CN113125024A - Low-noise temperature detection circuit and method - Google Patents

Low-noise temperature detection circuit and method Download PDF

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CN113125024A
CN113125024A CN201911413703.6A CN201911413703A CN113125024A CN 113125024 A CN113125024 A CN 113125024A CN 201911413703 A CN201911413703 A CN 201911413703A CN 113125024 A CN113125024 A CN 113125024A
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triode
pmos tube
resistor
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宋宇
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HI-TREND TECHNOLOGY (SHANGHAI) CO LTD
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    • G01MEASURING; TESTING
    • G01KMEASURING TEMPERATURE; MEASURING QUANTITY OF HEAT; THERMALLY-SENSITIVE ELEMENTS NOT OTHERWISE PROVIDED FOR
    • G01K7/00Measuring temperature based on the use of electric or magnetic elements directly sensitive to heat ; Power supply therefor, e.g. using thermoelectric elements
    • G01K7/01Measuring temperature based on the use of electric or magnetic elements directly sensitive to heat ; Power supply therefor, e.g. using thermoelectric elements using semiconducting elements having PN junctions

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Abstract

The invention provides a low-noise temperature detection circuit and a method, comprising the following steps: the first triode is connected between the drain electrode of the first PMOS tube and the ground; the second triode is connected between the first end of the first resistor and the ground, and the second end of the first resistor is connected with the drain electrode of the second PMOS tube; the source electrodes of the first PMOS tube and the second PMOS tube are connected with a power supply voltage; the operational amplifier is respectively connected with the drain electrodes of the first PMOS tube and the second PMOS tube, and the output end of the operational amplifier is connected with the grid electrodes of the first PMOS tube and the second PMOS tube; and one end of the second resistor is connected with the drain electrode of the second PMOS tube, and the other end of the second resistor is grounded. Generating a current with a positive temperature coefficient based on the first triode, the second triode and the first resistor to obtain a detection voltage which is in direct proportion to the absolute temperature; and adjusting the width-length ratio of the first PMOS tube and the second PMOS tube and the resistance value of the second resistor to reduce the output noise. The invention effectively reduces the low-frequency noise of the temperature detection circuit on the basis of no need of a complex structure and an additional area, and is suitable for a low-noise circuit.

Description

Low-noise temperature detection circuit and method
Technical Field
The invention relates to the field of integrated circuit design, in particular to a low-noise temperature detection circuit and a low-noise temperature detection method.
Background
The temperature is a physical quantity representing the cold and hot degree of an object, and is not related to the temperature everywhere in daily life and industrial production of people. Particularly, in the field of integrated circuits, with the continuous development of integrated circuits, the reliability requirement on the integrated circuits is higher and higher, and the temperature is an important parameter affecting the performance of the integrated circuits, so that the temperature needs to be detected and further controlled to improve the performance of the integrated circuits.
As shown in FIG. 1, a typical temperature detection circuit in the prior art is based on PTAT (Pr)open to Absolute Temperature) circuit, based on two bipolar transistors, operating under unequal current density, the difference of their base-emitter voltages is in direct proportion to Absolute Temperature, and then positive Temperature coefficient voltage is obtained. Base-emitter voltage V of a bipolar transistorBECan be used as a voltage reference for detecting temperature change.
Base-emitter voltage V of a bipolar transistorBEMay significantly affect the performance of the low noise circuit. For example, if a high-precision a/D converter uses the voltage as a reference for comparison with an analog signal, noise of the reference is directly applied to the input terminal; even if a large capacitance is added between the output terminal and ground, the low frequency 1/f noise component cannot be suppressed, which is a serious difficulty in low noise applications.
Thus, how to reduce the base-emitter voltage V of the bipolar transistorBEHas become one of the problems to be solved by those skilled in the art.
Disclosure of Invention
In view of the above-mentioned shortcomings of the prior art, it is an object of the present invention to provide a low noise temperature detection circuit and method for solving the problem of large output noise of the base-emitter voltage of the bipolar transistor in the prior art.
To achieve the above and other related objects, the present invention provides a low noise temperature detection circuit, comprising: the transistor comprises a first triode, a second triode, a first resistor, a first PMOS (P-channel metal oxide semiconductor) tube, a second PMOS tube, an operational amplifier and a second resistor;
the first triode is connected between the drain electrode of the first PMOS tube and the ground, and the source electrode of the first PMOS tube is connected with power supply voltage;
the second triode is connected between the first end of the first resistor and the ground, the second end of the first resistor is connected with the drain electrode of the second PMOS tube, and the source electrode of the second PMOS tube is connected with the power supply voltage;
the first input end and the second input end of the operational amplifier are respectively connected with the drain electrodes of the first PMOS tube and the second PMOS tube, and the output end of the operational amplifier is connected with the grid electrodes of the first PMOS tube and the second PMOS tube;
one end of the second resistor is connected with the drain electrode of the second PMOS tube, and the other end of the second resistor is grounded;
the ratio of the width-to-length ratio of the first PMOS tube to the second PMOS tube is N, and N is a real number greater than 1.
Optionally, the first triode and the second triode are PNP triodes; the base electrode and the collector electrode of the first triode are grounded, and the emitter electrode of the first triode is connected with the drain electrode of the first PMOS tube; and the base electrode and the collector electrode of the second triode are grounded, and the emitter electrode of the second triode is connected with the first resistor.
Optionally, the first triode and the second triode are NPN triodes; the emitter of the first triode is grounded, and the base and the collector are connected with the drain of the first PMOS tube; the emitting electrode of the second triode is grounded, and the base electrode and the collector electrode are connected with the first resistor.
More optionally, an emitter junction area ratio of the first transistor to the second transistor is 1: n, wherein n is a real number greater than 1.
In order to achieve the above and other related objects, the present invention provides a low noise temperature detection method, based on the above low noise temperature detection circuit, including at least:
generating a current with a positive temperature coefficient based on the first triode, the second triode and the first resistor, and further obtaining a detection voltage in direct proportion to the absolute temperature;
and adjusting the ratio of the width-to-length ratio of the first PMOS tube to the second PMOS tube and the resistance value of the second resistor to reduce the output noise.
Optionally, noise contributed by the first PMOS transistor to the base-emitter voltage of the first triode satisfies the following relation:
Figure BDA0002350638280000021
wherein (V)BE,P1)2Noise, V, contributed by the first PMOS transistor to the base-emitter voltage of the first triodeBEIs the base electrode-emitter voltage of the first triode, P1 is the first PMOS tube, k is Boltzmann constant, T is Kelvin absolute temperature, Gm1 is the transconductance of the first PMOS tube, Gm2 is the transconductance of the second PMOS tube, C is the voltage of the base electrode-emitter of the first triode, and the voltage of the first PMOS tube is the voltage of the second PMOS tubeoxIs a gate oxide capacitance per unit area, Wp1Is the channel width, L, of the first PMOS tubep1The length of the channel of the first PMOS transistor is f is frequency, Rx1 is the equivalent impedance of the first transistor, and Rx2 is the equivalent impedance of the second transistor, the first resistor and the second resistor.
Optionally, noise contributed by the second PMOS transistor to the base-emitter voltage of the first triode satisfies the following relation:
Figure BDA0002350638280000031
wherein (V)BE,P2)2Noise, V, contributed by the second PMOS transistor to the base-emitter voltage of the first triodeBEIs the base electrode-emitter voltage of the first triode, P2 is the second PMOS tube, k is Boltzmann constant, T is Kelvin absolute temperature, Gm1 is the transconductance of the first PMOS tube, Gm2 is the transconductance of the second PMOS tube, C is the emitter voltage of the first triode, and the second PMOS tubeoxIs a gate oxide capacitance per unit area, Wp2Is the channel width, L, of the second PMOS tubep2The length of the channel of the second PMOS transistor is f is frequency, Rx1 is the equivalent impedance of the first transistor, and Rx2 is the equivalent impedance of the second transistor, the first resistor and the second resistor.
Optionally, noise contributed by the first resistor to the base-emitter voltage of the first triode satisfies the following relation:
Figure BDA0002350638280000032
wherein (V)BE,R1)2Noise, V, contributed by the first resistor to the base-emitter voltage of the first transistorBEThe voltage of a base electrode and an emitter electrode of the first triode is represented by k, a Boltzmann constant, T, Kelvin absolute temperature, R1, R2, Gm1, Gm2 and Rx1, wherein the K is a Boltzman constant, the T is a resistance value of the first resistor, the R2 is a resistance value of the second resistor, the Gm1 is transconductance of the first PMOS tube, the Gm2 is transconductance of the second PMOS tube, and the Rx1 is equivalent impedance of the first triode.
Optionally, noise contributed by the second resistor to the base-emitter voltage of the first triode satisfies the following relation:
Figure BDA0002350638280000033
wherein (V)BE,R2)2Noise, V, contributed by the second resistor to the base-emitter voltage of the first transistorBEIs the base-emitter voltage of the first triode, k is Boltzmann constant, T is Kelvin absolute temperature, R1 is the resistance of the first resistor, R2 is the resistance of the second resistor, RQ2And Gm1 is the equivalent impedance of the second triode, Gm2 is the transconductance of the first PMOS tube, Rx1 is the equivalent impedance of the first triode, and Rx2 is the equivalent impedance of the second triode, the first resistor and the second resistor.
As described above, the low noise temperature detection circuit and method of the present invention have the following advantages:
the low-noise temperature detection circuit and the method effectively reduce the low-frequency noise of the temperature detection circuit on the basis of no need of a complex structure and an additional area, and are suitable for the low-noise circuit.
Drawings
Fig. 1 is a schematic diagram of a temperature detection circuit in the prior art.
Fig. 2 is a schematic structural diagram of the low noise temperature detection circuit of the present invention.
FIG. 3 is a schematic diagram showing the noise analysis of the conventional temperature detection circuit at 1 Hz-100 KHz.
FIG. 4 is a schematic diagram showing the noise analysis of the low noise temperature detection circuit of the present invention at 1 Hz-100 KHz.
Description of the element reference numerals
1 low noise temperature detection circuit
11 operational amplifier
Detailed Description
The embodiments of the present invention are described below with reference to specific embodiments, and other advantages and effects of the present invention will be easily understood by those skilled in the art from the disclosure of the present specification. The invention is capable of other and different embodiments and of being practiced or of being carried out in various ways, and its several details are capable of modification in various respects, all without departing from the spirit and scope of the present invention.
Please refer to fig. 2-4. It should be noted that the drawings provided in the present embodiment are only for illustrating the basic idea of the present invention, and the components related to the present invention are only shown in the drawings rather than drawn according to the number, shape and size of the components in actual implementation, and the type, quantity and proportion of the components in actual implementation may be changed freely, and the layout of the components may be more complicated.
As shown in fig. 2, the present invention provides a low-noise temperature detection circuit 1, wherein the low-noise temperature detection circuit 1 includes: the transistor comprises a first triode Q1, a second triode Q2, a first resistor R1, a first PMOS tube P1, a second PMOS tube P2, an operational amplifier 11 and a second resistor R2.
As shown in fig. 2, the first transistor Q1 is connected between the drain of the first PMOS transistor P1 and ground, and the second transistor Q2 is connected between the first end of the first resistor R1 and ground.
Specifically, in the present embodiment, the first transistor Q1 and the second transistor Q2 are PNP transistors; the base electrode and the collector electrode of the first triode Q1 are grounded, and the emitter electrode is connected with the drain electrode of the first PMOS tube P1; the base and the collector of the second triode Q2 are grounded, and the emitter is connected with the first resistor R1. In practical use, the first transistor Q1 and the second transistor Q2 may be NPN transistors; the emitter of the first triode Q1 is grounded, and the base and the collector are connected with the drain of the first PMOS tube P1; the emitter of the second triode Q2 is grounded, and the base and the collector are connected with the first resistor R1. Any device capable of realizing temperature detection is suitable for the invention, and the connection relation can be adaptively adjusted based on the specific device, which is not repeated herein.
More specifically, the emitter junction area ratio of the first transistor Q1 to the second transistor Q2 is 1: n, wherein n is a real number greater than 1.
As shown in fig. 2, the source of the first PMOS transistor P1 is connected to a power supply voltage, and the gate is connected to the output terminal of the operational amplifier 11; the second end of the first resistor R1 is connected with the drain electrode of the second PMOS tube P2; the source of the second PMOS transistor P2 is connected to the power supply voltage, and the gate is connected to the output terminal of the operational amplifier 11.
Specifically, the ratio of the width-to-length ratio of the first PMOS transistor P1 to the second PMOS transistor P2 is N, where N is a real number greater than 1, and a specific value of N may be set according to actual needs, and is not limited herein. The width-to-length ratio of the PMOS transistor in the prior art is 1.
As shown in fig. 2, the operational amplifier 11 has a first input terminal and a second input terminal respectively connected to the drains of the first PMOS transistor P1 and the second PMOS transistor P2, and an output terminal connected to the gates of the first PMOS transistor P1 and the second PMOS transistor P2.
Specifically, in this embodiment, the operational amplifier 11 has an inverting input terminal connected to the drain of the PMOS transistor P1, a non-inverting input terminal connected to the drain of the second PMOS transistor P2, and an output terminal connected to the gates of the first PMOS transistor P1 and the second PMOS transistor P2. The corresponding relationship between the input terminal polarity of the operational amplifier 11 and the input signal is adjustable, and the same logic can be realized by adding an inverter, which is not limited to this embodiment.
As shown in fig. 2, one end of the second resistor R2 is connected to the drain of the second PMOS transistor P2, and the other end is grounded.
The invention also provides a low-noise temperature detection method, based on the low-noise temperature detection circuit 1, the low-noise temperature detection method comprises the following steps:
the current with positive temperature coefficient is generated based on the first triode Q1, the second triode Q2 and the first resistor R1, and then the detection voltage which is in direct proportion to the absolute temperature is obtained;
the ratio of the width to length ratios of the first PMOS transistor P1 and the second PMOS transistor P2 and the resistance value of the second resistor R2 are adjusted to reduce the output noise.
Specifically, the voltage across the first resistor R1 is a difference between the first transistor Q1 and the second transistor Q2, the current across the first resistor R1 has a positive temperature coefficient, and a voltage proportional to the absolute temperature is obtained based on the second PMOS transistor P2. Output noise is adjusted based on the first PMOS transistor P1, the second PMOS transistor P2, and the second resistor R2.
Specifically, the base-emitter voltage V of the first transistor Q1 by the first PMOS transistor P1, the second PMOS transistor P2, the first resistor R1 and the second resistor R2 is calculated respectivelyBEThe structure of the operational amplifier 11 is the same as the prior art, so the influence of the noise inside the operational amplifier 11 on the output noise is approximately the same as the prior art, and no calculation is performed here.
The first PMOS pipe P1 couples the base-emitter voltage V of the first triodeBEThe contributing noise satisfies the following relation:
Figure BDA0002350638280000061
the second PMOS pipe P2 couples the base-emitter voltage V of the first triodeBEThe contributing noise satisfies the following relation:
Figure BDA0002350638280000062
the first resistor R1 couples the base-emitter voltage V of the first triodeBEThe contributing noise satisfies the following relation:
Figure BDA0002350638280000063
the second resistor R2 couples the base-emitter voltage V of the first triodeBEThe contributing noise satisfies the following relation:
Figure BDA0002350638280000064
noise at the input end of the operational amplifier 11 is applied to the base-emitter voltage V of the first triode Q1BEThe contributing noise satisfies the following relation:
Figure BDA0002350638280000065
wherein (V)BE,P1)2A base-emitter voltage V of the first transistor Q1 for the first PMOS transistor P1BEThe noise contributed; (V)BE,P2)2The base-emitter voltage V of the first triode is applied to the second PMOS pipe P2BEThe noise contributed; (V)BE,R1)2A base-emitter voltage V of the first triode for the first resistor R1BEThe noise contributed; (V)BE,R2)2For the second resistor R2 to the base-emitter voltage V of the first triodeBEThe noise contributed; k is Boltzmann constant; t is Kelvin absolute temperature; gamma is a process parameter; gm1 is the transconductance of the first PMOS transistor P1; gm2 is the transconductance of the second PMOS transistor P2; coxIs a gate oxide capacitance per unit area; wp1The channel width of the first PMOS transistor P1; l isp1The channel length of the first PMOS tube P1; wp2The channel width of the second PMOS pipe P2; l isp2The channel length of the second PMOS pipe P2; f is the frequency; rx1 is the equivalent impedance of the first transistor Q1; rx2 is the equivalent impedance of the second triode Q2, the first resistor R1 and the second resistor R2, and satisfies the following conditions:
Figure BDA0002350638280000071
r1 is the resistance of the first resistor R1; r2 is the resistance of the second resistor R2; rQ2Is the equivalent impedance of the second triode Q2; n is noise; (V)n,tot)2For the noise at the input end of the operational amplifier in the prior art to the base-emitter voltage V of the triodeBEThe contributing noise.
Due to different structures, the first PMOS transistor P1, the second PMOS transistor P2, the first resistor R1 and the second resistor R2 couple the base-emitter voltage V of the first triode Q1BEThe amount of noise reduction contributed is not particularly contrasted. Since the structure of the operational amplifier 11 is the same, comparing the noise contribution of the operational amplifier 11 in the present invention and the prior art, in the present embodiment, the resistance of the second resistor R2 is adjusted to make Rx2 equal to Rx1, because the structure of the operational amplifier 11 is the same as that of the prior art
Figure BDA0002350638280000072
The noise at the input of the operational amplifier 11 will have an influence on the base-emitter voltage V of the first transistor Q1BEThe noise contribution is reduced to
Figure BDA0002350638280000073
Each device is coupled to the base-emitter voltage V of the first triode Q1BEThe superposition of the contributing noise results in a total output noise, from which it can be seen that the total output noise is greatly reduced.
Fig. 3 shows the noise analysis of the conventional temperature detection circuit of fig. 1 at 1 Hz-100 KHz, and fig. 4 shows the noise analysis of the low-noise temperature detection circuit 1 of the present invention at 1 Hz-100 KHz, from which it can be seen that the total output noise of the prior art is 4.84104e-10, while the total output noise of the present application is 7.26133e-11, which greatly reduces the output noise of the present invention, and can obtain lower output noise after further optimizing the device parameters of the present invention, which is not repeated herein.
In summary, the present invention provides a low noise temperature detection circuit and method, including: the transistor comprises a first triode, a second triode, a first resistor, a first PMOS (P-channel metal oxide semiconductor) tube, a second PMOS tube, an operational amplifier and a second resistor; the first triode is connected between the drain electrode of the first PMOS tube and the ground, and the source electrode of the first PMOS tube is connected with power supply voltage; the second triode is connected between the first end of the first resistor and the ground, the second end of the first resistor is connected with the drain electrode of the second PMOS tube, and the source electrode of the second PMOS tube is connected with the power supply voltage; the first input end and the second input end of the operational amplifier are respectively connected with the drain electrodes of the first PMOS tube and the second PMOS tube, and the output end of the operational amplifier is connected with the grid electrodes of the first PMOS tube and the second PMOS tube; one end of the second resistor is connected with the drain electrode of the second PMOS tube, and the other end of the second resistor is grounded; the ratio of the width-to-length ratio of the first PMOS tube to the second PMOS tube is N, and N is a real number greater than 1. Generating a current with a positive temperature coefficient based on the first triode, the second triode and the first resistor, and further obtaining a detection voltage in direct proportion to the absolute temperature; and adjusting the ratio of the width-to-length ratio of the first PMOS tube to the second PMOS tube and the resistance value of the second resistor to reduce the output noise. The low-noise temperature detection circuit and the method effectively reduce the low-frequency noise of the temperature detection circuit on the basis of no need of a complex structure and an additional area, and are suitable for the low-noise circuit. Therefore, the invention effectively overcomes various defects in the prior art and has high industrial utilization value.
The foregoing embodiments are merely illustrative of the principles and utilities of the present invention and are not intended to limit the invention. Any person skilled in the art can modify or change the above-mentioned embodiments without departing from the spirit and scope of the present invention. Accordingly, it is intended that all equivalent modifications or changes which can be made by those skilled in the art without departing from the spirit and technical spirit of the present invention be covered by the claims of the present invention.

Claims (9)

1. A low-noise temperature detection circuit, comprising at least: the transistor comprises a first triode, a second triode, a first resistor, a first PMOS (P-channel metal oxide semiconductor) tube, a second PMOS tube, an operational amplifier and a second resistor;
the first triode is connected between the drain electrode of the first PMOS tube and the ground, and the source electrode of the first PMOS tube is connected with power supply voltage;
the second triode is connected between the first end of the first resistor and the ground, the second end of the first resistor is connected with the drain electrode of the second PMOS tube, and the source electrode of the second PMOS tube is connected with the power supply voltage;
the first input end and the second input end of the operational amplifier are respectively connected with the drain electrodes of the first PMOS tube and the second PMOS tube, and the output end of the operational amplifier is connected with the grid electrodes of the first PMOS tube and the second PMOS tube;
one end of the second resistor is connected with the drain electrode of the second PMOS tube, and the other end of the second resistor is grounded;
the ratio of the width-to-length ratio of the first PMOS tube to the second PMOS tube is N, and N is a real number greater than 1.
2. The low-noise temperature detection circuit according to claim 1, wherein: the first triode and the second triode are PNP triodes; the base electrode and the collector electrode of the first triode are grounded, and the emitter electrode of the first triode is connected with the drain electrode of the first PMOS tube; and the base electrode and the collector electrode of the second triode are grounded, and the emitter electrode of the second triode is connected with the first resistor.
3. The low-noise temperature detection circuit according to claim 1, wherein: the first triode and the second triode are NPN triodes; the emitter of the first triode is grounded, and the base and the collector are connected with the drain of the first PMOS tube; the emitting electrode of the second triode is grounded, and the base electrode and the collector electrode are connected with the first resistor.
4. A low noise temperature detection circuit according to any one of claims 1 to 3, wherein: the emitter junction area ratio of the first triode to the second triode is 1: n, wherein n is a real number greater than 1.
5. A low-noise temperature detection method based on the low-noise temperature detection circuit as claimed in any one of claims 1 to 4, wherein the low-noise temperature detection method at least comprises:
generating a current with a positive temperature coefficient based on the first triode, the second triode and the first resistor, and further obtaining a detection voltage in direct proportion to the absolute temperature;
and adjusting the ratio of the width-to-length ratio of the first PMOS tube to the second PMOS tube and the resistance value of the second resistor to reduce the output noise.
6. The low-noise temperature detection method according to claim 5, wherein: the noise contributed by the first PMOS tube to the base-emitter voltage of the first triode satisfies the following relational expression:
Figure FDA0002350638270000021
wherein (V)BE,P1)2Noise, V, contributed by the first PMOS transistor to the base-emitter voltage of the first triodeBEIs the base electrode-emitter voltage of the first triode, P1 is the first PMOS tube, k is Boltzmann constant, T is Kelvin absolute temperature, gamma is process parameter, Gm1 is transconductance of the first PMOS tube, Gm2 is transconductance of the second PMOS tube, C is the second PMOS tubeoxIs a gate oxide capacitance per unit area, Wp1Is the channel width, L, of the first PMOS tubep1The length of the channel of the first PMOS transistor is f is frequency, Rx1 is the equivalent impedance of the first transistor, and Rx2 is the equivalent impedance of the second transistor, the first resistor and the second resistor.
7. The low-noise temperature detection method according to claim 5, wherein: the noise contributed by the second PMOS tube to the base electrode-emitter electrode voltage of the first triode satisfies the following relational expression:
Figure FDA0002350638270000022
wherein (V)BE,P2)2Noise, V, contributed by the second PMOS transistor to the base-emitter voltage of the first triodeBEIs the base electrode-emitter voltage of the first triode, P2 is the second PMOS tube, k is Boltzmann constant, T is Kelvin absolute temperature, gamma is process parameter, Gm1 is transconductance of the first PMOS tube, Gm2 is transconductance of the second PMOS tube, C is the first triode, andoxis a gate oxide capacitance per unit area, Wp2Is the channel width, L, of the second PMOS tubep2The length of the channel of the second PMOS transistor is f is frequency, Rx1 is the equivalent impedance of the first transistor, and Rx2 is the equivalent impedance of the second transistor, the first resistor and the second resistor.
8. The low-noise temperature detection method according to claim 5, wherein: the noise contributed by the first resistor to the base-emitter voltage of the first triode satisfies the following relation:
Figure FDA0002350638270000023
wherein (V)BE,R1)2Noise, V, contributed by the first resistor to the base-emitter voltage of the first transistorBEIs the base electrode-emitter voltage of the first triode, k is Boltzmann constant, T is Kelvin absolute temperature, R1 is the resistance value of the first resistor, R2 is the resistance value of the second resistor, Gm1 is the transconductance of the first PMOS tube, Gm2 is the transconductance of the second PMOS tube,rx1 is the equivalent impedance of the first transistor.
9. The low-noise temperature detection method according to claim 5, wherein: the noise contributed by the second resistor to the base-emitter voltage of the first triode satisfies the following relation:
Figure FDA0002350638270000031
wherein (V)BE,R2)2Noise, V, contributed by the second resistor to the base-emitter voltage of the first transistorBEIs the base-emitter voltage of the first triode, k is Boltzmann constant, T is Kelvin absolute temperature, R1 is the resistance of the first resistor, R2 is the resistance of the second resistor, RQ2And Gm1 is the equivalent impedance of the second triode, Gm2 is the transconductance of the first PMOS tube, Rx1 is the equivalent impedance of the first triode, and Rx2 is the equivalent impedance of the second triode, the first resistor and the second resistor.
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