CN103294099B - Second-order curvature temperature-compensation circuit for band-gap reference - Google Patents

Abstract

The invention relates to a second-order curvature temperature compensation circuit suitable for a bandgap reference. Aiming at the problem that the second-order curvature temperature compensation circuit of the existing bandgap reference is not suitable for some specific processes, the invention discloses a novel second-order curvature temperature compensation circuit. The technical solution of the present invention is that the second-order curvature temperature compensation circuit used for the bandgap reference includes PMOS transistors: M15, M16, M17, M18, M19, and NMOS transistors: M20 and M21. Wherein, the gate of M15 is connected to the bandgap reference voltage signal after part of the first-order temperature compensation, and serves as the input end of the second-order curvature compensation circuit. The gate of M16 serves as the output terminal of the second-order curvature compensation circuit. In the present invention, voltage superposition is realized by the PMOS transistors M15 and M16 working in the sub-threshold region, and a voltage quantity with both first-order and second-order temperature compensation effects is superimposed on the basis of the bandgap reference voltage that has been partially first-order temperature compensated. This produces the final second-order curvature-compensated bandgap reference output voltage.

Description

Second-Order Curvature Temperature Compensation Circuit for Bandgap Reference

technical field

The invention relates to integrated circuit technology, in particular to a second-order curvature temperature compensation circuit suitable for bandgap references.

Background technique

The reference source is a very important module in the electronic system, and its characteristics are directly related to the overall performance of the system. Therefore, high-performance reference sources play an important role in many applications, covering the fields of analog circuits, digital circuits and mixed-signal circuits. Among the many reference sources, the bandgap reference source is the most widely used. In order to improve the output accuracy of the bandgap reference, a variety of high-order curvature compensation methods have been proposed in academia, such as square-term temperature compensation, exponential temperature compensation, piecewise linear compensation, and temperature-dependent resistance ratio compensation.

The bandgap reference second-order curvature temperature compensation circuit in the prior art is usually realized by superimposing second-order temperature compensation items on the basis of first-order temperature compensation (or part of first-order temperature compensation). The typical circuit structure is shown in Figure 1 shown. Figures 1a and b show two commonly used circuit structures, including a current source, a resistor R, and transistors T ₁ and T ₂ . The current source can be a positive temperature current source and/or a negative temperature current source, and is usually composed of a circuit including a PMOS transistor (P-type field effect transistor), an NMOS transistor (N-type field effect transistor) and a bipolar transistor. Figure 1a and b show two second-order curvature temperature compensation circuits using a positive temperature current source. The currents generated by the positive temperature current source are I ₁ and I ₂ respectively, and I ₁ =c ₁ T, I ₂ =c ₂ T. The circuit shown in Figure 1 can realize exponential second-order curvature temperature compensation. The expression of its output reference voltage VREF is

$\mathrm{<span\; class="notranslate">\; VREF</span>}<span\; class="notranslate">\; \&ap;</span>{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; BE</span>}\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; c</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}\mathrm{<span\; class="notranslate">\; RT</span>}<span\; class="notranslate">\; +</span>\frac{{\mathrm{<span\; class="notranslate">\; c</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; R</span>}}{{\mathrm{<span\; class="notranslate">\; \&beta;</span>}}_{<span\; class="notranslate">\; \&infin;</span>}}\mathrm{<span\; class="notranslate">\; T\; exp</span>}<span\; class="notranslate">\; (</span>\frac{{\mathrm{<span\; class="notranslate">\; \&Delta;E</span>}}_{\mathrm{<span\; class="notranslate">\; G</span>}}}{\mathrm{<span\; class="notranslate">\; kT</span>}}<span\; class="notranslate">\; )</span>$

Among them, V _BE1 is the voltage between the base and emitter of NPN transistor T ₁ , c ₁ and c ₂ are constants independent of temperature, T is the absolute temperature, β _∞ is the maximum value of common emitter current gain, ΔE _G is the bandgap reduction factor of the emitter, and k is the Boltzmann constant. The term c ₁ RT in the above formula is used for first-order temperature compensation of the BE junction voltage of the triode, The term realizes the exponential second-order curvature temperature compensation for the BE junction voltage of the triode. Although the structure of this circuit is simple, it requires the use of resistors, and has high requirements on the process, so it must be realized by using a bipolar process or a BiCMOS process. Circuit scope and flexibility are greatly limited.

Contents of the invention

The technical problem to be solved by the present invention is that the second-order curvature temperature compensation circuit for the existing bandgap reference needs to use resistors, which is not suitable for some specific processes (processes without resistance or inaccurate resistance models, such as standard digital CMOS processes) To solve the problem, a new type of second-order curvature temperature compensation circuit is provided.

The present invention solves the technical problem, and adopts the technical solution that is used for the second-order curvature temperature compensation circuit of the bandgap reference, including PMOS tubes: M15, M16, M17, M18, M19, and NMOS tubes: M20, M21; , the gate of M15 is connected to the bandgap reference voltage signal through part of the first-order temperature compensation, and is used as the input terminal of the second-order curvature compensation circuit, the source of M15 is connected to the substrate and connected to the drain of M17 and the drain of M18 pole and the source of M16, the drain of M15 is connected to the ground potential; the gate of M17 is connected to the output node of the positive temperature current source, and the source of M17 is connected to the power supply voltage; the gate of M18 is connected to the output node of the negative temperature current source and connected with The gate of M19 is connected, the source of M18 is connected to the power supply voltage; the source of M16 is connected to the substrate, the gate of M16 is connected to the drain and connected to the drain of M20, as the output end of the second-order curvature compensation circuit; The drain of M19 is connected to the gate and drain of M21 and the gate of M20, the source of M19 is connected to the power supply voltage; the sources of M20 and M21 are both connected to the ground potential.

Specifically, the positive temperature current source includes PMOS transistors: M00, M4, M5, NMOS transistors: M0, M1, M2, M3, PNP transistors: Q1, Q2, Q3; wherein, the gate of M00 is a positive temperature current The output node of the source, the gate of M00 is connected to the drain, and connected to the drain of M0, the gate of M5 and the gate of M4, the source of M00 is connected to the power supply voltage; the gate of M0 is connected to the drain of M5 and The drain of M3, the source of M0 is connected to the emitter of Q3; the source of M5 is connected to the power supply voltage; the drain of M4 is connected to the drain and gate of M2, the gate of M3 and the gate of M1, and the source of M4 Connect the power supply voltage; the source of M3 is connected to the emitter of Q2; the collector and base of Q3 are connected to the ground potential; the source of M2 is connected to the drain of M1; the source of M1 is connected to the emitter of Q1; Both collector and base are connected to ground potential.

Specifically, the negative temperature current source includes, PMOS transistors: M10, M11, M14, NMOS transistors: M6, M7, M8, M9, M12, M13; wherein the gate of M14 is the output node of the negative temperature current source, and the gate of M14 The gate is connected to the drain, and is connected to the drain of M13, the gate of M10 and the gate of M11, the source of M14 is connected to the power supply voltage; the gate of M13 is connected to the drain of M10 and the drain of M8, and the source of M13 The pole is connected to the drain and gate of M12; the source of M10 is connected to the power supply voltage; the drain of M11 is connected to the drain and gate of M9, the gate of M8 and the gate of M7, and the source of M11 is connected to the power supply voltage; M8 The source of M6 is connected to the drain and gate of M6; the source of M9 is connected to the drain of M7; the sources of M6, M7 and M12 are all connected to the ground potential.

The beneficial effect of the invention is that the application range and flexibility of the circuit are significantly improved. Compared with the existing second-order curvature temperature compensation circuit, the second-order curvature temperature compensation circuit of the present invention does not need to use resistors in terms of circuit structure, and can be applied to standard digital CMOS technology in terms of technology.

Description of drawings

Fig. 1 is a schematic structural diagram of a bandgap reference exponential type second-order curvature temperature compensation circuit in the prior art;

Fig. 2 is a schematic structural diagram of a bandgap reference second-order curvature temperature compensation circuit according to an embodiment of the present invention;

The structure diagram of the positive temperature current source circuit of the embodiment of the present invention of Fig. 3;

FIG. 4 is a structural diagram of a negative temperature current source circuit according to an embodiment of the present invention.

Among them, M00, M4, M5, M10, M11, M14, M15, M16, M17, M18, M19 are PMOS tubes; M0, M1, M2, M3, M6, M7, M8, M9, M12, M13, M20, M21 is NMOS tube; Q1, Q2, Q3 are PNP transistors; T1, T2 are NPN transistors; R is resistance.

Detailed ways

The present invention will be further described in detail below in conjunction with the accompanying drawings and embodiments.

The second-order curvature temperature compensation circuit for the bandgap reference of the present invention, as shown in FIG. 2 , includes PMOS transistors: M15, M16, M17, M18, M19, and NMOS transistors: M20 and M21. Among them, the gate of M15 is connected to the bandgap reference voltage signal VREF1 through part of the first-order temperature compensation as the input terminal of the second-order curvature temperature compensation circuit of the present invention, and the source is connected to the substrate and then connected to the drain of M17 and the drain of M18 And the source of M16 is connected to the substrate, and the drain of M15 is connected to the ground potential VSS. The gate of M17 is connected to the output node VP of the positive temperature current source, and the source is connected to the power supply voltage VDD. The gate of M18 is connected to the output node VC of the negative temperature current source and connected to the gate of M19, and the source of M18 is connected to the power supply voltage VDD. The source of M16 is connected to the substrate, the gate of M16 is connected to the drain and is connected to the drain of M20, and the gate of M16 is also the output terminal VREF2 of the second-order curvature temperature compensation circuit of the present invention. The drain of M19 is connected to the gate and drain of M21 and the gate of M20, and the source of M19 is connected to the power supply voltage VDD. Both the source of M20 and the source of M21 are connected to the ground potential VSS.

A circuit implementation scheme of the above-mentioned positive temperature current source is shown in Figure 3, including PMOS transistors: M00, M4, M5, NMOS transistors: M0, M1, M2, M3, and PNP transistors: Q1, Q2, Q3. The gate of M00 is the output node VP of the positive temperature current source, and the node VP is connected to the drain, and is connected to the drain of M0, the gates of M5 and the gates of M4, and the source of M00 is connected to the power supply voltage VDD. The gate of M0 is connected to the drain of M5 and the drain of M3, and the source of M0 is connected to the emitter of Q3. The source of M5 is connected to the power supply voltage VDD. The drain of M4 is connected to the drain and gate of M2, the gate of M3 and the gate of M1, and the source of M4 is connected to the power supply voltage VDD. The source of M3 is connected to the emitter of Q2. Both the collector and the base of Q3 are connected to the ground potential VSS. The source of M2 is connected to the drain of M1. The source of M1 is connected to the emitter of Q1. The collectors and bases of Q2 and Q1 are both connected to the ground potential VSS.

A circuit implementation scheme of the above-mentioned negative temperature current source is shown in FIG. 4 , including PMOS transistors: M10, M11, M14, and NMOS transistors: M6, M7, M8, M9, M12, and M13. The gate of M14 is the output node VC of the negative temperature current source, the output node VC is connected to the drain, and is connected to the drain of M13, the gates of M10 and M11, and the source of M14 is connected to the power supply voltage VDD. The gate of M13 is connected to the drain of M10 and the drain of M8, and the source of M13 is connected to the drain and gate of M12. The source of M10 is connected to the power supply voltage VDD. The drain of M11 is connected to the drain and gate of M9, the gate of M8 and the gate of M7, and the source of M11 is connected to the power supply voltage VDD. The source of M8 is connected to the drain and gate of M6. The source of M9 is connected to the drain of M7. The source of M6, the source of M7, and the source of M12 are all connected to the ground potential VSS.

In Figure 2, I _P is F times of the current I _bias generated by the positive temperature current source, and F is a quantity independent of temperature. I _C1 and I _C2 are the currents generated by the negative temperature current source. Here I _C1 and I _C2 are generated by the same negative temperature current source, as follows: I _C1 =I _C2 =I _C . The PMOS transistors M15 and M16 working in the sub-threshold region implement voltage superposition, and on the basis of the bandgap reference voltage VREF1 that has been partially compensated for the first-order temperature, a voltage quantity with both first-order and second-order temperature compensation effects is superimposed, thereby generating The final second-order curvature temperature compensated bandgap reference output voltage VREF2.

As shown in Figure 3, the positive temperature current I _bias generated by the positive temperature current source can be expressed as

${\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; bias</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; \&delta;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; T</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; T</span>}}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; \&delta;</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; T</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; no</span>}}$

in

${\mathrm{<span\; class="notranslate">\; \&delta;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; \&mu;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}\mathrm{<span\; class="notranslate">\; N</span>}}{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; OX</span>}}{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; W</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; L</span>}<span\; class="notranslate">\; )</span>}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}{\mathrm{<span\; class="notranslate">\; 2</span>}{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; W</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; L</span>}<span\; class="notranslate">\; )</span>}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; +</span>\sqrt{\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; +</span>{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; W</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; L</span>}<span\; class="notranslate">\; )</span>}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; /</span>{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; W</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; L</span>}<span\; class="notranslate">\; )</span>}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; ln</span>}\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}$

${\mathrm{<span\; class="notranslate">\; \&delta;</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; \&mu;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}\mathrm{<span\; class="notranslate">\; N</span>}}{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; OX</span>}}{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; W</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; L</span>}<span\; class="notranslate">\; )</span>}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}{\mathrm{<span\; class="notranslate">\; 2</span>}{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; W</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; L</span>}<span\; class="notranslate">\; )</span>}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; +</span>\sqrt{\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; +</span>{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; W</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; L</span>}<span\; class="notranslate">\; )</span>}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; /</span>{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; W</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; L</span>}<span\; class="notranslate">\; )</span>}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}{<span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; k</span>}}{\mathrm{<span\; class="notranslate">\; q</span>}}\mathrm{<span\; class="notranslate">\; ln</span>}\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}$

V _T is the thermal voltage, Indicates the width-to-length ratio of the MOS tube, C _OX is the capacitance per unit area of the gate oxide of the MOS tube, m is the ratio of the emitter area of the PNP transistor Q1 and Q2, and q is the unit charge. The electron mobility in the NMOS tube can be expressed as μ _N (T) = μ _0N T ^-n , μ _0N is a constant independent of temperature, n is a constant related to doping concentration, and its value is about 1.5 in general processes.

As shown in Figure 4, the current I _C can be expressed as in

${\mathrm{<span\; class="notranslate">\; \&delta;</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; \&mu;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}\mathrm{<span\; class="notranslate">\; N</span>}}{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; OX</span>}}{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; W</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; L</span>}<span\; class="notranslate">\; )</span>}_{\mathrm{<span\; class="notranslate">\; 7</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}{\mathrm{<span\; class="notranslate">\; 2</span>}{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; W</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; L</span>}<span\; class="notranslate">\; )</span>}_{\mathrm{<span\; class="notranslate">\; 9</span>}}}{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; +</span>\sqrt{\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; +</span>{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; W</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; L</span>}<span\; class="notranslate">\; )</span>}_{\mathrm{<span\; class="notranslate">\; 9</span>}}<span\; class="notranslate">\; /</span>{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; W</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; L</span>}<span\; class="notranslate">\; )</span>}_{\mathrm{<span\; class="notranslate">\; 7</span>}}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}$

V _THN is the threshold voltage of the NMOS tube. The threshold voltage of the NMOS transistor can be expressed as

V _THN (T)=V _THN (T ₀₀ )-α _VTN (TT ₀₀ )=β-α _VTN T

Where T ₀₀ is the reference temperature, α _VTN is the threshold voltage temperature coefficient of the NMOS transistor, α _VTN >0, β=V _THN (T ₀₀ )+α _VTN T ₀₀ . Therefore, the current I _C can be further expressed as

${\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; C</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; \&delta;</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}{\mathrm{<span\; class="notranslate">\; T</span>}}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; no</span>}}{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&beta;</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}_{\mathrm{<span\; class="notranslate">\; VTN</span>}}\mathrm{<span\; class="notranslate">\; T</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; \&delta;</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}_{\mathrm{<span\; class="notranslate">\; VTN</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; T</span>}}^{\mathrm{<span\; class="notranslate">\; 0.5</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}_{\mathrm{<span\; class="notranslate">\; VTN</span>}}{\mathrm{<span\; class="notranslate">\; \&beta;\; T</span>}}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 0.5</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&beta;</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>$

Wherein, α _VTN << β.

The drain current _ID of the PMOS transistor working in the sub-threshold region can be expressed as The voltage between source and gate Wherein, I _D0 =μ _P (T)C _OX (η-1)V _T ² , V _THP is the threshold voltage of the PMOS tube, μ _P (T) is the hole mobility in the PMOS tube, and η is the subthreshold region slope. In Fig. 2, PMOS transistors M15 and M16 both work in the sub-threshold region and have the same width-to-length ratio. Current I _D15 =I _P =FI _bias flowing through M15, and I _D16 =I _C =I _C1 =I _C2 flowing through M16. Among them, F is a quantity independent of temperature, and its value can be adjusted by changing the width-to-length ratio of the MOS tube. then there is

$\begin{array}{c}\mathrm{<span\; class="notranslate">\; VREF</span>}\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; VREF</span>}\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; SG</span>}\mathrm{<span\; class="notranslate">\; 15</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; SG</span>}\mathrm{<span\; class="notranslate">\; 16</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; \&eta;V</span>}}_{\mathrm{<span\; class="notranslate">\; T</span>}}\mathrm{<span\; class="notranslate">\; ln</span>}<span\; class="notranslate">\; (</span>\frac{{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; D.</span>}\mathrm{<span\; class="notranslate">\; 15</span>}}}{{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; D.</span>}\mathrm{<span\; class="notranslate">\; 16</span>}}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; \&eta;V</span>}}_{\mathrm{<span\; class="notranslate">\; T</span>}}\mathrm{<span\; class="notranslate">\; ln</span>}<span\; class="notranslate">\; (</span>\frac{{\mathrm{<span\; class="notranslate">\; FI</span>}}_{\mathrm{<span\; class="notranslate">\; bias</span>}}}{{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; C</span>}}}<span\; class="notranslate">\; )</span>\\ <span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; \&eta;V</span>}}_{\mathrm{<span\; class="notranslate">\; T</span>}}\mathrm{<span\; class="notranslate">\; ln</span>}<span\; class="notranslate">\; (</span>\frac{{\mathrm{<span\; class="notranslate">\; F\&delta;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; T</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; T</span>}}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; no</span>}}}{{\mathrm{<span\; class="notranslate">\; \&delta;</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; TH</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; T</span>}}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; no</span>}}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; \&eta;V</span>}}_{\mathrm{<span\; class="notranslate">\; T</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; ln</span>}\frac{{\mathrm{<span\; class="notranslate">\; \&delta;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}{{\mathrm{<span\; class="notranslate">\; \&delta;</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; ln</span>}\frac{{\mathrm{<span\; class="notranslate">\; FV</span>}}_{\mathrm{<span\; class="notranslate">\; T</span>}}}{{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; TH</span>}}}<span\; class="notranslate">\; )</span>\\ <span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; \&eta;V</span>}}_{\mathrm{<span\; class="notranslate">\; T</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; ln</span>}\frac{{\mathrm{<span\; class="notranslate">\; \&delta;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}{{\mathrm{<span\; class="notranslate">\; \&delta;</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; ln</span>}\frac{\mathrm{<span\; class="notranslate">\; f</span>}}{\mathrm{<span\; class="notranslate">\; q\&beta;</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; ln</span>}\frac{\mathrm{<span\; class="notranslate">\; T</span>}}{\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&theta;T</span>}}<span\; class="notranslate">\; )</span>\\ <span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; T</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&eta;V</span>}}_{\mathrm{<span\; class="notranslate">\; T</span>}}\mathrm{<span\; class="notranslate">\; ln</span>}\frac{\mathrm{<span\; class="notranslate">\; T</span>}}{\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&theta;T</span>}}\end{array}$

in When a current I _bias flows through the emitter of the PNP transistor, the voltage between the emitter and the base

${\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; EB</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; T</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; T</span>}}\mathrm{<span\; class="notranslate">\; ln</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; bias</span>}}{\mathrm{<span\; class="notranslate">\; T</span>}}^{\mathrm{<span\; class="notranslate">\; \&epsiv;</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 4</span>}}\mathrm{<span\; class="notranslate">\; E\; exp</span>}\frac{{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; G</span>}\mathrm{<span\; class="notranslate">\; 0</span>}}}{{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; T</span>}}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; G</span>}\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; T</span>}}\mathrm{<span\; class="notranslate">\; ln</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; E.</span>}{\mathrm{<span\; class="notranslate">\; \&delta;</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&epsiv;</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; T</span>}}\mathrm{<span\; class="notranslate">\; ln</span>}\mathrm{<span\; class="notranslate">\; T</span>}$

Where E is a temperature-independent constant, and V _G0 is the bandgap voltage of silicon at a temperature of 0K. The base electron mobility in a PNP transistor can be expressed as μ(T)=μ ₀ T ^-ε , where μ ₀ is a constant independent of temperature, and ε is a constant related to doping concentration.

VREF1 is a bandgap reference voltage with partial first-order temperature compensation, VREF1=V _EB (T)+A ₀ V _T , A ₀ is a temperature-independent quantity, and the value of A ₀ can be adjusted by changing the width-to-length ratio of the MOS tube . then there is

$\mathrm{<span\; class="notranslate">\; VREF</span>}\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; G</span>}\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; +</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; T</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; T</span>}}\mathrm{<span\; class="notranslate">\; ln</span>}\mathrm{<span\; class="notranslate">\; T</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; 4</span>}}{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; T</span>}}\mathrm{<span\; class="notranslate">\; ln</span>}\frac{\mathrm{<span\; class="notranslate">\; T</span>}}{\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&theta;T</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>$

Wherein A ₁ =ln(Eδ ₁ ), A ₃ =n-ε+2, A ₄ =2η. Assuming that the temperature at zero temperature point is T ₀ , the expression of VREF2 can be rewritten as

$\mathrm{<span\; class="notranslate">\; VREF</span>}\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; G</span>}\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; T</span>}}<span\; class="notranslate">\; [</span>{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; 4</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; ln</span>}\frac{{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}{\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&theta;T</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}<span\; class="notranslate">\; +</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&theta;T</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ]</span><span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; T</span>}}\mathrm{<span\; class="notranslate">\; ln</span>}\frac{\mathrm{<span\; class="notranslate">\; T</span>}}{{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; 4</span>}}{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; T</span>}}\mathrm{<span\; class="notranslate">\; ln</span>}\frac{\mathrm{<span\; class="notranslate">\; T</span>}}{\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&theta;T</span>}}<span\; class="notranslate">\; .</span>$

Carrying out the second-order Taylor expansion of the above formula around T=T ₀ , we have

VREF2≌a+bT+cT ² (2)

in

$\mathrm{<span\; class="notranslate">\; a</span>}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; G</span>}\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; +</span>\frac{{\mathrm{<span\; class="notranslate">\; kA</span>}}_{\mathrm{<span\; class="notranslate">\; 4</span>}}{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; q</span>}{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&theta;T</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; -</span>\frac{{\mathrm{<span\; class="notranslate">\; kA</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; q</span>}}$

$\mathrm{<span\; class="notranslate">\; b</span>}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; k</span>}}{\mathrm{<span\; class="notranslate">\; q</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; -</span>\frac{{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; 4</span>}}}{{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&theta;T</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; )</span>$

$\mathrm{<span\; class="notranslate">\; c</span>}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; k</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; q</span>}}<span\; class="notranslate">\; (</span>\frac{{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; 4</span>}}}{{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&theta;T</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; -</span>\frac{{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}}{{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}<span\; class="notranslate">\; )</span>$

According to the formula (2), if you want to realize the first-order and second-order temperature compensation at the same time, you must have b=c=0, that is

${\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; -</span>\frac{{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; 4</span>}}}{{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&theta;T</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; 4</span>}}}{{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&theta;T</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; -</span>\frac{{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}}{{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; )</span>$

In formula (3), only T ₀ is a variable quantity, then the above formula can be established by adjusting the zero temperature point T ₀ . Specifically, calculate the partial derivative of formula (1) with respect to temperature and set the partial derivative to zero, namely get

$<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; ln</span>}{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; 4</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; ln</span>}\frac{{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}{\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&theta;T</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}<span\; class="notranslate">\; +</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&theta;T</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0</span>}$

Solve T ₀ =f(F,A ₀ ), which means that T ₀ is a function of F and A ₀ , that is to say, the width-to-length ratio of the MOS tube can be changed to adjust the size of F and A ₀ and then change the zero temperature point T ₀ , so that formula (3) holds. In this way, the second-order temperature compensation of the BE junction voltage of the triode can be realized.

In summary, it can be seen that the bandgap reference second-order curvature temperature compensation circuit proposed by the present invention does not need to use resistors, and can be realized in standard CMOS technology, so that its application range and flexibility are significantly improved.

Those of ordinary skill in the art will appreciate that the embodiment described here is to help the reader understand the principle of the present invention, and the protection scope of the present invention is not limited to such special statements and embodiments, such as the above-mentioned positive temperature current source and The negative temperature current source can be realized by using various circuits with different structures, and these deformations and combinations are still within the protection scope of the present invention.

Claims (1)

1., for the second order curvature temperature-compensation circuit of band-gap reference, comprise, PMOS: M15, M16, M17, M18, M19, NMOS tube: M20, M21; Wherein, the grid of M15 is connected through the bandgap voltage reference signal of part single order temperature compensation, and as the input end of described second order curvature compensating circuit, the source electrode of M15 is connected with substrate and is connected the source electrode of the drain electrode of M17, the drain electrode of M18 and M16, and the drain electrode of M15 connects earth potential; The grid of M17 connects the output node of positive temperature current source, and the source electrode of M17 connects supply voltage; The grid of M18 connects the output node of subzero temperature current source and is connected with the grid of M19, and the source electrode of M18 connects supply voltage; The source electrode of M16 is connected with substrate, and the grid of M16 is connected with drain electrode and is connected the drain electrode of M20, as the output terminal of described second order curvature compensating circuit; The drain electrode of M19 connects the grid of M21 and the grid of drain electrode and M20, and the source electrode of M19 connects supply voltage; The source electrode of M20 with M21 is all connected earth potential;

Described positive temperature current source comprises, PMOS: M00, M4, M5, NMOS tube: M0, M1, M2, M3, PNP type triode: Q1, Q2, Q3; Wherein, the grid of M00 is the output node of positive temperature current source, being connected with drain electrode of the grid of M00, and connects the grid of the drain electrode of M0, the grid of M5 and M4, the source electrode connection supply voltage of M00; The grid of M0 connects the drain electrode of M5 and the drain electrode of M3, and the source electrode of M0 connects the emitter of Q3; The source electrode of M5 connects supply voltage; The drain electrode of M4 connects the grid of the drain and gate of M2, the grid of M3 and M1, and the source electrode of M4 connects supply voltage; The source electrode of M3 connects the emitter of Q2; The collector of Q3 is all connected earth potential with base stage; The source electrode of M2 connects the drain electrode of M1; The source electrode of M1 connects the emitter of Q1; The collector of Q2, Q1 is all connected earth potential with base stage;

Described subzero temperature current source comprises, PMOS: M10, M11, M14, NMOS tube: M6, M7, M8, M9, M12, M13; Wherein the grid of M14 is the output node of subzero temperature current source, and the grid of M14 is connected with drain electrode, and connects the grid of the drain electrode of M13, the grid of M10 and M11, the source electrode connection supply voltage of M14; The grid of M13 connects the drain electrode of M10 and the drain electrode of M8, and the source electrode of M13 connects the drain and gate of M12; The source electrode of M10 connects supply voltage; The drain electrode of M11 connects the grid of the drain and gate of M9, the grid of M8 and M7, and the source electrode of M11 connects supply voltage; The source electrode of M8 connects the drain and gate of M6; The source electrode of M9 connects the drain electrode of M7; The source electrode of M6, M7, M12 all connects earth potential.