Method of regulating the supply voltage of a load and related voltage regulator

[0001] The present invention relates to voltage regulators, and more particularly to a method of regulation of the supply voltage of a load, a method of operating a regulator and a related voltage regulator.

[0002] Some types of electric loads are subject to rapid variations of the absorbed current. The variation may go from an almost null current to the nominal maximum current and vice versa. The regulator (generally a switching regulator) that supplies these loads must be capable of maintaining the regulated voltage in a pre-defined range of accuracy (dynamic precision), which is often very narrow. For instance, processors used in portable computers supplied by batteries mostly in a stand-by mode during which their consumption is relatively low and from which they resume operation when instructions must be carried out.

[0003] The commonly used regulators have a closed loop control of the output voltage V_OUT to ensure under steady state conditions, i.e. with a constant load, that the regulated voltage is equal to the desired voltage V_REF independently from the load and the input voltage of the regulator. Of course, during a load transient this is no longer true. The speed with which the regulator adjusts the output voltage to the desired voltage V_REF, depends on the type of control used by the regulator and on the characteristics of the power stage.

[0004] Regulators that implement a control with hysteresis of the output voltage, as the regulator depicted in FIG. 1, generally provide for the fastest response to a load transient and are the most commonly used. Because of the importance of these regulators, in the ensuing description reference will be made to regulators with hysteresis, but the discussion also applies to regulators without hysteresis. Moreover, it will be discussed in detail the operation of known regulators with a high side power switch (HS) that switches the inductor to the supply voltage source. However, this is influential in identifying the particular technical problem being addressed and which is present also in regulators of different topology (for instance step-up regulators) wherein the inductor is switched to ground by a low side (LS) switch instead of to the supply voltage source.

[0005] A comparator with hysteresis of the output voltage V_OUT and the reference voltage V_REF determines the turn on and the turn off of the switch HS of the branch toward the node at the highest potential of an output half-bridge. If a constant turn on time (T_ON) control is carried out, a comparator without hysteresis is used instead and the switch HS remains on for a fixed time T_ON once it is turned on, while in a constant turn off time (T_OFF) control mode, the comparator switches off the switch HS. The kinds of controls mentioned above contemplate also variants in which the equivalent voltage at the input of the comparator is the integral-proportional voltage error (V² control) or the sum of the integral-proportional error and of a voltage proportional to the current in the inductor (current-mode control).

[0006] In a so-called forced turn on control (or forced turn off), a clock signal is provided to the command logic CONTROL LOGIC that forces the turn on (the turn off) of the switch HS with a period T_S, while the turn off (turn on) instant is determined by the comparator. Sometimes a minimum turn on time T_ON,MIN (minimum turn off time T_OFF,MIN) of the switch HS is imposed. Typically, in these kinds of synchronous control a current mode control is implemented. A saw-tooth signal synchronous with the clock is usually applied to an input of the comparator for preventing sub-harmonic instability.

[0007] In a PWM control, a modulator varies the duty-cycle proportionally to a control (voltage) signal applied to an input thereof. The turn on of the switch HS is usually synchronous with an external clock. The voltage integral-proportional error is applied at the control input. These regulators are relatively slow at regulating the output voltage to its reference value after a load variation has occurred, because they are never capable of reacting sufficiently fast to a very fast load transient.

[0008] For these reasons, an output capacitor in parallel to the load is capable, within certain limits, of allowing for an abrupt increase of the current absorption of the load while limiting the error on the output voltage. In general, the output capacitor has a non-negligible parasitic series resistance ERS dependent on the capacitance of the output capacitor C_OUT. The corresponding time constant T_C=ESR·C_OUT depends on the type of capacitor (tantalum, ceramic, organic electrolytic, etc.) and is to a large extent independent of the capacitance.

[0009] The power switch (or switches) has also an influence, besides the controller, in determining the effective response speed of the regulator. There is in fact a limit to the speed (slew-rate limitation) of variation of the current that the output power stage may furnish to the electric parallel of the load and of the output capacitor. For instance, if the switch HS is turned on, the current i_L circulating in the inductor cannot increase at a speed greater than $\begin{array}{cc}\frac{d{i}_L}{dt}\le m_p=\frac{V_{\mathrm{IN}}-V_{\mathrm{OUT}}}{L}& \left(1\right)\end{array}$

• • [0010] while, if the switch HS is turned off, the current cannot fall at a speed smaller than $\begin{array}{cc}\frac{d{i}_L}{dt}\ge -m_m=-\frac{V_{\mathrm{OUT}}}{L}.& \left(2\right)\end{array}$

[0011] In a regulator with constant turn on time, phases of duration T_ON during which the switch HS is turned on alternate with phases of duration T_OFF,MIN during which the switch is turned off, thus the mean speed variation of the output current is $\begin{array}{cc}{m}_p=\left(T_{\mathrm{ON}}·\frac{V_{\mathrm{IN}}-V_{\mathrm{OUT}}}{L}-T_{\mathrm{OFF},\mathrm{MIN}}·\frac{V_{\mathrm{OUT}}}{L}\right)·\frac{1}{T_{\mathrm{ON}}+T_{\mathrm{OFF},\mathrm{MIN}}}.& \left(3\right)\end{array}$

[0012] If for example the output current undergoes to a step increase ΔI_OUT, the output voltage V_OUT drops abruptly by an amount equal to ESR·ΔI_OUT. Depending on the response speed of the regulator, the output voltage V_OUT may thereafter raise back to the reference voltage or continue falling. For instance, in a regulator with hysteresis (e.g. with a constant turn on time T_ON), if the voltage V_OUT is lower than the reference voltage, the output current I_OUT increases with a slope given by eq. 1 (eq. 3). The output voltage will not fall further if $\begin{array}{cc}{m}_p\ge \frac{\Delta I_{\mathrm{OUT}}}{\mathrm{ESR}·C_{\mathrm{OUT}}}.& \left(4\right)\end{array}$

[0013] FIG. 2 depicts the waveforms of the main signals of the regulator with hysteresis of FIG. 1 after a load increase, being:

• • [0014] ΔI_OUT=20A; L=1.2 μH; V_IN=12V; V_REF0.5V; ESR=4 mΩ;
  • [0015] hysteresis=20 mV; C_OUT=2 mF.

[0016] Eq. 4 is verified, thus the output voltage cannot fall more than ESR·ΔI_OUT. FIG. 3 is the response of the regulator of FIG. 1 after a load reduction of the same absolute value. By substituting m_m to m_p, eq. 4 is no longer satisfied, thus the overshoot exceeds ESR·ΔI_OUT. Indicating with ΔV_OUT,MAX the maximum variation of the output voltage and with ΔI_OUT,MAX the maximum variation of the output current, to satisfy the dynamic specifications the capacitance of the output capacitor must be such to ensure that $\begin{array}{cc}\mathrm{ESR}·\Delta I_{\mathrm{OUT},\mathrm{MAX}}\le \frac{1}{2}\Delta V_{\mathrm{OUT},\mathrm{MAX}}& \left(5\right)\end{array}$

• • [0017] wherein the voltage V_OUT must range between V_REF±ΔV_OUT,MAX/2.

[0018] The area occupied by the output capacitor C_OUT and the costs thereof (which are proportional to the capacitance, and inversely proportional to the parasitic resistance ESR) have a great importance in this kind of application. The so-called “voltage positioning” technique, often used for reducing the capacitance of the output capacitor, consists in modifying the controller so that the output resistance of the regulator under steady state conditions R_O is not null, and in choosing the reference voltage V′_REF: $\begin{array}{cc}{V}_{\mathrm{REF}}^{\prime }=V_{\mathrm{REF}}+\frac{\Delta V_{\mathrm{OUT},\mathrm{MAX}}}{2}.& \left(6\right)\end{array}$

[0019] In this way, the null load voltage is higher than the desired voltage V_REF while at maximum load, under steady state conditions, is lower.

[0020] If
R_O=ESR  (7)

• • [0021] then the static variation, i.e. the voltage variation after the load transient has terminated, is equal to the dynamic variation, i.e. the variation that immediately follows the load transient.

[0022] Finally, if an appropriate controller for making the regulator operate as a pure resistance of value ESR even under transient conditions is realized, that is for making the output impedance Z_OUT=ESR, then the variation of the output voltage after a step variation ΔI_OUT of the output current is a voltage step variation ESR·ΔI_OUT. An example of response of a regulator with Z_OUT=ESR is depicted in FIG. 6. The specifications of dynamic accuracy are now satisfied if
ESR·ΔI_OUT,MAX≦ΔV_OUT,MAX  (8)

[0023] Therefore, it is possible to use a capacitor whose capacitance is half the value of the previous evaluation.

[0024] The condition Z_OUT=ESR ensures that the output voltage V_OUT remains in the dynamic accuracy range even if two load transients, from zero to the maximum load and vice versa, occur in rapid succession. On the contrary, if R_O=ESR, these transients should be spaced by a time interval long enough to allow the output voltage V_OUT to stabilize itself. To have an output voltage with a step variation, the current in the inductor L must have an exponential profile with maximum slope ΔI_OUT,MAX/T_C at the transient instant. It is possible to have this kind of response only if the following equation, similar to eq. 4, is verified $\begin{array}{cc}\frac{\Delta I_{\mathrm{OUT},\mathrm{MAX}}}{\mathrm{ESR}·C_{\mathrm{OUT}}}\le m=\min \left(m_p,m_m\right).& \left(9\right)\end{array}$

[0025] A procedure for determining the capacitance of the output capacitor based on the above considerations is described in: Redl et al., “Optimizing the load transient of the buck converter” IEEE PESC 1998; Redl et al., “Cost-optimized design of the Pentium II converter for load transient specification” PCIM 1998-Tokio; Redl et al., Analog Devices, U.S. Pat. No. 6,064,187 May 16, 2000; and Redl et al., Analog Devices, U.S. Pat. No. 6,221,302 May 8, 2001. There are also several examples about how it may be possible to realize the regulator such that Z_OUT=ESR. In U.S. Pat. No. 6,064,187, a similar procedure is illustrated for the case in which, depending on the kind of the capacitor, the time constant T_C=ESR·C_OUT is too small to satisfy eq. 9. In this case it is not possible to have Z_OUT=ESR and Z_OUT is chosen such that $\begin{array}{cc}{Z}_{\mathrm{OUT}}=\mathrm{ESR}+\frac{R_O-\mathrm{ESR}}{1+{\mathrm{sR}}_O{C}_{\mathrm{OUT}}}& \left(10\right)\end{array}$

• • [0026] wherein R_O is the output resistance in steady state conditions, that must be greater than ESR, and s is the complex frequency. The consequence is that the response of the regulator to a variation ΔI_OUT,MAX is a voltage step whose amplitude is ESR·Δ_OUT,MAX followed by a further exponential increment as long as the value R_O·ΔI_OUT,MAX is finally reached.

[0027] Therefore, to satisfy the specifications on the maximum voltage variation ΔV_OUT,MAX it must be $\begin{array}{cc}{R}_O=\frac{\Delta V_{\mathrm{OUT},\mathrm{MAX}}}{\Delta I_{\mathrm{OUT},\mathrm{MAX}}}.& \left(11\right)\end{array}$

[0028] The current in the inductor has an exponential waveform but the maximum variation speed now is ΔI_OUT,MAX/R_O·C_OUT). It is then possible to choose the capacitor C_OUT such that the variation speed is equal to m, obtaining $\begin{array}{cc}{C}_{\mathrm{OUT}}=\frac{\Delta I_{\mathrm{OUT},\mathrm{MAX}}}{m·R_O}=\frac{\Delta V_{\mathrm{OUT},\mathrm{MAX}}}{m·R_O^2}.& \left(12\right)\\ & \end{array}$

[0029] For greater values of the capacitor C_OUT, a smaller slope will be obtained, thus eq. 12 gives the minimum value which is necessary and sufficient to satisfy the specifications. It is easy to verify that, with the chosen values, it is indeed ESR<R_O.

[0030] Generally, a regulator operates to nullify a comparison signal V_COMP that is determined in function of the output voltage V_OUT and of the current flowing in the inductor I_L through linear filtering operations. The comparison signal V_COMP is in general given by:
V_COMP=(V_OUT−V′_REF)·B(s)+R_SA(S)I_L  (13)

• • [0031] wherein s is the complex frequency and R_S is a sensing resistance in series to the inductor L. The sensing resistance may even be substituted by other circuit means capable of providing a voltage signal proportional to the current circulating in the inductor, for instance a circuit having an auxiliary winding magnetically coupled to the inductor. In this case the following formulas are valid, provided that R_S is the (constant) ratio between the voltage signal and the current circulating in the inductor L.

[0032] For sake of simplicity, in the ensuing description reference will be made to the case in which the voltage signal is generated by a sensing resistance (R_S).

[0033] The output impedance is given by: $\begin{array}{cc}\frac{1}{Z_{\mathrm{OUT}}}=\frac{V_{\mathrm{OUT}}-V_{\mathrm{REF}}^{\prime }}{I_{\mathrm{OUT}}}=\frac{C\left(s\right)}{R_S}+\frac{1}{\frac{1}{{\mathrm{sC}}_{\mathrm{OUT}}}+\mathrm{ESR}}& \left(14\right)\end{array}$

• • [0034] wherein $C\left(s\right)=\frac{B\left(s\right)}{A\left(s\right)}.$

[0035] In order to have Z_OUT=ESR it must be $\begin{array}{cc}C\left(s\right)=\frac{R_S}{\mathrm{ESR}}·\frac{1}{1+{\mathrm{sC}}_{\mathrm{OUT}}·\mathrm{ESR}}.& \left(15\right)\end{array}$

[0036] On the contrary, if C(s) is given by $\begin{array}{cc}C\left(s\right)=\frac{R_S}{R_O}·\frac{1}{1+{\mathrm{sC}}_{\mathrm{OUT}}·\mathrm{ESR}}& \left(16\right)\end{array}$

• • [0037] an output impedance Z_OUT given by eq. 10 is obtained.

[0038] It is worth noting that only the ratio B(s)/A(s) is determined, thus it is possible to choose B(s) or A(s).

[0039] A very simple way for obtaining a voltage drop proportional to the output current consists in connecting in series to the inductor and in cascade to the feedback input of the logic command circuit CONTROL LOGIC of the switches, a resistance equal to ESR. It is easy to notice that in this way it is not possible to satisfy the condition Z_OUT=ESR.

[0040] In U.S. Pat. No. 6,064,187 to Redl et al., many solutions are proposed, in which the coefficients A(s) and B(s) are $\begin{array}{cc}\{\begin{array}{c}A\left(s\right)=1\\ B\left(s\right)=\frac{R_S}{R_O}·\frac{1}{1+{\mathrm{sC}}_{\mathrm{OUT}}\mathrm{ESR}}\end{array}& \left(17\right)\end{array}$

• • [0041] and in which the resistance R_O is given by eq. 11 or by eq. 7. The comparator is input with a filtered and attenuated error signal and with the voltage read on the sensing resistor. Several examples are depicted in FIGS. 4 and 5. For example, the circuit of FIG. 5 satisfies eq. 17, with R_O given by eq. 7 or by eq. 11, if $\begin{array}{cc}\{\begin{array}{c}{C}_1\frac{1}{\frac{1}{R_1}+\frac{1}{R_2}}=\mathrm{ESR}·C_{\mathrm{OUT}}\\ \frac{R_1}{R_1+R_2}=\frac{R_S}{R_O}\end{array}.& \left(18\right)\end{array}$

[0042] If R_O=ESR, eq. 18 imposes that ESR be greater than R_S. In other words, an equivalent output resistance R_O equal to ESR is obtained using a sensing resistance R_S smaller than ESR. To reduce power dissipation, it is better to choose a small sensing resistance R_S, considering that R_S cannot be too small otherwise the voltage drop on it would be very low.

[0043] It is worth noting that hysteretic controls are stable and operate correctly when the ripple of the comparison signal V_COMP has a substantially triangular shape. From the above equations, this ripple V_COMP,R is given by $\begin{array}{cc}{V}_{\mathrm{COMP},R}=I_{\mathrm{RIPPLE}}·A\left(s\right)·R_S·\frac{1+{\mathrm{sR}}_O{C}_{\mathrm{OUT}}}{{\mathrm{sR}}_O{C}_{\mathrm{OUT}}}& \left(19\right)\end{array}$
wherein I_RIPPLE is the ripple of the current in the inductor, that generally varies according to a triangular waveform. If A(s)=1, to have a substantially triangular signal V_COMP, it is necessary that
R_OC_OUT>>T_S  (20)
where T_S is the switching period of switches.

[0044] A problem that burdens known regulators, independently from the position in respect to the supply voltage source of the switches that drive the inductor, consists in that the comparator has an offset voltage that reduces the accuracy with which the output voltage is regulated. The offset voltage considered, V_OFFSET,CMP, comprises the statistical offset, the delay effect of the comparator and an induced parasitic voltage due to the magnetic flux generated by the inductor through the circuit that generates the comparison signal V_COMP. The error on the output voltage caused by this offset voltage V_OFFSET,CMP is $\begin{array}{cc}\frac{R_O}{R_S}·V_{\mathrm{OFFSET},\mathrm{CMP}}.& \left(21\right)\end{array}$

[0045] To reduce the parasitic voltage, which is always present, the area of this circuit is reduced as much as possible and/or this circuit is moved away from the inductor. Both expedients complicate remarkably the realization of the regulator. Another type of inaccuracy of the known regulators is caused by the oscillations of signal V_COMP due to the oscillations of the current flowing in the inductor. Referring to a constant turn on time T_ON regulator, the power switch (or switches) is switched to nullify the lower peak of the voltage V_COMP. Therefore, the mean value of V_COMP is half the peak-to-peak amplitude of the ripple.

[0046] In prior art regulators implementing the voltage positioning according to eqs. 13 and 17, this implies an error on the mean value of the output voltage equal to ½·R_O·I_RIPPLE, in respect to the desired value V′_REF−R_O·I_O, equivalent to an error on the mean value of the current equal to ½·I_RIPPLE. Similar considerations may be done for synchronous and T_OFF constant controllers.

[0047] An object of the invention is to enhance the accuracy of known controllers. It has been found that disturbances on the signal V_COMP due to the magnetic field generated by the inductor, the offset of the comparator and the oscillations of the signal V_COMP do not produce any effect on the output voltage if the difference between the output voltage and the reference voltage is integrated. This happens because disturbances are eliminated if they manifest themselves as (equivalent) voltages superposed to the voltage V_COMP (that is if these voltages are introduced downstream of the integrator), independently from their mean value, because of the infinite DC gain of the integrator. Disturbances induced upstream of the integrator do not produce any output error because their mean value is zero.

[0048] An object of this invention is to provide a method of regulating the supply voltage of a load via a switching voltage regulator having an inductor driven by at least a power switch for delivering current to an output capacitor having a certain parasitic series resistance, connected between the output node of the regulator and ground and to an electric load eventually connected in parallel to the output capacitor. The method includes the operations of establishing a reference voltage, generating a comparison signal as the sum of a first voltage signal proportional to the current circulating in the inductor and of a second voltage signal depending on the difference between the output voltage and the reference voltage and on the first voltage signal, comparing the comparison signal with at least a threshold for generating a logic signal that switches between an active state and an inactive state and vice versa each time that the threshold is crossed, and commanding the turn on or the turn off of the switch as a function of the state of the logic signal. The second voltage signal is generated by integrating the sum between said first signal and the difference, scaled by a certain quantity, between the output voltage of the regulator and the reference voltage.

[0049] The method of the invention is implemented by defining accordingly the design functions A(s) and B(s). After having determined C_OUT in the known manner according to the above indicated criteria, the functions A(s) and B(s) are determined, according to this invention, as follows: $\begin{array}{cc}\{\begin{array}{c}A\left(s\right)=\frac{K_{\mathrm{INT}}}{S}+1\\ B\left(s\right)=\alpha \frac{K_{\mathrm{INT}}}{S}\end{array}& \left(22\right)\end{array}$
where $\begin{array}{cc}\{\begin{array}{c}{K}_{\mathrm{INT}}=\frac{1}{\mathrm{ESR}·C_{\mathrm{OUT}}}\\ \alpha =\frac{R_S}{R_O}\end{array}& \left(23\right)\end{array}$
with R_O given by eq. 7 or eq. 11. By substituting eqs. 22 in 23, eq. 13 may be rewritten in the form $\begin{array}{cc}\{\begin{array}{c}{V}_{\mathrm{COMP}}=V_{\mathrm{INT}}+R_S{I}_L\\ V_{\mathrm{INT}}=\frac{K_{\mathrm{INT}}}{S}·\left[\alpha \left(V_{\mathrm{OUT}}-V_{\mathrm{REF}}^{\prime }\right)+R_S{I}_L\right]\end{array}.& \left(24\right)\end{array}$

[0050] According to this invention, an integrator is introduced in the control circuit instead of the low-pass filter with finite DC gain that is used in the known circuits.

[0051] Another object of this invention is a switching voltage regulator comprising an inductor driven by at least a power switch, a logic control circuit of the switch, circuit means capable of generating a voltage signal proportional to the current flowing in the inductor according to a certain proportionality coefficient, an output capacitor having a certain parasitic series resistance connected between the output node and ground, second circuit means capable of generating an amplified and filtered error signal, and a comparator comparing the amplified and filtered error signal and the voltage signal proportional to the current flowing in the inductor and generating a logic signal applied to an input of the logic control circuit of the power switch.

[0052] The regulator of the invention reduces the effects on the regulated output voltage of disturbances that corrupts the error signal, because said circuit means comprise an integrator of the sum between the voltage signal and the difference, scaled by a certain quantity, between the output voltage and the reference voltage. The turn on or the turn off of the switch is commanded in function of the state of the logic signal according to whether a regulator with a constant turn on time or with a constant turn off time is implemented. In case of a constant turn on time (T_ON) control, the signal generated by the comparator forces the turning on while the turning off is forced by a timer of by a clock after a certain time T_ON from the turning on instant. In case of a constant turn off time (T_OFF) control, the comparator forces the turning off while the turning on is forced by a timer or a clock a certain time after the turning off instant. If the comparator has hysteresis, it will determine both the turn on and turn off instants. In case a clock signal is used to determine the turn on and/or the turn off instants, the comparator should be input also with a “slope compensation” signal.

[0065] Two embodiments of the regulator of this invention are depicted in FIGS. 7 and 8. For the purpose of illustrating how to realize a regulator according to the method of this invention, reference will be made to a step-down regulator. As will be evident to any skilled person, the illustrated circuits may be easily adapted to realize switching regulators of different topology, for instance regulators employing transformers as long as they employ an inductor driven in PWM mode to deliver current to an output capacitor and to a load eventually connected in parallel to the output capacitor.

[0066] A common feature of all the voltage regulator topologies is the presence of an inductance through which, at least during a phase of the cycle, stored energy is discharged towards an output buffer capacitor and thus towards the electric load. For example, in step-up regulators, the current I_SW injected in the output capacitor through a switch is the current that flows through the inductor during a discharge phase of the inductance. The invention is directly applicable to step-up regulators whenever the control process contemplates that the comparator determines the start of a charge phase of the inductor, for example with a constant turn on time T_ON. In case of a constant turn off time T_OFF mode, the voltage V_COMP may be generated according to the following relations $\begin{array}{cc}\{\begin{array}{c}{V}_{\mathrm{COMP}}=R_S{I}_L+V_{\mathrm{INT}}\\ V_{\mathrm{INT}}=\frac{K_{\mathrm{INT}}}{S}\left(\alpha \left(V_{\mathrm{OUT}}-V_{\mathrm{REF}}^{\prime }\right)+R_S{I}_{\mathrm{SW}}\right)\end{array}.& \left(24b\right)\end{array}$

[0067] The parameters R1, R2, g_m, C_INT are preferably chosen such that $\begin{array}{cc}\{\begin{array}{c}\frac{g_m}{C_{\mathrm{INT}}}=\frac{1}{\mathrm{ESR}·C_{\mathrm{OUT}}}\\ \frac{R_1}{R_1+R_2}=\frac{R_S}{R_O}\end{array}.& \left(25\right)\end{array}$

[0068] In the case in which the error amplifier g_m of the mentioned figures is capable of supplying a maximum current ±I_INT,MAX, it must be ensured that $\begin{array}{cc}\frac{I_{\mathrm{INT},\mathrm{MAX}}}{C_{\mathrm{INT}}}>R_S\frac{\Delta I_{\mathrm{OUT},\mathrm{MAX}}}{R_O{C}_{\mathrm{OUT}}}& \left(26\right)\end{array}$
to make the current flowing in the inductor vary with the desired speed.

[0069] Now the ripple of the signal V_COMP is given by $\begin{array}{cc}{V}_{\mathrm{COMP},R}=I_{\mathrm{RIPPLE}}·R_S\frac{1+{\mathrm{sR}}_O{C}_{\mathrm{OUT}}}{{\mathrm{sR}}_O{C}_{\mathrm{OUT}}}·\frac{1+{\mathrm{sT}}_C}{{\mathrm{sT}}_c}.& \left(27\right)\end{array}$

[0070] For reasons of stability, it must be
T_C>>T_S  (28)

[0071] This condition is more restrictive of the condition R_OC_OUT>>T_S required by known regulators, but it is satisfied for all kinds of commonly used capacitors (e.g. tantalum capacitors) as output capacitors.

[0072] Optionally, the regulators of FIG. 7 or 8 may be provided with a clamping device CLAMP for limiting the product R_S·I_L and, as a consequence also the current delivered by the regulator to the parallel of the output capacitor C_OUT and the load. In this way, the first addend of eq. 24 is prevented from exceeding certain bounds, thus avoiding excessive undervoltages or overvoltages in situations such as the turning on of the regulator or the changing of the reference voltage (an event that is contemplated for certain types of microprocessors and typically carried out with a null load). In general, the clamping device CLAMP is useful in all these conditions in which the current in the inductor increases at the maximum allowed speed, that is in slew-rate conditions.

[0073] The lower threshold of intervention of the clamp determines the current with which the regulator discharge C_OUT when the reference voltage is reduced, and thus must be negative, while the upper threshold of intervention must be positive and greater than the product R_S·I_OUT,MAX. The latter limit depends from the maximum current I_OUT,MAX that is delivered for instance in the case of a short-circuit of the output or when the reference voltage is increased. In any case, the intervention thresholds of the clamp must be fixed so that it does not intervene during a load transient.

[0074] It is possible to obtain a limitation of the maximum positive and negative current that may flow in the inductor even by employing comparators of maximum positive and negative current, respectively, not shown in the figure. In this case, the intervention thresholds of the clamp must define a range that contains the range of variation determined by the maximum and minimum current comparators.

[0075] In general, eq. 27, modified to take into account the presence of the clamp, becomes
V_COMP=V_INT+R_SI_L  (29)

• • [0076] wherein V_INT is $\begin{array}{cc}{V}_{\mathrm{INT}}=\frac{K_{\mathrm{INT}}}{S}\left[\alpha \left(V_{\mathrm{OUT}}-V_{\mathrm{REF}}^{\prime }\right)+R_S{I}_L-F_{\mathrm{CLAMP}}\left(V_{\mathrm{INT}}\right)\right].& \left(30\right)\end{array}$

[0077] A switching regulator may operate in continuous current mode (CCM), in which the current in the inductor is never null, or in discontinuous current mode (DCM) in which for a certain time interval the current is null. FIGS. 9 and 10 show waveforms of the current flowing in the inductor and of the output voltage in the case of a constant turn-on time TON control in both situations. For a discontinuous control mode, it is necessary to use a zero-cross comparator (not shown in FIGS. 7 and 8) that turns off the switch LS when the current flowing in it becomes null.

[0078] The discontinuous current mode (DCM) intervenes under low load conditions, that is when the current in the inductor is smaller than I_RIPPLE/2, being I_RIPPLE the peak-to-peak amplitude of the current ripple in the inductor in the continuous current mode (CCM). In case of a constant turn-on time TON control, the switching frequency in DCM is reduced in respect to the frequency in CCM when the load diminishes, allowing for an increase of the efficiency of the regulator under low load conditions. In DCM, the current provided to the parallel of the output capacitor C_OUT and the load cannot be negative. Therefore, it is convenient to make the regulator work temporarily in CCM if the reference voltage must be lowered and if the load is very low.

[0079] The circuit of FIG. 7 or of FIG. 8 may operate in DCM with constant turn on time T_ON, but not with constant turn off time T_OFF. In DCM, with a very low load, the interval in which I_L=0 is rather long and the integral at the right side of eq. (30) assumes even larger negative values. This may slow the response to a load transient if it takes place during this interval. To prevent this inconvenience it is preferable to choose the lower threshold of the clamp equal to zero or negative with a relatively small absolute value. On the contrary, if the inductor is driven in CCM even at low load (for instance, to change the reference voltage), the lower intervention threshold of the clamp must be negative to ensure that the current in the inductor may be negative and of sufficiently high level to discharge rapidly the output capacitor C_OUT.

[0080] FIGS. 11 and 12 are diagrams of the main signals of the circuit of FIG. 8 in discontinuous current mode at very low load, for a constant turn on time T_ON control with the following electrical parameters:

• • [0081] L=0.6 μH; V_IN=12V; R_S=1.5 mΩ; ESR=2 mΩ; resistance of the clamp≈0.5/g_m; C_OUT=2 mF.

[0082] It may be noted that the lower peak of the output voltage V_OUT is regulated at the voltage V′_REF, given by eq. 6, thus the output voltage V_OUT is slightly greater than V′_REF. This fact must be taken into account when choosing the reference voltage V′_REF. In these conditions, the control behaves as the known ones.

[0083] Lowering the frequency at low load conditions in a constant turn off time T_OFF control or in a forced turn on synchronous control, is more complicated than described above. For instance, DCM functioning in case of a synchronous control keeps constant the frequency while reducing the peak current. For this reason DCM driving is not able per se to ensure a high efficiency under low load conditions, even if at a constant frequency and at low load it is more efficient than the CCM mode. In this case, when the load current is smaller than a certain threshold, it is possible to let the regulator operate in burst mode, that is with intervals in which the regulator operates in CCM (or DCM) forcing the current in the inductor equal to the threshold value, alternate with intervals in which the current is null (there are not any switchings).

[0084] To this end, it is possible to choose a positive upper intervention threshold corresponding to the load threshold. The switched driving mode is stopped or resumed by a hysteresis comparator of the quantity F_CLAMP(V_INT) defined hereinbefore. In the circuits of this invention, such a comparator compares the current flowing in the clamp with two suitable thresholds.

[0085] The advantages of the circuits made according to this invention derive from the high (theoretically infinite) DC gain of the integrator that eliminates the effects on the output of the offset of the comparator and of the current ripple. The integrator, that may be realized with a transconductance amplifier loaded with an integration capacitance, and the clamp are components that are commonly present in classic V² or current-mode controls wherein the present invention may be readily implemented. The regulator of the invention solves the technical problems of inaccuracy caused by the offset of the comparator. As stated before, in known regulators the error on the output voltage V_OUT, in respect to the reference, due to the offset voltage V_OFFSET,CMP is given by: $\begin{array}{cc}\frac{R_O}{R_S}·V_{\mathrm{OFFSET},\mathrm{CMP}}& \left(21\right)\end{array}$
This offset voltage is due to many causes, such as the statistical offset, the effect of the delay of the comparator and the induced parasitic voltage.

[0086] Statistical offset and delay are generally tied to each other, that is a comparator designed to have a reduced statistical offset, has in general a relatively high delay time. Conversely, the offset of the integrator, which influences the output according to an equation similar to eq. 21, may be made (almost) arbitrarily small because there are not particular speed constraints in the design of the integrator.

[0087] According to this invention, the error I_RIPPLE/2 present in known regulators with constant turn on time T_ON control is eliminated by the presence of the integrator. The improvements in terms of accuracy that are accomplished by the invention tend to vanish when the load becomes very low and the regulator operates in discontinuous mode, because of the intervention of the clamp. However, in these cases, the equivalent offset due to the delay of the comparator is minimum while the offset due to the induced voltage is null.

[0088] FIG. 13 compares the voltage-current characteristics of a regulator of this invention and of a known regulator controlled with constant turn on time T_ON. The dash line curves refer to a DCM control while the continuous line curves refer to a CCM control. The curve 1 is that of a regulator of this invention. It reproduces the ideal conditions in which
V_OUT=V′_REF−R_OUT·I_OUT  (31)
The curve 2 corresponds to that of a known regulator, in which precautionary measures have been taken to nullify the offset and the voltage that the inductor induces in the circuit that generates the signal V_COMP: the voltage E_RIPPLE is the difference between these two characteristics and is equal to ½ESR·I_RIPPLE, corresponding to an error on the measured current equal to ½I_RIPPLE.

[0089] The curve 3 is the voltage-current characteristic of a known regulator in which these precautionary measures have not been taken. As it is possible to notice, in this last case the curve 3 exceeds the curve 2 by a quantity corresponding to the offset voltage E_OFFSET. The curve 4 is a voltage-current characteristic of a regulator of the invention having a minimum current clamp with a threshold corresponding to a null output current and a resistance equal to the inverse of the transconductance of the integrator. The curve 4 accounts for only the ripple effect on the current, while the curve 5 accounts for also the offset voltage, the delay and the induced voltage.

[0090] These voltage-current curves may be compared with the corresponding characteristics 6 and 7 of known regulators. As noted above, there are not accuracy improvements in respect to the known regulators when the regulator functions in discontinuous mode and the load is very low. However, when the load increases the voltage-current characteristic of the regulator of this invention tends to the ideal curve 1, while the characteristics of the known regulators remain far from it.