Valeo explains how to enhance pixelated automotive front lighting with multiphase buck converters

By Sebastian Krick, Valeo

While alternative technologies like Valeo's PictureBeam Monolithic can very precisely control the intensity of the projected light, automotive headlights can flexibly and automatically adjust the light intensity to highlight road signs and other objects to attract the driver's attention. Each pixel can be managed individually to adjust the light flux accordingly. A major challenge facing such technologies involves the precise control and power supply of the LEDs.

Converter topologies: from LED string drivers to pixelated LEDs

In the latest LED drivers for automotive headlamps, there is typically a buck converter driving a single LED string with currents up to 1.5 A. The buck converter acts as a current source for the single LED string (Figure 1). There are several buck converters for different lighting functions.

The buck converter acts like a current source for a single LED string

Since the LED string voltage usually exceeds the battery voltage Vin, you need an upstream boost circuit. You will find this topology in all headlight LED drivers because they have the highest flexibility in terms of LED number and LED current control. The boost voltage is usually around 45 V and can power up to 10 buck converters.

Multi-Phase Buck for Pixelated LEDs

For pixelated LEDs, you now need a buck converter as a voltage source with an output voltage slightly higher than the forward voltage of a single LED. Each LED has its own current control. However, the current of the buck converter is much higher—potentially in the range of 10 A or more when you need thousands of LEDs in parallel (Figure 2).

2. Pixelated headlight solution using a buck converter as the voltage source to power thousands of LEDs (pixels) with a total current greater than 10 A.

To handle the high currents, one possible solution is to use multiple step-down phases instead of a single-coil buck converter (Figure 3).

3. Single-phase buck converter with controlled output voltage.

Thus, we can benefit from the cost advantages of small coils and keep the reflow process for SMDs instead of the selective soldering of “pin-through-hole” components like high-power coils.

Multiple phases reduce ripple (current and voltage) and therefore RMS current in the input filter. The number of buck phases can be adjusted to suit the power required by the application and allows for better heat dissipation to the PCB. Converter ICs with integrated switching, feedback and protection functions can be used in multiphase systems.

In this case, one IC is the master (MS) (Figure 4). It ensures a closed loop and controls the slaves (SL) by controlling the voltage VC, which sets the peak current of the coil current. The master will therefore set the same peak current for each phase. In a practical implementation, the phases are shifted over time to avoid switching all phases at the same time.

4. Multi-phase step-down, one master and one slave to control the output voltage.

Stability of Small Signal Models

The stability of all types of closed-loop systems must be studied, and there is a large literature on how to do this using small-signal models of buck converters.

Another approach is to use a powerful tool like SIMPLIS. It allows you to get an AC simulation without having to create a small circuit model of the converter. We can draw the schematic almost as is and start the AC simulation, and finally get a Bode plot of the power stage (PS) transfer function.

However, unlike the small-signal model, it is difficult to understand where the poles and zeros come from. Many publications discuss different small-signal models, but only single-phase versions are discussed. This paper presents an improved small-signal model by extending the existing small-signal model to the multiphase case.

In our case of fixed frequency current mode control with a switching period of TS, Raymond B. Ridley1 developed the control-to-output function that shows the relationship between the control voltage vCS and the output voltage vO:

A graphical representation of Ps and its inductor, load, and capacitor is shown in Figure 5. PS includes the current sensing gain Ri for current control, slope compensation for the external slope Se, and the natural slope Sn.

5. Buck converter with its power stage, inductor, output capacitor, and load.

Here, mc is defined as mc = 1 + (Se/Se) and D' = 1 – D, where D is the duty cycle of the converter.

The power stage also contains “sampling” modeled by He(s) which is caused by the converter “sampling” the inductor current at the switching frequency fs.

Therefore, the transfer function consists of:

The first part is the DC gain.

The second part, Fp(s), contains the power level for a given output load and capacitor.

The third part simulates the sampling He(s).

We now add a second identical stage to analyze the effect on the system (Figure 6). The load and output capacitance remain the same. If we want the same output voltage, this also means that the control voltage must be different. It is named Vcn.

6. Two-phase buck converter; output capacitance and load remain unchanged.

Each phase of the converter now provides half the output current. Even though both power stages are identical to Figure 5, their small signal models are different because each power stage only sees half the output current. This is why they are labeled PS.

Figure 6 can be plotted by splitting the load without changing anything about each phase of the converter. At output voltage Vo, each phase still provides half the output current (Figure 7).

7. Two-phase buck converter; output capacitor and load are separated.

We can now apply Ridley's control-to-output function, extending the phase from 2 to n and replacing R with nR, C with C/n, and RC with nRC.

The static gain is modified by replacing R with nR, thus:

The transfer function Fp(s) is affected; even though n in the numerator cancels out, the pole ωp is affected:

Hp(s) is not affected – it depends only on the switching frequency.

Therefore, we now derive the new control-to-output function for n phases in parallel:

Check with SIMPLIS

We can do some checks by comparing the control to output transfer function with the SIMPLIS model and sweeping some parameters, such as the output current Io.

We swept from 1 A to 10 A, which means we changed R in the transfer function. As expected, this affects the DC gain and the pole of FP(s) (Figure 8). The DC gain drops from 27 dB to 14 dB, and the pole moves from 800 Hz to 3.3 kHz. Clearly, the small signal and SIMPLIS transfer functions match perfectly up to half the switching frequency.

Figure 8. Bode plots of a four-phase buck converter for 1A (blue) and 10A (red) output currents. SIMPLIS and small-signal simulations match exactly until 250 kHz (half the switching frequency).

In fact, for frequencies above half the switching frequency, the two models no longer match due to the simplified modeling of sampling effects by He(s). As detailed in Ridley's book, this was a conscious choice to reduce model complexity.

We can repeat this check by changing another parameter: increasing the number of output caps (CO) by a factor of three. From the transfer function, we can infer that the DC gain is not affected, only the pole of Fp(s) changes. This is confirmed by the plot in Figure 9. The pole moves from about 2 kHz to 600 Hz. We can see that the small signal and SIMPLIS transfer functions match perfectly until half the switching frequency.

Figure 9. Bode plot of a four-phase buck converter with nominal output capacitor count (blue) and tripled output capacitor count (red).

in conclusion

By varying a few parameters, we show that the SIMPLIS model and the small signal give exactly the same results, validating the multiphase model derived from Raymond B. Ridley’s single-phase model. Therefore, we can use the multiphase small signal model to better understand the converter during the design phase, since we know how each system parameter will affect the transfer function.