Distributed control of a voltage regulator

Abstract

A controller is disclosed for a voltage regulator module including a power unit and providing an output current, I.sub.out, at an output voltage, V.sub.out, from an input current/voltage and being configured for use in a multi-module voltage regulator having a neighbouring voltage regulator module having a respective output connected in parallel, the controller comprising: a reference voltage source for providing a reference voltage; a current balancing unit, configured to receive a respective output current from the or each neighbouring voltage regulator module and to determine an adjusted reference voltage, from the reference voltage and for balancing the output current with the at least one respective output current; and a control unit configured to use the adjusted reference voltage to control the voltage regulator module, to provide the output current at the output voltage from the input current at the input voltage, based on adaptive voltage positioning regulation.

Claims

1. A controller, for a first voltage regulator module including a power unit and providing, at an output, an output current, Iout, at an output voltage, Vout, from an input current at an input voltage, the first voltage regulator module being configured for use in a multi-module voltage regulator including a second voltage regulator module having an output connected in parallel with the output of the first voltage regulator module, the controller comprising: a reference voltage source for providing a reference voltage (Vref); a current balancing unit, configured to receive an output current from the second voltage regulator module, to determine an adjusted reference voltage, Vref′, from the reference voltage, and to balance the output current with the output current from the second voltage regulator module; and a control unit configured to use the adjusted reference voltage to control the voltage regulator module and to provide the output current wherein the current balancing module is configured to determine a difference, the difference being a difference between the output current and the output current from the second voltage regulator module, and to adjust the reference voltage in proportion to the difference to provide the adjusted reference voltage.

2. The controller as claimed in claim 1, wherein the current balancing module is configured to determine a difference, the difference being a difference between the output current and the sum of half the output currents from the second voltage regulator module and a third voltage regulator module, and to adjust the reference voltage in proportion to the difference to provide the adjusted reference voltage.

3. The controller as claimed in claim 2, wherein the current balancing module is further configured to detect a failure of communication from either the second voltage regulator module or the third voltage regulator module, and in response to the failure of communication determine the difference to be a difference between the output current and the output current from the other of either the second voltage regulator module or the third voltage regulator module.

4. The controller as claimed in claim 1, wherein the current balancing module is configured to determine a difference, the difference being a difference between the output current and a weighted average of the output currents from the second voltage regulator module and a third voltage regulator module, and to adjust the reference voltage in proportion to the difference to provide the adjusted reference voltage.

5. The controller as claimed in claim 1 wherein the control unit is configured to control the voltage regulator module to provide the output current from the input current, and the adjusted reference voltage by a control loop having a finite feedback gain, H.

6. The controller as claimed in claim 5 wherein the control loop of the control unit has an infinite DC gain.

7. The controller of claim 6: further comprising the voltage regulator module; and wherein the controller is embedded in the voltage regulator module.

8. The controller of claim 6: wherein the controller is embedded in the multi-module voltage regulator including the first and second voltage regulator modules having respective controllers arranged in a logical daisy-chain, wherein the respective controller of each voltage regulator modules includes a separate reference voltage source, and the output voltage of the regulator modules is common.

9. The controller as claimed in claim 1, wherein the current balancing unit is configured to adjust the reference voltage by the difference multiplied by a finite loop gain value, H,Rdiff to determine the adjusted reference voltage.

10. The controller as claimed in claim 9, wherein the output voltage is determined, by voltage droop regulation, as the difference between the adjusted reference voltage divided by the feedback gain, and the output current multiplied by an output impedance, Rout:
Vout=Vref′/H−Rout.Math.Iout.

11. The controller as claimed in claim 1: wherein the controller is embedded in a multi-module voltage regulator including at least three voltage regulator modules operable with distributed control whose controllers are arranged in a logical daisy-chain, and wherein the reference voltage source, the output current, the common output voltage and the respective output currents from two immediately neighbouring voltage regulator modules in the daisy-chain are the only control inputs for controlling the output current.

12. The voltage regulator module comprising the controller as claimed in claim 1, and further comprising the power unit having at least one controllable switch and an impedance.

13. The voltage regulator module as claimed in claim 12, wherein the second voltage regulator module is supplied from the input voltage.

14. A controller, for a first voltage regulator module including a power unit and providing, at an output, an output current, Iout, at an output voltage, Vout, from an input current at an input voltage, the first voltage regulator module being configured for use in a multi-module voltage regulator including a second voltage regulator module having an output connected in parallel with the output of the first voltage regulator module, the controller comprising: a reference voltage source for providing a reference voltage (Vref); a current balancing unit, configured to receive an output current from the second voltage regulator module, to determine an adjusted reference voltage, Vref′, from the reference voltage, and to balance the output current with the output current from the second voltage regulator module; and a control unit configured to use the adjusted reference voltage to control the voltage regulator module and to provide the output current; wherein the current balancing module is configured to determine a difference, the difference being a difference between the output current and a weighted average of the output currents from the second voltage regulator module and a third voltage regulator module, and to adjust the reference voltage in proportion to the difference to provide the adjusted reference voltage.

15. A controller, for a first voltage regulator module including a power unit and providing, at an output, an output current, Iout, at an output voltage, Vout, from an input current at an input voltage, the first voltage regulator module being configured for use in a multi-module voltage regulator including a second voltage regulator module having an output connected in parallel with the output of the first voltage regulator module, the controller comprising: a reference voltage source for providing a reference voltage (Vref); a current balancing unit, configured to receive an output current from the second voltage regulator module, to determine an adjusted reference voltage, Vref′, from the reference voltage, and to balance the output current with the output current from the second voltage regulator module; and a control unit configured to use the adjusted reference voltage to control the voltage regulator module and to provide the output current; wherein the controller is embedded in a multi-module voltage regulator including at least three voltage regulator modules operable with distributed control whose controllers are arranged in a logical daisy-chain; and wherein the reference voltage source, the output current, the common output voltage and the respective output currents from two immediately neighbouring voltage regulator modules in the daisy-chain are the only control inputs for controlling the output current.

Description

BRIEF DESCRIPTION OF DRAWINGS

(1) Embodiments will be described, by way of example only, with reference to the drawings, in which

(2) FIG. 1 shows, in schematic form, an arrangement of multiple regulators connected in parallel.

(3) FIG. 2(a) illustrate a voltage-current characteristic showing the concept of voltage droop;

(4) FIG. 3(a) shows an arrangement of multiple regulators connected in parallel with shared wired voltage references

(5) FIG. 3(b) illustrates the voltage-current characteristic of the modules of FIG. 3(a);

(6) FIG. 4(a) shows an arrangement of multiple regulators connected in parallel with daisy-chain current communication;

(7) FIG. 4(b) illustrates the voltage-current characteristic of the modules of FIG. 4(a);

(8) FIG. 5 shows an arrangement of multiple regulators connected in parallel with local voltage references and current sharing communication according to one or more embodiments;

(9) FIG. 6 shows, schematically, the DC operation of a module according to one or more embodiments;

(10) FIG. 7 shows a DC model of a single module;

(11) FIG. 8 shows a DC model of n modules connected in parallel;

(12) FIG. 9 shows the control scheme of a controller according to embodiments;

(13) FIG. 10 shows a switched mode buck converter; and

(14) FIG. 11 shows a switched mode buck converter operating under AVP.

(15) It should be noted that the Figures are diagrammatic and not drawn to scale. Relative dimensions and proportions of parts of these Figures have been shown exaggerated or reduced in size, for the sake of clarity and convenience in the drawings. The same reference signs are generally used to refer to corresponding or similar features in modified and different embodiments.

DETAILED DESCRIPTION OF EMBODIMENTS

(16) An idealised voltage regulator may operate as a perfect voltage source—that is to say, the output voltage remains constant irrespective of the current supplied. However, the outputs of two such regulators could not be connected in parallel, since this would result in very high—theoretically infinite —currents flowing between the two, to try to offset any, even very small, differences in output voltage.

(17) To enable two or more such regulator modules to be connected in parallel (or be “parallelized”), they must not be operated as ideal voltage sources. Instead, the concept of “voltage droop” is utilised. This is illustrated in FIG. 2. The regulator is designed to have a “virtual output impedance” R.sub.out, such that the output voltage V.sub.out decreases, or “droops”, from an initial value V.sub.out0, with increasing load current Iload up to a maximum allowed load current Iload.sub.max:
V.sub.out=V.sub.out0−R.sub.out.Math.Iload  (1)

(18) The control of such voltage regulators may be described as being by “voltage droop regulation”, which is also referred to as Adaptive Voltage Positioning (AVP) regulation. AVP allows parallel connection with well-controlled differential currents flowing from one module to another due to internal offsets or mismatches. AVP naturally provides some degree of current sharing and better transient response as well as improved system power efficiency, so that it is presently used in CPU/GPU (central processor unit/general processor unit) power supplies.

(19) As will be discussed in more detail below, AVP regulation with multiple modules can be implemented with each module having its own reference voltage. The output voltage is then proportional to the average of the reference voltages. However, parallelizing with AVP typically provides only a poor level of current sharing. Current imbalance is given by mismatches from the reference voltages and the output droops (i.e. virtual output impedance). Therefore, some communication links are required to improve the current sharing. That is why distributed, or decentralized, controllers are typically configured to be modular with standard connections—which allows the use of an unlimited number of elements.

(20) Methods of improving the current sharing for multi-module VRs are known. One such method is averaging the reference voltage in a shared wire, as shown in FIG. 3. This figure shows a multi-module voltage regulator, having several regulator modules 310, each of which includes its own local voltage reference Vref 320 in addition to a control and power unit 330. The power and control unit 330 may have separate control unit 322 and power unit 324 as shown. The local voltage references are tied together by a shared wire 340.

(21) Such an approach cancels out differential currents, at the nominated output current I.sub.out0, due to voltage reference mismatch, as shown in FIG. 3b, by the imposition of a common value of Vref; however, mismatches in the virtual output impendences of the modules, combined with droop mismatch, result in the modules providing a range of current outputs I.sub.outk, from each of the modules at a different operational voltage V.sub.out.

(22) Shared wire approaches are in general not fault tolerant, since the shared wire is a single-point-of-failure, and such approaches still have poor current sharing because of the mismatches in the output currents resulting from the differences between each converter's output impedance. Further, although a single wire could be added for current balancing, this would also be a single point of failure (SPOF) and thus not fault-tolerant.

(23) An alternative approach has been proposed by one of the present inventors (Cousineau, Marc, and Zijian Xiao. “Fully Decentralized Modular Approach for Parallel Converter Control.” In Applied Power Electronics Conference and Exposition (APEC), 2013 Twenty-Eighth Annual IEEE, 237-243. IEEE, 2013). This is illustrated in FIG. 4(a).

(24) In this approach, the outputs from AVP converter-module control and power units 430 are connected in parallel at 450, and the currents are balanced using a circular chain, or daisy-chain, communication 460, such that each element balances the current with the average of its neighbours' current. This approach has two strengths: firstly it cancels out voltage offsets and droop mismatches, secondly it is fault tolerant on the current sharing—since there is no single wire, a fault on the inter-module communication 460 can be detected and isolated. However, it relies on a single voltage reference 420 that is shared with all modules, so it does not achieve high accuracy and fault tolerance on the reference.

(25) The voltage-current characteristic of the modules are shown in FIG. 4(b). In this approach, the modules can be controlled to each provide the same current Iload/n, at the operating voltage V.sub.out, as seen at 470. It is noted that one of the modules acts as master, with its V-I characteristic 480, and thus this approach is not entirely fault-tolerant.

(26) In contrast to the known approaches, embodiments of the present disclosure may provide for truly distributed control, with fault tolerance, and the potential for high accuracy. Once such embodiment is shown in FIG. 5, which shows an arrangement 500 of multiple regulator modules 510 connected in parallel, each with a local voltage reference 520 and control and power unit 530, and current sharing, or daisy-chain, communication 560. The control and power unit may be subdivided, as shown, into a control unit 532, which controls the voltage regulation, and a power unit 534, which regulates the voltage. As non-limiting examples, in a linear regulator the power unit 534 may include a power-dissipating impedance, whereas in a switched mode power converter the power unit may includes one or more switches and an impedance.

(27) In this arrangement, each of the regulator modules 510 may be identical, and there is no artificial limit to the number which may be combined. The output from the modules are connected in parallel. Each module regulates independently its the output voltage, using its own reference voltage 520. Each module has a non-null virtual output impedance R.sub.out, to facilitate voltage droop, or AVP, regulation as discussed above. A common output voltage value V.sub.out is proportional to the average of the voltage references. The averaging occurs automatically at the output without a need for added communication between the modules, as will be explained in more detail below. Using an average of several voltage references may yield an accuracy that is improved compared to the accuracy of one module; this benefit may further increase with an increasing number of modules. A current sharing loop 560 is based on local current sensing 565 of the current output from each module, and typically provides communication of current values between neighbouring modules along a circular chain, or daisy-chain. An finite DC loop gain H, but having an infinite output resistance R.sub.out such that H*R.sub.out is infinite, is further used to reduce differential currents while preserving the output voltage accuracy. That is to say, in steady state (or “DC”) the control loops force the output currents to be the same.

(28) The control will now be explained, with reference to FIGS. 6 to 9.

(29) FIG. 6 shows, schematically, the main control loop, in DC operation, of a module according to one or more embodiments. Each module comprises a voltage reference V.sub.ref, and a regulation loop with non-null output impedance. Various forms of voltage reference, such as a band-gap reference, will be known to the skilled person. The output impedance R.sub.out is determined by a current loop with local current sensing of the output current. The loop gain G shows a high DC gain—typically greater than 1000; which is effectively an infinite DC gain. Feedback gain H defines the ratio between the reference voltage V.sub.ref and the output voltage V.sub.out. Then:

(30) $\begin{array}{cc}H.Math.V_{\mathrm{out}}=V_{\mathrm{ref}}-H.Math.R_{\mathrm{out}}.Math.I_{\mathrm{out}}⟹V_{\mathrm{out}}=\frac{V_{\mathrm{ref}}}{H}-R_{\mathrm{out}}.Math.I_{\mathrm{out}}& \left(2\right)\end{array}$

(31) The DC operation of a single module can be simplified and modelized with a voltage source V.sub.ref/H, followed by an output impedance, as illustrated in FIG. 7. An arrangement of “n” modules gives the association of “n” voltage sources connected together to the output node through their output impedance, as illustrated in FIG. 8, where, “n” is an integer greater or equal to two.

(32) The following relationships can then be seen:

(33) For all of the local references, V.sub.refk, k=1 to n, the following holds:
∀k∈[1:n]V.sub.ref.sub.k=V.sub.ref.Math.(1+ε.sub.vref.sub.k)  (3)

(34) where:

(35) $\begin{array}{cc}.Math.V_{\mathrm{ref}}.Math.=\frac{1}{n}\underset{k=1}{\overset{n}{.Math.}}\mathrm{and}\underset{k=1}{\overset{n}{.Math.}}{\epsilon }_{{\mathrm{vref}}_k}=0& \left(4\right)\end{array}$

(36) The output impedances of the modules are, similarly:
∀k∈[1:n]R.sub.out.sub.k=R.sub.out.Math.(1+ε.sub.rout.sub.k)  (5)

(37) where:

(38) $\begin{array}{cc}.Math.R_{\mathrm{out}}.Math.=\frac{1}{n}\underset{k=1}{\overset{n}{.Math.}}{R}_{{\mathrm{out}}_k}\mathrm{and}\underset{k=1}{\overset{n}{.Math.}}{\epsilon }_{{\mathrm{rout}}_k}=0& \left(6\right)\end{array}$

(39) Moreover, the local feedback gains can be shown to be:

(40) $\begin{array}{cc}\forall k\in \left[1:n\right]H_k=.Math.H.Math..Math.\left(1+{\epsilon }_{h_k}\right)& \left(7\right)\end{array}$

(41) where

(42) $\begin{array}{cc}.Math.H.Math.=\frac{1}{n}\underset{k=1}{\overset{n}{.Math.}}{H}_k\mathrm{and}\underset{k=1}{\overset{n}{.Math.}}{\epsilon }_{h_k}=0& \left(8\right)\end{array}$

(43) And finally, the local output currents are:
∀k∈[1:n]I.sub.out.sub.k=I.sub.out.Math.(1+ε.sub.lout.sub.k)  (9)

(44) where

(45) $\begin{array}{cc}.Math.I_{\mathrm{out}}.Math.=\frac{1}{n}\underset{k=1}{\overset{n}{.Math.}}{I}_{{\mathrm{out}}_k}=\frac{I_{\mathrm{load}}}{n}\mathrm{and}\underset{k=1}{\overset{n}{.Math.}}{\epsilon }_{I_{{\mathrm{out}}_k}}=0& \left(10\right)\end{array}$

(46) From the above, it can be shown that the output voltage V.sub.out is proportional to the average of the voltage references:

(47) $\begin{array}{cc}{I}_{\mathrm{load}}=\underset{k=1}{\overset{n}{.Math.}}{I}_{{\mathrm{out}}_k}=\underset{k=1}{\overset{n}{.Math.}}\frac{V_{{\mathrm{ref}}_k}/H_k-V_{\mathrm{out}}}{R_{{\mathrm{out}}_k}}& \left(11\right)\end{array}$

(48) so that (equation 12)

(49) $I_{\mathrm{load}}=\frac{.Math.V_{\mathrm{ref}}.Math.}{.Math.H.Math..Math..Math.R_{\mathrm{out}}.Math.}\underset{k=1}{\overset{n}{.Math.}}\frac{\left(1+{\epsilon }_{{\mathrm{vref}}_k}\right)}{\left(1+{\epsilon }_{h_k}\right).Math.\left(1+{\epsilon }_{{\mathrm{rout}}_k}\right)}-\frac{V_{\mathrm{out}}}{.Math.R_{\mathrm{out}}.Math.}.Math.\underset{k=1}{\overset{n}{.Math.}}\frac{1}{\left(1+{\epsilon }_{{\mathrm{rout}}_k}\right)}$

(50) that is:

(51) $\begin{array}{cc}{I}_{\mathrm{load}}=\frac{n.Math..Math.V_{\mathrm{ref}}.Math.}{.Math.H.Math..Math..Math.R_{\mathrm{out}}.Math.}-\frac{n.Math.V_{\mathrm{out}}}{.Math.R_{\mathrm{out}}.Math.}& \left(13\right)\end{array}$

(52) and finally

(53) 0$\begin{array}{cc}{V}_{\mathrm{out}}=\frac{.Math.V_{\mathrm{ref}}.Math.}{.Math.H.Math.}-\frac{.Math.R_{\mathrm{out}}.Math.}{n}.Math.I_{\mathrm{load}}& \left(14\right)\end{array}$

(54) In other words, the output reference is proportional to the average of the local references and the output droop is also proportional to the average of the local droops.

(55) Differential Currents:

(56) Potential mismatches between modules (voltage references V.sub.ref, feedback ratio H, output impedance R.sub.out) generate undesirable differential currents (current flowing from a module to another, and thus not transferred to the load). Equation (16) below describes the differential current attached to module “k” as a function of small shifts observed in the reference voltage value, feedback gain value and output impedance value. Differential currents are limited because the output impedance is not null. Equation (18) below shows that the bigger the output resistance is, the lower are the differential currents. However, a circuit for reducing the differential currents may be desirable, especially if choosing an output impedance of high value is not possible for the application.

(57) Differential current in one module can be described through:

(58) $\begin{array}{cc}{I}_{{\mathrm{out}}_k}-\frac{I_{\mathrm{load}}}{n}=\frac{\frac{V_{{\mathrm{ref}}_k}}{H_k}-V_{\mathrm{out}}}{R_{{\mathrm{out}}_k}}-\frac{I_{\mathrm{load}}}{n}=\frac{.Math.V_{ref}.Math..Math.\left(1+{\epsilon }_{{\mathrm{vref}}_k}\right)-.Math.H.Math..Math.\left(1+{\epsilon }_{h_k}\right).Math.V_{out}}{.Math.H.Math..Math.\left(1+{\epsilon }_{h_k}\right).Math..Math.R_{out}.Math.\left(1+{\epsilon }_{{\mathrm{rout}}_k}\right)}-\frac{I_{\mathrm{load}}}{n}& \left(15\right)\end{array}$
from which it follows that

(59) $\begin{array}{cc}{I}_{{\mathrm{out}}_k}-\frac{I_{\mathrm{load}}}{n}=\frac{.Math.V_{\mathrm{ref}}.Math.}{.Math.H.Math..Math..Math.R_{\mathrm{out}}.Math.}.\frac{\left(1+{\epsilon }_{{\mathrm{vref}}_k}\right)}{\left(1+{\epsilon }_{h_k}\right).Math.\left(1+{\epsilon }_{{\mathrm{rout}}_k}\right)}-\frac{V_{\mathrm{out}}}{.Math.R_{\mathrm{out}}.Math.}.Math.\frac{1}{\left(1+{\epsilon }_{{\mathrm{rout}}_k}\right)}-\frac{I_{\mathrm{load}}}{n}& \left(16\right)\end{array}$

(60) Using a first order approximation gives:

(61) $\begin{array}{cc}{I}_{{\mathrm{out}}_k}-\frac{I_{\mathrm{load}}}{n}\approx \frac{\frac{.Math.V_{\mathrm{ref}}.Math.}{.Math.H.Math.}-V_{\mathrm{out}}}{.Math.R_{\mathrm{out}}.Math.}+\frac{.Math.V_{\mathrm{ref}}.Math.}{.Math.H.Math..Math..Math.R_{\mathrm{out}}.Math.}.Math.\frac{\left(1+{\epsilon }_{vre{f}_k}\right)}{\left(1+{\epsilon }_{h_k}\right).Math.\left(1+{\epsilon }_{{\mathrm{rout}}_k}\right)}-\frac{V_{\mathrm{out}}}{.Math.R_{\mathrm{out}}.Math.}.Math.\frac{1}{\left(1+{\epsilon }_{{\mathrm{rout}}_k}\right)}-\frac{I_{\mathrm{load}}}{n}& \left(17\right)\end{array}$

(62) From (15) to (17), it follows that

(63) $\begin{array}{cc}{I}_{{\mathrm{out}}_k}-\frac{I_{\mathrm{load}}}{n}\approx \frac{\left({\epsilon }_{h_k}+{\epsilon }_{{\mathrm{rout}}_k}-{\epsilon }_{{\mathrm{vref}}_k}\right).Math..Math.V_{\mathrm{ref}}.Math.-{\epsilon }_{{\mathrm{rout}}_k}.Math..Math.H.Math..Math.V_{\mathrm{out}}}{.Math.H.Math..Math..Math.R_{out}.Math.}& \left(18\right)\end{array}$

(64) Equation (18) can be rewritten as:

(65) $\begin{array}{cc}{I}_{{\mathrm{out}}_k}-\frac{I_{\mathrm{load}}}{n}\approx \frac{\left({\epsilon }_{h_k}-{\epsilon }_{{\mathrm{vref}}_k}\right).Math..Math.V_{\mathrm{ref}}.Math.+{\epsilon }_{{\mathrm{rout}}_k}\left[.Math.V_{\mathrm{ref}}.Math.-.Math.H.Math..Math.V_{\mathrm{out}}\right]}{.Math.H.Math..Math..Math.R_{\mathrm{out}}.Math.}& \left(18a\right)\end{array}$

(66) This shows that the impact of ε.sub.vref.sub.k the current error is much higher than the impact of ε.sub.rout.sub.k because V.sub.ref tends to be 10 times bigger than the droop at full load: [V.sub.ref−H.Math.V.sub.out].

(67) Typically, the droop may be as little as one tenth, or less, of Vref. So it is in general preferable to match Vref to reduce, ε.sub.vref.sub.k.

(68) Current Sharing:

(69) According to embodiments of the present disclosure, a current sharing—or current matching—circuit is implemented, to reduce differential currents. The current sharing circuit corrects the local reference voltage from sensing the local output current and comparing it with currents from other modules. The most convenient approach is to compare with the two immediately neighbouring modules, typically using bi-directional communication around a daisy-chain or circular chain). However, it is possible to compare with just a single neighbour (for instance, using uni-directional communication around the daisy-chain), or with additional, more remote, modules. An example of the latter would be a “leap-frog” communication chain in which each module would communicate with its immediate next-neighbours and its next-but-one neighbours, such that a k-th module communicates with, or more particularly receives current sense information from, modules (k−2), (k−1), (k+1) and (k=2). Conversely, in the bi-direction immediate neighbour arrangement, the k-th module receives current sense information from modules (k−1) and (k+1), whilst in the unidirectional communication, the k-th module receives current sense information from only the (k−1)th module.

(70) In embodiments in which the local output current is compared with the currents from with the two neighbouring modules, the average of those currents are typically used for the comparison: (I.sub.k+1+I.sub.k−1)/2, as shown in FIG. 9. Conversely, in embodiments where the comparison is with just one neighbour, that neighbour's current is used directly (I.sub.k−1). In general, a weighted average may be used:

(71) $\frac{w_1.Math.I_1+w_2.Math.I_2+{\mathrm{.Math.w}}_{k-1}.Math.I_{k-1}+w_{k+1}.Math.I_{k+1}+.Math.+w_n.Math.I_n}{w_1+w_2+.Math.+w_{k-1}+w_{k+1}+.Math.+w_n}$

(72) where w1, w2 are weighting factors chosen to suit the application. In the above preferred cases, n=2 and w.sub.1=w.sub.2=1, or n=1 and w.sub.1=1, respectively.

(73) FIG. 9 shows, schematically, the control of a “k-th” voltage regulator module, according to embodiments of the present disclosure. The primary control loop 910 implements AVP or voltage droop regulation as discussed above. However, instead of controlling directly from the reference voltage V.sub.refk, the control is carried out based on an adjusted reference voltage V.sub.refk′. The adjusted reference voltage is determined by the current sharing, or current balancing, loop, 920. As shown, the current balancing loop uses the difference between the output current I.sub.outk from the local voltage regulator, and an average current from other voltage regulator modules in the multi-module voltage regulator—in this example, the mean of the currents I.sub.outk+1, and I.sub.outk−1, from the two neighbouring modules.

(74) Proportional correction (finite DC gain) is applied in this current sharing loop.

(75) The use of a finite DC gain (that is to say, as measured in Ohms, Hk.Math.Rdiff ∜∞ avoids impacting the main voltage loop accuracy: otherwise, one of the modules might go into saturation under this loop operation, and it could impose its current as a new reference for all the modules currents. That would result in a shifting of the sum of the output currents, so the output voltage would be offset from the average of the references, which would generally not be desirable.

(76) With a finite DC gain in the current sharing loop, correction of the differential currents does not affect the accuracy of the output voltage, because the sum of the corrections from sharing operations is null as showed by equations (20) to (27) below.

(77) It follows from the circular-chained property, that (eq19):

(78) $\underset{k=1}{\overset{n}{.Math.}}\left(I_{{\mathrm{out}}_k}-\frac{1}{2}{I}_{{\mathrm{out}}_{k-1}}-\frac{1}{2}{I}_{{\mathrm{out}}_{k+1}}\right)=\underset{k=1}{\overset{n}{.Math.}}\left(I_{{\mathrm{out}}_k}\right)-\frac{1}{2}\underset{k=1}{\overset{n}{.Math.}}\left(I_{{\mathrm{out}}_k}\right)-\frac{1}{2}\underset{k=1}{\overset{n}{.Math.}}\left(I_{{\mathrm{out}}_k}\right)=0A$

(79) And using a first order approximation, this results in:

(80) $\begin{array}{cc}{.Math.}_{k=1}^n{V}_{i_k}={.Math.}_{k=1}^n{H}_k.Math.R_{\mathrm{diff}}.Math.\left(I_{{\mathrm{out}}_k}-\frac{1}{2}{I}_{{\mathrm{out}}_{k-1}}-\frac{1}{2}{I}_{{\mathrm{out}}_{k+1}}\right)=0V& \left(20\right)\end{array}$

(81) Calculation of the output voltage with the current sharing loop:

(82) $\begin{array}{cc}{I}_{\mathrm{load}}={.Math.}_{k=1}^n\frac{\frac{\left(V_{{\mathrm{ref}}_k}-V_{i_k}\right)}{H_k}-V_{\mathrm{out}}}{R_{{\mathrm{out}}_k}},& \left(21\right)\end{array}$

(83) from which it follows that:

(84) 0$\begin{array}{cc}{I}_{\mathrm{load}}=\frac{.Math.V_{\mathrm{ref}}.Math.}{.Math.H.Math..Math..Math.R_{\mathrm{out}}.Math.}{.Math.}_{k=1}^n\frac{\left(1+{\epsilon }_{{\mathrm{vref}}_k}\right)}{\left(1+{\epsilon }_{h_k}\right).Math.\left(1+{\epsilon }_{{\mathrm{rout}}_k}\right)}-\frac{1}{.Math.H.Math..Math..Math.R_{\mathrm{out}}.Math.}{.Math.}_{k=1}^n{V}_{i_k}-\frac{V_{\mathrm{out}}}{.Math.R_{\mathrm{out}}.Math.}.Math.{.Math.}_{k=1}^n\frac{1}{\left(1+{\epsilon }_{\mathrm{rou}{t}_k}\right)}.& \left(22\right)\end{array}$

(85) From (20) and (22) one gets:

(86) $\begin{array}{cc}{V}_{\mathrm{out}}=\frac{.Math.V_{\mathrm{ref}}.Math.}{.Math.H.Math.}-\frac{.Math.R_{\mathrm{out}}.Math.}{n}.Math.I_{\mathrm{load}}& \left(23\right)\end{array}$

(87) Calculation of the differential current with the correction:

(88) $\begin{array}{cc}{I}_{{\mathrm{out}}_k}-\frac{I_{\mathrm{load}}}{n}=\frac{\frac{\left(V_{re{f}_k}-V_{i_k}\right)}{H_k}-V_{\mathrm{out}}}{R_{{\mathrm{out}}_k}}-\frac{I_{\mathrm{load}}}{n},& \left(24\right)\end{array}$

(89) from which it follows that

(90) $\begin{array}{cc}{I}_{{\mathrm{out}}_k}-\frac{I_{\mathrm{load}}}{n}=\frac{\left({\epsilon }_{h_k}+{\epsilon }_{{\mathrm{rout}}_k}-{\epsilon }_{{\mathrm{vref}}_k}\right).Math..Math.V_{\mathrm{ref}}.Math.}{.Math.H.Math..Math..Math.R_{\mathrm{out}}.Math.}-\frac{\left(1-{\epsilon }_{{\mathrm{rout}}_k}-{\epsilon }_{h_k}\right).Math.V_{i_k}}{.Math.H.Math..Math..Math.R_{\mathrm{out}}.Math.}-\frac{{\epsilon }_{{\mathrm{rout}}_k}.Math.V_{\mathrm{out}}}{.Math.R_{\mathrm{out}}.Math.}& \left(25\right)\end{array}$$\begin{array}{cc}{V}_{i_k}=H_k.Math.R_{\mathrm{diff}}\left(I_{{\mathrm{out}}_k}-\frac{I_{\mathrm{load}}}{n}\right)& \left(26\right)\end{array}$

(91) Equation (21) and (23) lead to:

(92) $\begin{array}{cc}{I}_{{\mathrm{out}}_k}-\frac{I_{\mathrm{load}}}{n}\approx \frac{\left({\epsilon }_{h_k}+{\epsilon }_{{\mathrm{rout}}_k}-{\epsilon }_{{\mathrm{vref}}_k}\right).Math..Math.V_{\mathrm{ref}}.Math.-{\epsilon }_{{\mathrm{rout}}_k}.Math..Math.H.Math..Math.V_{\mathrm{out}}}{.Math.H.Math..Math.\left(.Math.R_{\mathrm{out}}.Math.+R_{\mathrm{diff}}\right)}& \left(27\right)\end{array}$

(93) Equation (27), compared with equation (18), shows that the introduction of the current sharing operation can reduce differential currents as if an additional output impedance Rdiff was added in the modules, while common mode operation is not affected (equation (23)).

(94) It can thus be seen that embodiments according to the present disclosure may result in improved output voltage accuracy based on multiple reference voltages, reduced differential currents, and complete modular decentralized control with inter-module communication—typically along a daisy-chain or circular chain.

(95) The control methods and apparatus disclosed herein may be used with linear regulators, or switched mode regulators. FIG. 10 shows, as a non-limiting example, one such voltage regulator. The figure shows a switched mode buck converter 1000, having a half-bridge node SW which is switched between a supply voltage Vin and ground, by PWM controller 1110, to switchedly supply current through an inductor Lf, to an output by a filter Rdcr,Resr,Cout, where Rdcr is the parasitic resistance of the inductor Lf, and Resr if the parasitic resistance of the capacitor Cout The current through the inductor provides an output voltage V.sub.out, and is sensed (Isense).

(96) Control of such a VR, by AVP or voltage droop regulation, is illustrated in FIG. 11. FIG. 11 depicts a buck 1100 converter, the half-bridge switches of which are driven by high and low-side drivers Driver HS, and Driver_LS. The drivers are controlled by logic control 1110. The logic takes input from an oscillator 1140. An infinite gain (G=∞) DC control loop 1120 is provided with a feedback loop 1130, based on the output impedance Rout, to control the PWM signal in dependence on the output current I.sub.i. The other details of such a buck converter will be familiar to the skilled person.

(97) From reading the present disclosure, other variations and modifications will be apparent to the skilled person. Such variations and modifications may involve equivalent and other features which are already known in the art of voltage regulators, and which may be used instead of, or in addition to, features already described herein.

(98) Although the appended claims are directed to particular combinations of features, it should be understood that the scope of the disclosure of the present invention also includes any novel feature or any novel combination of features disclosed herein either explicitly or implicitly or any generalisation thereof, whether or not it relates to the same invention as presently claimed in any claim and whether or not it mitigates any or all of the same technical problems as does the present invention.

(99) Features which are described in the context of separate embodiments may also be provided in combination in a single embodiment. Conversely, various features which are, for brevity, described in the context of a single embodiment, may also be provided separately or in any suitable sub-combination. The applicant hereby gives notice that new claims may be formulated to such features and/or combinations of such features during the prosecution of the present application or of any further application derived therefrom.

(100) For the sake of completeness it is also stated that the term “comprising” does not exclude other elements or steps, the term “a” or “an” does not exclude a plurality, a single processor or other unit may fulfil the functions of several means recited in the claims and reference signs in the claims shall not be construed as limiting the scope of the claims.

LIST OF REFERENCE SIGNS

(101) 100,300, 400 multi-module voltage regulator 110 regulator module 120 load 310 regulator module with local reference voltage 320 local voltage reference 330 control and power unit 332 control unit 334 power unit 340 shared wired 420 single voltage reference 430 AVP converter module control and power unit 460 parallel connection between control and power unit outputs 460 daisy-chain communication 470 operating point V.sub.out with current Iload/n 480 master module V-I characteristic 500 arrangement of multiple regulator modules 510 regulator module 515 controller 520 local voltage reference 530 control and power unit 532 control unit 534 power unit 550 current balancing unit 560 current sharing, or daisy-chain communication 565 local current sensing 1000 buck converter 1010 PWM controller 1100 buck converter with AVP regulation 1110 logic control 1120 Infinite DC gain 1130 feedback loop based in output impedance 1140 oscillator