Average-current-mode control of two-input buck ... - Semantic Scholar
IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 46, NO. 3, JUNE 1999
569
Average-Current-Mode Control of Two-Input Buck Postregulators Used in Power-Factor Correctors Javier Sebasti´an, Member, IEEE, Pedro Jos´e Villegas, Member, IEEE, Marta Hernando, Member, IEEE, Fernando Nu˜no, Member, IEEE, and Francisco Fern´andez-Linera, Member, IEEE Abstract—The use of the average-current-mode control in the recently introduced two-input buck postregulator is studied in this paper. Using this type of control, the attenuation of the input voltage ripple (100–120 Hz) increases in relation to the one obtained when a conventional voltage-mode control (with or without feedforward) is used and, therefore, lower bulk capacitors can be used to obtain a very low voltage ripple at the output, which is very important when a battery is connected at the output. This is very common in distributed power supply systems. Index Terms— Average-current-mode control, power-factor correction, two-input buck postregulators.
I. INTRODUCTION
T
HE two-input buck (TIBuck) postregulator has been recently proposed as a postregulator to be used in several dc-to-dc and ac-to-dc converters [1]–[3]. Thus, using a TIBuck as a postregulator, a precise static and dynamic output voltage can be obtained in converters such as multiple-output switching-mode power supplies or power-factor correctors (PFC’s) (see Fig. 1). In the latter type of converters, the static output voltage is accurately regulated by a voltage feedback loop, but this output voltage exhibits poor dynamic regulation. This is due to the fact that a low-pass filter must be included in the output voltage feedback loop when the bulk capacitor used to remove the low-frequency ripple (100–120 Hz) is placed at the output [4]. To improve dynamic regulation and to decrease bulk capacitor size, several new topologies have recently been proposed [5]–[9]. The use of a TIBuck postregulator for the same purpose is also possible [1]–[3]. Table I summarizes its main characteristics. The very high efficiency achieved (96–99%) and the low voltage stress across semiconductors ) should be noted. (only One of the applications in which the structure “main twooutput PFC TIBuck” can be most useful is in distributed power supplies with batteries connected at the dc bus (see Fig. 2). In this case, the dc bus must exhibit a low voltage ripple in order to avoid battery damage. To have a low line voltage ripple at the output when two relatively small and ) have been used implies a bulk capacitors ( wide bandwidth in the TIBuck postregulator. Two ways to Manuscript received November 7, 1997; revised January 28, 1998. Abstract published on the Internet March 1, 1999. This work was supported by CICYT under Project TIC97-0936. The authors are with the Departamento de Ingenier´ıa El´ectrica, Electr´onica, de Computadores y Sistemas, Universidad de Oviedo, 33204 Gij´on, Spain (e-mail: [email protected]). Publisher Item Identifier S 0278-0046(99)04137-4.
increase this bandwidth are either to increase the switching frequency in order to diminish the TIBuck output filter or to explore new types of control strategies. The former decreases TIBuck efficiency because switching losses increase. On the other hand, an adequate choice of the control strategy can increase the bandwidth with no efficiency penalty. Thus, using a feedforward input voltage loop [2], [3], the output ripple obtained when only a classical output voltage loop had been used can be easily divided by two. The experimental results obtained in [2] and [3] show that the postregulator attenuates the voltage ripple by 20–30 dB. However, no more control strategies have been proposed in [1] and [3]. In this paper, the use of the average-current-mode control (ACMC) [10], [11] in the TIBuck postregulator is studied. Using this type of control, the line voltage ripple will be attenuated by 66 dB in a prototype (around 100 times more than with the above-mentioned control methods). II. A SHORT REVIEW OF ACMC APPLIED TO A BUCK CONVERTER Nowadays, two types of current-mode control are being widely used: peak-current-mode control (PCMC) and ACMC [11]. Comparing both control methods, ACMC exhibits better noise immunity, it does not need a compensating ramp, and it does not have peak-to-average-current error. The main drawbacks are that the current sensor to be used is slightly more complex and that there is a limit to loop gain at the switching frequency in order to achieve stability (the slopes of the waveforms applied to the two inputs of the pulsewidth modulation (PWM) comparator must be appropriately related). However, ACMC is becoming more and more popular. Fig. 3 shows a general scheme of the ACMC applied to a buck converter. The gain of the current loop error amplifier must be set in such a way that the amplified inductor current downslope at one input of the PWM comparator must not exceed the oscillator ramp slope at the other comparator input. This criterion puts an upper limit on the current at the switching frequency amplifier gain , indirectly establishing the maximum current loop . From [10] and [11], gain crossover frequency (1) (2) is the voltage-to-current gain of the current sensor, where is the oscillator ramp peak-to-peak voltage, and is the
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IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 46, NO. 3, JUNE 1999
(a)
(b)
(c)
(d) Fig. 1. Power-factor corrector proposed in [1]–[3]. (a) General scheme. (b) Two-output flyback push–pull TIBuck postregulator. (d) Two boost converters in parallel TIBuck postregulator.
+
+
+ TIBuck
postregulator. (c) Two-output current-fed
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BUCK
AND
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TABLE I TIBUCK CHARACTERISTICS.
Fig. 4. Equivalent circuit for a converter with ACMC.
Fig. 2. TIBuck postregulator used in a distributed power supply system, where a very low voltage ripple across the battery is required.
Fig. 5. ACMC in a TIBuck postregulator.
III. THE AVERAGE-CURRENT-MODE CONTROL APPLIED TO THE TIBUCK POSTREGULATOR Fig. 5 shows the basic diagram for the TIBuck postregulator with ACMC. In order to obtain a small-signal model of this converter, the same process as the one explained in [10] and [11] will be followed in this section. Thus, the average value of the input voltage of the output LC filter, , will be (5) This equation can be perturbed as follows: (6)
Fig. 3. ACMC in a buck converter.
converter duty cycle. The transfer function between the current control voltage and the current injected into the RC output cell (see Fig. 4), , can be written as follows [10], [11]: (3) where
where quantities with hats are the perturbed ones, whereas quantities in capitals are their steady-state values. From this equation, the main transfer functions of this converter can be found, as is going to be analyzed in the following sections. A. Transfer Function Between Control Voltage and Output Voltage In this case, both input voltages are assumed to be constant . Therefore, (6) becomes
is (4)
(7)
has a pole at It should be noted that . The transfer function between the current control and the output voltage , has another pole voltage due to the output RC cell. Finally, the at is the crossover frequency optimum design is achieved if and, from this condition and from (1), (2) can be easily obtained.
The perturbed value of the current passing through the inductor (and, therefore, injected into the RC output cell) is (8) is the input impedance of the LC output filter. where The perturbed duty cycle can be expressed as a function of
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IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 46, NO. 3, JUNE 1999
At lower frequencies, increases (as in the case of a has been designed with a pole at buck converter [12], being the crossover the origin and a zero at ). On the other hand, decreases frequency of (at least while it is inductive) and, therefore, [see Fig. 6(a)]. As a result, from (10), and and do not affect at these frequencies [see Fig. 6(c)]. Therefore, (10) and (12) lead to (13)
(a)
can be approached by a first-order function, Therefore, , as in as Fig. 7(a) shows, with a pole at the case of a buck converter. The only difference is the value expressed by (12) instead of (4). of Similarly, the transfer function between the control voltage and the output voltage , has another pole at due to the output RC cell [see Fig. 7(b)]. in the The condition for setting the crossover frequency ) is also valid case of the buck converter (that is, is here. The final expression for
(b)
(14) The inductor current downslope
for a TIBuck is given by (15)
(c) Fig. 6. Obtaining transfer function Gi (s). (a) Bode plots of Z (s); Req (s); and Z (s)=Req (s). (b) Error amplifier of the current loop. (c) Bode plots of Req (s)=Z (s) and Gi (s).
The criterion of the amplified inductor current downslope at one input of the PWM comparator being lower than the oscilator ramp slope at the other comparator input becomes and from (15)) (from Fig. 5, from the definition of (16)
the perturbed voltage as follows:
at the input of the PWM comparator (9)
is the oscillator ramp peak-to-peak voltage. From where Fig. 5 and from (7)–(9), the transfer function can be easily obtained (10) where
(see Table I), from the From (16), from the value of value of the crossover frequency and from (12), the relationship between and can be easily obtained (17) Therefore, the relationship between the same as in the buck converter.
and
in this case is
is given by (11)
and of the LC output filter [10] An adequate design of by . This is because allows us to approach can be approached by its inductive component at frequencies equals [at least in around the frequency in which is standard designs; see Fig. 6(a)]. At such frequencies, [see Fig. 6(b)] and, usually designed as a constant value becomes therefore, (12)
B. Transfer Functions Between Input Voltages and Output Voltage To calculate these transfer functions, only the input voltages and will be directly perturbed, whereas the control will be mantained constant . However, voltage the duty cycle will also be perturbed (although indirectly) will be due to the current feedback loop. Thus, the voltage expressed as a function of ˆı as follows: (18) From (6), (8), (9), and (18), the transfer functions between and can be easily the current and both input voltages
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(a)
(a)
(b) Fig. 7. Effects of approaching Z (s)=Req (s) by Ls=Reqc . (a) Bode plots of transfer function Gi (s). (b) Bode plots of transfer function Gvi (s).
calculated (19)
(20) As in the case of (10), (19) and (20) can be approached as follows: (21)
(b) Fig. 8. (a) Comparing Gv1 (s) and Gv2 (s) with Gvi (s). (b) Comparing Gv1 (s) with ACMC and with VMC.
(22) Therefore, these functions have a pole at . At frequencies below and become and and, from (11) and from Fig. 6(a), it can be easily deduced . Due to that they have a zero at the origin and a pole at and decrease when frequency this fact, both decreases, achieving very good immunity at low frequency. Finally, the transfer functions between the input voltages and and output voltage will be
(a)
(23) (b)
(24)
Fig. 9. Block diagram of a TIBuck postregulator with ACMC. (a) Basic diagram. (b) Diagram after moving the output RC cell before the summing junction.
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Fig. 10.
Prototype of a two-output flyback PFC
+
a TIBuck postregulator.
Fig. 12. Bode plots of
Fig. 11.
Bode plots of
Gi (s)
K Gvi (s)
(K =
020 7). :
.
These transfer functions have a zero at the origin, a pole at (both from the pole and zero, respectively), and and (at the same frequency as ). two poles at and plotted together. Fig. 8(a) shows
(a)
C. Block Diagram Fig. 9(a) shows the basic block diagram of the small-signal model of a TIBuck postregulator with ACMC. It should be noted that the current loop has been included in the model developed and, therefore, only the voltage feedback loop appears in this figure. By moving the position of the RC output cell before the summing junction, the block diagram shown in Fig. 9(b) can be easily obtained. IV. COMPARING OPEN-LOOP TRANSFER FUNCTIONS BETWEEN INPUT AND OUTPUT VOLTAGES WITH VOLTAGE-MODE CONTROL (VMC) AND ACMC The transfer functions between input and output voltages using VMC have been studied in [1] and [3]
(b) Fig. 13. Voltage ripple waveforms (output current 2.5 A). (a) Using VMC. (b) using ACMC.
with the feedback loop open, better natural immunity to input voltage variations is achieved using ACMC, as Fig. 8(b) shows. V. EXPERIMENTAL RESULTS
(25) (26) Comparing these transfer functions with the ones obtained with ACMC, (23), and (24), it can be easily deduced that,
The ACMC has been applied to the TIBuck postregulator used in a converter formed by a flyback PFC and the TIBuck postregulator (Fig. 10). Several experimental and theoretical transfer functions are shown in Figs. 11 and 12. Thus, the transfer function between the variations of the control voltage and the variations of the current injected into the RC output
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Fig. 14.
575
(a)
(b)
(c)
(d)
(e)
(f)
Transient response at different scales. (a)–(c) Using VMC. (d)–(f) Using ACMC.
cell (see Fig. 4) are shown in Fig. 11, whereas Fig. 12 shows the transfer function between the same control voltage and the output voltage. As Fig. 12 shows, the crossover frequency of is larger than 10 kHz. Both Bode plots have been obtained at the following conditions:
variations presented by the ACMC. The output current step was 3.67–1.85 A, 25 mA/ s.
VI. CONCLUSION W V
V V
The low-frequency voltage ripple at the inputs and at the output of the postregulator is given in Fig. 13(a) for the case of using VMC with feedforward (an attenuation of 26 dB has been achieved), whereas 66 dB of attenuation have been obtained using ACMC, as Fig. 13(b) shows. That means that the attenuation is 100 times higher using ACMC instead of VMC. Finally, the transient response using both types of control are shown in Fig. 14. As this figure shows, the transient response is very similar in both cases (similar bandwidth) and, however, the low-frequency output voltage ripple (lower trace in each figure) is much lower using ACMC than using VMC. This is a consequence of the natural immunity to the input voltage
The study of the ACMC applied to the TIBuck postregulator between the current shows that the transfer function has the same poles control voltage and the output voltage as the buck converter (two poles). The lower frequency pole is placed at the same frequency in both converters, whereas the frequency where the other pole is placed can be computed (buck) for the difference by changing the input voltage (TIBuck) in the definition between input voltages , (4) and (12). Moreover, the maximum crossover of in both buck and TIBuck converters can be frequency by the same expression, related to the switching frequency (2) and (17). The influence of the variations of the input voltages on the output votage has also been studied. This study shows that ACMC exhibits better behavior than VMC when the voltage feedback loop is open and, therefore, ACMC is “naturally” more immune than VMC to input voltage variations.
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In summary, the use of the ACMC applied to the TIBuck postregulator allows an important increase in the attenuation of the 100–120-Hz voltage ripple at the output. This attenuation permits a reduction in the size of both bulk capacitors to obtain very low output voltage ripples.
Javier Sebasti´an (M’87), for a photograph and biography, see this issue, p. 568.
Pedro Jos´e Villegas (M’96), for a photograph and biography, see this issue, p. 568.
REFERENCES [1] J. Sebasti´an, P. Villegas, F. Nu˜no, and M. M. Hernando, “Very efficient two-input dc-to-dc switching post-regulators,” in Proc. IEEE PESC’96, 1996, pp. 874–880. [2] J. Sebasti´an, P. Villegas, F. Nu˜no, O. Garc´ıa, and J. Arau, “Improving dynamic response of power factor preregulators by using two-input high-efficient post-regulators,” IEEE Trans. Power Electron., vol. 12, pp. 1007–1016, Nov. 1997. [3] J. Sebasti´an, P. Villegas, F. Nu˜no, M. M. Hernando, E. Ol´ıas, and J. Arau, “A study of the two-input dc-to-dc switching post-regulators,” in Proc. IEEE Int. Power Electronics Congr., 1996, pp. 35–45. [4] L. H. Dixon, “High power factor preregulators for off-line power supplies,” in Unitrode Power Supply Design Seminar, Unitrode Corp., Merrimack, NH, 1988, pp. 6.1–6.16. [5] M. Madigan, R. Erickson, and E. Ismail, “Integrated high quality rectifier-regulators,” in Proc. IEEE PESC’92, 1992, pp. 1043–1051. [6] R. Redl, L. Balogh, and N. Sokal, “A new family of single-stage isolated power-factor correctors with fast regulation of the output voltage,” in Proc. IEEE PESC’94, 1994, pp. 1137–1144. [7] M. H. Kheraluwala, R. L. Steigerwald, and R. Gurumoorthy, “A fastresponse high power factor converter with a single power stage,” in Proc. IEEE PESC’91, 1991, pp. 769–779. [8] Y. Jiang, F. C. Lee, G. Hua, and W. Tang, “A novel single-phase power factor correction scheme,” in Proc. IEEE APEC’93, 1993, pp. 287–292. [9] Y. Jiang and F. C. Lee, “Single-stage single-phase parallel power factor correction scheme,” in Proc. IEEE PESC’94, 1994, pp. 1145–1151. [10] D. O’Sulivan, H. Spruijt, and A. Crausaz, “Pulse-Width-Modulation (PWM) conductance control,” Eur. Space Agency J., vol. 13, no. 1, pp. 33–46, 1989. [11] L. H. Dixon, “Average current mode control of switching power supplies,” in Unitrode Power Supply Design Seminar, Unitrode Corp., Merrimack, NH, 1988, pp. 5.1–5.14. [12] L. H. Dixon, “Switching power supply control loop design,” in Unitrode Power Supply Design Seminar, Unitrode Corp., Merrimack, NH, 1991, pp. 7.1–7.10.
Marta Hernando (M’94), for a photograph and biography, see this issue, p. 568.
Fernando Nuno ˜ (M’96) was born in Pola de Siero, Spain, in 1963. He received the M.Sc. and Ph.D. degrees in electrical engineering from the University of Oviedo, Gij´on, Spain, in 1988 and 1991, respectively. From 1988 to 1993, he was an Assistant Professor at the University of Oviedo, where, since May 1993, he has been an Associate Professor. His research interests are switching-mode power supplies, resonant power conversion, modeling of magnetic devices, and high-power-factor rectifiers.
Francisco Fern´andez-Linera (M’96) was born in Cangas de Narcea, Spain, in 1966. He received the M.Sc. and Ph.D. degrees in electrical engineering from the University of Oviedo, Gij´on, Spain, in 1990 and 1997, respectively. He is currently an Assistant Professor at the University of Oviedo. His main interests are switchingmode power supplies, converter modeling, and digital control.
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Average-Current-Mode Control of Two-Input Buck Postregulators Used in Power-Factor Correctors Javier Sebasti´an, Member, IEEE, Pedro Jos´e Villegas, Member, IEEE, Marta Hernando, Member, IEEE, Fernando Nu˜no, Member, IEEE, and Francisco Fern´andez-Linera, Member, IEEE Abstract—The use of the average-current-mode control in the recently introduced two-input buck postregulator is studied in this paper. Using this type of control, the attenuation of the input voltage ripple (100–120 Hz) increases in relation to the one obtained when a conventional voltage-mode control (with or without feedforward) is used and, therefore, lower bulk capacitors can be used to obtain a very low voltage ripple at the output, which is very important when a battery is connected at the output. This is very common in distributed power supply systems. Index Terms— Average-current-mode control, power-factor correction, two-input buck postregulators.
I. INTRODUCTION
T
HE two-input buck (TIBuck) postregulator has been recently proposed as a postregulator to be used in several dc-to-dc and ac-to-dc converters [1]–[3]. Thus, using a TIBuck as a postregulator, a precise static and dynamic output voltage can be obtained in converters such as multiple-output switching-mode power supplies or power-factor correctors (PFC’s) (see Fig. 1). In the latter type of converters, the static output voltage is accurately regulated by a voltage feedback loop, but this output voltage exhibits poor dynamic regulation. This is due to the fact that a low-pass filter must be included in the output voltage feedback loop when the bulk capacitor used to remove the low-frequency ripple (100–120 Hz) is placed at the output [4]. To improve dynamic regulation and to decrease bulk capacitor size, several new topologies have recently been proposed [5]–[9]. The use of a TIBuck postregulator for the same purpose is also possible [1]–[3]. Table I summarizes its main characteristics. The very high efficiency achieved (96–99%) and the low voltage stress across semiconductors ) should be noted. (only One of the applications in which the structure “main twooutput PFC TIBuck” can be most useful is in distributed power supplies with batteries connected at the dc bus (see Fig. 2). In this case, the dc bus must exhibit a low voltage ripple in order to avoid battery damage. To have a low line voltage ripple at the output when two relatively small and ) have been used implies a bulk capacitors ( wide bandwidth in the TIBuck postregulator. Two ways to Manuscript received November 7, 1997; revised January 28, 1998. Abstract published on the Internet March 1, 1999. This work was supported by CICYT under Project TIC97-0936. The authors are with the Departamento de Ingenier´ıa El´ectrica, Electr´onica, de Computadores y Sistemas, Universidad de Oviedo, 33204 Gij´on, Spain (e-mail: [email protected]). Publisher Item Identifier S 0278-0046(99)04137-4.
increase this bandwidth are either to increase the switching frequency in order to diminish the TIBuck output filter or to explore new types of control strategies. The former decreases TIBuck efficiency because switching losses increase. On the other hand, an adequate choice of the control strategy can increase the bandwidth with no efficiency penalty. Thus, using a feedforward input voltage loop [2], [3], the output ripple obtained when only a classical output voltage loop had been used can be easily divided by two. The experimental results obtained in [2] and [3] show that the postregulator attenuates the voltage ripple by 20–30 dB. However, no more control strategies have been proposed in [1] and [3]. In this paper, the use of the average-current-mode control (ACMC) [10], [11] in the TIBuck postregulator is studied. Using this type of control, the line voltage ripple will be attenuated by 66 dB in a prototype (around 100 times more than with the above-mentioned control methods). II. A SHORT REVIEW OF ACMC APPLIED TO A BUCK CONVERTER Nowadays, two types of current-mode control are being widely used: peak-current-mode control (PCMC) and ACMC [11]. Comparing both control methods, ACMC exhibits better noise immunity, it does not need a compensating ramp, and it does not have peak-to-average-current error. The main drawbacks are that the current sensor to be used is slightly more complex and that there is a limit to loop gain at the switching frequency in order to achieve stability (the slopes of the waveforms applied to the two inputs of the pulsewidth modulation (PWM) comparator must be appropriately related). However, ACMC is becoming more and more popular. Fig. 3 shows a general scheme of the ACMC applied to a buck converter. The gain of the current loop error amplifier must be set in such a way that the amplified inductor current downslope at one input of the PWM comparator must not exceed the oscillator ramp slope at the other comparator input. This criterion puts an upper limit on the current at the switching frequency amplifier gain , indirectly establishing the maximum current loop . From [10] and [11], gain crossover frequency (1) (2) is the voltage-to-current gain of the current sensor, where is the oscillator ramp peak-to-peak voltage, and is the
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(a)
(b)
(c)
(d) Fig. 1. Power-factor corrector proposed in [1]–[3]. (a) General scheme. (b) Two-output flyback push–pull TIBuck postregulator. (d) Two boost converters in parallel TIBuck postregulator.
+
+
+ TIBuck
postregulator. (c) Two-output current-fed
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BUCK
AND
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TABLE I TIBUCK CHARACTERISTICS.
Fig. 4. Equivalent circuit for a converter with ACMC.
Fig. 2. TIBuck postregulator used in a distributed power supply system, where a very low voltage ripple across the battery is required.
Fig. 5. ACMC in a TIBuck postregulator.
III. THE AVERAGE-CURRENT-MODE CONTROL APPLIED TO THE TIBUCK POSTREGULATOR Fig. 5 shows the basic diagram for the TIBuck postregulator with ACMC. In order to obtain a small-signal model of this converter, the same process as the one explained in [10] and [11] will be followed in this section. Thus, the average value of the input voltage of the output LC filter, , will be (5) This equation can be perturbed as follows: (6)
Fig. 3. ACMC in a buck converter.
converter duty cycle. The transfer function between the current control voltage and the current injected into the RC output cell (see Fig. 4), , can be written as follows [10], [11]: (3) where
where quantities with hats are the perturbed ones, whereas quantities in capitals are their steady-state values. From this equation, the main transfer functions of this converter can be found, as is going to be analyzed in the following sections. A. Transfer Function Between Control Voltage and Output Voltage In this case, both input voltages are assumed to be constant . Therefore, (6) becomes
is (4)
(7)
has a pole at It should be noted that . The transfer function between the current control and the output voltage , has another pole voltage due to the output RC cell. Finally, the at is the crossover frequency optimum design is achieved if and, from this condition and from (1), (2) can be easily obtained.
The perturbed value of the current passing through the inductor (and, therefore, injected into the RC output cell) is (8) is the input impedance of the LC output filter. where The perturbed duty cycle can be expressed as a function of
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At lower frequencies, increases (as in the case of a has been designed with a pole at buck converter [12], being the crossover the origin and a zero at ). On the other hand, decreases frequency of (at least while it is inductive) and, therefore, [see Fig. 6(a)]. As a result, from (10), and and do not affect at these frequencies [see Fig. 6(c)]. Therefore, (10) and (12) lead to (13)
(a)
can be approached by a first-order function, Therefore, , as in as Fig. 7(a) shows, with a pole at the case of a buck converter. The only difference is the value expressed by (12) instead of (4). of Similarly, the transfer function between the control voltage and the output voltage , has another pole at due to the output RC cell [see Fig. 7(b)]. in the The condition for setting the crossover frequency ) is also valid case of the buck converter (that is, is here. The final expression for
(b)
(14) The inductor current downslope
for a TIBuck is given by (15)
(c) Fig. 6. Obtaining transfer function Gi (s). (a) Bode plots of Z (s); Req (s); and Z (s)=Req (s). (b) Error amplifier of the current loop. (c) Bode plots of Req (s)=Z (s) and Gi (s).
The criterion of the amplified inductor current downslope at one input of the PWM comparator being lower than the oscilator ramp slope at the other comparator input becomes and from (15)) (from Fig. 5, from the definition of (16)
the perturbed voltage as follows:
at the input of the PWM comparator (9)
is the oscillator ramp peak-to-peak voltage. From where Fig. 5 and from (7)–(9), the transfer function can be easily obtained (10) where
(see Table I), from the From (16), from the value of value of the crossover frequency and from (12), the relationship between and can be easily obtained (17) Therefore, the relationship between the same as in the buck converter.
and
in this case is
is given by (11)
and of the LC output filter [10] An adequate design of by . This is because allows us to approach can be approached by its inductive component at frequencies equals [at least in around the frequency in which is standard designs; see Fig. 6(a)]. At such frequencies, [see Fig. 6(b)] and, usually designed as a constant value becomes therefore, (12)
B. Transfer Functions Between Input Voltages and Output Voltage To calculate these transfer functions, only the input voltages and will be directly perturbed, whereas the control will be mantained constant . However, voltage the duty cycle will also be perturbed (although indirectly) will be due to the current feedback loop. Thus, the voltage expressed as a function of ˆı as follows: (18) From (6), (8), (9), and (18), the transfer functions between and can be easily the current and both input voltages
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(a)
(a)
(b) Fig. 7. Effects of approaching Z (s)=Req (s) by Ls=Reqc . (a) Bode plots of transfer function Gi (s). (b) Bode plots of transfer function Gvi (s).
calculated (19)
(20) As in the case of (10), (19) and (20) can be approached as follows: (21)
(b) Fig. 8. (a) Comparing Gv1 (s) and Gv2 (s) with Gvi (s). (b) Comparing Gv1 (s) with ACMC and with VMC.
(22) Therefore, these functions have a pole at . At frequencies below and become and and, from (11) and from Fig. 6(a), it can be easily deduced . Due to that they have a zero at the origin and a pole at and decrease when frequency this fact, both decreases, achieving very good immunity at low frequency. Finally, the transfer functions between the input voltages and and output voltage will be
(a)
(23) (b)
(24)
Fig. 9. Block diagram of a TIBuck postregulator with ACMC. (a) Basic diagram. (b) Diagram after moving the output RC cell before the summing junction.
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Fig. 10.
Prototype of a two-output flyback PFC
+
a TIBuck postregulator.
Fig. 12. Bode plots of
Fig. 11.
Bode plots of
Gi (s)
K Gvi (s)
(K =
020 7). :
.
These transfer functions have a zero at the origin, a pole at (both from the pole and zero, respectively), and and (at the same frequency as ). two poles at and plotted together. Fig. 8(a) shows
(a)
C. Block Diagram Fig. 9(a) shows the basic block diagram of the small-signal model of a TIBuck postregulator with ACMC. It should be noted that the current loop has been included in the model developed and, therefore, only the voltage feedback loop appears in this figure. By moving the position of the RC output cell before the summing junction, the block diagram shown in Fig. 9(b) can be easily obtained. IV. COMPARING OPEN-LOOP TRANSFER FUNCTIONS BETWEEN INPUT AND OUTPUT VOLTAGES WITH VOLTAGE-MODE CONTROL (VMC) AND ACMC The transfer functions between input and output voltages using VMC have been studied in [1] and [3]
(b) Fig. 13. Voltage ripple waveforms (output current 2.5 A). (a) Using VMC. (b) using ACMC.
with the feedback loop open, better natural immunity to input voltage variations is achieved using ACMC, as Fig. 8(b) shows. V. EXPERIMENTAL RESULTS
(25) (26) Comparing these transfer functions with the ones obtained with ACMC, (23), and (24), it can be easily deduced that,
The ACMC has been applied to the TIBuck postregulator used in a converter formed by a flyback PFC and the TIBuck postregulator (Fig. 10). Several experimental and theoretical transfer functions are shown in Figs. 11 and 12. Thus, the transfer function between the variations of the control voltage and the variations of the current injected into the RC output
´ et al.: AVERAGE-CURRENT-MODE CONTROL OF TIBUCK POSTREGULATORS USED IN PFC’S SEBASTIAN
Fig. 14.
575
(a)
(b)
(c)
(d)
(e)
(f)
Transient response at different scales. (a)–(c) Using VMC. (d)–(f) Using ACMC.
cell (see Fig. 4) are shown in Fig. 11, whereas Fig. 12 shows the transfer function between the same control voltage and the output voltage. As Fig. 12 shows, the crossover frequency of is larger than 10 kHz. Both Bode plots have been obtained at the following conditions:
variations presented by the ACMC. The output current step was 3.67–1.85 A, 25 mA/ s.
VI. CONCLUSION W V
V V
The low-frequency voltage ripple at the inputs and at the output of the postregulator is given in Fig. 13(a) for the case of using VMC with feedforward (an attenuation of 26 dB has been achieved), whereas 66 dB of attenuation have been obtained using ACMC, as Fig. 13(b) shows. That means that the attenuation is 100 times higher using ACMC instead of VMC. Finally, the transient response using both types of control are shown in Fig. 14. As this figure shows, the transient response is very similar in both cases (similar bandwidth) and, however, the low-frequency output voltage ripple (lower trace in each figure) is much lower using ACMC than using VMC. This is a consequence of the natural immunity to the input voltage
The study of the ACMC applied to the TIBuck postregulator between the current shows that the transfer function has the same poles control voltage and the output voltage as the buck converter (two poles). The lower frequency pole is placed at the same frequency in both converters, whereas the frequency where the other pole is placed can be computed (buck) for the difference by changing the input voltage (TIBuck) in the definition between input voltages , (4) and (12). Moreover, the maximum crossover of in both buck and TIBuck converters can be frequency by the same expression, related to the switching frequency (2) and (17). The influence of the variations of the input voltages on the output votage has also been studied. This study shows that ACMC exhibits better behavior than VMC when the voltage feedback loop is open and, therefore, ACMC is “naturally” more immune than VMC to input voltage variations.
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IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 46, NO. 3, JUNE 1999
In summary, the use of the ACMC applied to the TIBuck postregulator allows an important increase in the attenuation of the 100–120-Hz voltage ripple at the output. This attenuation permits a reduction in the size of both bulk capacitors to obtain very low output voltage ripples.
Javier Sebasti´an (M’87), for a photograph and biography, see this issue, p. 568.
Pedro Jos´e Villegas (M’96), for a photograph and biography, see this issue, p. 568.
REFERENCES [1] J. Sebasti´an, P. Villegas, F. Nu˜no, and M. M. Hernando, “Very efficient two-input dc-to-dc switching post-regulators,” in Proc. IEEE PESC’96, 1996, pp. 874–880. [2] J. Sebasti´an, P. Villegas, F. Nu˜no, O. Garc´ıa, and J. Arau, “Improving dynamic response of power factor preregulators by using two-input high-efficient post-regulators,” IEEE Trans. Power Electron., vol. 12, pp. 1007–1016, Nov. 1997. [3] J. Sebasti´an, P. Villegas, F. Nu˜no, M. M. Hernando, E. Ol´ıas, and J. Arau, “A study of the two-input dc-to-dc switching post-regulators,” in Proc. IEEE Int. Power Electronics Congr., 1996, pp. 35–45. [4] L. H. Dixon, “High power factor preregulators for off-line power supplies,” in Unitrode Power Supply Design Seminar, Unitrode Corp., Merrimack, NH, 1988, pp. 6.1–6.16. [5] M. Madigan, R. Erickson, and E. Ismail, “Integrated high quality rectifier-regulators,” in Proc. IEEE PESC’92, 1992, pp. 1043–1051. [6] R. Redl, L. Balogh, and N. Sokal, “A new family of single-stage isolated power-factor correctors with fast regulation of the output voltage,” in Proc. IEEE PESC’94, 1994, pp. 1137–1144. [7] M. H. Kheraluwala, R. L. Steigerwald, and R. Gurumoorthy, “A fastresponse high power factor converter with a single power stage,” in Proc. IEEE PESC’91, 1991, pp. 769–779. [8] Y. Jiang, F. C. Lee, G. Hua, and W. Tang, “A novel single-phase power factor correction scheme,” in Proc. IEEE APEC’93, 1993, pp. 287–292. [9] Y. Jiang and F. C. Lee, “Single-stage single-phase parallel power factor correction scheme,” in Proc. IEEE PESC’94, 1994, pp. 1145–1151. [10] D. O’Sulivan, H. Spruijt, and A. Crausaz, “Pulse-Width-Modulation (PWM) conductance control,” Eur. Space Agency J., vol. 13, no. 1, pp. 33–46, 1989. [11] L. H. Dixon, “Average current mode control of switching power supplies,” in Unitrode Power Supply Design Seminar, Unitrode Corp., Merrimack, NH, 1988, pp. 5.1–5.14. [12] L. H. Dixon, “Switching power supply control loop design,” in Unitrode Power Supply Design Seminar, Unitrode Corp., Merrimack, NH, 1991, pp. 7.1–7.10.
Marta Hernando (M’94), for a photograph and biography, see this issue, p. 568.
Fernando Nuno ˜ (M’96) was born in Pola de Siero, Spain, in 1963. He received the M.Sc. and Ph.D. degrees in electrical engineering from the University of Oviedo, Gij´on, Spain, in 1988 and 1991, respectively. From 1988 to 1993, he was an Assistant Professor at the University of Oviedo, where, since May 1993, he has been an Associate Professor. His research interests are switching-mode power supplies, resonant power conversion, modeling of magnetic devices, and high-power-factor rectifiers.
Francisco Fern´andez-Linera (M’96) was born in Cangas de Narcea, Spain, in 1966. He received the M.Sc. and Ph.D. degrees in electrical engineering from the University of Oviedo, Gij´on, Spain, in 1990 and 1997, respectively. He is currently an Assistant Professor at the University of Oviedo. His main interests are switchingmode power supplies, converter modeling, and digital control.
