Patent Publication Number: US-2023163767-A1

Title: Control circuit for an electronic converter, related integrated circuit, electronic converter and method

Description:
PRIORITY CLAIM 
     This application claims the priority benefit of Italian Application for Patent No. 102021000029294, filed on Nov. 19, 2021, the content of which is hereby incorporated by reference in its entirety to the maximum extent allowable by law. 
     TECHNICAL FIELD 
     The embodiments of the present description refer to a control device for a buck voltage converter. 
     BACKGROUND 
     Power-supply circuits, such as AC/DC or DC/DC switched mode power supplies, are well known in the art. There exist many types of electronic converters, which are mainly divided into isolated and non-isolated converters. For instance, non-isolated electronic converters are the converters of the “buck”, “boost”, “buck-boost”, “Ćuk”, “SEPIC”, and “ZETA” type. Instead, isolated converters are, for instance, converters of the “flyback”, “forward”, “half-bridge”, and “full-bridge” type. Such types of converters are well known to the person skilled in the art, as evidenced e.g., by the application note AN513/0393 “Topologies for Switched Mode Power Supplies”, L. Wuidart, 1999, STMicroelectronics (incorporated herein by reference). 
       FIG.  1    is a schematic illustration of a DC/DC electronic converter  20 . In particular, a generic electronic converter  20  comprises two input terminals  200   a  and  200   b  for receiving a DC voltage V in  and two output terminals  202   a  and  202   b  for supplying a DC voltage V out . For example, the input voltage V in  may be supplied by a DC voltage source  10 , such as a battery, or may be obtained from an AC voltage by means of a rectifier circuit, such as a bridge rectifier, and possibly a filtering circuit. Instead, the output voltage V out  may be used to supply a load  30 . 
       FIG.  2    shows the circuit schematic of a typical buck voltage converter  20 . In particular, a buck converter  20  comprises two input terminals  200   a  and  200   b  for receiving a DC input voltage V in  and two output terminals  202   a  and  202   b  for supplying a regulated voltage V out , where the output voltage is equal to or lower than the input voltage yin. 
     In particular, typically, a buck converter  20  comprises two electronic switches Q 1  and Q 2  (with the current path thereof) connected (e.g., directly) in series between the input terminals  200   a  and  200   b , wherein the intermediate node between the electronic switches Q 1  and Q 2  represents a switching node Lx. Specifically, the electronic switch Q 1  is a high-side switch connected (e.g., directly) between the (positive) terminal  200   a  and the switching node Lx, and the electronic switch Q 2  is a low-side switch connected (e.g., directly) between the switching node Lx and the (negative) terminal  200   b , which often represents a ground GND. The (high-side) switch Q 1  and the (low-side) switch Q 2  hence represent a half-bridge configured to connect the switching node Lx to the terminal  200   a  (voltage V in ) or the terminal  200   b  (ground GND). 
     For example, the switches Q 1  and/or Q 2  are often transistors, such as Field-Effect Transistors (FETs), such as Metal-Oxide-Semiconductor Field-Effect Transistors (MOSFETs), e.g., n-channel FETs, such as NMOS transistors. Frequently, the second electronic switch Q 2  is also implemented just with a diode, where the anode is connected to the terminal  200   b  and the cathode is connected to the switching node Lx. 
     In the example considered, an inductance L, such as an inductor, is connected (e.g., directly) between the switching node Lx and the (positive) output terminal  202   a . Instead, the (negative) output terminal  202   b  is connected (e.g., directly) to the (negative) input terminal  200   b.    
     In the example considered, to stabilize the output voltage V out , the converter  20  typically comprises a capacitor Cout connected (e.g., directly) between the output terminals  202   a  and  202   b.    
     In this context,  FIG.  3    shows exemplary waveforms of the signals of such an electronic converter, where: waveform a) shows the signal DRV 1  for switching the electronic switch Q 1 ; waveform b) shows the signal DRV 2  for switching the second electronic switch Q 2 ; waveform c) shows the current I Q1  that traverses the electronic switch Q 1 ; waveform d) shows the voltage V Lx  at the switching node Lx (i.e., the voltage at the second switch Q 2 ); and waveform e) shows the current I L  that traverses the inductor L. 
     In particular, when the electronic switch Q 1  is closed at an instant t 1  (ON state), the current I L  in the inductor L increases (substantially) linearly. The electronic switch Q 2  is at the same time opened. Instead, when the electronic switch Q 1  is opened after an interval Tom at an instant t 2  (OFF state), the electronic switch Q 2  is closed, and the current I L  decreases (substantially) linearly. Finally, the switch Q 1  is closed again after an interval T OFF1 . In the example considered, the switch Q 2  (or a similar diode) is hence closed when the switch Q 1  is open, and vice versa. 
     The current I L  can thus be used to charge the capacitor Cout, which supplies the voltage V out  at the terminals  202   a  and  202   b.    
     In the example considered, the electronic converter  20  comprises thus a control circuit  22  configured to drive the switching of the switch Q 1 , and possibly of the switch Q 2 , for repeating the intervals T ON1  and T OFF1  periodically. For example, typically the buck converter  20  comprises also a feedback circuit  24 , such as a voltage divider (Div), configured to generate a feedback signal FB indicative of (and preferably proportional to) the output voltage V out , and the control circuit  22  is configured to generate the drive signals DRV 1  and optionally DRV 2  by comparing the feedback signal FB with a reference signal, such as a reference voltage V REF . 
     A significant number of driving schemes are known for generating the drive signal DRV 1  and optionally DRV 2 . These solutions have in common the possibility of regulating the output voltage V out  by regulating the duration of the interval Tom and/or the interval T OFF1 . 
     For example, in many applications, the control circuit  22  generates a Pulse-Width Modulation (PWM) signal DRV 1 , wherein the duration of the switching interval T SW =T ON1 +T OFF1  is constant, but the duty cycle T ON /T SW  is variable. For example, a typical control scheme involves that the duration of the interval Tom is varied via a regulator circuit having at least an integral component, such as a PI (Proportional-Integral) or PID (Proportional-Integral-Derivative) regulator. 
     Specifically, as well known, a buck converter may be operated in a Continuous-Conduction Mode (CCM), Discontinuous-Conduction Mode (DCM) or Transition Mode (TM). 
     As shown in  FIG.  4 A , when the control circuit  20  operates the converter in the CCM mode, the current I L  flowing through the inductance L has a value different from zero at the end of the interval T OFF1  (see  FIG.  3   ). In this case, the control circuit  20  uses two switching phases T 1  and T 2 , with T SW =T 1 +T 2 , wherein: during the phase T 1  (T 1 =T ON1 =T OFF2 ) the switch Q 1  is closed and the switch/diode Q 2  is opened; and during the phase T 2  (T 2 =T OFF1 =T ON2 ) the switch Q 1  is opened and the switch/diode Q 2  is closed. 
     For example, in CCM, the control circuit  20  may use switching cycles T SW  with fixed duration, but the switch-on duration T ON1 =T 1  may be varied via a PID regulator, i.e., the signal DRV 1  is a PWM signal with (fixed or predetermined frequency) but the switch-on duration/duty cycle is determined as a function of the output voltage (and the reference signal V REF ). Conversely, the optional signal DRV 2  may correspond to the inverted version of the signal DRV 1 . 
     Conversely, as shown in  FIG.  4 B , when the control circuit  20  operates the converter in the DCM mode, the current I L  flowing through the inductance L reaches zero during the interval T OFF1  and remains at zero until the end of the interval T OFF1  (see  FIG.  3   ). In this case, the control circuit  20  uses indeed three switching phases T 1 , T 2  and T 3 , with T SW =T 1 +T 2 +T 3 , wherein: during the phase T 1  (T 1 =T ON1 ) the switch Q 1  is closed and the switch/diode Q 2  is opened; during the phase T 2  (T 2 =T ON2 ) the switch Q 1  is opened and the switch/diode Q 2  is closed; and during the phase T 3  (T OFF1 =T 2 +T 3  and T OFF2 =T 3 +T 1 ) the switch Q 1  is opened and the switch/diode Q 2  is opened. 
     For example, when using a diode as switch Q 2 , this diode will automatically open when the current I L  reaches zero, thereby ending the interval T 2 . Conversely, when using a controllable electronic switch Q 2 , usually the control circuit  20  comprises (or is connected to) a demagnetization detection circuit configured to determine the instant when the current I L  reaches zero (corresponding to the end of the interval T 2  and the beginning of the interval T 3 ). For example, such a demagnetization detection circuit may monitor the current I L . For example, in  FIG.  2    is shown a current sensor  24   b  connected in series with the electronic switch Q 2 , such as a shunt resistor, which thus generates a measurement signal CS indicative of (and preferably proportional to) the current I L  flowing during the interval T 2  through the inductance L. 
     Accordingly, in DCM, the control circuit  20  may again use switching cycles T SW  with fixed duration, where the switch-on duration T ON1 =T 1  may again be varied via a PID regulator, i.e., the signal DRV 1  is a PWM signal with fixed or predetermined frequency, and the switch-on duration/duty cycle is determined as a function of the output voltage (and the reference signal V REF ). However, when using a controllable electronic switch Q 2 , the control circuit  20  may be configured to open the electronic switch Q 2  when the signal CS indicates a demagnetization of the inductance L. 
     The CCM and the DCM modes of a buck converter have thus in common that often a fixed frequency PWM signal DRV 1  may be used to drive the electronic switch Q 1 . Conversely, an optional drive signal DRV 2  may be determined as a function of the drive signal DRV 1  and (when operated in DCM) an additional signal CS indicative of the demagnetization of the inductance L. 
     In general, also (usually fixed) dead times may be introduced between the switching of the drive signals, e.g., between the falling edge of the signal DRV 1  and the rising edge of the signal DRV 2 , and similarly (in CCM mode) between the falling edge of the signal DRV 2  and the rising edge of the signal DRV 1 . Insofar as these intervals are usually short compared to the durations T ON  and T OFF , these intervals will not be considered in the following. However, also in this case, the drive signal DRV 2  may be determined as a function of the drive signal DRV 1 . 
     Other electronic converters often using a PWM modulation are for example boost, buck-boost, flyback or forward converters, various types of half-bridge converter, etc. 
     For example,  FIG.  5    shows an example of a boost converter. Specifically, in the example considered, an inductance L, such as an inductor, is connected (e.g., directly) between the positive input terminal  200   a  and a switching node Lx. The switching node Lx is connected (e.g., directly) via (the current path of) a first electronic switch S 1  to the negative input terminal  200   b , which in turn is usually connected (e.g., directly) to the negative output terminal  202   b . The switching node Lx is also connected (e.g., directly) via (the current path of) a second electronic switch S 2  to the positive output terminal  202   a . For example, the electronic switches S 1  and S 2  may be MOSFET. Generally, the electronic switch S 2  may also be implemented only with a diode. Usually a capacitance Cout, such as a capacitor, is connected between the output terminals  202   a  and  202   b.    
     Also in this case the electronic switch S 1  may be driven via a PWM signal DRV 1 , wherein the duty cycle is determined as a function of the output voltage V out  and a reference voltage V REF . Conversely, when a controllable electronic switch S 2  is used, the electronic switch S 2  may be driven via a signal DRV 2 , which: in CCM may correspond to the inverted version of the signal DRV 1 ; or in DCM may be determined as a function of the signal DRV 1  and a signal CS indicative of the demagnetization of the inductance L, such as a current measurement signal CS being proportional to the current I L  flowing through the inductance L. 
     In this respect,  FIG.  6    shows a generic electronic converter  20  using a PWM signal DRV with fixed or predetermined frequency. Specifically, the electronic converter  20  comprises a switching stage  26  connected between the input terminals  200   a ,  200   b  and the output terminal  202   a , and  202   b . Such a switching stage  26  comprises one or more electronic switches SW 26  and at least one inductance L 26 , such as inductors or transformers, and optionally one or more capacitances C 26 , such as capacitors. For example, in a buck converter ( FIG.  2   ), these components are the switch Q 1 , the switch or diode Q 2 , the inductance L and the capacitance Cout. Conversely, in a boost converter ( FIG.  5   ), these components are the switch S 1 , the switch or diode S 2 , the inductance L and the capacitance Cout. 
     In the example considered, the control circuit  22  comprises a driver circuit  222  configured to generate one or more drive signals for the switching stage  26  as a function of: the PWM signal DRV, which has switching cycles T SW  (with fixed or predetermined period) wherein the signal DRV is set to a first logic level (e.g., high) for a first duration T ON  and to a second logic level (e.g., low) for a second duration T OFF , with T SW =T ON +T OFF  (see also  FIG.  7   ) and an optional measurement signal CS indicative of the demagnetization of the inductance L 26 . 
     For example, as mentioned before, the PWM signal DRV may be used to drive the switch Q 1  of  FIG.  2    and the switch S 1  of  FIG.  5   . Conversely, the measurement signal CS may be used when the electronic converter is operated in the DCM mode, e.g., for driving the electronic switch Q 2  of  FIG.  2    or the switch S 2  of  FIG.  5   . 
     In line with the description of  FIG.  2   , usually a feedback circuit  24  is used to generate a feedback signal FB indicative of (and preferably proportional to, e.g., corresponding to) the output voltage V out . Next a regulator circuit  220 , such as a PID regulator, may vary the duration T ON  of the PWM signal DRV as a function of the feedback signal FB and a reference signal V REF . 
     For example, as described in document U.S. Pat. No. 9,091,741 B2 (incorporated by reference), such PID regulators are often implemented with an error amplifier comprising an operational amplifier and a feedback network comprising one or more capacitors and resistors. 
     Recently another type of regulator circuit  220  has been used, wherein a time-based regulation is used to generate the PWM signal DRV. Time-based DC-DC converters are gaining popularity, because this type of control scheme offers many advantages. By virtue of the continuous-time digital nature of the time-based regulators, they combine the advantages of conventional analog and digital controller circuit  220 . Basically, they operate with (e.g., CMOS-level) digital signals, but without adding any quantization error typically found in digital controllers. Deploying simple circuits such as ring oscillators, delay lines, and flip-flops, time-based regulator circuits  220  eliminate the need for wide bandwidth error amplifiers and PWM blocks in analog regulator circuits, or high-resolution analog-to-digital converters (ADCs) and digital PWM blocks in digital regulator circuits. Using time as the processing variable, this new type of control provides an attractive solution for implementing wide-bandwidth high-switching frequency PWM-based electronic converters, because it obviates the need for power and area demanding wide bandwidth amplifiers and high-speed comparators present in conventional PID controllers. 
     For example, such a time based PID is described in United States Application for Patent Publication No. 2021/0226531 A1 (incorporated by reference). 
     There is a need in the art to provide a time-based control device for a PWM driven electronic converter, such as a buck or boost converter. 
     SUMMARY 
     According to one or more embodiments, a control circuit for an electronic converter is provided. Embodiments moreover concern a related integrated circuit, electronic converter and method. 
     Various embodiments of the present disclosure relate to a control circuit for a switching stage of an electronic converter configured to provide via two output terminals an output voltage. For example, the electronic converter may be a buck or boost converter. 
     In various embodiments, the control circuit, e.g., implemented in an integrated circuit, comprises one or more terminals configured to provide one or more respective drive signals to one or more electronic switches of the switching stage of the electronic converter, and a terminal configured to receive from a feedback circuit a first feedback signal proportional to the output voltage. 
     In various embodiments, the control circuit comprises a driver circuit configured to generate the one or more drive signals as a function of a Pulse-Width Modulation (PWM) signal, and a PWM signal generator circuit configured to generate the PWM signal as a function of the first feedback signal and a reference voltage. 
     Specifically, in various embodiments, the PWM signal generator circuit comprises a first current-controlled oscillator having an input terminal for receiving a first current and configured to generate a first clock signal as a function of the first current, and a second current-controlled oscillator having an input terminal for receiving a second current and configured to generate a second clock signal as a function of the second current. 
     Moreover, in various embodiments, the PWM signal generator circuit comprises a first operational transconductance amplifier and a phase detector. Specifically, the first operational transconductance amplifier has a first output terminal and is configured to provide at the first output terminal a third current indicative of the difference between the reference voltage and the first feedback signal, wherein the first output terminal of the first operational transconductance amplifier is connected to the input terminal of the first current-controlled oscillator. The phase detector has inputs coupled to the first oscillator and the second oscillator and provides at an output the PWM signal. 
     Specifically, according to various embodiment, the PWM signal generator circuit further comprises a first bias current generator having an output terminal and configured to provide at the output terminal a first bias current, and a second bias current generator having an output terminal and configured to provide at the output terminal a second bias current. Specifically, in various embodiments, a switching circuit is configured to receive a clock signal and determine the logic level of the clock signal. In response to determining that the logic level of the clock signal has a first logic level, the switching circuit connects the output terminal of the first bias current generator to the input terminal of the first current-controlled oscillator and connects the output terminal of the second bias current generator to the input terminal of the second current-controlled oscillator. Conversely, in response to determining that the logic level of the clock signal has a second logic level, the switching circuit connects the output terminal of the first bias current generator to the input terminal of the second current-controlled oscillator and connects the output terminal of the second bias current generator to the input terminal of the first current-controlled oscillator. 
     For example, in various embodiments, the clock signal is derived from the first clock signal or the second clock signal. For example, the clock signal may correspond to the first clock signal or the second clock signal. 
     In various embodiments, the PWM signal generator circuit may also comprise one or more first delay lines connected between the first oscillator and the phase detector, and/or one or more second delay lines connected between the second oscillator and the phase detector. For example, these delay lines may be used to implement a Proportional and/or Derivative component of the regulator. For example, in order to implement a Proportional component, the one or more first delay lines and/or the one or more second delay lines may be driven as a function of the difference between the reference voltage and the first feedback signal. Conversely, in order to implement a Derivative component, the control circuit may comprise a third terminal configured to receive from an analog differentiator a second feedback signal proportional to the derivative of the output voltage. In this case the one or more first delay lines and/or the one or more second delay lines may be driven as a function of the difference between the reference voltage and the second feedback signal. 
     For example, in various embodiments, the one or more first delay lines and the one or more second delay lines are current-controlled delay lines. In this case, the PWM signal generator circuit may comprise a second operational transconductance amplifier configured to generate a fourth current indicative of the difference between the reference voltage and the first feedback signal and/or a third operational transconductance amplifier configured to generate a fifth current indicative of the difference between the reference voltage and the second feedback signal. Accordingly, the fourth current and the fifth current may be provided to the one or more first delay lines and/or the one or more second delay lines. 
     Generally, also differential operational amplifiers may be used. For example, the first operational transconductance amplifier may be a differential operational transconductance amplifier comprising a second output terminal, wherein the first operational transconductance amplifier is configured to provide at the second output terminal a sixth current, wherein the difference between the sixth current and the third current is proportional to the difference between the reference voltage and the first feedback signal. In this case, the second output terminal of the first operational transconductance amplifier may thus be connected to the input terminal of the second current-controlled oscillator. 
     Similarly, in order to implement the Proportional component, the second operational transconductance amplifier may indeed generate two currents, wherein a first current is applied to one or more first delay lines and a second current is applied to the one or more second delay lines, wherein the difference between these currents is proportional to the difference between the reference voltage and the first feedback signal. Conversely, in order to implement the Derivative component, the third operational transconductance amplifier may generate two currents, wherein a first current is applied to one or more first delay lines and a second current is applied to the one or more second delay lines, wherein the difference between these currents is proportional to the difference between the reference voltage and the second feedback signal. In various embodiments, the first current generated by the second operational transconductance amplifier and the first current generated by the third operational transconductance amplifier may be summed and applied to the same one or more first delay lines. Similarly, the second current generated by the second operational transconductance amplifier and the second current generated by the third operational transconductance amplifier may be summed and applied to the same one or more second delay lines. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The embodiments of the present disclosure will now be described with reference to the annexed plates of drawings, which are provided purely to way of non-limiting example and in which: 
       The features and advantages of the present invention will become apparent from the following detailed description of practical embodiments thereof, shown by way of non-limiting example in the accompanying drawings, in which: 
         FIG.  1    shows an example of an electronic converter; 
         FIG.  2    shows an example of a buck converter; 
         FIG.  3    shows exemplary waveforms of the buck converter of  FIG.  2   ; 
         FIG.  4 A  shows waveforms when the buck converter of  FIG.  2    is operated in a CCM mode; 
         FIG.  4 B  shows waveforms when the buck converter of  FIG.  2    is operated in a DCM mode; 
         FIG.  5    shows an example of a boost converter; 
         FIG.  6    shows an example of an electronic converter using a PWM signal; 
         FIG.  7    shows an example of PWM signal of the electronic converter of  FIG.  6   ; 
         FIG.  8    shows a first example of a time-based control circuit for the electronic converter of  FIG.  6   ; 
         FIG.  9    shows exemplary waveforms of the control circuit of  FIG.  8   ; 
         FIG.  10    shows a second example of a time-based control circuit for the electronic converter of  FIG.  6   ; 
         FIG.  11    shows exemplary waveforms of the control circuit of  FIG.  10   ; 
         FIG.  12    shows a possible implementation of the time-based control circuit of  FIG.  10   ; 
         FIG.  13    shows an embodiment of a modified time-based control circuit; and 
         FIG.  14    shows an embodiment of a switching circuit used in the time-based control circuit of  FIG.  13   . 
     
    
    
     DETAILED DESCRIPTION 
     In the ensuing description, various specific details are illustrated aimed at enabling an in-depth understanding of the embodiments. The embodiments may be provided without one or more of the specific details, or with other methods, components, materials, etc. In other cases, known structures, materials, or operations are not shown or described in detail so that various aspects of the embodiments will not be obscured. 
     Reference to “an embodiment” or “one embodiment” in the framework of this description is meant to indicate that a particular configuration, structure, or characteristic described in relation to the embodiment is comprised in at least one embodiment. Hence, phrases such as “in an embodiment”, “in one embodiment”, or the like that may be present in various points of this description do not necessarily refer to one and the same embodiment. Moreover, particular conformations, structures, or characteristics may be combined in any adequate way in one or more embodiments. 
     The references used herein are only provided for convenience and hence do not define the sphere of protection or the scope of the embodiments. 
     In  FIGS.  8  to  14    described below, parts, elements or components that have already been described with reference to  FIGS.  1  to  7    are designated by the same references used previously in these figures. The description of these elements has already been made and will not be repeated in what follows in order not to burden the present detailed description. 
     As explained in the foregoing, various embodiments of the present disclosure relate to an improved time-based control circuit  22   a  for an electronic converter. For a general description of electronic converters using a PWM signal reference can be made to the previous description of  FIGS.  1  to  7   . Conversely, for a general description of time-based PID regulators, reference can be made to the previously cited United States Patent Application Publication No. 2021/0226531 A1 (incorporated by reference). 
     For example,  FIG.  8    schematically shows an example of a time-based control circuit  22   a , e.g., in the form of an integrated circuit. Specifically, also in this case, the control circuit  22   a  comprises: a PWM signal generator  220   a  configured to generate a PWM signal DRV as a function of a feedback signal FB indicative of the output voltage V out  generated by the switching stage (SS)  26  of the electronic converter and a reference voltage V REF ; and a driver circuit  222  configured to drive a switching stage  26  as a function of the PWM signal DRV. 
     Specifically, in the embodiment considered, the PWM signal generator  220   a  comprises: a first voltage-controlled oscillator  2220  configured to generate a first clock signal CLK 1  as a function of the feedback signal FB; an analog differentiator  2222  configured to generate a signal indicative of (and preferably proportional to) the derivative of the feedback signal FB, e.g., implemented with a capacitor C D  and a resistor R D  connected in series between the feedback signal FB and a reference voltage, e.g., ground (which may correspond e.g., to the negative input terminal  200   b  or the negative output terminal  202   b ), wherein the intermediate node between the capacitor C D  and the resistor R D  corresponds to the signal indicative of the derivative of the feedback signal FB; a first delay line  2224  having a delay as a function of the feedback signal FB and a second delay line  2226  having a delay as a function of the signal indicative of the derivative of the feedback signal FB, wherein the first and second delay lines are connected in cascade and generate a delayed first clock signal CLK 1 ′; a second voltage-controlled oscillator  2228  configured to generate a second clock signal CLK 2  as a function of the reference voltage V REF ; and a phase detector (PD) circuit  2230  configured to generate the PWM signal DRV, wherein the duty cycle of the PWM signal DRV is determined as a function of the phase difference Φ between the clock signal CLK 2  and the delayed clock signal CLK 1 ′. 
     Delay lines having a programmable delay as a function of a voltage or current signal are well known in the art. For example, in this context may be cited U.S. Pat. Nos. 5,650,739 A and 7,696,799 B2 (incorporated by reference). 
     For example, as shown in  FIG.  9   , the phase detector circuit  2230  may be configured to set the signal DRV to high when the second clock signal CLK 2  is high and the delayed first clock signal CLK 1 ′ is low. For example, the phase detector  2230  may be implemented with one or more logic gates and/or one or more latches. 
     In the embodiment considered, the second voltage-controlled oscillator  2228  provides thus a clock signal CLK 2  having a given (fixed or settable) frequency as a function of the reference voltage V REF . Conversely, the first voltage-controlled oscillator  2220  varies the frequency of the first clock signal CLK 1  until the feedback signal FB corresponds to the reference voltage V REF , and in this steady condition the frequency of the first clock signal CLK 1  corresponds to the frequency of the second clock signal CLK 2 , but the clock signals are phase shifted by a given phase Φ I . The first oscillator  2220  thus implements a regulator with I (integral) component of the phase Φ I . Conversely, the first delay line  2224  and the second delay line  2226  introduce an additional phase Φ P  being proportional to the feedback signal FB and an additional phase Φ D  being proportional to the derivative of the feedback signal FB, i.e., the total phase shift Φ corresponds to: Φ=Φ I +Φ P +Φ D ; wherein, as shown in  FIG.  9   , the phase shift Φ is proportional to (and preferably corresponds to) the switch on duration T ON  (e.g., T ON =T SW (Φ/2π), i.e., the signal DRV is a PWM signal wherein the switch-on duration T ON /the duty cycle is varied via a time-based control (with PID regulation) of the phase shift Φ as a function of the feedback signal FB and the reference voltage V REF . Accordingly, the phase detector  2230  may also perform other operations, such as a down-scaling operation of the frequency of the clock signals CLK 1 /CLK 2 , and it is only relevant that the phase detector  2230  is configured to generate a PWM signal DRV, wherein the switch-on duration T ON  of the signal DRV is determined as a function of the phase shift Φ. 
       FIG.  10    shows a second example of a time-based PWM signal generator  220   a.    
     Specifically, in the embodiment considered, the following modifications have been performed, which also may be used separately: the voltage-controlled oscillators  2220  and/or delay lines  2224  and  2226  have been replaced with current-controlled oscillators and/or delay lines; the delay lines  2224  and  2226  have been combined into the same delay line  2234 ; and a differential approach is used, wherein the oscillators  2220 / 2228  and/or the delay lines  2234 / 2235  are driven with differential signal. 
     Specifically, in the embodiment considered, again a feedback circuit  24  is used to determine a feedback signal FB proportional to the output voltage V out . For example, in various embodiments, the feedback circuit  24  is implemented with a voltage divider  24  comprising two or more resistors R FB1  and R FB2  connected in series between the terminals  202   a  and  202   b , wherein the voltage V FB  at one of the resistors, e.g., resistor R FB2 , corresponds to the feedback signal FB. 
     In the embodiment considered, the feedback signal FB and the reference voltage V REF  are provided to a first differential transconductor  2236 , such as a differential operational transconductance amplifier (OTA). For example, in various embodiments, the differential transconductor  2236  provides: a first current i I+ =i I0 +i I /2; and a second current i I− =i I0 −i I /2. 
     Specifically, in a differential transconductor  2236  the difference i I =i I+ −i I−  between the currents and is proportional to the difference between the respective input voltages, i.e., the reference voltage V REF  and the feedback voltage V FB , i.e., i I =G MI (V REF −V FB ). 
     In the embodiment considered, the current i I+  is provided to the current-controlled oscillator  2228  and the current i I−  is provided to the current-controlled oscillator  2220 , such as two ring-oscillators. Accordingly, the oscillator  2228  generates a clock signal CLK 2  having a frequency proportional to the current and the oscillator  2220  generates a clock signal CLK 1  having a frequency proportional to the current i I− . Thus, when the feedback voltage V FB  corresponds to the reference voltage V REF , both oscillators are supplied with the current i I0 , which thus determines the steady state frequency of the clock signals CLK 1  and CLK 2 . 
     Similarly, the feedback signal FB and the reference voltage V REF  are provided to a second differential transconductor  2238 , such as a differential operational transconductance amplifier (OTA). For example, in various embodiments, the differential transconductor  2238  provides: a first current i P+ =i P0 +i P /2; and a second current i P− =i P0 −i P /2. 
     Specifically, in the differential transconductor  2238  the difference i P =i P+ −i P−  between the currents i P+  and i P−  is proportional to the difference between the respective input voltages, i.e., the reference voltage V REF  and the feedback voltage V FB , i.e., i P =G MP (V REF −V FB ). 
     In the embodiment considered, again an analog differentiator  2222  is used to generate a signal V D  proportional to the derivative of the output voltage V out . For example, in the embodiment considered, the analog differentiator  2222  is implemented with a capacitor C D  and a resistor R D  connected between the output voltage V out  or the feedback signal FB, and a reference voltage, such as ground or preferably the reference voltage V REF . For example, when connecting the resistor R D  to the reference voltage V REF  the derivative signal V D  has an offset of V REF  to which the derivative component of the output voltage V out  is added. 
     In the embodiment considered, the derivative signal V D , e.g., the voltage at the intermediate node between the capacitor C D  and the resistor R D , and the reference voltage V REF  are provided to a third differential transconductor  2240 , such as a differential operational transconductance amplifier (OTA). For example, in various embodiments, the differential transconductor  2240  provides: a first current i D+ =i D0 +i D /2; and a second current i D− =i D0 −i D /2. 
     Specifically, in the differential transconductor  2240  the difference i D =i D+ −i D−  between the currents i D+  and i D−  is proportional to the difference between the respective input voltages, i.e., the reference voltage V REF  and the derivative signal V D , i.e., i P =G MD (V REF −V D ). 
     Similar to the description of  FIG.  8   , the currents i P+  and i D+  and/or the currents i P−  and i D− , i D−  may be provided to respective delay lines, such as: two delay lines connected in series (essentially corresponding to the delay lines  2224  and  2226 ) may be configured to generate a delayed version CLK 1 ′ of the clock signal CLK 1  as a function of the currents i P−  and i D− , respectively; and/or two delay lines connected in series may be configured to generate a delayed version CLK 2 ′ of the clock signal CLK 2  as a function of the currents i P+  and i D+ . 
     Generally, the term “and/or” highlights the possibility that these delay lines may be provided for each clock signal (as shown in  FIG.  10    for a differential approach) or only for a single clock signal (as shown in  FIG.  8   ). 
     Conversely, in the embodiment considered, the currents i P+  and i D+  are provided to a first summation node, which thus provides a current I R =i P+ +i D+ , and/or the currents i P−  and i D−  are provided to a second summation node, which thus provides a current I F =i P− +i D− . In the embodiment considered, the current I R  is provided to the delay line  2235  and/or the current I F  is provided to the delay line  2234 , such as a sequence of delay stages having a delay as a function of a respective supply current, i.e., the currents I F  and I R . 
     Accordingly, in the embodiment considered and as also shown in  FIG.  11   , the delay stage  2235  generates a delayed clock signal CLK 2 ′ having a delay t d2  with respect to the clock signal CLK 2  and/or the delay stage  2234  generates a delayed clock signal CLK 1 ′ having a delay tai with respect to the clock signal CLK 1 . 
     In the embodiment considered, the delayed clock signals CLK 2 ′ and CLK 1 ′ are then provided to a phase detector, which e.g., is configured to: set the signal DRV to a first logic level (e.g., high) at the rising edge of CLK 2 ′; and set the signal DRV to a second logic level (e.g., low) at the rising edge of the signal CLK 1 ′. 
     Thus, in the embodiment considered, in steady state, the feedback signal V FB  corresponds to the reference voltage V REF , and by connecting the analog differentiator to the reference voltage V REF , also the signal V D  corresponds to the reference voltage V REF . Thus, in the steady state, the differential currents i D , i P  and i I  are zero, and (when using a differential approach) the delay t d1  of the delay line  2234  corresponds to the delay t d2  of the delay line  2235 . Moreover, the oscillators  2220  and  2228  provide two clock signals CLK 1  and CLK 2  having the same frequency and a phase-shift Φ I . Due to the fact, that the delay lines  2234  and  2235  introduce the same delay t d1 =t d2  in the embodiment considered, the phase shift Φ between the delayed clock signals CLK 1 ′ and CLK 2 ′ corresponds to Φ I , e.g., the duration T ON  corresponds to (or is proportional to) the delay Φ I , e.g., T ON =T SW (Φ I /2π). Accordingly, the duty cycle D=T ON /T SW  of the signal DRV corresponds thus to Φ I /2π. For example, in a buck converter, the duty cycle may be determined (approximately) as a function of the input and output voltage, i.e., D=Φ I /2π=V out /V in . 
     As mentioned before, also only one of the delay lines  2234  or  2235  could be used or one of the delay lines could introduce a constant delay, i.e., one of the delays t d1  to or t d2  could be zero or at least constant. In fact, in this case, the oscillators  2220  and  2228  would generate clock signals having a phase shift Φ I  which also compensate the constant delay t d1  or t d2 . Thus, in general, in various embodiments, one or more first delay lines  2234  are connected between the oscillator  2220  and the phase detector  2230  and/or one or more second delay lines  2235  are connected between the oscillator  2228  and the phase detector  2230 , wherein the one or more first delay lines  2234  and/or the one or more second delay lines  2235  are driven via the currents i P  and i D . 
     As mentioned before, in various embodiments, the feedback signal FB and the reference voltage V REF  are provided to a first differential transconductor  2236 , such as a differential operational transconductance amplifier (OTA). For example, in various embodiments, the differential transconductor  2236  provides: a first current i I+ =i I0 +i I /2; and a second current i I− =i I0 −i I /2. 
       FIG.  12    shows in this respect an embodiment for implementing the above biasing of the current i I0 . 
     Specifically, in the embodiment considered, the differential transconductor  2236  just provides the differential component i I , i.e.: a first (positive) terminal of the differential transconductor  2236  provides a first current i I /2, wherein the first terminal is connected to the current controlled oscillator  2228 ; and a second (negative) terminal of the differential transconductor  2236  provides a first current −i I /2, wherein the first terminal is connected to the current controlled oscillator  2220 . 
     In the embodiment considered, a first current source  2250  providing a current I BIAS+ =i I0  is thus connected to the first terminal of the differential transconductor  2236 , whereby the current controlled oscillator  2228  receives a current i I+ =i I0 +i I /2. Similarly, a second current source  2252  providing a current I BIAS− =i I0  is connected to the second terminal of the differential transconductor  2236 , whereby the current controlled oscillator  2220  receives a current i I− =i I0 −i I /2. 
     Generally, the differential transconductor  2236  may also provide a common mode current, which thus would also be added to the currents provided to the current controlled oscillators  2220  and  2228 . However, without loss of generality, this common mode current is usually small and will be neglected in the following. Accordingly, neglecting the common mode current provided by the differential transconductor  2236 , the current controlled oscillators  2220  and  2228  are equally biased with a common-mode current I BIAS+ =I BIAS− , so that in steady state (i.e., when the loop is closed, FB=V REF ) the differential current i I  provided by the differential transconductor  2236  is zero, i.e., the current controlled oscillators  2220  and  2228  oscillate with the same frequency F SW . Accordingly, the frequency F SW  is nominally constant across the entire input and output voltage range and only determined by the bias currents I BIAS+  and I BIAS−  (and the actual common mode current of the differential transconductor  2236 ). This applies also in case of the single ended configuration, when the differential amplifier  2236  just provides a current I I  to one of the current controlled oscillators  2220  or  2228 . 
     Conversely, focusing on the delay-lines  2234  and  2235 , in steady-state the (differential) currents i D  and i P  provided by the (differential) transconductors  2238  and  2240  are zero. Supposing the delay lines are matched, they both introduce the same delay t d1 =t d2  and therefore the same phase-shift. 
     In this respect, in steady state, the regulator circuit should generate a PWM signal DRV, which ensures that the electronic converter generates the requested output voltage V out . As mentioned before, in this case, the two oscillators  2220  and  2228  provide two clock signals CLK 1  and CLK 2  with the same frequency F SW  and the phase-shift Φ is related to the converter duty-cycle D PWM , e.g., in case of a buck and without considering efficiency: 
         D   PWM   =T   ON /( T   ON   +T   OFF ))=Φ/2π= V   out   /V   in  
 
     Again, it is important to note that the phase-shift Φ is dictated by the integral Φ I  action only, while the proportional Φ P  and derivative Φ P  actions have effects just during transients. 
     However, it will be noted that, in the steady state condition, the output voltage V out  may be subject to an offset. 
     On the one hand, as mentioned before, typically a resistive voltage divider R FB1  and R FB2  is used to generate the feedback signal FB, which is provided to the transconductor  2236  (and similarly the transconductor  2238 ). Such a voltage divider may thus introduce an offset due to an unexpected divider ratio. However, thanks to the integral action, the regulator circuit varies the currents I I−  and I I+  until the feedback signal FB corresponds to the reference voltage V REF . Accordingly, a mismatch between the resistors R FB1  and R FB2 , translates into an offset error of the regulated output voltage V out . Similar issues may also exist with other feedback circuits  24 , such as level-shifters. Such a feedback mismatch is well-known in the context of PID regulators, and is not limited to time-based controllers. Although integrated resistors may be matched very well, trimming actions on the feedback divider  24  or other calibration methods may be exploited to minimize the residual output voltage offset. 
     On the other hand, in time-based controllers, another major source of an offset of the output voltage V out  are possible unequal common-mode currents of the current-controlled oscillators  2220  and  2228 . For example, when the bias currents I BIAS+  and I BIAS−  are not equal, the control loop has to take care of such an unbalanced bias of the current-controlled oscillators  2220  and  2228 . Substantially, in this case, the control loop has to provide, even in the steady state, a current I I  being different from zero, thereby imposing again currents I I+ =I I−  on the current-controlled oscillators, whereby an undesired offset is introduced in the output voltage V out . 
     Similar issues do not apply to the delay lines (for the proportional and derivative regulation), because even though the delays t d1  and t d2  may not be equal (e.g., due to an unequal common mode current), such an effect is compensated by the integral regulation and therefore does not contribute to the output offset. 
     In this respect, the offset introduced via such unmatched bias currents may also be rather significant. Accordingly, in order to reduce such a voltage offset, the bias current sources  2250  and  2252  should be matched. 
     For example, in various embodiments, the current sources  2250  and  2252  may be implemented via two output stages of the same current mirror, wherein the two output transistors of the current mirror are matched transistors. However, also in this case, the currents I BIAS+  and I BIAS−  may not be perfectly matched and, e.g., a trimming or calibration operation of the currents I BIAS+  and I BIAS−  may be required. 
     However, unfortunately, the nominal operating frequency F SW  of such a time-based regulator circuit should often be settable, e.g., programmable, which thus implies that also the current sources  2250  and  2252  should provide settable currents I BIAS+  and I BIAS− . For example, in various embodiments, the current generators  2250  and  2252  may be variable current generators, wherein the values of the currents I BIAS+  and I BIAS−  are settable/programmable, e.g., as a function of a digital or analog control signal. For example, in the context of a current mirror with two output transistors, the current fed to the input stage of the current mirror may be settable. 
     Such a programming may be required, e.g., due to changing operating conditions, and may often be performed also dynamically (i.e., on-the-fly, in real-time). This translates into an output regulation offset that usually changes with the operating frequency F SW . 
     Moreover, the current offset between the current sources  2250  and  2252  is usually process-voltage-temperature (PVT) dependent. Accordingly, a robust solution is required in order to avoid this uncontrolled output offset over various operating conditions of the regulator circuit  220   a.    
     In this respect, simply performing a trimming action to compensate such offset may thus be practically impossible, especially in case of multiple applicative scenarios as discussed above. Moreover, trimming solutions are, by definition, time consuming and add extra cost for the final test. Finally, a trimming solution usually is not robust and reliable, because it is an open-loop solution that does not take into account temperature variations, aging and all the other possible phenomena that may occur after the final testing (e.g., packaging and assembly, soldering, etc.). In addition, the discrete and finite nature of a trimming action usually does not permit to reach a zero residual error. 
       FIG.  13    shows an embodiment of a different solution. 
     As mentioned before, a mismatch between the current I BIAS+  and I BIAS−  usually cannot be avoided, in particular over all operation condition. 
     In the embodiment considered, the regulator circuit  220   a  is configured to perform an averaging operation of the bias currents provided to the current controlled oscillators  2220  and  2228 . Specifically, for this purpose is used a time-based averaging operation, wherein over a given time period the current I BIAS+  is provided for 50% to the current-controlled oscillator  2220  and for 50% to the current-controlled oscillator  2228 . Similarly, the current I BIAS−  is provided for 50% to the current-controlled oscillator  2228  and for 50% to the current-controlled oscillator  2220 . 
     For example, this is schematically shown in  FIG.  13   , wherein the current generators  2250  and  2252  are connected via a switching circuit  2254 , such as a butterfly switching circuit, to the output terminals of the differential transconductor  2236 , i.e., the input terminals of the current-controlled oscillators  2220  and  2228 . 
     Accordingly, as schematically shown in  FIG.  14   , such a switching circuit  2254  comprises four terminals, wherein: a terminal N 1  is connected to the positive output terminal of the transconductor  2236 /the current-controlled oscillator  2228 ; a terminal N 2  is connected to the negative output terminal of the transconductor  2236 /the current-controlled oscillator  2220 ; a terminal N 3  is connected to the current generator  2250 ; and a terminal N 4  is connected to the current generator  2252 . 
     Moreover, the switching circuit  2254  is configured to: in a first switching condition, connect the terminal N 1  to the terminal N 4 , i.e., the current generator  2252  to the oscillator  2228 , and the terminal N 2  to the terminal N 3 , i.e., the current generator  2250  to the oscillator  2220 ; and in a second switching condition, connect the terminal N 1  to the terminal N 3 , i.e., the current generator  2250  to the oscillator  2228 , and the terminal N 2  to the terminal N 4 , i.e., the current generator  2252  to the oscillator  2220 . 
     For example, as schematically shown in  FIG.  14   , the switching circuit  2254  may comprise for this purpose two deviator switches SW 1  and SW 2 . For example, a deviator switch be implemented with two electronic switches, such as FET. 
     As mentioned before, the switching between these two switching conditions should be performed based on the logic level of a PWM signal having a 50% duty cycle, such as a clock signal CLK. 
     In an embodiment of the implementation, averaging may be performed with a frequency, which remains outside of the bandwidth of the control loop, i.e., so that the averaging process should not influence the control-loop. It will be noted that the clock signal CLK should not be too high, in order to allow the currents provided to the oscillators  2220  and  2228  to correctly settle within half of the clocking period (at least). 
     In an example embodiment, the clock signal CLK may correspond to one of the clock signals already used within the regulator circuit  220   a , such as the clock signal CLK 1  or the clock signal CLK 2  generated by the oscillators  2220  and  2228 , respectively. In this respect, the selection of the clock signal CLK 1  or the clock signal CLK 2  is rather irrelevant, because in steady state, both clock signals should have the same frequency. Generally, the clock signal CLK may also correspond to a down-scaled version of the clock signal CLK 1  or CLK 2 , i.e., the clock signal CLK may be generated via a frequency divider receiving at input the clock signal CLK 1  or CLK 2 , whereby the period of the clock signal CLK is a multiple of the period of the clock signal CLK 1  or CLK 2 . 
     On the one hand, this avoids the need of an additional clock generator. On the other hand, this ensures that the averaging action is automatically performed according to the converter switching frequency F SW , which is usually also higher than the loop bandwidth. In this way, if the DC-DC converter supports different switching frequencies F SW  (i.e., different common-mode bias currents I BIAS+  and I BIAS−  feeding the oscillators  2220  and  2228 ), there is no need to recalibrate/retune the averaging action, because it remains automatically aligned with the DC-DC switching frequency F SW . 
     Accordingly, the proposed solutions allow to avoid mismatches and non-idealities of the common-mode current generators  2250  and  2252 , thus ensuring in steady state average values of the current I I−  and I I+ , which correspond, i.e., AVG(I I− )=AVG(I I+ ). As a consequence, the negative feedback loop does not need to provide any balancing action and therefore the (differential) current I I  provided by the transconductor  2236  remains zero in steady state (i.e., I I =0). This also implies that no offset is produced in the output voltage V out  due to this mismatch. 
     In various embodiments, the proposed solution is auto consistent and automatically performs the averaging action ensuring that, steadily, the output offset is zeroed. Being the solution based on an averaging operation, the output offset is cancelled irrespective of any PVT variation, aging, components derating or any other phenomena that may happen after the final test and packaging/assembly. Accordingly, the solution is robust with respect to the operating conditions, in particular the switching frequency F SW , the input and output voltages V in  and V out , and the values of the inductance(s) L 26  and capacitance(s) C 26  of the switching stage  26 , and loop compensation choices, in particular the gain G mI  of the transconductor  2236 . 
     It will be noted that the proposed solution has practically a zero impact on the quiescent current consumption (nor efficiency and neither power consumption). In fact, in various embodiments, the solution requires only the actuation of a butterfly switch  2254 , without the need of any other complex analog or digital circuits. Moreover, in various embodiments, also no separated clock signal CLK has to be generated. Accordingly, in terms of system complexity and area, basically there are no substantial difference with respect to an implementation without the proposed solution. 
     It will also be noted that the proposed solution not only improves the static performances of the converter, but also the dynamic performances. In fact, without a matching of the bias currents, the transconductor  2236  would remain unbalanced in steady state. Accordingly, the transconductor  2236  would be forced to operate in a bias condition that inherently exacerbates its non-linearity and emphasizes its non-idealities. Non-linearities within the loop negatively affect the whole DC-DC transient response and should be always minimized. Conversely, with the proposed averaging solution, the unbalancing of the transconductor  2236  due to different common-mode bias currents I BIAS+  and I BIAS−  for the oscillators  2220  and  2228  is mitigated, and therefore the system linearity is improved, as well as the converter transient response. 
     Finally, as mentioned before, the current generators  2250  and  2252  may be implemented as two output stages of the same current mirror. In this respect, the proposes solutions permit that this current mirror may have a less complex design, because also bigger mismatches between the output stages of the current mirror are compensated by the disclosed averaging operation. 
     Of course, without prejudice to the principle of the invention, the details of construction and the embodiments may vary widely with respect to what has been described and illustrated herein purely by way of example, without thereby departing from the scope of the present invention, as defined by the ensuing claims. 
     For example, while the previous embodiments have been described with respect to a PID regulator, the embodiments mainly relate to the implementation of the I component with the transconductor  2236  and the current-controlled oscillators  2220  and  2228 . Accordingly, the D and/or P components are purely optional. For example, this implies that one or even both of the transconductor  2238  and  2240  may be omitted. 
     Moreover, the solutions may also be applied to the PID regulator shown in  FIG.  8    by simply replacing the oscillators  2220  and  2228  with current controlled oscillators. For example, this implies that also voltage-controlled delay lines may be used. Moreover, instead of using differential amplifiers, also a single ended configuration may be used for one or more of the components P, I and D. 
     The claims form an integral part of the technical teaching of the description provided herein.