMI. Application circuits are simple, and only few small capacitors are needed. Because there's no inductor, the final pc-board component height is generally smaller than a comparable switching converter.

Finally, the constant-current regulator approach adds excellent current matching to these features (typically 0.2% to 1%)?that is, excellent brightness uniformity. When evaluating the power consumption of a charge-pump-based LED driver, consider the input power consumption for a given brightness level. In charge pumps, input power relates directly to the gain with which the device is operating. As for magnetic dc-dc converters, input power depends on the LED forward voltage.