1. Buck Regulator Architectures
4.2 Multi-Phase Buck Regulators
Author's Original Notes:

2. Multi-phase Overview
The idea of a multi-phase buck regulator is to put several buck regulators in parallel but have them operate in an interleaving manner. See figure below. The three-phase synchronous buck regulator has identical components for each phase, but the switching actions are 120 degrees out of phase.
The main reason to go multi-phase in low voltage high output current applications is to be able to supply the huge output current required without suffering from severe efficiency loss or thermal problems. The idea is to distribute the load current among a number of phases or channels so that current, power dissipation and heat dissipation in each phase are within the capability of a modern single-phase solution.
By interleaving the switching action of the channels, we create "phases." The interleaving approach helps reduce input and output ripple currents and is a free gift of a multi-channel topology. The interleaving approach also helps reduce the size of the output filter without sacrificing load transient performance.
At the time this course is written, most people still prefer to use as few phases as possible. The main concern is the cost of extra inductors, FET drivers and sometimes extra FETs. This is because an inductor with twice the current carrying capability does not cost twice as much. The same applies to FET drivers. A 3A driver does not cost three times as a 1A driver, maybe not even twice as much. Encouraged by the advantages of the multi-phase approach, efforts are being made to integrate the inductors and the FET drivers into single packages to reduce cost. The discussions that follow address only the pure technical side of the comparison. Some of the advantages may not matter in certain applications. But there are also numerous cases where multi-phase is the only choice.
In mobile CPU applications, the multi-phase approach is the standard approach. Depending on the thermal budget, the system designer may choose to allow 12A to 25A per channel when designing the power supply. So to power the latest Merom processor that requires up to 32A continuous current, most people use two phases.
Examples of National's multi-phase controllers include the LM27214 (up to four phases), the LM27212 (two phases) and the LM27292 (two phases).

3. Power FETs and Their Drivers
How fast a driver can turn on and turn off the power FETs has an impact on switching loss. The idea of using multiple drivers to drive FETs grouped into different phases is introduced and the benefits explained.
Power FETs share current fairly well, primarily due to their positive temperature coefficient. It is common practice to use a single FET driver to drive two or more FETs. The typical reason for this is the designer cannot find a single FET that has a low enough Rds_on to meet the power dissipation requirement. In addition, having the power switch distributed in two or more packages also helps eliminate local hot spots.
However, there is a limit. As the load current goes higher and more power FETs are paralleled, the driver sees an increasingly larger gate charge. The large gate charge slows down the switching process and causes more transition loss in the top FETs. So putting more FETs in parallel may not improve the overall efficiency at all. To keep the top FETs' switching loss at a reasonable level, the driver needs to be able to supply higher current. With today's technology, merely increasing the die size of the driver has hit a diminishing return on its peak current capability due to the resistance in the interconnect inside the driver chip.

4. Power FETs and Their Drivers
Theoretically, we may use the same trick power FETs use, i.e. to distribute. We may drive each pair of power FETs (top and bottom) with a separate synchronous driver.
The problem with this approach is the two groups of power FETs cannot be guaranteed to switch exactly at the same time. Therefore there can be potential shoot-through problems.
Author's Original Notes:

5. Power FETs and Their Drivers
The idea of using a separate driver for each group of FETs will work if the groups of FETs do not share the same switch node. This is precisely the case in a multi- phase configuration. Not only does each group of FETs not need to switch simultaneously with the rest of the groups, but all the groups are intentionally switched at different times to gain other benefits which we will discuss later in this course.
So by going multi-phase, we are able to use existing driver technology to drive more power FETs, without incurring excessive switching loss in the top FETs. As a side benefit, we are also distributing heat dissipation across a larger PCB area, reducing the number of local hot spots.

6. Output Filter
The output filter is a major portion of the power train and a major cost contributor. The following concepts will be explained:
Ripple cancellation
Physical size tradeoff
Load transient response performance improvement
When the load current gets too large, the power inductor can be troublesome. Assume the inductance does not change. Whenever the current doubles, the energy storage in the inductor quadruples, which roughly translates into quadrupled inductor size.

7. Output Filter
In reality, since the number of output capacitors typically doubles when the maximum load current doubles, the inductance value of the inductor may be cut in half without increasing the output voltage ripple. So in many cases when the maximum load current doubles, the physical size of the inductor only needs to double and not quadruple.
Still, this can quickly become a problem as the maximum load current keeps going up. New inductor structures are being invented to handle the huge current more effectively. However, such inductors are huge compared with their lower-current counterparts.
The idea of distribution may bring some advantage here. Instead of using a single 0.5uH/30A inductor, we may use two 0.5uH/15A inductors and have them connected to separate switch nodes that are toggling out of phase. That way, the output voltage ripple will be the same or smaller, but the sum of the physical size of the inductors will be half that of the single inductor and the total energy storage in the inductors will also be half of that in the single inductor. Low profile designs will be easier to achieve and output capacitance can potentially be reduced.

8. Example of Multi-Phase Benefits Using COT
A typical worst-case load transient is when the CPU current snaps from full load to no load, causing the control loop to immediately shrink the duty cycle to zero, and the energy stored in the inductor dumped into the output capacitors. The left figure below shows such a load transient in a single-phase buck regulator where the inductor is 0.5uH. Obviously the less energy stored in the inductor the fewer capacitors will be necessary. The right side is the power stage of the single-phase circuit and the control scheme is current mode hysteretic.
Large and ultra-fast load transient characteristics are typical of low voltage, high current digital processors. For example, in a CPU, load current can change between 3A and 40A in a matter of 100ns or less. The feedback control loop of today's switching power supply does not have the speed or linear headroom to contain the output voltage excursion without getting into duty cycle saturation. Faced with such an extreme load transient, what typically happens is that the control loop quickly sends the duty cycle to zero or its maximum allowed value, i.e. saturating the duty cycle. Once the duty cycle is saturated, the only way to contain the output voltage excursion is to have enough output capacitors.

9. Choose Multi-Phase Stage
Going multi-phase has a clear technical advantage here. Let's first take a look at the combined output ripple (total ripple) current versus the ripple current in each individual inductor (phase ripple).
The figure below shows the relationship between the duty cycle and the ratio of the total ripple to the phase ripple. At certain duty cycle values there is total cancellation of the ripple current. Those points are located where the conversion ratio (Vin/Vout) is equal to the ratio of the number of phases to any positive integer that is less than it. For example, in the case of a 4-phase regulator, at conversion ratios of 4:1, 4:2 and 4:3, output ripple is zero. Remember duty cycle is approximately equal to Vout/Vin, i.e., the reciprocal of the conversion ratio.

10. Inductor Size Improvement
What is probably more important than achieving zero ripple at certain given points is the fact that the output ripple current is always less than phase ripple current. This means we can safely replace the single-phase inductor with multiple physically smaller inductors that are of the same inductance value, without increasing the output ripple current.
The figure below shows a comparison between the inductor arrangement of a single-phase regulator and that of a two-phase regulator.

11. Overshoot Improvement
Load transient response also benefits from the multi-phase approach. The figure below shows the load transient response of a two-phase circuit experiencing exactly the same load step as in the single-phase example.
This time, instead of a single 0.5uH, 36A inductor, two 0.5uH, 18A inductors are used. Energy storage in the inductors is reduced by half, so the output voltage overshoot is also significantly reduced.

12. Input Capacitors
In a single-phase buck regulator, the input ripple RMS current can be calculated as follows.
The figure below shows that if we go multi-phase, input ripple RMS current will be reduced. In the two-phase case, the magnitude of the input ripple current is half that of the single-phase solution because each phase is only carrying half the load current. Of course, there is one more current pulse each clock cycle.
Ripple cancellation also happens to the input capacitors. Figures and equations are presented to illustrate this concept.
The input capacitors supply the majority of the input ripple current that the buck regulator creates. As a result, heat is generated in the input capacitors. The input capacitors typically have a figure of merit called “rated ripple RMS current." For a given type of input capacitor, usually the higher that rating is, the more expensive the capacitor will be. The power dissipated in the input capacitors is simply the combined ESR (Equivalent Serier Resistance) multiplied by the square of the ripple RMS current.

13. Input Capacitors
The figure below shows the relationship between the duty cycle and the ratio of input ripple RMS current to the output current.
We can tell that more phases generally can get us less ripple RMS current, and more chances to hit zero ripple points. The zero ripple points happen at conversion ratios (Vin / Vout) that are equal to the number of phases divided by any positive integer that is less than the number of phases. For example, in the case of a two-phase buck regulator, if Vin is 10V and Vout is 5V (i.e. conversion ratio is 2), then input ripple current is theoretically zero.

14. Current Sharing
Current sharing is a potential issue that is not a concern in a single-phase solution. It is also a lesson learned for the IC industry in certain applications. In prior discussions we assumed that in a multi-phase regulator all the phases will carry exactly the same amount of current, in other words, perfect load current sharing. In reality, that is not a given. The situation is similar to paralleling two batteries of the same type and expecting them to supply equal shares of current.
See figure below. Assume the two batteries have about 5 mOhm internal resistance each, but the battery voltages are slightly different, one being 1.36V, the other 1.32V. The seemingly small difference (40mV) in the two voltages will result in a 4A circulating current between the two batteries. The reason is simple - the battery internal resistance is so small (5 mOhm) that any slight mismatch in the battery voltages will result in a large circulating current. In this case, the 1.36V battery is supplying 4.056A while the 1.32V battery is absorbing 3.944A. The payload is only 112mA but the two batteries have to deal with much larger currents, which will no doubt lead to much shorter battery life.

15. Current Sharing
In the case of a multi-phase buck regulator, a very similar mechanism exists. The figure below shows a voltage mode two-phase synchronous buck.
The two channels share the same error amplifier, that is, the control signal is common to both. This is actually a real world example. In the process of the IC design, every effort was made to ensure that the two drivers see the same duty cycle value. But on the bench, the two channels share the load current poorly, to the extent that one channel supplies a current that is more than the load while the other channel sucks current. This kind of behavior is totally unacceptable because it may cause the inductors to saturate, it will overheat all the power components and it has a poor efficiency

16. Current Sharing
The cure for this current sharing problem is to sense the current in each phase and use some kind of feedback to force the sensed currents to be equal. The traditional peak-current mode control achieves this automatically and guarantees matching of the currents cycle by cycle.
Note the top FETs are turned on by the PWM clocks, not by the PWM comparators in the figure. The schematic has been simplified to just show that sensed instantaneous currents are compared with the control voltage (error amplifier output) to determine the turn-off instant of each cycle. The sensed currents can also be used to modify the PWM ramps in a voltage mode buck so that the duty cycles will be the right values to give balanced inductor currents. This approach is employed in the LM27231.

17. Summary
The idea of a multi-phase buck regulator is to put several buck regulators in parallel and have them operate in an interleaving manner. The three- phase synchronous buck regulator below has identical components for each phase, but the switching actions are 120 degrees out of phase.
The main reason to go multi-phase in low voltage high output current applications is to be able to supply the huge output current required without suffering from severe efficiency loss or thermal problems. The idea is to distribute the load current among a number of phases or channels so that current, power dissipation and heat dissipation in each phase are within the capability of a modern single-phase solution.
By interleaving the switching action of the channels, we create "phases." The interleaving approach helps reduce input and output ripple currents and is a free gift of a multi-channel topology. The interleaving approach also helps reduce the size of the output filter without sacrificing load transient performance.
At the time this course is written, most people still prefer to use as few phases as possible. The main concern is the cost of extra inductors, FET drivers and sometimes extra FETs. This is because an inductor with twice the current carrying capability does not cost twice as much. The same applies to FET drivers. A 3A driver does not cost three times as a 1A driver, maybe not even twice as much. Encouraged by the advantages of the multi-phase approach, efforts are being made to integrate the inductors and the FET drivers into single packages to reduce cost. The discussions that follow address only the pure technical side of the comparison. Some of the advantages may not matter in certain applications. But there are also numerous cases where multi-phase is the only choice.
In mobile CPU applications, the multi-phase approach is the standard approach. Depending on the thermal budget, the system designer may choose to allow 12A to 25A per channel when designing the power supply. So to power the latest Merom processor that requires up to 32A continuous current, most people use two phases.
Examples of National's multi-phase controllers include the LM27214 (up to four phases), the LM27212 (two phases) and the LM27292 (two phases).

18. Thank you!
Author's Original Notes: