Patent Publication Number: US-2019196388-A1

Title: Fixing apparatus, image forming apparatus, and fixing apparatus control method

Description:
The entire disclosure of Japanese patent Application No. 2017-244975, filed on Dec. 21, 2017, is incorporated herein by reference in its entirety. 
     BACKGROUND 
     Technological Field 
     The present invention relates to a fixing apparatus, an image forming apparatus, and a method for controlling the fixing apparatus. More specifically, the present invention relates to a fixing apparatus equipped with a fixing member including a heater as a heat source, and relates to an image forming apparatus, and a method for controlling the fixing apparatus. 
     Description of the Related Art 
     An electrophotographic image forming apparatus includes: a multi function peripheral (MFP) having a scanner function, a facsimile function, a copying function, a printer function, a data communication function, and a server function; a facsimile machine; a copying machine; and a printer. 
     An image forming method using a general image forming apparatus is as follows. The image forming apparatus charges a photoconductor using a charging apparatus and forms an electrostatic latent image on the photoconductor by using a laser beam generated from an exposure apparatus. The image forming apparatus uses a developing apparatus to develop the electrostatic latent image to form a toner image, and then uses a transfer roller to transfer the toner image to a sheet. The image forming apparatus uses the fixing apparatus to fix the toner image on the sheet so as to form an image on the sheet. 
     A heater (in particular, a halogen heater) for heating the fixing member (fixing roller and fixing belt) in the fixing apparatus has a property that the resistance value of the filament increases with a temperature rise. Accordingly, the resistance value of the filament is low in a state where the heater temperature is comparatively low immediately after power supply. For this reason, immediately after power is supplied to the heater, an inrush current several times as much as the rated current momentarily flows to the heater. Thereafter, the current flowing through the heater decreases with the temperature rise of the heater and converges to the rated current or less. The inrush current flowing immediately after power is supplied to the heater causes flicker (blinking phenomenon of light generated by a fluorescent lamp or the like). 
     In recent years, there is a rising demand for reducing the temperature warm-up time of the fixing apparatus from the viewpoint of reducing energy consumption and reducing the time before starting printing by the image forming apparatus. In order to reduce the warm-up time of the fixing apparatus, there is a trend to use a lower heat-capacity fixing member on the fixing apparatus. With the use of a lower heat-capacity fixing member, it is possible to warm up the fixing apparatus in a shorter time. On the other hand, however, it is difficult to store sufficient thermal energy in the fixing member, leading to an increased frequency of heater switching on/off. This results in a trend of recent image forming apparatuses having increasing frequency of occurrence of flicker. 
     Conventional techniques capable of suppressing inrush currents are disclosed in JP 2004-191710 A and JP 2011-81143 A, for example. JP 2004-191710 A proposes soft start by using phase control. JP 2004-191710 A discloses a technique of executing phase control of the AC power by using a soft start method at power-on of a heater that generates heat by using the power supplied from an AC power supply, and after continuous execution of the phase control for a predetermined time at a predetermined duty ratio, switching to half-wave control with the same duty ratio as the predetermined duty ratio. 
     JP 2011-81143 A proposes soft start by using pulse width modulation (PWM) control. JP 2011-81143 A discloses an image forming apparatus including: a fixing heater temperature detection unit for detecting the temperature of a fixing heater, a fixing heater temperature control unit for inputting a temperature control signal to an inverter circuit for driving a fixing heater, a switching duty change unit for changing the on-duty of the temperature control signal in synchronization with zero cross of an input power supply, and a switching frequency change unit for changing the frequency of the temperature control signal on the basis of a detection result of the fixing heater temperature detection unit. The duty of the input PWM signal is changed in synchronization with the zero cross of the input AC power supply and is changed every half cycle of the input AC power supply. 
     In JP 2004-191710 A and JP 2011-81143 A, an inrush current is suppressed by applying soft start being a control of gradually increasing the power to be supplied to the heater in accordance with the elapsed time from the start of the power supply to the heater. However, this technique has a problem that, in a case where soft start is implemented, it takes time to warm up the fixing apparatus because the power supplied to the heater is small immediately after the start of power supply. 
     SUMMARY 
     The present invention has been made to solve this problem, and an object of the present invention is to provide a fixing apparatus, an image forming apparatus, and a method for controlling a fixing apparatus, capable of reducing a warm-up time while suppressing an inrush current. 
     To achieve the abovementioned object, according to an aspect of the present invention, a fixing apparatus reflecting one aspect of the present invention comprises: a fixing member including a heater as a heat source; and a hardware processor that uses pulse width modulation (PWM) control to control power supplied to the heater; wherein the hardware processor changes a duty of the PWM control within a half cycle of an input current of the PWM control. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The advantages and features provided by one or more embodiments of the invention will become more fully understood from the detailed description given hereinbelow and the appended drawings which are given by way of illustration only, and thus are not intended as a definition of the limits of the present invention: 
         FIG. 1  is a cross-sectional view schematically illustrating a configuration of an image forming apparatus  1  according to a first embodiment of the present invention; 
         FIGS. 2A and 2B  are diagrams illustrating a configuration of a power controller  50  according to an embodiment of the present invention; 
         FIG. 3  is a diagram schematically illustrating a temporal change in a current flowing through a heater in a first comparative example; 
         FIG. 4  is a diagram schematically illustrating a temporal change in a current flowing through a heater in a second comparative example; 
         FIGS. 5A and 5B  are schematic diagrams respectively illustrating a temporal change in a current flowing in a heater in a first wave, and a temporal change in a duty in a first wave, according to an embodiment of the present invention; 
         FIG. 6  is a diagram schematically illustrating a temporal change in a current flowing through a heater according to an embodiment of the present invention; 
         FIG. 7  is a diagram illustrating a relationship between a value of the order n of a half cycle and a crest factor in each of an embodiment of the present invention example, the first comparative example, and the second comparative example; 
         FIG. 8  is a diagram illustrating a relationship between the order n of a half cycle and power supplied to a heater HT in each of an embodiment of the present invention example, the first comparative example, and the second comparative example; 
         FIG. 9  is a diagram illustrating a relationship between elapsed time from the start of power supply to the heater HT and the temperature of a fixing apparatus  40  in each of an embodiment of the present invention example and the second comparative example; and 
         FIG. 10  is a diagram schematically illustrating a plurality of relationships RL 1 , RL 2 , and RL 3  of elapsed time and duty within a half cycle of an input current stored in a storage  374  in a modification of one embodiment of the present invention. 
     
    
    
     DETAILED DESCRIPTION OF EMBODIMENTS 
     Hereinafter, one or more embodiments of the present invention will be described with reference to the drawings. However, the scope of the invention is not limited to the disclosed embodiments. 
     The following embodiments describe a case where the image forming apparatus on which the fixing apparatus is mounted is an MFP. The image forming apparatus on which the fixing apparatus is mounted may be a facsimile machine, a copying machine, a printer, or the like, other than an MFP, and may be for monochrome or color devices. 
       FIG. 1  is a cross-sectional view schematically illustrating a configuration of an image forming apparatus  1  according to a first embodiment of the present invention. 
     Referring to  FIG. 1 , the image forming apparatus  1  in the present embodiment is an MFP and can execute a copy job, a print job, a scan job, a fax job, a box job, or the like. The box job is a job executed by using data stored in a box (folder) provided in the image forming apparatus  1 . The image forming apparatus  1  mainly includes a sheet conveyance unit  10 , a toner image forming part  20  (an example of an image forming part), a fixing apparatus  40 , a scanner  45 , an auto document feeder (ADF)  46 , and a power controller  50 . The image forming apparatus  1  executes image formation on the basis of print settings. The print settings refer to a collection of setting values corresponding to a plurality of setting items related to image formation. 
     The sheet conveyance unit  10  conveys a sheet M (an example of a recording material) along conveyance paths TR 1  and TR 2 . The sheet conveyance unit  10  includes a plurality of sheet feeding trays  11   a  to  11   c , a sheet feeding roller  12 , a conveyance roller  13 , a registration roller  14 , and a sheet discharge roller  15 . The plurality of sheet feeding trays  11   a  to  11   c  each accommodates sheet on which an image is to be formed. There may be a plurality of sheet feeding trays or a single sheet feeding tray. The sheet feeding roller  12  is arranged between each of the sheet feeding trays  11   a  to  11   c  and the conveyance path TR 1 . The conveyance roller  13  and the registration roller  14  are provided along the conveyance path TR 1 . The sheet discharge roller  15  is provided at a most downstream portion of the conveyance path TR 1 . 
     The toner image forming part  20  combines images of four colors of yellow (Y), magenta (M), cyan (C), and black (K) by a tandem system to form a toner image on the sheet M conveyed. The toner image forming part  20  forms an image on the sheet M supplied from the sheet conveyance unit  10  on the basis of read data generated by the scanner  45  or print data obtained from the outside by an interface unit of the controller  37 . The toner image forming part  20  includes an image forming unit  21  for each of colors of Y, M, C, and K, an intermediate transfer belt  22 , a primary transfer roller  23  for each of colors of Y, M, C, and K, and a secondary transfer roller  24 . 
     The image forming unit  21  for each of the colors of Y, M, C, and K includes a photoconductive dram  25 , a charging apparatus  26 , an exposure apparatus  27 , a developing apparatus  28 , and a cleaning apparatus  29 . The photoconductive drum  25  is rotationally driven in a direction indicated by an arrow a in  FIG. 1 . The photoconductive drum  25  is surrounded by the charging apparatus  26 , the developing apparatus  28 , and the cleaning apparatus  29 . The exposure apparatus  27  is provided at a right-hand side of the photoconductive drum  25 . 
     The intermediate transfer belt  22  is provided at the left-hand side of the image forming units  21  of individual colors of Y, M, C, and K. The intermediate transfer belt  22  is annular, and is disposed across a rotating roller  22   a . The intermediate transfer belt  22  is rotationally driven in a direction indicated by an arrow in  FIG. 1 . Each of the primary transfer rollers  23  for each of colors of Y, M, C, K faces each of the photoconductive drums  25  with the intermediate transfer belt  22  interposed therebetween. The secondary transfer roller  24  is in contact with the intermediate transfer belt  22  in the conveyance path TR 1 . 
     The fixing apparatus  40  conveys a sheet M on which a toner image is formed while gripping the sheet M with a fixing nip, and thereby fixes the toner image on the sheet M. The fixing apparatus  40  includes a fixing roller  41  (an example of a fixing member) and a pressure roller  42 . The fixing roller  41  and the pressure roller  42  are pressed against each other to form a nip portion (fixing nip portion). The toner image is fixed by passing the sheet through the fixing nip portion. The fixing roller  41  internally includes a heater HT as a heat source of the fixing roller  41 . The heater HT includes a halogen heater, for example. 
     The scanner  45  is disposed between the ADF  46  and the toner image forming part  20 . The scanner  45  reads an image of the document conveyed by the ADF  46 , and generates read data. 
     The ADF  46  is provided above the scanner  45 . The ADF  46  automatically conveys the document placed on a document table  46   a  to a reading position of the scanner  45 . 
     The power controller  50  controls power to be supplied to each of members of the image forming apparatus  1 . 
     The image forming apparatus  1  rotates the photoconductive drum  25  to charge the surface of the photoconductive drum  25  with the charging apparatus  26 . The image forming apparatus  1  applies laser light by the exposure apparatus  27  onto a surface of the charged photoconductive drum  25  so as to form an electrostatic latent image on the surface of the photoconductive drum  25 . 
     Next, the image forming apparatus  1  supplies toner from the developing apparatus  28  to the photoconductive drum  25  on which an electrostatic latent image is formed, and then performs development so as to form a toner image corresponding to the electrostatic latent image, on the surface of the photoconductive dram  25 . 
     Next, the image forming apparatus  1  causes the primary transfer roller  23  to sequentially transfer the toner image formed on the photoconductive drum  25  to the surface of the intermediate transfer belt  22  (primary transfer). In the case of a full-color image, the image forming units  21  of individual colors of Y, M, C, and K operate in synchronized timings with each other, so as to form a toner image in which toner images of the individual colors of Y, M, C, and K are combined, on the surface of the intermediate transfer belt  22 . The image forming apparatus  1  causes the cleaning apparatus  29  to remove the toner remaining on the surface of the photoconductive drum  25  without being transferred to the intermediate transfer belt  22 . 
     Subsequently, the image forming apparatus  1  rotates the intermediate transfer belt  22  to convey the toner image formed on the surface of the intermediate transfer belt  22  to a position facing the secondary transfer roller  24 . 
     Meanwhile, the image forming apparatus  1  causes the sheet feeding roller  12  to feed a sheet accommodated in one of the sheet feeding trays  11   a  to  11   c  and causes the conveyance roller  13  to convey the sheet along the conveyance path TR 1 . The image forming apparatus  1  the causes the registration roller  14  to correct the tilt of the sheet and then guides the sheet to a portion between the intermediate transfer belt  22  and the secondary transfer roller  24  at a predetermined timing. Then, the image forming apparatus  1  causes the secondary transfer roller  24  to transfer the toner image formed on the surface of the intermediate transfer belt  22  to the surface of the sheet M. 
     The image forming apparatus  1  guides the sheet M on which a toner image is formed to the fixing apparatus  40 , and causes the fixing apparatus  40  to fix the toner image onto the surface of the sheet M. Thereafter, the image forming apparatus  1  causes the conveyance roller  13  to convey the sheet M on which the toner image is fixed, to the downstream side. 
     In the case of single-sided printing, the image forming apparatus  1  causes the sheet discharge roller  15  to discharge the sheet M having the toner image fixed on its surface as it is to the outside of the image forming apparatus  1 . In the case of duplex printing, the image forming apparatus  1  guides the sheet M having the toner image formed on its surface to a reversing path TR 2 . The image forming apparatus  1  guides the sheet M to the conveyance path TR 1  again from a joining position with the reversing path TR 2  provided on more toward the downstream side than the secondary transfer roller  24  in the conveyance path TR 1 . Thereafter, the image forming apparatus  1  causes the toner image forming part  20  to form a toner image on the back surface of the sheet M, causes the fixing apparatus  40  to fix the toner image on the back side of the sheet M, and causes the sheet discharge roller  15  to discharge the sheet to the outside of the image forming apparatus  1 . 
       FIGS. 2A and 2B  are diagrams illustrating a configuration of a power controller  50  according to an embodiment of the present invention.  FIG. 2A  is a circuit diagram illustrating a configuration of the power controller  50 .  FIG. 2B  is a block diagram illustrating a functional configuration of the controller  37 . 
     With reference to  FIGS. 2A and 2B , the power controller  50  includes a DC power control device  50   a , an AC power control device  50   b , and a controller  37  (an example of controller). 
     The DC power control device  50   a  includes a rectification input current detection circuit  60 , a zero cross detection circuit  62 , a capacitor input type rectifier circuit  65 , a switching circuit  68 , a transformer  70 , a diode  72 , a smoothing capacitor  74 , and a secondary side output circuit  76 . 
     The rectifier circuit  65  rectifies the AC power output from a AC power supply  200  (an example of a power supply) and outputs a resulting DC power to a load  78 . The rectifier circuit  65  includes: a bridge diode  64  formed with four diodes; and a smoothing capacitor  66 . 
     AC power output from the AC power supply  200  is full-wave rectified by the bridge diode  64  and smoothed by the smoothing capacitor  66 . A charging current Ic flows through the smoothing capacitor  66 . The output from the rectifier circuit  65  goes through the switching circuit  68 , the transformer  70 , the diode  72 , and the smoothing capacitor  74  to be adjusted to a stable DC voltage, and goes through the secondary side output circuit  76  to be output to the load  78 . 
     The rectification input current detection circuit  60  detects a current Ii 1  of the AC power output from the AC power supply  200  and input to the rectifier circuit  65 , and then, outputs a signal Sii 1  corresponding to the current Ii 1 , to the controller  37 . 
     The zero cross detection circuit  62  detects a timing at which the AC voltage Vi 1  output from the AC power supply  200  is switched between a positive value and a negative value, and outputs a signal Sz indicating the detection result to the controller  37 . 
     The AC power control device  50   b  outputs power obtained by performing PWM control of applying amplitude modulation on AC power from the AC power supply  200 , to the heater HT. The AC power control device  50   b  includes a rectifier circuit  81  (an example of a rectifier circuit), a filter  82 , a chopper circuit  83 , an ammeter  84  (an example of a current measurement part), a thermometer  85  (an example of a temperature detector). 
     The rectifier circuit  81  is connected to the AC power supply  200  and rectifies the AC current output from the AC power supply  200 . 
     The filter  82  is, for example, a H type filter, and is cascade-connected to the output side of the rectifier circuit  81 . The filter  82  includes a coil L 1  and capacitors C 1  and C 2 . The coils L 1  and L 2 , the heater HT, and a switching device  831  of the chopper circuit  83  are connected in series in this order. The capacitors C 1  and C 2  are connected in parallel to the heater HT. 
     The chopper circuit  83  is a step-down chopper circuit, for example, being cascade-connected to the output side of the filter  82 . The heater HT is connected between the output terminals of the chopper circuit  83 . The chopper circuit  83  includes a coil L 2  (an example of a reactor), a flyback device D 1 , a switching device  831 , and a drive circuit  832 . The chopper circuit  83  can operate (turning on/off) of the switching device  831  to control the current flowing through the heater HT. The coil L 2  is connected in series between the coil L 1  and the heater HT. The flyback device D 1  is a diode, for example, and is connected in parallel with the heater HT, at a position between the coil L 1  and the coil L 2 . More specifically, the cathode of the flyback device D 1  is connected between the coil L 1  and the coil L 2 , and the anode of the flyback device D 1  is electrically connected between the heater HT and the collector of the switching device  831 . The switching device  831  is, for example, an insulated gate bipolar transistor (IGBT) or a metal-oxide-semiconductor field-effect transistor (MOS-FET). A collector of the switching device  831  is connected to the heater HT, and an emitter of the switching device  831  is connected to the output side of the rectifier circuit  81 . 
     The drive circuit  832  is connected to a gate of the switching device  831 . The drive circuit  832  drives the switching device  831  under the control of the controller  37 . 
     The ammeter  84  is connected between the coil L 1  and the coil L 2 . The ammeter  84  is used to measure a value of an input current of the PWM control in a modification to be described below, and outputs the measured value to the controller  37 . 
     The thermometer  85  detects the temperature of the fixing roller  41  and outputs the detected temperature to the controller  37 . 
     The controller  37  uses the drive circuit  832  to control the operation of the switching device  831 , thereby controlling the power supplied to the heater HT by using the PWM control. The controller  37  includes a duty controller  371  (an example of a selection controller), a selector  372  (an example of a selector), a counter  373  (an example of a counter), a storage  374  (an example of a storage device). 
     The duty controller  371  sets the duty of the PWM control of the heater HT. 
     The selector  372  selects one relationship among a plurality of relationships between the elapsed time and the duty within the half cycle of the input current stored in the storage  374  in a modification described below. 
     The counter  373  counts the elapsed time from a point when the power supplied to the heater HT is most recently stopped in the modification described below. 
     The storage  374  stores various types of information such as the relationship between the elapsed time and the duty within the half cycle of the input current. 
     The controller  37  detects a half cycle of the input current of the PWM control by using the timing detected by the zero cross detection circuit  62 . The controller  37  sets the duty of the PWM control and the drive frequency of the switching device  831  on the basis of the detected half cycle, and transmits these setting values to the drive circuit  832 . The duty of the PWM control is set on the basis of a table stored in the storage  374 , the value of the input current of the PWM control measured by the ammeter  84 , the temperature of the fixing roller  41  measured by the thermometer  85 , or the like. 
     Subsequently, a method for controlling the power supplied to the heater HT in the present embodiment will be described in comparison with a comparative example. 
       FIG. 3  is a diagram schematically illustrating a temporal change in the current flowing through the heater HT in a first comparative example. In  FIGS. 3 to 6 , the rated power of the heater HT is 720 W, the rated voltage is 100V, and the rated current is 7.2 A. In the following description, the order of the half cycle of the input current of the PWM control from the start of the power supply to the heater HT will be represented as the n-th wave (n is a natural number). 
     Referring to  FIG. 3 , the first comparative example is an exemplary case where power is supplied to heater HT under the condition that the switching device  831  is constantly turned on (without control by the controller  37 ). A waveform LN 1  represents a current (periodically fluctuating DC current) flowing through the heater HT in the first comparative example, being the current corresponding to the input current of the PWM control in the present embodiment. A waveform LN 2  represents a steady current of the current flowing through the heater HT. 
     In the first comparative example, an inrush current with a high crest factor of 300% flows through the heater HT at the first wave immediately after power is supplied to the heater HT. The inrush current is attributed to the state immediately after power supply where the temperature of the heater HT is comparatively low and therefore the resistance value of the filament of the heater HT is low. In accordance with the lapse of time from the start of the power supply to the heater HT, the temperature of the filament rises and the resistance value of the filament increases, causing the crest factor of the current flowing through the heater HT to converge to 100%. In the ninth and subsequent waves, a rated current with a crest factor of 100% flows through the heater HT. 
     Note that the crest factor represents the ratio of the effective current flowing through the heater HT to the steady current of the PWM-controlled input current. 
       FIG. 4  is a diagram schematically illustrating temporal changes in the current flowing through the heater HT in a second comparative example. 
     Referring to  FIG. 4 , the second comparative example is an exemplary case where the power is supplied to heater HT under the condition (conventional PWM control condition) that performs soft start while keeping the duty within a half cycle of the input current of PWM control at a constant value. A waveform LN 3  represents a current flowing through the heater HT in the second comparative example. Since the duty within the half cycle of the input current of the PWM control is kept to a constant value in the second comparative example, the waveform LN 3  becomes the same sine wave as the waveform LN 1 . 
     In the second comparative example, the duty is set to 10% within the first wave. As a result, the crest factor in the first wave is 30%, and the power supplied to the heater HT in the first wave is 216 W. In the first and subsequent waves, the duty within the half cycle is increased to 15%, 20%, 28%, . . . , at each of timings when a time corresponding to a half cycle of the input current of the PWM control elapses. As a result, the crest factor within the half cycle increases to 35%, 40%, 47%, . . . , also increasing the power supplied to the heater HT. In the tenth wave and beyond, the duty within the half cycle is set to 100%. As a result, the crest factor of the tenth wave and thereafter is 100%, and the power supplied to the heater HT is 720 W. In the second comparative example, the total value of the power supplied to the heater HT (output voltage of the heater HT) during the time (first wave to tenth wave) until the inrush current converges to a steady current, is 4190 W. 
       FIGS. 5A and 5B  are schematic diagrams respectively illustrating a temporal change in a current flowing in the heater HT in a first wave and a temporal change in a duty in the first wave, according to an embodiment of the present invention.  FIG. 5A  is a diagram illustrating a temporal change in the current flowing through the heater HT within the first wave.  FIG. 5B  is a diagram schematically illustrating a relationship between the elapsed time and the duty in the first wave. Note that the length of the half cycle of the input current of the PWM control in  FIGS. 5A and 5B  is 10 ms. 
     With reference to  FIGS. 5A and 5B , the controller  37  in the present embodiment supplies power to the heater HT under a condition of performing soft start while varying the duty within a half cycle of the input current of the PWM control. The controller  37  maintains the crest factor within a half cycle of the input current of the PWM control to be constant and increases a lower limit value of the duty within the n-th wave in accordance with the increase of n. 
     Specifically, the controller  37  preliminarily stores a relationship RL ( FIG. 5B ) between the elapsed time and the duty within the half cycle of the input current into the storage  374 , and then sets the duty of the PWM control in accordance with this relationship. A waveform LN 4  represents a current flowing through the heater HT in the present embodiment. 
     In the present embodiment, the lower limit value of the duty is set to 10% within the first wave, and the duty is changed within the range of 10% to 100%. The change in the duty within the first wave is divided into the following first to fifth sections. 
     In the first section (section of elapsed time from 0 ms to 0.3 ms), the duty is set to a local maximum (here, 100%). The value of the sine wave input current (waveform LN 1 ) is low in this section, and thus, a large amount of current would not flow through the heater HT even when the duty is set to 100%. 
     In the second section (section of elapsed time from 0.3 ms to 5 ms), the duty is gradually decreased from the local maximum. Since the input current gradually increases in this section, the duty is decreased in accordance with the increase of the input current. 
     In the third section (section of elapsed time of 5 ms), the duty is set to a local minimum. In this section, the input current takes its local maximum, and thus, setting the duty to the lower limit value of 10% minimizes the current flowing through the heater HT. 
     In the fourth section (the section of elapsed time from 5 ms to 9.7 ms), the duty is gradually increased from the local minimum. Since the input current gradually decreases in this section, the duty is increased with the decrease of the input current. 
     In the fifth section (section of elapsed time of 9.7 ms to 10 ms), the duty is set to the local maximum (100% in the first wave). The value of the sine wave input current is low in this section, and thus, a large amount of current would not flow through the heater HT even when the duty is set to 100%. 
     As a result of the above control, the waveform LN 4  has a trapezoidal shape, and the crest factor of the first wave to the tenth wave is maintained at 30% which is the same as that of the second modification. Note that the crest factor in the half cycle need not necessarily be a constant value but may vary. 
       FIG. 6  is a diagram schematically illustrating a temporal change in a current flowing through the heater HT according to an embodiment of the present invention. 
     With reference to  FIG. 6 , in the present embodiment, the duty is set to 10% to 100% (the lower limit value of the duty is set to 10%) within the first wave. As a result, the crest factor in the first wave is 30%, and the power supplied to the heater HT in the first wave is 152 W. Even after the first wave, the PWM control is performed in a similar manner as the PWM control in the first wave illustrated in  FIG. 5B . In the first and subsequent waves, the lower limit value of the duty within the half cycle is increased to 15%, 20%, 28%, . . . , at a lapse of each of periods corresponding to a half cycle of the input current of the PWM control (in other words, the lower limit of the duty is increased in accordance with an increase of n). As a result, the crest factor within the half cycle increases to 35%, 40%, 47%, . . . , also increasing the power supplied to the heater HT. In the tenth and subsequent waves, the duty and crest factor within the half cycle are set to 100%. As a result, the power supplied to the heater HT after the tenth wave is 720 W. In the present embodiment, the total value of the power (output voltage of the heater HT) supplied to the heater HT during the time between first and tenth waves, which is the time until the inrush current converges to the steady current, is 5334 W, being 27% higher than in the second comparative example. 
     According to the present embodiment, it is possible to increase the output power of the heater HT while suppressing the crest factor in the half cycle of the input current of the PWM control to the level of the conventional soft start. As a result, it is possible to reduce the temperature warm-up time of the fixing apparatus  40  while suppressing the inrush current, achieving suppression of power consumption of the image forming apparatus. According to the present embodiment, it is possible to increase the output voltage of the heater HT by effectively utilizing the inrush current which rises and falls early as the current flowing to the heater HT. Hereinafter, effects of the present embodiment will be specifically described. 
       FIG. 7  is a diagram illustrating a relationship between a value of the order n of a half cycle and a crest factor in each of an embodiment of the present invention example, the first comparative example, and the second comparative example.  FIG. 8  is a diagram illustrating a relationship between the order n of a half cycle and power supplied to a heater HT in each of an embodiment of the present invention example, the first comparative example, and the second comparative example.  FIG. 9  is a diagram illustrating a relationship between elapsed time from the start of power supply to the heater HT and the temperature of a fixing apparatus  40  in each of an embodiment of the present invention example and the second comparative example. 
     Referring to  FIG. 7 , the crest factor within a half cycle of each of the first to tenth waves in an embodiment of the present invention is equal to the crest factor within a half cycle of each of the first to tenth waves in the second comparative example. From this result, it can be seen that the crest factor in the half cycle of the input current of the PWM control can be suppressed to the level of the conventional soft start, making it possible suppress the inrush current. 
     Referring to  FIG. 8 , the power supplied to heater HT in each of the first wave to the tenth wave in the present embodiment is higher than the power supplied to the heater HT in each of the first wave to the tenth wave in the second comparative example. From this result, it can be seen that the output power of the heater HT is successfully increased. 
     Referring to  FIG. 9 , the elapsed time from the start of the power supply to the heater HT to the time when the temperature of the fixing apparatus  40  reaches a target temperature is shorter by time AT in the embodiment of the present invention than in the second comparative example. From this result, it can be seen that the warm-up time of the fixing apparatus  40  is successfully reduced. 
     [Others] 
       FIG. 10  is a diagram schematically illustrating a plurality of relationships RL 1 , RL 2 , and RL 3  of elapsed time and the duty within a half cycle of an input current stored in the storage  374  in a modification of one embodiment of the present invention. Although the relationship within the first wave is simply illustrated in  FIG. 10 , each of the plurality of relationships RL 1 , RL 2 , and RL 3  is result of actually defining the relationship between the elapsed time until an inrush current converges to a steady current (period from the first wave to the tenth wave) and the duty within a half cycle of the input current. 
     Referring to  FIG. 10 , as an alternative method for setting the duty, the controller  37  may store the plurality of relationships RL 1 , RL 2 , and RL 3  of the elapsed time and the duty within the half cycle of the input current, into the storage  374 . 
     The controller  37  may use the selector  372  to select one of the plurality of relationships RL 1 , RL 2 , and RL 3  stored in the storage  374  on the basis of the temperature detected by the thermometer  85 , and may use the duty controller  371  to set the duty on the basis of the selected relationship. 
     Alternatively, the controller  37  may use the selector  372  to select one of the plurality of relationships RL 1 , RL 2 , and RL 3  stored in the storage  374  on the basis of the time counted by the counter  373  and may use the duty controller  371  to set the duty on the basis of the selected relationships. 
     Note that the lower the temperature detected by the thermometer  85  or the longer the time counted by the counter  373 , the higher the possibility of occurrence of greater inrush current. Accordingly, it is more desirable to select the relationship in which the duty is set to a lower value (corresponding to the relationship RL 3  among the relationships RL 1 , RL 2 , and RL 3 ). 
     As another modification, the controller  37  may set the duty of the PWM control on the basis of the value of the input current of the PWM control measured by the ammeter  84 . 
     The circuit configuration for implementing the PWM control of the heater HT may be other than those described above. The rectifier circuit may have any configuration, and it may be a half-wave rectifier circuit in addition to the full-wave rectifier circuit as in the above-described embodiment. The input current of the PWM control may be an AC current. 
     Although embodiments of the present invention have been described and illustrated in detail, the disclosed embodiments are made for purposes of illustration and example only and not limitation. The scope of the present invention should be interpreted by terms of the appended claims. The scope of the present invention is intended to include all modifications within the meaning and scope, which are equivalent to the scope of claims.