Patent Publication Number: US-2021165366-A1

Title: Humidity detection device and image forming apparatus

Description:
TECHNICAL FIELD 
     The present invention relates to a humidity detection device and an image forming apparatus. 
     BACKGROUND 
     A humidity detection circuit described in Patent Document 1 detects a humidity based on divided voltages between a humidity sensor element and a resistor. Further, a humidity detection device described in Patent Document 2 detects a humidity by utilizing a logarithmic characteristic of a relationship between a forward voltage of a diode and a current. 
     RELATED ART 
     Patent Document(s) 
     
         
         [Patent Doc. 1] JP Laid-Open Patent Application Publication 2009-180560 
         [Patent Doc. 2] JP Laid-Open Patent Application Publication S58-179344 
       
    
     SUBJECT(S) TO BE SOLVED 
     Conventionally, in the case where a humidity is detected based on a divided voltage between a humidity sensor element and a resistor, since an impedance of the humidity sensor element increases exponentially as the humidity decreases, there is a problem that detection accuracy of a low humidity is poor. 
     Further, in the case of utilizing a logarithmic characteristic of a relationship between a forward voltage of a diode and a current, although the detection accuracy of a low humidity is improved, the forward voltage of the diode is not constant due to manufacturing variations. Therefore, for example, a voltage can be obtained with an error of ±1% in class F in a case of a resistor, whereas an error of a forward voltage of a diode becomes large, and, as compared to the case where a humidity is detected based on a divided voltage between a humidity sensor element and a resistor, there is a problem that detection accuracy of a high humidity is poor. 
     Therefore, one or more aspects of the present invention are intended to prevent deterioration in detection accuracy at a high humidity and to enable detection from a high humidity to a low humidity. 
     SUMMARY 
     A humidity detection device, disclosed in the application, includes; a humidity sensor that detects a humidity; having at least two sides to be connected, a resistor that is connected to one-side of the humidity sensor; a first switching part that switches between an ON state and OFF state, and is connected to the resistor; a diode that is connected to the first switching part; a second switching part that switches between ON state and OFF state, and is connected to the other-side of the humidity sensor; a potential difference generating part that is connected to the second switching part; a power supply that supplies a voltage, and a control part that applies the voltage from the power supply as an alternating voltage to the humidity sensor by controlling the first switching part and the second switching part, wherein the control part applies a current to the diode, the resistor and the humidity sensor in a first direction by connecting the second switching part to the ground, and applies the current to the resistor and the humidity sensor in a second direction, which is an opposite direction from the first direction, by connecting the first switching part to the ground. 
     An image forming apparatus, disclosed in the application, includes the humidity detection device discussed above. 
     According to one or more aspects of the present invention, it is possible to prevent deterioration in detection accuracy at a high humidity and to perform detection from a high humidity to a low humidity. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a configuration diagram of image forming apparatuses according to first-third embodiments. 
         FIG. 2  is a block diagram of control circuits of the image forming apparatuses according to the first-third embodiments. 
         FIG. 3  is a circuit diagram of a temperature and humidity sensor in the first embodiment. 
         FIG. 4  is a flow diagram illustrating an operation of calculating an impedance of a humidity sensor in the first embodiment. 
         FIG. 5  is a schematic diagram illustrating an example of an impedance table. 
         FIG. 6  is a schematic diagram illustrating waveforms of a PWM signal, an inverted PWM signal and a HUM signal, and AD conversion timing in the first and second embodiments. 
         FIG. 7  is a circuit diagram of a temperature and humidity sensor in the second embodiment. 
         FIG. 8  is a flow diagram illustrating an operation of calculating an impedance of a humidity sensor in the second embodiment. 
         FIG. 9  is a schematic diagram in which an approximate expression of a forward voltage of a diode at each temperature is illustrated. 
         FIG. 10  is a circuit diagram of a temperature and humidity sensor in the third embodiment. 
         FIG. 11  is a schematic diagram illustrating waveforms of a PWM signal, an inverted PWM signal and a HUM signal, and AD conversion timing in the third embodiment. 
         FIG. 12  is a circuit diagram illustrating a modified embodiment of the temperature and humidity sensor in the third embodiment. 
     
    
    
     BRIEF DESCRIPTION OF THE PREFERRED EMBODIMENT(S) 
     First Embodiment 
       FIG. 1  is a configuration diagram of an image forming apparatus  100  according to a first embodiment. The image forming apparatus  100  is, for example, an image forming apparatus of a color electrophotographic direct transfer type. In the first embodiment, the image forming apparatus  100  forms black, magenta, yellow and cyan images. In the following description, “K” is added to a reference numeral symbol indicating an element for forming a black image; “M” is added to a reference numeral symbol indicating an element for forming a magenta image; “Y” is added to a reference numeral symbol indicating an element for forming a yellow image; and “C” is added to a reference numeral symbol indicating an element for forming a cyan image. 
     The development unit cartridges  101 K,  101 Y,  101 M,  101 C each form a toner image as a developer image. The development unit cartridges  101 K,  101 Y,  101 M,  101 C are each detachable from the image forming apparatus  100 . Since the development unit cartridges  101 K,  101 Y,  101 M,  101 C have the same configuration except for a color of a toner which is a developer, in the following, the development unit cartridge  101 K is described. 
     The development unit cartridge  101 K includes a charging roller  102 K, a development roller  103 K, a supply roller  104 K, a development blade  105 K, a cleaning blade  106 K, and a photosensitive drum  107 K. 
     The charging roller  102 K charges the photosensitive drum  107 K. The development roller  103 K forms a toner image by adhering toner to the photosensitive drum  107 K. The supply roller  104 K supplies toner to the development roller  103 K. The development blade  105 K forms a toner layer, which is a uniform developer layer, on a surface of the development roller  103 K. The cleaning blade  106 K removes unwanted substances such as toner remaining on the photosensitive drum  107 K. The photosensitive drum  107 K is an image carrier. 
     LED heads  108 K,  108 Y,  108 M,  108 C are exposure parts that respectively form electrostatic latent images on the surfaces the corresponding photosensitive drums  107 K,  107 Y,  107 M,  107 C. The LED heads  108 K,  108 Y,  108 M,  108 C are respectively detachable from the corresponding development unit cartridges  101 K,  101 Y,  101 M,  101 C. 
     Toner cartridges  109 K,  109 Y,  109 M,  109 C are developer containers that respectively supply toners of corresponding colors to the corresponding development unit cartridges  101 K,  101 Y,  101 M,  101 C. 
     A sheet which is a medium on which an image is formed is stored in a sheet cassette  110  which is a medium container. A hopping roller  111  takes out a sheet from the sheet cassette  110 . The sheet taken out by the hopping roller  111  is carried by a pair of registration rollers  112 ,  113  to a transfer unit  114 . In the transfer unit  114 , in order to control a timing of performing transfer of a toner image, a sheet detection sensor  121  that detects a sheet is provided. 
     The transfer unit  114  carries a sheet, and transfers to the sheet a toner image from at least one of the development unit cartridges  101 K,  101 Y,  101 M,  101 C. The transfer unit  114  includes a transfer belt  115 , a driving roller  116 , a stretching roller  117 , transfer rollers  118 K,  118 Y,  118 M,  118 C, a cleaning blade  119 , and a waste toner container  120 . 
     The transfer belt  115  is stretched over the driving roller  116  and the stretching roller  117 , and carries a sheet fed out from the pair of registration rollers  112 ,  113  by moving in a direction indicated by an arrow in  FIG. 1  due to a driving force of the driving roller  116 . The driving roller  116  provides the driving force for moving the transfer belt  115 . The stretching roller  117  together with the driving roller  116  stretches the transfer belt  115  therebetween. 
     The transfer rollers  118 K,  118 Y,  118 M,  118 C respectively transfer toner images from the corresponding development unit cartridges  101 K,  101 Y,  101 M,  101 C to the sheet carried by the transfer belt  115 . The cleaning blade  119  removes unwanted substances such as toner adhering to the transfer belt  115 . The waste toner container  120  stores unwanted substances removed by the cleaning blade  119 . 
     The sheet to which a toner image has been transferred by the transfer unit  114  is carried from the transfer unit  114  to a fuser  122 . The fuser  122  fuses the toner image onto the sheet by applying heat and pressure. The sheet onto which the toner image has been fused by the fuser  122  is carried forward along a carrying guide  123  and is ejected to a sheet ejection tray  124 . 
     Further, in the image forming apparatus  100 , a density sensor  125  and a temperature and humidity sensor  150  are provided. The density sensor  125  detects a density of a toner image transferred to a sheet. The temperature and humidity sensor  150  detects a temperature and a humidity. 
       FIG. 2  is a block diagram illustrating a control circuit of the image forming apparatus  100 . The control circuit of the image forming apparatus  100  includes a host interface part  130 , a command image processing part  131 , an LED head interface part  132 , a storage part  133 , and a printer engine control part  134 . 
     The host interface part  130  receives print data as image formation data from an external device such as a personal computer as a host. The command image processing part  131  generates an image from the image data included in the print data received by the host interface part  130 . According to an instruction from the command image processing part  131 , the LED head interface part  132  transmits a signal to at least one of the LED heads  108 K,  108 Y,  108 M,  108 C to form an electrostatic latent image on the surfaces of the corresponding photosensitive drums  107 K,  107 Y,  107 M,  107 C. 
     The storage part  133  stores programs and data required for processing in the image forming apparatus  100 . The printer engine control part  134  controls entire processing in the image forming apparatus  100  using the programs and data stored in the storage part  133 . For example, the printer engine control part  134  controls the command image processing part  131  and the LED head interface part  132  to perform processing related to an image formed on a sheet. 
     Further, the printer engine control part  134  controls a low voltage power supply  140  that supplies a relatively low voltage to each part in the control circuit. Further, the printer engine control part  134  controls a high voltage power supply  141  that supplies a relatively high voltage to the development unit cartridges  101 K,  101 Y,  101 M,  101 C and the transfer rollers  118 K,  118 Y,  118 M,  118 C. 
     The printer engine control part  134  controls a hopping motor  142  that drives the hopping roller  111 , a registration motor  143  that drives one of the registration rollers  112 ,  113 , a belt motor  144  that drives the transfer belt  115 , a fuser motor  145  that drives the fuser  122 , and a drum motor  146  that drives the photosensitive drums  107 K,  107 Y,  107 M,  107 C. 
     Print data in a predetermined format described in a page description language (PDL) or the like is input to the image forming apparatus  100  illustrated in  FIG. 1  from an external device (not illustrated in the drawings) via the host interface part  130  illustrated in  FIG. 2 . The input print data is converted into an image of bitmap data by the command image processing part  131 . 
     The printer engine control part  134  starts a printing operation after a thermal fusing roller of the fuser  122  is brought to a predetermined temperature by controlling a fuser heater according to a detection value of a thermistor. 
     From the sheet cassette  110  illustrated in  FIG. 1 , a sheet is fed by the hopping roller  111 . The sheet is carried onto the transfer belt  115  by the pair of registration rollers  112 ,  113  at a timing synchronized with an image forming operation to be described below. 
     The development unit cartridges  101 K,  101 Y,  101 M,  101 C respectively form toner images on the photosensitive drums  107 K,  107 Y,  107 M,  107 C by electrophotographic processing. In this case, the corresponding LED heads  108 K,  108 Y,  108 M,  108 C are lit according to the bitmap data. 
     The toner images developed by the development unit cartridges  101 K,  101 Y,  101 M,  101 C are transferred to the sheet carried by the transfer belt  115  by biases applied to the corresponding transfer rollers  118 K,  118 Y,  118 M,  118 C when the sheet passes through corresponding nips. 
     A sheet to which a toner image has been transferred is carried to the fuser  122 , and the toner image is fused onto the sheet by the fuser  122 . Then, the sheet is carried forward along the carrying guide  123  and is ejected to the sheet ejection tray  124 . 
     The printer engine control part  134  detects a temperature and a humidity via the temperature and humidity sensor  150  prior to the above printing operation. The printer engine control part  134  varies a voltage of each bias output from the high voltage power supply  141  according to the detected temperature and humidity. An impedance of a sheet for image transfer varies depending on the temperature and humidity. Therefore, the printer engine control part  134  controls a voltage of a bias to a value according to the temperature and humidity in order to apply an optimum bias. 
       FIG. 3  is a circuit diagram of temperature and humidity sensor  150 . The temperature and humidity sensor  150  is controlled by a processor such as a microcomputer, an ASIC (Application Specific Integrated Circuit) or an FPGA (Field Programmable Gate Array) that functions as a control part  135  included in the printer engine control part  134 . A humidity detection device is formed by the temperature and humidity sensor  150  and the control part  135 . 
     The control part  135  includes an ADC0 port  135   a , an ADC1 port  135   b , a Port0 port  135   c , an SCI port  135   d , a Port1 port  135   e , and a memory  135   f.    
     The ADC0 port  135   a  is a first AD conversion port that performs AD (Analog Digital) conversion. The ADC1 port  135   b  is a second AD conversion port that performs AD conversion. The Port0 port  135   c  is a first output port that performs output from the control part  135 . The SCI port  135   d  is a serial port that performs data transmission in serial communication. The Port1 port  135   e  is a second output port that performs output from the control part  135 . The memory  135   f  is a volatile or non-volatile memory that stores information required for processing in the control part  135 . The memory  135   f  functions as a storage part of the control part  135 . 
     The temperature and humidity sensor  150  includes a temperature sensor  151 , a 3.3 V power supply  152 , an operational amplifier  153 , a diode  154 , an analog switch  155 , a digital-to-analog converter (DAC)  156 , an operational amplifier  157 , an analog switch  158 , a resistor  159 , and a humidity sensor  160 . 
     The 3.3 V power supply  152  is a power supply that supplies a voltage of 3.3 V. The diode  154  is connected to the analog switch  155 . The analog switch  155  is connected to the resistor  159  and functions as a first switching part. The analog switch  158  is connected to an other-side of the humidity sensor  160  and functions as a second switching part. The resistor  159  is connected to a one-side of the humidity sensor  160  so as to be in series with the humidity sensor  160 . The humidity sensor  160  is a resistance-varying humidity sensor of which an impedance varies according to a humidity. 
     The DAC  156  and the operational amplifier  157  function as a potential difference generating part connected to the analog switch  158 . For example, by functioning as a potential difference generating part, the DAC  156  and the operational amplifier  157  equalize a magnitude of a current flowing from a first direction to the humidity sensor  160  with a magnitude of a current flowing from a second direction, which is an opposite direction with respect to the first direction, to the humidity sensor  160 . Specifically, when a current is applied to the resistor  159  and the humidity sensor  160  from the second direction, the DAC  156  and the operational amplifier  157  function as a potential difference generating part by providing a voltage drop corresponding to a forward voltage of the diode  154  to a voltage from the 3.3 V power supply  152  before the voltage from the 3.3 V power supply  152  is applied to the humidity sensor  160 . 
     The control part  135  applies a current from the first direction to the diode  154 , the resistor  159  and the humidity sensor  160  by connecting the analog switch  158  to the ground (GND), and applies a current from the second direction to the resistor  159  and the humidity sensor  160  by connecting the analog switch  158  to the GND. This is specifically described below. 
     The control part  135  sets an output voltage of the DAC  156  by 3-wire serial communication. The DAC  156  is a 10-bit 3.3 V digital-to-analog converter. The DAC  156  outputs a voltage of 3.3 V by receiving a setting of hexadecimal setting value of “0x3FF” from the control part  135 . 
     The operational amplifier  157  has rail-to-rail characteristics and can vary an output voltage in a range of 0 V-3.3 V. The operational amplifier  157  converts an output of the DAC  156  to a lower impedance. 
     From the Port0 port  135   c  and the Port1 port  135   e  of the control part  135 , PWM (Pulse Width Modulation) signals of 1 kHz and 50% duty with phases inverted from each other are output. In the following, a signal output from the Port0 port  135   c  is simply referred to as a PWM signal, and a signal output from the Port1 port  135   e  is referred to as an inverted PWM signal. The PWM signal alternates on and off of the analog switch  155 , and the inverted PWM signal alternates on and off of the analog switch  158 . 
     The analog switch  155  connects a common (COM) terminal  155   a  and a normally closed (NC) terminal  155   b  when an input PWM signal is L (Low), and connects the COM terminal  155   a  and a normally open (NO) terminal  155   c  when the PWM signal is H (High). 
     The analog switch  158  connects a COM terminal  158   a  and a NC terminal  158   b  when an input inverted PWM signal is L, and connects the COM terminal  158   a  and an NO terminal  158   c  when the inverted PWM signal is H. 
     By the PWM signal and the inverted PWM signal from the control part  135 , the two analog switches  155 ,  158  alternately apply voltages to a series circuit of the resistor  159  and the humidity sensor  160 . As a result, an alternating voltage is applied to this series circuit. 
     The diode  154  is inserted between the 3.3 V power supply  152  and the analog switch  155 . When the PWM signal input to the analog switch  155  is H and the NO terminal  155   e  and the COM terminal  155   a  are connected, a voltage of 3.3 V from the 3.3 V power supply  152  produces a voltage drop equal to a forward voltage of the diode  154 . Then, a voltage obtained by subtracting the forward voltage from 3.3 V is applied to the COM terminal  555   a  of the analog switch  155 . 
     With respect to the series circuit of the resistor  159  and the humidity sensor  160 , in order to prevent deterioration of the humidity sensor  160 , it is necessary to apply equal bidirectional currents. Therefore, the control unit  135  sets the output voltage of the DAC  156  to a voltage lower by the forward voltage of the diode  154  (that is, 3.3 V—the forward voltage). 
     Based on the forward voltage of the diode  154  when a current is applied from the first direction to the diode  154 , the resistor  159  and the humidity sensor  160 , the control part  135  calculates a first impedance, which is an impedance of the humidity sensor  160 , and identifies a first humidity from the first impedance. In this case, the PWM signal input to the analog switch  155  is H, and the inverted PWM signal input to the analog switch  158  is L. 
     Further, when a current is applied from the second direction, which is an opposite direction with respect to the first direction, to the resistor  159  and the humidity sensor  160 , based on a voltage obtained between the resistor  159  and the humidity sensor  160 , the control part  135  calculates a second impedance, which is an impedance of the humidity sensor  160 , and identifies a second humidity from the second impedance. In this case, the PWM signal input to the analog switch  155  is L, and the inverted PWM signal input to the analog switch  158  is H. 
     Then, the control part  135  selects one of the first humidity and the second humidity as a humidity detected by the humidity sensor  160 . For example, when the voltage obtained between the resistor  159  and the humidity sensor  160  is greater than or equal to a predetermined threshold, the control part  135  may select the second humidity as the humidity detected by the humidity sensor  160 , and, when the voltage is less than the predetermined threshold, the control part  135  may select the first humidity as the humidity detected by the humidity sensor  160 . Further, when the second humidity is greater than or equal to a predetermined threshold, the control part  135  may select the second humidity as the humidity detected by the humidity sensor  160 , and, when the second humidity is less than the predetermined threshold, the control part  135  may select the first humidity as the humidity detected by the humidity sensor  160 . Further, when the second impedance is less than or equal to a predetermined threshold, the control part  135  may select the second humidity as the humidity detected by the humidity sensor  160 , and, when the second impedance is greater than the predetermined threshold, the control part  135  may select the first humidity as the humidity detected by the humidity sensor  160 . 
       FIG. 4  is a flow diagram illustrating an operation of calculating an impedance of the humidity sensor  160  in the first embodiment. First, the control part  135  enables an ADC1 detection interrupt of the ADC1 port  135   b , and outputs a PWM signal from the Port0 port  135   c , and outputs an inverted PWM signal from the Port1 port  135   e  (S 10 ). 
     Then, by controlling the DAC  156  via the SCI port  135   d , the control part  135  sets a DAC setting value to Vdac, sets the 10-bit DAC setting value to a maximum value of 0x3FF, and outputs 3.3 V from the DAC  156  (S 11 ). 
     Next, the control part  135  determines whether or not the ADC1 detection interrupt has occurred (S 12 ). When the ADC1 detection interrupt has occurred (Yes in S 12 ), the process proceeds to S 13 . 
     In S 13 , the control part  135  determines whether or not the PWM signal output from the Port0 port  135   c  when the ADC1 detection interrupt occurs is L. When the PWM signal is L (Yes in S 13 ), the process proceeds to S 14 , and when the PWM signal is H (No in S 13 ), the process proceeds to S 15 . 
     In S 14 , the control part  135  sets a voltage value indicated by a signal input from the ADC1 port  135   b  to Va. On the other hand, in S 15 , the control part  135  sets the voltage value indicated by the signal input from ADC1 port  135   b  to Vb. 
     Next, the control part  135  determines whether or not both Va and Vb have been acquired (S 16 ). When both Va and Vb have been acquired (Yes in S 16 ), the process proceeds to S 17 , and, when at least one of Va and Vb has not been acquired (No in S 16 ), the process returns to S 12 . 
     In S 17 , the control part  135  determines whether or not (Vdac−Va) is less than Vb. When (Vdac−Va) is less than Vb (Yes in S 17 ), the process proceeds to step S 18 , and, when (Vdac−Va) is greater than or equal to Vb (No in S 17 ), the process proceeds to S 19 . 
     In S 18 , the control part  135  adds 1 to the 10-bit DAC setting value. 
     In S 19 , the control part  135  determines whether or not (Vdac−Va) is greater than Vb. When (Vdac−Va) is greater than Vb (Yes in S 19 ), the process proceeds to S 20 , and, when (Vdac−Va) is less than or equal to Vb (No in S 19 ), the process proceeds to S 21 . 
     In S 20 , the control part  135  subtracts 1 from the 10-bit DAC setting value. On the other hand, in S 21 , the control part  135  calculates the impedance of the humidity sensor  160  from Va, Vb and Vdac. 
     According to the flow diagram illustrated in  FIG. 4 , the voltage output from the DAC  156  is adjusted to (3.3 V—the diode forward voltage). 
     Although Vdac−Va=Vb is set in the flow diagram, the first embodiment is not limited to such an example. A width may be provided in the matching between the voltage output from the DAC  156  and (3.3 V—the diode forward voltage). 
     For example, the ADC of the DAC  156  and the ADC1 port  135   b  having 3.3 Visa 10-bit, and has 3.22 mV (=3.3 V÷1023) per digit. Therefore, the control part  135  may determine whether or not (Vdac−Va) is less than Vb÷3 in S 17 , and determine whether or not (Vdac−Va) is greater than Vb+3 in S 19 . In this case, an error width of about 10 mV can be provided. 
     By the above processing, the output voltages of the COM terminals  155   a ,  158   a  of the analog switches  155 ,  158  are substantially equal to each other, and the positive and negative currents flowing through the humidity sensor  160  are substantially equal to each other. 
     In the flow diagram illustrated in  FIG. 4 , the voltage output from the DAC  156  is 3.3V in an initial state, and the positive and negative currents flowing through the humidity sensor  160  are not equal to each other. However, for example, when the forward voltage of the diode  154  is 0.6 V and a change in the output of the DAC  156  is 3.22 mV per digit, then 0.6 V÷3.22 mV=186 mV. Since the PWM signal is 1 kHz, the voltage output from the DAC  156  is equal to (3.3 V—the diode forward voltage) within 200 msec. For a short time period of 0.2 seconds, deterioration of the humidity sensor  160  due to polarization can be avoided. 
     Further, the forward voltage of the diode  154  differs depending on a forward current. However, since it is known, when an initial value of the DAC setting value is set to 3.0 V or the like, the 200 msec calculated as described above can be shortened to 100 msec. Further, the control part  135  can achieve further shortening by storing the DAC setting value in the memory  135   f  and using the stored value as the initial value in the next operation. 
     Next, calculation of an impedance is described. First, calculation of an impedance based on resistance divided voltage using the resistor  159  is described. Once the values of Va, Vb, and Vdac are determined, the control part  135  can calculate the following equations (1) and (2). 
       (0 x 3 FF−Vdac )×3.3÷1023= VF   (1)
 
       ( Va× 3.3÷1023)÷( Vdac ×3.3÷1023)= R ÷( R+HUM )  (2)
 
     wherein VF is the forward voltage of the diode  154 , R is the resistance value of the resistor  159 , and HUM is the impedance of the humidity sensor  160  at a frequency of 1 kHz. 
     For example, when Vdac=0x345 and Va=0x100, VF=0.30585 according to Eq. (1). Further, when R=100 k Ω, HUM≈227 k Ω according to Eq. (2). For example, when the resistor  159  of 100 k Ω is class F (having an accuracy of ±1%), the impedance of the humidity sensor  160  is 226 kΩ−228 kΩ. 
     Next, calculation of an impedance based on the forward voltage VF of the diode is described. The forward voltage VF of the diode can be expressed by the following Eq. (3). 
         VF=nkT ln( I/I 0)  (3)
 
     wherein n is an emission coefficient; k is the Boltzmann coefficient (8.6171×10 −5  [eV/K]); T is the absolute temperature; ln is a natural logarithm symbol; I is the current; and I0 is the reverse saturation current. The emission coefficient n and the reverse saturation current I0 have different values for each diode type, and the values are disclosed by semiconductor manufacturers for use in circuit simulators. 
     By rearranging Eq. (3), Eq. (4) is obtained. 
         I=I 0×exp( VF/nkT )  (4)
 
     wherein exp is an exponential function symbol. 
     When Eq. (4) is calculated assuming the forward voltage VF=3.3−(Vdac×3.3÷1023)=0.60, n=1.54, I0=2 pA, and the temperature is 25° C. (or 298K), I=7.769×10 −6 =7.769 μA is obtained. 
     The impedance HUM of the humidity sensor  160  becomes HUM=247 kΩ by substituting VF=0.6V and R=100 kΩ into the following Eq. (5). 
       3.3− VF =(7.769 μA)×( R+HUM )  (5)
 
     The forward voltage of the diode has a large variation and usually has a variation of several tens of mV. Although it is caused by a variation of the reverse saturation current I0, it is not realistic to measure this value for each set. For example, the variation of the forward voltage of the diode  154  is assumed to be ±50 mV for VF=0.6 V. First, let VF=0.605V. When the current value is calculated according to Eq. (4), I=8.816×10 −6 =8.816 μA is obtained. Here, when VF=0.605 V and R=100 kΩ are substituted into the following Eq. (6), HUM=206 kΩ is obtained. 
       3.3− VF =(8.816 μA)×( R+HUM )  (6)
 
     Next, let VF=0.595 V. When the current value is calculated according to Eq. (4), I=6.846×10− −6 =6.846 μA is obtained. Here, when VF=0.595 V and R=100 kΩ are substituted into the following Eq. (6′), HUM=295 kΩ is obtained. In this case, the impedance of the humidity sensor  160  has a larger error than that obtained from the voltage across the series circuit of the humidity sensor  160  and the resistor  159 . 
       3.3− VF= 6.846 μA×( R+HUM )  (6′)
 
       FIG. 5  is an impedance table (impedance information) showing the impedance of the humidity sensor  160  in a humidity range of 90% RH-10% RH for a temperature range of 5° C.-45° C. For example, the control part  135  stores such an impedance table in the memory  135   f.    
     Then, the control part  135  detects with the ADC0 port  135   a  a signal output from the temperature sensor  151 , acquires a temperature thereof, and selects a humidity from an impedance corresponding to the acquired temperature by referring to the impedance table. In the first embodiment, the control part  135  refers to the impedance table that shows an impedance for every 1° C. and every 1% RH. However, it is also possible to save the capacity of the memory  135   f , for example, by using a method in which the humidity is calculated using an arithmetic expression. 
     Since the impedance obtained from resistance divided voltage using the resistor  159  according to the above Eqs. (1) and (2) is 227 kΩ, from the impedance table illustrated in  FIG. 5 , 50% RH=218.48 kΩ and 49% RH=247.23 kΩ. Therefore, the humidity is determined to be 50% RH. In general, for a humidity detection accuracy required for electrophotography, digits after the decimal point are not required, thus, such a determination is performed. 
     On the other hand, when the variation of the forward voltage of the diode  154  is included as described above, the impedance is 206 kΩ-295 kΩ from the forward voltage of the diode  154 . Therefore, from the impedance table illustrated in  FIG. 5 , it is determined that the humidity is 50% RH at 206 kΩ and 48% RH at 295 kΩ, and thus, an error of about 2% RH occurs. 
     As described above, when the impedance of the humidity sensor  160  is about 200 kΩ, the humidity calculated from the divided voltage by the resistor  159  is more accurate. 
     The variation of ±50 mV of the diode occurs even for a normal production variation, and, as product specifications, the variation becomes even larger, and there is a problem that a diode with high accuracy as in a case of a resistor cannot be easily obtained. 
     However, when the impedance of the humidity sensor  160  is high, it is difficult to detect the impedance based on the divided voltage directly connected to the resistor  159 . For example, assume that the impedance of the humidity sensor  160  is 10 MΩ. In this case, when the forward voltage of the diode  154  is 0.468 V, the voltage across the series circuit of the humidity sensor  160  and the resistor  159  is 3.3−0.468=2.832 V. 
     In this case, Va is 0.0280396 V (=2.832×100000÷(100000+10000000)). In the 10-bit ADC, it is 0x008−0x009, and the control part  135  detects Va as 0x008 or 0x009. By converting only 1 digit, a value detected as Va is shifted by about 10%. 
     For example, when the control part  135  detects Va as 0x008, since 0x008×3.3÷1023=0.0258065, HUM=10804230≈10.8 M Ω according to the following Eq. (7). 
       100000×2.814÷0.0258065−10000  (7)
 
     On the other hand, when the control part  135  detects Va as 0x009, since 0x009×3.3÷1023=0.0290323, HUM=9592653≈9.6 M Ω according to the following Eq. (8). 
       100000×2.814÷0.0290323−10000  (8)
 
     Therefore, in the resistance divided voltage, the accuracy of the humidity deteriorates. 
     Further, the accuracy of the ADC of a general microcomputer is about ±3 LSB. Therefore, it is necessary to expect that a value of 0x008−0x009 is to be detected in a range of about 0x005−0x00A. When the control part  135  detects Va as 0x005, since 0x005×3.3÷1023=0.016129032, HUM=17346800≈17.3 M Ω according to the following Eq. (9). 
       100000×2.814÷0.016129032−100000  (9)
 
     On the other hand, when the control part  135  detects Va as 0x00A, since 0x00A×3.3÷1023=0.032258065, HUM=8623399≈8.6 M Ω according to the following Eq. (10). 
       100000×2.814÷0.032258065−100000  (10)
 
     Therefore, a nearly doubled variation occurs in the calculated impedance. 
     Here, assuming that a variation of ±50 mV has occurred with respect to VF=0.468 V, the impedance is calculated from VF=0.473 V and VF=0.463 V. The temperature is 25° C. 
     First, when VF=0.473 V, the current I=3.313×10 −7 =0.3313 μA according to the following Eq. (11). 
       2×10 −12 ×exp(0.473÷(1.54×8.6171×10 −5 ×(273+25)))  (11)
 
     Then, when VF=0.473 V and R=100 kΩ are substituted into the following Eq. (12), HUM=8.5 MΩ is obtained. 
       3.3− VF =(0.3313 μA)×( R+HUM )  (12)
 
     Next, when VF=0.463 V, the current I=2.431×10 −7 =0.2431 μA according to the following Eq. (13). 
       2×10 −12 ×exp(0.463÷(1.54×8.6171×10 −5 ×(273+25)))  (13)
 
     Then, when VF=0.463 V and R=100 kΩ are substituted into the following Eq. (14), HUM=11.7 MΩ is obtained. 
       3.3− VF =(0.2431 μA)×( R+HUM )  (14)
 
     The variation of VF is ±50 mV and has a width of 100 mV. For a 10-bit AD value, 100 mV has a width of 31 digits. When an error in AD conversion accuracy is ±3 LSB, the width is about ±10 mV. Therefore, the variation of VF=0.473 V-0.463 V appears as a detection error of VF=0.474 V-0.462 V. 
     Therefore, similar to the above, the impedance is calculated from VF=0.474 V and VF=0.462 V. The temperature is 25° C. 
     First, when VF=0.474 V, the current I=3.211×10 −7 =0.3211 μA according to the following Eq. (15). 
       2×10 −12 ×2 exp(0.474÷(1.54×8.6171×10 −5 ×(273+25)))  (15)
 
     Then, when VF=0.474 V and R=100 kΩ are substituted into the following Eq. (16), HUM=8.8 MΩ is obtained. 
       3.3− VF =(0.3311 μA)×( R+HUM )  (16)
 
     Next, when VF=0.462 V, the current I=2.37×10 −7 =0.237 μA according to the following Eq. (17). 
       2×10 −12 ×2 exp(0.462÷(1.54×8.6171×10 −5 ×(273+25)))  (17)
 
     Then, when VF=0.462 V and R=100 kΩ are substituted into the following Eq. (18), HUM=12.0 MΩ is obtained. 
       3.3− VF =(0.237 μA)×( R+HUM )  (18)
 
     As described above, when the impedance of the humidity sensor  160  is 10 MΩ, the impedance can be obtained more accurately by obtaining it from the forward voltage. Since a detection limit based on the resistance divided voltage is determined by a ratio with respect to the resistance value of the resistor  159 , when the resistor  159  is set to 50 kΩ, the impedance of the humidity sensor  160  is 5 MΩ, and the same error occurs. 
     When the impedance obtained from the resistance divided voltage is 8.6 MΩ, from  FIG. 5 , the humidity is 19% RH, and, when the impedance is 17.3 MΩ, the humidity is 17% RH. When the impedance obtained from the forward voltage of the diode  154  is 8.8 MΩ, the humidity is 19% RH, and when the impedance is 12.0 MΩ, the humidity is 18% RH. 
     As described above, when the impedance of the humidity sensor  160  is about 10 MΩ and a ratio to a divided voltage resistance is about 100 times, a value calculated from the forward voltage of the diode  154  is more accurate. 
     When the impedance of the humidity sensor  160  becomes further higher, a voltage output by divided voltage becomes close to zero. For example, assume that the impedance of the humidity sensor  160  is 100 MΩ. In this case, when the forward voltage of the diode  154  is 0.379 V, the voltage across the series circuit of the humidity sensor  160  and the resistor  159  is 3.3-0.379=2.921 V. 
     In this case, Va is 0.002918 V (=2.921×100000÷(100000+10000000)). This value is 0x001 for a 10-bit ADC. When an error of ±3 LSB occurs in the ADC, a value detected by the control part  135  is 0x000-0x004. 
     When the control part  135  detects Va as 0x000, 0x000×3.3÷1023=0.0, and HUM=∞Ω. On the other hand, when the control part  135  detects Va as 0x004, 0x004×3.3÷1023=0.0129032, and HUM=22537795≈22.5 M Ω according to the following Eq. (19). 
       1000000×2.921÷0.0129032−100000  (19)
 
     As described above, since a detected value is ⅕ on a lower side and zero on a higher side with respect to an actual value, the control part  135  cannot perform detection. As described above, as is also clear from the example in which the impedance is 10 MΩ, in the resistance divided voltage, a ratio of about 100 times with respect to the resistance value of the resistor  159  is a detection limit, and, when the impedance is 100 MΩ, detection cannot be performed. 
     Next, the diode forward voltage is calculated. Here, assuming a case where a variation of ±60 mV has occurred for VF=0.379 V by combining a variation of ±50 mV of VF of the diode  154  and a variation of 10 mV of the detection accuracy of the ADC, from VF=0.385 V and VF=0.373 V, the impedance is calculated and the humidity is identified. The temperature is 25° C. 
     First, when VF=0.385 V, the current I=3.382×10 −8 =0.03382 μA according to the following Eq. (20). 
       2×10 −12 ×2 exp(0.385÷(1.54×8.6171×10 −5 ×(273+25)))  (20)
 
     Then, by substituting VF=0.385 V and R=100 kΩ into the following Eq. (21), HUM=86 MΩ is obtained. 
       3.3− VF =(0.03382 μA)×( R+HUM )  (21)
 
     Next, when VF=0.373 V, the current I=2.497×10 −8 =0.02497 μA according to the following Eq. (22). 
       2×10 −12 ×exp(0.373÷(1.54×8.6171×10 −5 ×(273+25)))  (22)
 
     Then, by substituting VF=0.373 V and R=100 kΩ into the following Eq. (23), HUM=117 MΩ is obtained. 
       3.3− VF =(0.02497 μA)×( R+HUM )  (23)
 
     Here, according to  FIG. 5 , in the case of 86 MΩ obtained from the diode forward voltage, it is 13% RH, and, in the case of 117 MΩ, it is 12% RH. 
     As described above, when the impedance of the humidity sensor  160  is about 10 MΩ and a ratio to the resistance value of the resistor  159  used as a divided voltage resistance is about 1000 times, the impedance of the humidity sensor  160  can be detected with only the forward voltage of the diode  154 . 
     Further, with respect to a unit humidity change, for example, as obtained from  FIG. 5 , an impedance change ratio between 49% RH and 48% RH is 50.70÷56.70=0.89, which is 11%, whereas an impedance change ratio between 20% RH and 19% RH is 5915.63÷8012.31=0.74, which is 26%. The amount of change in impedance with respect to a unit humidity change is larger when the humidity is lower and the impedance of the humidity sensor  160  is higher. 
     Highly accurate detection can be performed in the entire humidity region by detecting the impedance based on the divided voltage of the resistor  159  in a region where the humidity is high and the impedance is low and based on the forward voltage of the diode  154  in a region where the humidity is low and the impedance is high. 
     For example, as described above, the control part  135  identifies the humidity from the values of Va, Vb and Vdac by obtaining the impedance of the humidity sensor  160  from the calculation based on the resistance divided voltage. Then, when the identified humidity is 20% RH or higher, the humidity may be used; and, when the identified humidity is less than 20% RH, the control part  135  may further identify the humidity from the impedance calculated from the forward voltage of the diode. 
     Further, it is also possible that a threshold is set for the detection value of Va, and the control part  135  calculates the impedance from the resistance divided voltage when the detection value of Va is 0x20 or more, and calculates the impedance based on the forward voltage when the detection value of Va is less than 0x20. 
       FIG. 6  is a schematic diagram illustrating waveforms of the PWM signal, the inverted PWM signal and the HUM signal, and the AD conversion timing of the ADC1 port  135   b . As illustrated in  FIG. 6 , the ADC1 port  135   b  performs AD conversion of an input signal at a timing immediately before the PWM signal is switched, and the control part  135  detects the humidity. 
     Second Embodiment 
     As illustrated in  FIG. 1 , an image forming apparatus  200  according to a second embodiment is configured in the same manner as the image forming apparatus  100  according to the first embodiment, except for a temperature and humidity sensor  250 . As illustrated in  FIG. 2 , a control circuit of the image forming apparatus  200  according to the second embodiment is configured in the same manner as the control circuit of the image forming apparatus  100  according to the first embodiment, except for a printer engine control part  234 . The printer engine control part  234  in the second embodiment is different from the printer engine control part  134  in the first embodiment in a control part that controls the temperature and humidity sensor  250 . 
       FIG. 7  is a circuit diagram of the temperature and humidity sensor  250  in the second embodiment. The temperature and humidity sensor  250  is controlled by a processor such as a microcomputer, an ASIC or an FPGA that functions as a control part  235  included in the printer engine control part  234 . 
     The control part  235  includes an ADC0 port  135   a , an ADC1 port  135   b , a Port0 port  135   c , a Port1 port  135   e , and a memory  135   f . The ADC0 port  135   a , the ADC1 port  135   b , the Port0 port  135   c , the Port1 port  135   e  and the memory  135   f  of the control part  235  in the second embodiment are respectively the same as the ADC0 port  135   a , the ADC1 port  135   b , the Port0 port  135   c , the Port1 port  135   e  and the memory  135   f  of the control part  135  in the first embodiment. 
     The temperature and humidity sensor  250  includes a 3.3 V power supply  152 , a resistor  159 , a humidity sensor  160 , a thermistor  261 , resistors  262 ,  263 ,  264 , a PNP transistor  265 , an NPN transistor  266 , resistors  267 ,  268 , a PNP transistor  269 , an NPN transistor  270 , and diodes  271 ,  272 . 
     The 3.3 V power supply  152  supplies a voltage of 3.3 V. The thermistor  261  is a temperature sensor element of which a resistance value varies with temperature. Thermistor  261  detects an ambient temperature of the humidity sensor  160 . The resistor  262  forms a divided voltage circuit with the thermistor  261 , and a voltage level of a signal input to the ADC0 port  135   a  varies depending on the temperature. 
     Via the resistors  263 ,  264 , a PWM signal output from Port0 port  135   c  is input to a base of the PNP transistor  265  and the NPN transistor  266 . The PNP transistor  265  applies 3.3 V from the 3.3 V power supply  152  to the resistor  159  and humidity sensor  160  via the diode  271  when the PWM signal is L. The NPN transistor  266  connects the humidity sensor  160  to the GND when the PWM signal is H. 
     Further, via the resistors  267 ,  268 , an inverted PWM signal output from the Port1 port  135   e  is input to a base of the PNP transistor  269  and the NPN transistor  270 . The PNP transistor  269  applies 3.3 V from the 3.3 V power supply  152  to the humidity sensor  160  and the resistor  159  via the diode  272  when the inverted PWM signal is L. The NPN transistor  270  connects the humidity sensor  160  to the GND when the inverted PWM signal is H. 
     As a result, the PNP transistor  265  and the NPN transistor  266  function as a first switching part connected to a resistor. The diode  271  is a diode connected to the first switching part. The PNP transistor  269  and the NPN transistor  270  function as a second switching part connected to an other-side of the humidity sensor  160 . The diode  272  functions as a potential difference generating part connected to the PNP transistor  269  and the NPN transistor  270 . 
     As described above, an alternating voltage is applied to the humidity sensor  160 , and a voltage as a detection value thereof is input to the ADC1 port  135   b.    
     In the first embodiment, the control part  135  uses the DAC  156  to control a drop in the forward voltage of the diode  154 . However, in the second embodiment, both the diode  271  and the diode  272  are used to balance the alternating voltage. 
     Further, in the second embodiment, instead of the analog switches  155 ,  158  in the first embodiment, the voltage applied to the series circuit of the resistor  159  and the humidity sensor  160  is alternately switched by the PWM signal or the inverted PWM signal input using the NPN transistors  266 ,  270  and PNP transistors  265 ,  269 . 
     When the resistor  159  is 100 kΩ, a collector current of the transistors  265 ,  266 ,  269 ,  270  is at most 30 μA or less when it is on, and a collector-emitter voltage is 10 mV or less, and thus, the collector-emitter voltage is treated as 0 V. 
       FIG. 8  is a flow diagram illustrating an operation of calculating an impedance of the humidity sensor  160  in the second embodiment. First, the control part  235  enables an ADC1 detection interrupt of the ADC1 port  135   b , and outputs a PWM signal from the Port0  135   c , and outputs an inverted PWM signal from the Port1  135   e  (S 30 ). 
     Next, the control part  235  determines whether or not the ADC1 detection interrupt has occurred (S 31 ). When the ADC1 detection interrupt has occurred (Yes in S 31 ), the process proceeds to S 32 . 
     In S 32 , the control part  235  determines whether or not the PWM signal output from the Port0 port  135   c  when the ADC1 detection interrupt occurs is H. When the PWM signal is H (Yes in S 32 ), the process proceeds to S 33 , and when the PWM signal is L (No in S 32 ), the process proceeds to S 34 . 
     In S 33 , the control part  235  sets a voltage value indicated by a signal input from the ADC1 port  135   b  to Va. On the other hand, in S 34 , the control part  235  sets the voltage value indicated by the signal input from ADC1 port  135   b  to Vb. 
     Next, the control part  235  determines whether or not both Va and Vb have been acquired (S 35 ). When both Va and Vb have been acquired (Yes in S 35 ), the process proceeds to S 36 , and, when at least one of Va and Vb has not been acquired (No in S 35 ), the process returns to S 31 . 
     In S 36 , the control part  235  calculates the impedance of the humidity sensor  160  from Va and Vb. 
     In the second embodiment, Vain a state in which the NPN transistor  266  is on and the PNP transistor  265  is off is determined according to the following Eq. (24) based on the current flowing through the resistor  159 . 
         Va=IR   (24)
 
     Vb detected periodically when the PNP transistor  265  is on is determined according to the following Eq. (25) since now the same current flows in an opposite direction. 
         Vb= 3.3− VF−IR   (25)
 
     From Eqs. (24) and (25), the following Eq. (26) is obtained. 
         VF= 3.3− Va−Vb   (26)
 
     Therefore, since the current is obtained from the forward voltage of the diode  271 , and the voltage across the series circuit of the resistor  159  and the humidity sensor  160  is obtained from 3.3—VF, the impedance of the humidity sensor  160  can be obtained by the same calculation as in the first embodiment. Further, when the current value is obtained from Va=IR, from the voltage across the series circuit, an impedance due to divided voltage can also be obtained in the same manner as in the first embodiment. 
     As described in the first embodiment, when the impedance of the humidity sensor  160  is low, the impedance can be detected accurately by the resistance divided voltage. However, the diode  154  (see  FIG. 3 ) has a variation in the forward voltage and the accuracy is poor. 
     As a result of processing with n (emission coefficient), which is a characteristic value of the diode, and I (reverse saturation current) as fixed values in the equation for the forward voltage of the diode shown in the above Eq. (3), it is not possible to absorb the variation in the reverse saturation current, which fluctuates due to manufacturing variations. 
     Here, by processing with I0 as a variable, it is possible to suppress the variation. Specifically, when Va=x100 and VF=0.6 V, Va=256, and thus, Va=0.8258065 V(=256×3.3÷1023). From the above Eq. (24), I=8.258 μA is obtained. 
     By rearranging the above Eq. (3), the following Eq. (27) can be derived. 
         I 0= I ÷exp( VF÷nkT )  (27)
 
     When I=8.258×10 −6 , VF=0.6, n=1.54, k=8.6171×10 −5 , and T=298 are substituted into the above Eq. (27), I0=2.126 pA is obtained. It is assumed that the values of VF, n and k are stored in the memory  135   f.    
     The control part  235  calculates I in an environment in which the detection accuracy based on the resistance divided voltage is high, and stores the value in the memory  135   f . In a region where the humidity is low and the impedance is high, the control part  235  performs calculation using the stored value to correct the forward voltage of the diodes  271 ,  272 . Thereby, the variation can also be corrected. In the region where the detection accuracy based on the resistance divided voltage is high, the temperature is 15° C. or 288 K or higher. 
     Specifically, when the first impedance calculated when a current is passed from the first direction is less than or equal to a predetermined impedance, the control part  235  calculates a current value of the current flowing through the humidity sensor  160  or the resistor  159 , and calculates a characteristic of the forward voltage of the diode  271  from the calculated current value. Then, when the first impedance is larger than the predetermined impedance, the control part  235  calculates a current value of the current flowing through the humidity sensor  160  from the calculated characteristic, and calculates the first impedance and the second impedance. 
     The control part  235  may always perform storing of such a value when the humidity is high and the impedance of the humidity sensor  160  is low. Further, it is also possible that the control part  235  stores such a value only once when the image forming apparatus  200  is manufactured and then performs processing using the stored value thereafter. Further, it is also possible that a non-volatile memory or microcomputer is mounted on a substrate on which the temperature and humidity sensor  250  is mounted, and the value is stored during substrate testing. 
     As described above, in the first and second embodiments, the temperature and humidity sensor  250  is combined with the resistor  159 , which is used as a divided voltage resistance, and the diodes  154 ,  271 ,  272 , and, a voltage of the series circuit that does not include the forward voltage of the diodes  154 ,  271 ,  272  is detected in a half cycle of one cycle when an alternating voltage is applied, and a voltage of the series circuit including the forward voltage of the diodes  154 ,  271 ,  272  is detected in the other half cycle, thereby, the impedance of the humidity sensor  160  can be calculated without being affected by the variation in the forward voltage of the diodes  154 ,  271 ,  272 . Therefore, the humidity can be detected with high accuracy. 
     In the first and second embodiments described above, the forward voltage of the diodes  154 ,  271  is processed based on the above Eq. (3). However, embodiment(s) of the invention are not limited to such an example. For example, the forward voltage has a logarithmic characteristic with respect to the current, and thus can be expressed in a linear form by putting the change in current on a logarithmic axis. Specifically, in the case where I0=2.126 pA and n=1.54 as described above, VF can be approximated by the following Eq. (28). 
         VF= 0.0911× X+ 1.0629  (28)
 
     Equation (28) is an approximation of VF, wherein X is an exponent of a current value and I=10×. 
     When converted to a logarithm, the above 8.258 μA becomes −5.08313 according to the following Eq. (29). 
       LOG(8.258×10 −6 )=LOG(8.258)+LOG(10 −6 )=0.916875−6  (29)
 
     Therefore, VF≈0.6 according to the following Eq. (30). 
         VF= 0.0911×(−5.08313)+1.0629  (30)
 
       FIG. 9  shows an approximate expression of VF at each temperature. When used as an approximate expression, it is not appropriate to calculate I0 (reverse saturation current) each time with respect to the variation in VF. When using an approximate expression, the control part  235  stores a difference between the current value obtained from the resistor and the VF obtained from the approximate expression as a correction value in the memory  135   f , and uses a value obtained by adding the correction value to a VF detected thereafter as VF′ and substitutes VF′ into an approximate expression of  FIG. 9  to determine X. 
     For example, when the VF is detected as 0.61 Vat 25° C. and the VF obtained from the current value is 0.60 V, the correction value is −0.01 V. When the VF is detected as 0.4 V at a low humidity, a value 0.39 V, which is a sum of the detected voltage 0.4 V and the correction value −0.01 V, is used as VF′. 
     When the temperature is 25° C., from the above Eq. (28), X=−7.338639 (=(0.39−1.0629)÷0.0911), and the current value is 10 −7.38639 =4.10782×10 −8 . 
     From the measured value of VF of 0.4 V and the current value obtained using the approximate expression, the impedance=70.5 MΩ according to the following Eqs. (31) and (32). 
       3.3−0.4=4.10782×10 −8 ×(100000+ R )  (31)
 
         R =(2.9−4.10782×10 −3 )+(4.10782×10 −8 )  (32)
 
     In this case, according to  FIG. 5 , the control part  235  determines that the humidity=13% RH. 
     Third Embodiment 
     As illustrated in  FIG. 1 , an image forming apparatus  300  according to a third embodiment is configured in the same manner as the image forming apparatus  100  according to the first embodiment, except for a temperature and humidity sensor  350 . As illustrated in  FIG. 2 , a control circuit of the image forming apparatus  300  according to the third embodiment is configured in the same manner as the control circuit of the image forming apparatus  100  according to the first embodiment, except for a printer engine control part  334 . The printer engine control part  334  in the third embodiment is different from the printer engine control part  134  in the first embodiment in a control part that controls the temperature and humidity sensor  350 . 
       FIG. 10  is a circuit diagram of the temperature and humidity sensor  350  in the third embodiment. The temperature and humidity sensor  350  is controlled by a processor such as a microcomputer, an ASIC or an FPGA that functions as a control part  335  included in the printer engine control part  334 . 
     The control part  335  includes an ADC0 port  135   a , an ADC1 port  135   b , a Port0 port  135   c , and a memory  135   f . The ADC0 port  135   a , the ADC1 port  135   b , the Port0 port  135   c  and the memory  135   f  of the control part  335  in the third embodiment are respectively the same as the ADC0 port  135   a , the ADC1 port  135   b , the Port0 port  135   c  and the memory  135   f  of the control part  135  in the first embodiment. 
     The temperature and humidity sensor  350  includes a 3.3 V power supply  152 , a 100 kΩ resistor  159 , a humidity sensor  160 , a 1 kΩ resistor  373 , 750Ω resistors  374 ,  375 , an NPN type digital transistor  376 , diodes  377 ,  378 , a 5.6 kΩ resistor  380 , a 4.7 kΩ resistor  381 , NPN transistors  382 ,  383 , operational amplifiers  384 ,  385 , a thermistor  386 , and a resistor  387 . 
     In the third embodiment, the NPN transistor  383  functions as a first switching part connected to the resistor  159 . The diode  378  is a diode connected to the first switching part. The NPN transistor  382  functions as a second switching part connected to the other-side of the humidity sensor  160 . The diode  377  functions as a potential difference generating part. 
     In the third embodiment, a package  379  including two circuits of the diodes  377 ,  378  is used. By using the diodes  377 ,  378  of the package  379  with two circuits, characteristics of the diodes  377 ,  378  can be aligned. In other words, in the first embodiment, the control part  135  uses the DAC  156  to control the drop in the forward voltage of the diode  154 . However, in the third embodiment, by using the diodes  377 ,  378  having aligned forward voltage characteristics in the package  379  with two circuits, the alternating voltage is balanced. 
     Further, in the third embodiment, by the PWM signal input using the NPN transistors  382 ,  383  instead of the analog switches  155 ,  158  in the first embodiment, the voltage applied to the series circuit of the resistor  159  and the humidity sensor  160  is alternately switched. 
     When the NPN transistor  382  is off, the voltage from the 3.3 V power supply  152  is applied to the humidity sensor  160  via the diode  377  and the resistor  374 . On the other hand, when the NPN transistor  382  is on, a current flows through the diode  377  and the resistor  374 , and a voltage drop due to the resistor  374  and a voltage drop due to the forward voltage of the diode  377  bring an emitter voltage of the NPN transistor  382  close to 0 V, and the humidity sensor  160  is connected to the GND. 
     When the NPN transistor  383  is off, the voltage from the 3.3 V power supply  152  is applied to the humidity sensor  160  via the diode  378 , the resistor  375  and the resistor  159 . On the other hand, when the NPN transistor  383  is on, a current flows through the diode  378  and the resistor  375 , and a voltage drop due to the resistor  375  and a voltage drop due to the forward voltage of the diode  378  bring an emitter voltage of the NPN transistor  383  close to 0 V, and the humidity sensor  160  is connected to the GND. 
     When the characteristics of the diode  377  are n=1.54, k=8.6171×10 −5 , T=298, I0=2×10 −12 , at a temperature of 25° C. and I=3.16 mA, VF=0.894 V according to the following Eq. (33). 
         VF=nkT ln( I/I 0)=1.54×8.6171×10 −5 ×298×ln(3.2×10 −3 ÷2×10 −12 )  (33)
 
     Here, n is the emission coefficient of the diode  377 , k is the Boltzmann constant, and T is the absolute temperature. 
     Further, the voltage drop of the 750Ω resistor  374  is 2.37 V according to the following Eq. (34). 
         V=IR= 750×3.16×10 −3   (34)
 
     A sum of the forward voltage of the diode  377  and the voltage drop of the resistor  374  is 3.264 V(0.894+2.37). 
     When a collector current is about 3 mA, a collector-emitter voltage is not negligible as in the first embodiment, and a collector-emitter voltage of the NPN transistor  382  is about 40 mV. In the second embodiment, the collector-emitter voltage of the NPN transistor  382  is assumed to be 40 mV. 
     Since this value differs depending on the temperature and the type of the transistor, the value may be obtained by performing appropriate measurement at the time of design. For a collector current of 3.16 mA, a base current is used in a saturation region, and a sufficiently large value is selected. Assuming a base-emitter voltage of 0.7 V, since the resistor  380  is 5.6 kΩ, the resistor  373  is 1 kΩ, and the resistor  381  is 4.7 kΩ, a base current of the NPN transistor  382  is about 460 μA in any case. 
     When the NPN transistor  382  is on, when a flowing current of about 3 mA is also off, when a current is applied from the 3.3 V power supply  152  to the humidity sensor  160  and the 100 kΩ resistor  159 , a current corresponding to the impedance of the humidity sensor  160  flows, and the operation is the same as in the first embodiment. 
     When the above-described 40 mV is a collector-emitter saturation voltage Vce=40 mV, a current flowing through a divided voltage circuit is I, AD conversion values as shown in the timing chart illustrated in  FIG. 11  are Va and Vb as in the first embodiment, and the impedance of the humidity sensor  160  to be determined is HUM, Va and Vb can be determined according to the following Eqs. (35) and (36). 
         Va=I× 100000+0.04=3.3−( VF +(750+ HUM )× I   )(35)
 
         Vb= 3.3−( VF +(750+100000)× I )= HUM×I+ 0.04  (36)
 
     From Eqs. (35) and (36), the following Eqs. (37) and (38) can be obtained. 
         I =( Va− 0.04)÷100000  (37)
 
         HUM =( Vb− 0.04)÷ I   (38)
 
     From Eqs. (37) and (38), similar to the first embodiment, the impedance due to the resistance divided voltage can be obtained. 
     Further, by rearranging the above Eq. (36), the following Eq. (39) can be obtained. 
         VF= 3.3− Vb −(750+100000)× I   (39)
 
     VF can be obtained according to the above Eqs. (35) and (39). The following processing is the same as in the first embodiment, and thus a description thereof is omitted. 
     As described above, also in the third embodiment, similar to the first embodiment, detection and correction with respect to the variation of VF can be performed in a region where the humidity is high. 
       FIG. 12  is a circuit diagram illustrating a modified embodiment of the temperature and humidity sensor  350  in the third embodiment. A temperature and humidity sensor  350 # illustrated in  FIG. 12  includes a 3.3 V power supply  152 , a 100 kΩ resistor  159 , a humidity sensor  160 , a 750Ω resistor  375 , a 5.6 kΩ resistor  380 , NPN transistors  382 ,  383 , operational amplifiers  384 ,  385 , a thermistor  386 , a resistor  387 , a 1 kΩ resistor  388 , a 2.8 kΩ resistor  389 , and a diode  340 . 
     The 3.3 V power supply  152 , the resistor  159 , the humidity sensor  160 , resistor  375 , the resistor  380 , the NPN transistors  382 ,  383 , the operational amplifiers  384 ,  385 , the thermistor  386  and the resistor  387  of the temperature and humidity sensor  350  are respectively the same as the 3.3 V power supply  152 , the resistor  159 , humidity sensor  160 , the resistor  375 , the resistor  380 , the NPN transistors  382 ,  383 , the operational amplifiers  384 ,  385 , the thermistor  386  and the resistor  387  of the temperature and humidity sensor  350  in the third embodiment. 
     In this modified embodiment, the NPN transistor  383  functions as a first switching part connected to the resistor  159 . The diode  340  is a diode connected to the first switching part. The NPN transistor  382  functions as a second switching part connected to the other-side of the humidity sensor  160 . The resistor  388  functions as a potential difference generating part. 
     When the NPN transistor  382  is off, a voltage from the 3.3 V power supply  152  is applied to the humidity sensor  160  via the resistor  388 . On the other hand, when the NPN transistor  382  is on, a current flows through the resistor  388 , and a voltage drop due to the resistor  388  brings an emitter voltage of the NPN transistor  382  close to 0 V, and the humility sensor  160  is connected to the GND. 
     When the NPN transistor  383  is off, the voltage from the 3.3 V power supply  152  is applied to the humidity sensor  160  via the resistor  375 , the diode  340  and the resistor  159 . On the other hand, when the NPN transistor  383  is on, a current flows through the resistor  375  and the diode  340 , and a voltage drop due to the resistor  375  and a voltage drop due to the forward voltage of the diode  340  bring an emitter voltage of the NPN transistor  383  close to 0 V, and the humidity sensor  160  is connected to the GND. 
     A current flowing through the humidity sensor  160  and the resistor  159  is 27 μA ((3.3−0.6)÷100000) or less when VF is 0.6 V. 
     At 30 μA, the voltage drop of the 750Ω resistor  375  is 0.0225 V, and the VF of the diode  340  is 0.697 V, and the total is 0.700 V. At 3 μA, the voltage drop of the 750Ω resistor  375  is 0.00225 V, and the VF of the diode  340  is 0.600 V, and the total is 0.600 V. At 300 nA, the voltage drop of the 750Ω resistor  375  is 0.000225 V, and the VF of the diode  340  is 0.503 V, and the total is 0.503V. At 30 nA, the voltage drop of the 750Ω resistor  375  is 0.0000225 V, and the VF of the diode  340  is 0.406 V, and the total is 0.406 V. 
     Since the impedance of the humidity sensor  160  at a temperature of 25° C. and a humidity of 50% RH is about 50 kΩ, when a current under this condition is calculated, VF=0.659 V, I=12 μA, and IR=0.009 V, and thus, a total voltage drop is 0.668 V. Therefore, a base current of the transistor  383  is adjusted such that the voltage drop of 1 kΩ resistor  388  is 0.668 V. 
     At I=688 μA, when abase voltage of the NPN transistor  383  is 0.7 V, a value obtained by subtracting the voltage drops of the resistor  388  and the NPN transistor  383  from 3.3 V is 1.932 V(=3.3-0.668-0.7). In this case, a resistance value of the resistor  389  is 2.8 kΩ according to the following Eq. (40). 
       1.932÷(688×10 −6 )  (40)
 
     Although left and right are slightly unbalanced due to a change in VF, the voltage applied to the humidity sensor  160  is 0.032 V on a high humidity side and is 0.068 V at a current of 3 μA, and is about 2.5% (=0.068÷(3.3-0.668)) in proportion. Therefore, deterioration of the humidity sensor  160  can be prevented. In a region of less than 3 μA, the current flowing through the humidity sensor  160  is also very small, so there is no problem. 
     Next, the impedance of the humidity sensor  160  in the temperature and humidity sensor  350 # is described. Also here, when AD conversion values as shown in the timing chart illustrated in  FIG. 11  are Va and Vb as in the first embodiment, and the impedance of the humidity sensor  160  to be determined is HUM, Va and Vb can be determined according to the following Eqs. (41) and (42). 
         Va=Ia× 100000+0.04=3.3−(0.668+ HUM×Ia )  (41)
 
         Vb= 3.3−( VF +(750+100000)× Ib )= HUM×Ib+ 0.04  (42)
 
     As described above, in the temperature and humidity sensor  350 #, since symmetry of the divided voltage circuit is lost, currents on both sides are not equal. Therefore, here, Ia≈Ib is assumed, and they are described separately. 
     Based on Eq. (41), Eq. (43) can be derived as follows. 
       3.3−(0.668+ HUM×Ia )= Ia× 100000+0.04
 
       3.3−0.688−0.04=(100000+ HUM )× Ia  
 
         HUM= 2.632÷ Ia− 100000  (43)
 
     Further, by rearranging Eq. (41), the following Eq. (44) is obtained. By substituting Eq. (44) into the above Eq. (43), the following Eq. (45) is derived. 
         Ia =( Va− 0.04)÷100000  (44)
 
         HUM= 2.632÷(( Va− 0.04)÷100000)−100000  (45)
 
     With Eq. (45), conversion in a region where the impedance of the humidity sensor  160  is low can be performed in the same manner as in the first embodiment. 
     Further, based on Eq. (42), Eq. (46) can be derived as follows. 
       3.3−( VF +(750+100000)× Ib )= HUM×Ib+ 0.04 VF= 3.26−( HUM+ 100750)× Ib   (46)
 
     Here, with Ib=Ia, the following Eq. (47) can be derived from Eqs (44) and (46). 
         VF= 3.26−( HUM+ 100750)×( Va− 0.04)÷100000  (47)
 
     The control part  335  determines VF using this Eq. (47). Specifically, the control part  335  determines the temperature from a value obtained with a divided voltage of the thermistor  386  and the resistor  387 , and, in the following, similar to the first embodiment, the control part  335  determines the current from the VF, calculates the impedance of the humidity sensor  160 , and identifies the humidity from the impedance. 
     As described above, by applying an alternating voltage to the series circuit of the resistor  159  and the humidity sensor  160  with a combination of transistors and resistors, the same effect can be obtained with fewer components than in the first embodiment. 
     In the first-third embodiments described above, a bipolar transistor or an analog switch is used as a switching part for applying an alternating voltage to a series circuit. However, the embodiments of the present invention are not limited to such an example. For example, other semiconductor devices such as a field effect transistor may be used as such a switching part. In the invention, the switching part may be realized with any device that functions to switch ON/OFF status of the device. Under ON statue, the device is able to convey a voltage or current to the downstream side. Under OFF state, the device is able to convey a voltage or current to the downstream side.