Abstract:
A proportional to absolute temperature (PTAT) sensor is capable of reducing a sensing error resulted from a mismatch between circuit components. The PTAT sensor includes a control unit, a sensing unit and a calculation unit. The control unit generates a control signal. The sensing unit, comprising at least a pair of circuit components having a matching relationship, senses an absolute temperature under the first connection configuration and the second connection configuration respectively to generate a first voltage value and a second voltage value, wherein the first connection configuration and the second connection configuration are decided by interchanging the circuit connections of the pair of circuit components according to the control signal. And the calculation unit, coupled to the sensing unit, calculates a PTAT voltage value according to the first voltage value and the second voltage values.

Description:
CROSS REFERENCE TO RELATED PATENT APPLICATION 
     This patent application is based on Taiwan, R.O.C. patent application No. 98106349 filed on Feb. 27, 2009. 
     FIELD OF THE INVENTION 
     The present invention relates to a temperature sensing circuit, and more particularly, to a proportional to absolute temperature (PTAT) sensor and a temperature sensing method thereof. 
     BACKGROUND OF THE INVENTION 
     A PTAT sensing circuit is a common temperature sensing circuit applied to a situation where accurate temperature detection is needed. For example, in a global position system (GPS) device, an oscillator frequency of a local oscillator needs to be extremely precise to maintain the accuracy of positioning. However, the oscillator frequency varies with the temperature. Therefore, the GPS device also needs to accurately sense the temperature to facilitate the local oscillator to generate a proper local frequency. 
     Referring to  FIG. 1 , a conventional PTAT sensing circuit applies a pair of bipolar junction transistors (BJTs) to sense the temperature. In a PTAT sensing circuit  10 , when collector current densities of transistors Q 4  and Q 5  are different, a collector voltage difference (ΔVEB) between the transistors Q 4  and Q 5  satisfies Formula 1:
 
Δ V   EB   =V   T  ln [( I   C4   /A   4 )/( I   C5   /A   5 )]
 
where V T  is equal to kT/q, V T  is a thermal voltage, k is the Boltzmann&#39;s constant, T is an absolute temperature, q is an electric charge, I C4  and I C5  are respectively collector currents of the transistors Q 4  and Q 5 , A 4  and A 5  are respectively emitter areas of the transistors Q 4  and Q 5 , and I C4 /A 4  and I C5 /A 5  are respectively current densities of the transistors Q 4  and Q 5 . Therefore, Formula 1 shows the relationship between the emitter-collector voltage difference ΔV EB  and the absolute temperature T. Furthermore, other components of the PTAT sensing circuit  10  amplify the emitter-collector voltage difference ΔV EB  to generate a PTAT voltage V PTAT . V PTAT  is obtained via a simple analysis:
 
 V   PTAT   =ΔV   EB *2*( M 4 /M 3)*( R   11   /R   9 ),
 
The following Formula 2 is obtained by substituting V PTAT  into Formula 1:
 
 V   PTA   =V   T  ln [( I   C4   /A   4 )/( I   C5   /A   5 )]*2*( M 4 /M 3)*( R   11   /R   9 ),
 
where M 4 /M 3  is a current proportion of a current mirror formed by the transistors M 3  and M 4 . The relationship between the PTAT voltage and the absolute temperature is thus established via Formula 2. Therefore, when the PTAT sensing circuit  10  operates, the absolute temperature being sensed is acquired according to the generated PTAT voltage.
 
     However, a sensing error in the PTAT sensing circuit  10  may be resulted from a mismatch between its circuit components. More particularly, when the PTAT sensing circuit  10  is implemented via an integrated circuit (IC), factors during the production process of the IC inevitably cause the mismatch between the circuit components such that it is even more difficult to avoid the error. Take  FIG. 1  for example. The mismatch circuit components may be the transistors Q 4  and Q 5 , two input ends (regarded as circuit components) of an amplifier  11 , the transistors M 3  and M 4 , the resistors R 8  and R 10 , and the resistors R 9  and R 11 . For example, suppose that the relationships of the foregoing  5  pairs of circuit components are: an emitter area ratio of transistors Q 4  and Q 5  A 5 /A 4  is 8, the amplifier  11  has no voltage offset between its two input ends, the current ratio of the current mirror formed by the transistors M 3  and M 4  M 4 /M 3  is 1.5, R 10 /R 8  is 1.5, and R 11 /R 9  is 1. 
     Due to the IC manufacturing process or other factors, the foregoing relationships may become invalid, and the following circumstances are generated instead. For example, A 5 /A 4 =8*(1+ΔA 4 ), the amplifier  11  has a voltage offset V offset (T) between its two input ends, where the V offset (T) changes according to the absolute temperature T, M 4 /M 3 =1.5*(1+ΔM 4 ), R 10 /R 8 =1+ΔR 8 , and R 11 /R 9 =1+ΔR 9 . ΔA 4 , V offset (T), ΔM 4 , ΔR 8  and ΔR 9  respectively represent a mismatching extent of each pair of circuit components. 
     Under the foregoing mismatching circumstances, a sensing error in the V PTAT  obtained from Formula 2 is caused to undesirably influence the accuracy of the PTAT sensing circuit  10 . Via a further experiment, it is found that the mismatch between the transistors Q 4  and Q 5  and between two input ends of the amplifier is a main source of the sensing error. 
     SUMMARY OF THE INVENTION 
     In view of the foregoing issues, one object of the present invention is to provide a PTAT sensor capable of reducing a sensing error resulted from a mismatch of circuit components and a temperature sensing method thereof. 
     A PTAT sensor is provided according to the present invention. The PTAT sensor comprises a control unit, a sensing unit, and a calculation unit. The control unit generates a control signal. The sensing unit coupled to the control unit comprises an amplifier, a first transistor and a second transistor, a switch unit, and a current module. The amplifier has a first input end, a second input end, and an output end. The first transistor has a collector, a emitter and a base, and a second transistor has a collector, a emitter and a base, wherein the collector of the first transistor and the collector of the second transistor are coupled, and the emitter of the first transistor and the emitter of the second transistor are respectively coupled to the first input end and the second input end of the amplifier. The switch unit, coupled to the output end of the amplifier and one of the first transistor and the second transistor, switches between a first connection configuration and a second connection configuration according to the control signal, wherein under the first connection configuration, the base of the first transistor is coupled to a bias voltage and the base of the second transistor is coupled to the output end of the amplifier, and under the second connection configuration, the base of the first transistor is coupled to the output end, and the base of the second transistor is coupled to the bias voltage. The current module, coupled to the first transistor and the second transistor, provides a first current and a second current to the emitter of the first transistor and the emitter of the second transistor respectively under the first connection configuration, and providing the second current and the first current to the emitter of the first transistor and the emitter of the second transistor respectively under the second connection configuration. The sensing unit senses an absolute temperature under the first and second connection configurations to generate corresponding first and second voltage values. The calculation unit coupled to the sensing unit generates a PTAT voltage value according to the first and second voltage values. 
     A PTAT sensor is further provided according to the present invention. The PTAT sensor comprises a control unit, an sensing unit and a calculation unit. The control unit generates a control signal. The sensing unit, coupled to the control unit, comprises an amplifier, having a first input end, a second input end, and an output end; a first transistor having a collector, a emitter, and a base, and a second transistor having a collector, a emitter and a base, wherein the collector of the first transistor is coupled to the collector of the second transistor, the base of the first transistor is coupled to a bias voltage, and the base of the second transistor is coupled to the output end; a switch unit, coupled to the first input end and the second input end of the amplifier and one of the first transistor and the second transistor, for switching between a first connection configuration and a second connection configuration according to the control signal, wherein under the first connection configuration, the emitters of the first and second transistors are respectively coupled to the first and second input ends of the amplifier, and under the second connection configuration, the emitters of the first and second transistors are respectively coupled to the second and first input ends of the amplifier; and a current module, coupled to the first transistor and the second transistor, for respectively providing a first current and a second current to the emitters of the first transistor and the second transistor; wherein the sensing unit senses an absolute temperature under the first connection configuration and the second connection configuration to generate a first voltage value and a second voltage value. The calculation unit, coupled to the sensing unit, calculates a PTAT voltage value according to the first voltage value and the second voltage value. 
     A PTAT sensor is yet provided according to the present invention. The PTAT sensor comprises a control unit for generating a control signal; a sensing unit, comprising at least a pair of circuit components having a matching relationship, for sensing an absolute temperature under the first connection configuration and the second connection configuration respectively to generate a first voltage value and a second voltage value, wherein the first connection configuration and the second connection configuration are decided by interchanging the circuit connections of the pair of circuit components according to the control signal; and a calculation unit, coupled to the sensing unit, for calculating a PTAT voltage value according to the first voltage value and the second voltage values. 
     A method for generating a PTAT voltage is provided according to the present invention. The method comprises switching a PTAT circuit to a plurality of connection configurations respectively to generate a plurality of voltage values corresponding to the plurality of connection configurations, wherein the plurality of connection configurations are formed by interchanging circuit connections of at least one pair of circuit components having a matching relationship; and calculating a PTAT voltage value according to the plurality of voltage values. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a circuit diagram of a conventional PTAT sensing circuit. 
         FIG. 2  is a schematic diagram of a PTAT sensor in accordance with an embodiment of the present invention. 
         FIG. 3A  and  FIG. 3B  are schematic diagrams of first and second connection configurations respectively. 
         FIG. 4A  and  FIG. 4B  are schematic diagrams of third and fourth connection configurations respectively. 
         FIG. 5  is a circuit diagram of an amplifier of a sensing unit in accordance with a preferred embodiment of the present invention. 
         FIG. 6  is a circuit diagram of an amplifying unit of a sensing unit in accordance with a preferred embodiment of the present invention. 
         FIG. 7  is a circuit diagram of a current module of a sensing unit in accordance with a preferred embodiment of the present invention. 
         FIG. 8  is a flow chart of a PTAT sensing method in accordance with an embodiment of the present invention. 
     
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT 
     As mentioned above, when an absolute temperature is sensed, a sensing error occurs for the reason of a mismatch between circuit components. Therefore, in a PTAT sensor according to the present invention, with respect to a pair or a plurality pairs of circuit components having matching relationships, switchable connection configurations are implemented to provide the pair or the plurality pairs of circuit components with interchangeable connection relationships. In this invention, a pair of circuit components A and B has interchangeable connection relationships. More specifically, the circuit components can replace each other, i.e, A can replace B, and B can replace A. The PTAT sensor respectively senses a temperature under various connection configurations to obtain corresponding voltage values and generates a final PTAT voltage value according to the voltage values obtained. For example, an average value calculated by the voltage values serves as a PTAT voltage value. Therefore, when the circuit components having matching relationships become mismatched due to the manufacturing process and other factors, the sensing error created by the mismatch is significantly reduced via a design according to the present invention. 
       FIG. 2  is a PTAT sensor  20  in accordance with an embodiment of the present invention. The PTAT sensor  20  comprises a control unit  21 , a sensing unit  22 , and a calculation unit  23 . The PTAT sensor  20  senses an absolute temperature and outputs a corresponding PTAT voltage value. The control unit  21  generates a control signal to control the sensing unit  22  to switch between a plurality of circuit configurations as described in detail below. The sensing unit  22  comprises an amplifier  221 , switch units  222  and  223 , transistors Q 1 , Q 2  and Q 3 , a current module  224 , and an amplifying unit  228 , where the transistors Q 1 , Q 2  and Q 3  are BJT transistors. The amplifier  221  has input ends  225  and  226 , and an output end  227 . A collector of the transistor Q 1  is coupled to a collector of the transistor Q 2 , and emitters of the transistors Q 1  and Q 2  are coupled to the switch unit  223  and the current module  224 . Bases of the transistors Q 1  and Q 2  are coupled to the switch unit  222  and the amplifying unit  228 . In the sensing unit  22 , a bias voltage is provided to the bases of the transistors Q 1  and Q 2  in order to keep an associated circuit working normally. The bias voltage value is determined according to a working voltage of the associated circuit. For example, the working voltage is an output voltage of the amplifier  221  or a working voltage of the amplifying unit  228 . In this embodiment, the transistor Q 3  is regarded as a bias circuit for providing the bias voltage. The emitter of the transistor Q 3  is coupled to the switch unit  222  and the collector and base of the transistor Q 3  are connected together to the collectors of the transistors Q 1  and Q 2 . The bias circuit can also apply serial resistors (not shown) for dividing a bias voltage to be provided to the transistors Q 1  and Q 2 . 
     The switch unit  222 , coupled between the output  227  and the transistors Q 1 , Q 2  and Q 3 , switches between a first connection configuration and a second connection configuration according to the control signal provided by the control unit  21 . The first connection configuration is that the base of the transistor Q 1  is coupled to the emitter of the transistor Q 3  and the base of the transistor Q 2  is coupled to the output end  227 , as illustrated in  FIG. 3A . The second connection configuration is that the base of the transistor Q 1  is coupled to the output end  227  and the base of the transistor Q 2  is coupled to the emitter of the transistor Q 3 , as illustrated in  FIG. 3B . In an embodiment of  FIG. 2 , the transistors Q 1  and Q 2  are designed to be a pair of circuit components having a matching relationship. For example, the transistors Q 1  and Q 2  have a same emitter area, and the first and second connection configurations are generated by interchanging connection relationships of the transistors Q 1  and Q 2 . Moreover, in order to interchange currents flowing through the transistors Q 1  and Q 2 , the current module  224  respectively provides a first current and a second current to the emitters of the transistors Q 1  and Q 2  under the first connection configuration, and respectively provides the second current and the first current to the emitters of the transistors Q 1  and Q 2  under the second connection configuration. 
     The switch unit  223 , coupled to the input ends  225  and  226  and the transistors Q 1  and Q 2 , switches between a third connection configuration and a fourth connection configuration according to the control signal provided by the control unit  21 . The third connection configuration is that the emitters of the transistors Q 1  and Q 2  are respectively connected to the input ends  225  and  226 , as illustrated in  FIG. 4A . The fourth connection configuration is that the emitters of the transistors Q 1  and Q 2  are respectively connected to the input ends  226  and  225 , as illustrated in  FIG. 4B . The input ends  225  and  226  of the amplifier  221  are regarded as circuit components having a matching relationship, and the third and four connection configurations are generated by interchanging connection relationships of the input ends  225  and  226 . 
     The switch units  222  and  223  are switched to generate the first, second, third and fourth connection configurations via the control signal generated by the control unit  21 . Therefore, the sensing unit  22  generates four (2×2) types of circuit configurations according to the control signal. The control signal is a digital signal having two bit values such as 00, 01, and 11, which respectively represents the four circuit configurations. 
     The sensing unit  22  respectively senses an absolute temperature under the four circuit configurations to generate four corresponding analog voltage values to be transmitted to the calculation unit  23 . The calculation unit  23  comprises an analog-to-digital converter (not shown) for converting the four analog voltages values transmitted from the sensing unit  22  to digital voltage values. The calculation unit  23  calculates an average value of the four digital voltage values, with the average value serving as the PTAT voltage value. 
     Following description takes the switch units  222  and  223  respectively switch to the first and third connection configurations for example. Referring to  FIG. 3A  and  FIG. 4A , operation of the sensing unit  22  is described below. The first current and the second current respectively flow through the emitters of the transistors Q 1  and Q 2 , and the transistors Q 1  and Q 2  can sense the absolute temperature. Therefore, the base-emitter voltage difference ΔV BE  between the transistors Q 1  and Q 2  satisfies Formula 3:
 
Δ V   BE   =V   T  ln [( I   C1   /A   1 )/( I   C2   /A   2 )],
 
Formula 3 is similar to Formula 1, where I C1  and I C2  are respectively collector currents of the transistors Q 1  and Q 2 , and A 1  and A 2  are emitter areas of the transistors Q 1  and Q 2 . In this embodiment, Q 1  and Q 2  have a same emitter area and I C1 /I C2  is equal to an emitter current proportion of the transistors Q 1  and Q 2 . Therefore, Formula 3 is simplified as:
 
Δ V   BE   =V   T  ln [( I   E1   /I   E2 )],
 
where I E1  and I E2  are respectively emitter currents of the transistors Q 1  and Q 2  (the first current and the second current). The emitters are respectively coupled to the input ends  225  and  226  of the amplifier  221 . Therefore, an emitter voltage V E1  of the transistors Q 1  is equal to an emitter voltage V E2  of the transistor Q 2 . Accordingly, ΔV BE  is represented as:
 
Δ V   BE   =V   BE1   −V   BE2 =( V   B1   −V   E1 )−( V   B2   −V   E2 )= V   B1   −V   B2 ,
 
where V BE1  and V BE2  are base-emitter voltages of the transistors Q 1  and Q 2 , V B1  and V B2  are base voltages of the transistors Q 1  and Q 2 , and V E1  and V E2  are the emitter voltages of the transistors Q 1  and Q 2 . Therefore, ΔV BE  is equal to a base voltage difference of the transistors Q 1  and Q 2 . Since the base voltage difference is very small, the sensing unit  22  transmits the base voltage difference to the amplifying unit  228  for amplification, so as to obtain a corresponding voltage value generated by sensing the absolute temperature under the first and third connection configurations. Other similar approaches are also applied to the sensing unit  22  under other circuit configurations to generate the corresponding voltage value.
 
     In a first preferred embodiment, the amplifier  221  in the sensing unit  22  has a pair of circuit components having a matching relationship and a corresponding switch unit. The switch unit interchanges connection relationships of the pair of circuit components according to the control signal generated by the control unit  21 , so as to generate a fifth connection configuration and a sixth connection configuration. For example, in the amplifier  221  illustrated in  FIG. 5 , P-channel metal-oxide semiconductor (PMOS) transistors M 1  and M 2  are circuit components having a matching relationship, and gates of the transistors M 1  and M 2  are coupled to each other. The switch unit  51  switches between the fifth and sixth connection configurations according to the control signal. The fifth connection configuration is that the gate of the transistor M 1  is coupled to a drain of the transistor M 1  and a drain of the transistor M 2  is coupled to the output end  227  of the amplifier  221 . The sixth connection configuration is that the gate of the transistor M 2  is coupled to a drain of the transistor M 2  and a drain of the M 1  is coupled to the output end  227 .  FIG. 5  shows the fifth connection configuration. Therefore, in the first preferred embodiment, the sensing unit  22  generates 8 (2 3 ) types of circuit configurations according to the control signal at least having 3 bits at this point. The sensing unit  22  senses an absolute temperature under eight circuit configurations respectively to generate eight corresponding voltage values. The voltage values are calculated by the calculation unit  23  to generate an average value to be served as a PTAT voltage value. 
     In a second preferred embodiment, the amplifying unit  228  of the sensing unit  22  is an instrument amplifier  60 . Referring to  FIG. 6 , an input voltage and an output voltage of the instrument amplifier  60  are respectively V in  (=V + -V_) and V out , and the instrument amplifier  60  comprises three amplifiers  61 ,  62  and  63  and resistors R 1 , R 2 , R 3  and R 4 . As mentioned above, two input ends of an amplifier are regarded as a pair of circuit components having a matching relationship, and the amplifier has a pair of internal circuit components having a matching relationship. Therefore, the instrument amplifier further comprises switch units  611 ,  612 ,  621 ,  622 ,  631  and  632 . The switch units  611 ,  621  and  631  are used for respectively interchanging connection relationships of input ends of the amplifiers  61 ,  62  and  63 . The switch units  612 ,  622  and  632  are used for respectively interchanging connection relationships of the pair of internal circuit components having the matching relationship in the amplifiers  61 ,  62  and  63 . In addition, the amplifiers  61  and  62  are regarded as a pair of circuit components having a matching relationship. Therefore, the instrument amplifier  60  further comprises a switch unit  601  having switches S 1  and S 2 , and a switch unit  602  having switches S 3 , S 4 , S 5  and S 6 . The switch units  601  and  602  are used for interchanging connection relationships between the amplifier  61  and  62 . That is, when the amplifiers  61  and  62  wish to interchange connection configurations as illustrated in  FIG. 6 , the switches S 1  and S 2  switch to P 6  and P 5  respectively, and the switches S 3 , S 4 , S 5  and S 6  switch to P 8 , P 7 , P 10  and P 9  respectively. All switch units inside the instrument amplifier  60  can perform switching according to the control signal generated by the control unit  21 . Consequently, the instrument amplifier  60  can generate 2 7  different circuit configurations. When the first preferred embodiment is incorporated to the second preferred embodiment, the sensing unit  22  can generate up to 2 3 ×2 7 =2 10  types of circuit configurations, where the control signal has at least 10 bits. 
     Voltages between the two input ends of the amplifiers  61 ,  62  and  63  are regarded as being equal to each other. Thus, voltages of P 1  and P 2  are respectively equal to V +  and V − , and voltages of P 3  and P 4  are equal to each other, supposing that the voltage of P 3  or P 4  is V d . In addition, no current flows through the two input ends of the amplifier  63  such that a current flows through R 1  is equal to a current flows through R 2  and a current flows through R 3  is equal to a current flows through R 4 . Therefore, Formula 4 and Formula 5 are respectively represented as:
 
( V   +   −V   d )/ R   1   =V   d   /R   2 , and
 
( V   −   −V   d )/ R 3=( V   d   −V   out )/ R   4 .
 
Formula 6 is deduced from Formula 4 and Formula 5:
 
               V   out     =         V   +     *       1   +       R   4       R   3           1   +       R   1       R   2             -       V   -     *         R   4       R   3       .               
Taking R 4 =20R 3  and R 2 =20 R 1  for example, Formula 6 is then:
 
 V   out   =V   + *20 −V   − *20=20 V   in .
 
That is, the instrument amplifier  60  (the amplifying unit  228 ) has a gain of 20.
 
     Furthermore, suppose that the sensing unit  22  has m pairs of circuit components having matching relationships, and a switch unit is designed to be corresponding to each pair of circuit components. By interchanging connection relationships of the circuit components according to the control signal generated by the control unit  21 , two different circuit configurations are generated, where the control signal has at least m bits. Accordingly, the sensing unit  22  can generate 2 m  types of circuit configurations and sense the absolute temperature under the 2 m  types of circuit configurations respectively, so as to generate 2 m  corresponding voltage values, which are then calculated by the calculation unit  23  to generate a PTAT voltage value. 
     In a third preferred embodiment, the current module  24  comprises a current source  2241 , resistors R 5 , R 6  and R 7 , and a switch unit  2242 , as illustrated in  FIG. 7 . The resistors R 5  and R 6  has one end thereof coupled to emitters of the transistors Q 1  and Q 2  respectively, and the resistor R 7  is coupled between the other ends of the resistors R 5  and R 6 . The switch unit  2242 , coupled between the current source  2241  and the resistor R 7 , switches to let the current source  2241  couple to a coupling point between the resistors R 6  and R 7  under the foregoing first connection configuration, and switches to let the current source  2241  couple to a coupling point between the resistors R 5  and R 7  under the foregoing second connection configuration. When the second current provided by the current module  224  is n (a positive number) times the first current, it is designed that R 5  and R 6  have a same resistance value and R 7  has a resistance value (n−1) times R 5 . That is, under the first connection configuration, a current (the second current at this point) flowing through R 6  and arriving at the emitter of the transistor Q 2  is n times a current (the first current at this point) flowing through R 7  and R 5  and arriving at the emitter of the transistor Q 2 . Under the second connection configuration, a current (the second current at this point) flowing through R 5  and arriving at the emitter of the transistor Q 1  is n times a current (the first current at this point) flowing through R 7  and R 6  and arriving at the emitter of the transistor Q 2 . 
     In a fourth preferred embodiment, the amplifier  221  of the sensing unit  22  is a differential output amplifier having input ends  225  and  226  and output ends  227 A and  227 B. The output ends  227 A and  227 B (comprised in the output  227  as shown in  FIG. 2 ) of the amplifier  221  are connected to the switch unit  222 . The switch unit  222 , coupled between the output ends  227 A and  227 B and the transistors Q 1  and Q 2 , switches between the first connection configuration and the second connection configuration according to the control signal provided by the control unit  21 . The first connection configuration is that the base of the transistor Q 1  is coupled to the output end  227 A of the amplifier and the base of the transistor Q 2  is coupled to the output end  227 B of the amplifier. The second connection configuration is that the base of the transistor Q 1  is coupled to the output end  227 B of the amplifier and the base of the transistor Q 2  is coupled to the output end  227 A of the amplifier. 
     In the foregoing embodiments, the connection relationships of the entire circuit are established on the basis that the transistors Q 1  and Q 2  are PNP transistors. The transistors Q 1  and Q 2  are replaced by NPN transistors by re-arranging the entire circuit in reverse or only replacing the transistors Q 1  and Q 2  with NPN transistors. With a reverse arrangement of the circuit, the connection relationships of the circuit remain unchanged. When the transistors Q 1  and Q 2  are replaced by NPN transistors, the emitters and collectors of the transistors Q 1  and Q 2  according to the foregoing embodiments change to collectors and emitters respectively, while other circuit relationships also remain unchanged. 
       FIG. 8  is a flow chart of a PTAT sensing method in accordance with an embodiment of the present invention. The method comprises steps below. In Step  80 , a circuit for sensing an absolute temperature is changed the connection to be a plurality of connection configurations such that a plurality of voltage values corresponding to the absolute temperature are generated. The plurality of connection configurations are generated by interchanging connection relationships between at least one pair of circuit components having a matching relationship. In Step  81 , a PTAT voltage value is generated according to the plurality of voltage values, and the PTAT voltage value can be an average value of the plurality of voltage values, for example. 
     While the invention has been described in terms of what is presently considered to be the most practical and preferred embodiments, it is to be understood that the invention needs not to be limited to the above embodiments. On the contrary, it is intended to cover various modifications and similar arrangements included within the spirit and scope of the appended claims which are to be accorded with the broadest interpretation so as to encompass all such modifications and similar structures.