Resistor circuit with temperature coefficient compensation

Abstract

The present invention discloses a resistor circuit with temperature coefficient compensation, which comprises a first series resistor composed of a first resistor and a second resistor interconnected in series, and a second parallel resistor composed of a third resistor and a fourth resistor interconnected in series, with the first series resistor and the second parallel resistor interconnected in series, wherein the first resistor and the second resistor respectively have a positive and negative temperature coefficient and make the positive and negative temperature coefficients of the first series resistor offset each other, and the third resistor and the fourth resistor respectively have a positive and negative temperature coefficient and make the positive and negative temperature coefficients of the second parallel resistor offset each other.

Claims

1. A resistor circuit with temperature coefficient compensation, comprising a first resistor array and a second resistor array connected in series; wherein the first resistor array is composed of a first resistor and a second resistor interconnected in series, and the second resistor array is composed of a third resistor and a fourth resistor interconnected in parallel; wherein the first resistor and the third resistor have positive temperature coefficient, and the second resistor and the fourth resistor have negative temperature coefficient, wherein the first resistor array forms a first-order temperature compensation by the first resistor and the second resistor in series connection; the second resistor array forms a first-order temperature compensation by the third resistor and the fourth resistor connected in parallel; wherein the first resistor array and the second array interconnected in series form a second-order temperature compensation.

2. The resistor circuit with temperature coefficient compensation according to claim 1, wherein the first positive temperature coefficient, the first negative temperature coefficient, the second positive temperature coefficient, and the second negative temperature coefficient are all first-order coefficients.

3. The resistor circuit with temperature coefficient compensation according to claim 2, wherein an absolute value of a product of the first positive temperature coefficient and a constant term of the first resistor is equal to an absolute value of a product of the first negative temperature coefficient and a constant term of the second resistor.

4. The resistor circuit with temperature coefficient compensation according to claim 3, wherein the absolute value of the first positive temperature coefficient is equal to that of the first negative temperature coefficient, and the constant term of the first resistor is equal to that of the second resistor.

5. The resistor circuit with temperature coefficient compensation according to claim 2, wherein the absolute value of the second positive temperature coefficient is equal to that of the second negative temperature coefficient, and the constant term of the third resistor is equal to that of the fourth resistor.

6. The resistor circuit with temperature coefficient compensation according to claim 2, wherein the absolute value of the second positive temperature coefficient is unequal to that of the second negative temperature coefficient; the constant terms of the third resistor and the fourth resistor are set according to the second positive temperature coefficient and the second negative temperature coefficient, and a first-order temperature coefficient of the second parallel resistor is set to be zero.

7. The resistor circuit with temperature coefficient compensation according to claim 2, wherein the first positive temperature coefficient is equal to the second positive temperature coefficient, and the first negative temperature coefficient is equal to the second negative temperature coefficient.

8. The resistor circuit with temperature coefficient compensation of claim 1, wherein the first resistor, the second resistor, the third resistor and the fourth resistor are formed with the CMOS process and integrated on one and the same silicon chip.

9. The resistor circuit with temperature coefficient compensation according to claim 8, wherein the first resistor is a polysilicon resistor, a diffusion resistor or an N-well resistor in the CMOS process; the third resistor is a polysilicon resistor, a diffusion resistor or an N-well resistor in the CMOS process; the second resistor is a polysilicon resistor; and the fourth resistor is a polysilicon resistor.

10. A resistor circuit with temperature coefficient compensation, comprising a first series resistor composed of a first resistor and a second resistor interconnected in series, and a second parallel resistor composed of a third resistor and a fourth resistor interconnected in series, with the first series resistor and the second parallel resistor interconnected in series; the first resistor has a first positive temperature coefficient, and the second resistor has a first negative temperature coefficient, with the first resistor, the second resistor, the first positive temperature coefficient and the first negative temperature coefficient set to make the positive and negative temperature coefficients of the first series resistor offset each other; and the third resistor has a second positive temperature coefficient, and the fourth resistor has a second negative temperature coefficient, with the third resistor, the fourth resistor, the second positive temperature coefficient and the second negative temperature coefficient set to make the positive and negative temperature coefficients of the second parallel resistor offset each other.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) The present invention will be further described below in detail with reference to drawings and specific embodiments.

(2) FIG. 1 shows an existing resistor circuit with temperature coefficient compensation;

(3) FIG. 2 shows a resistor circuit with temperature coefficient compensation of the example of the present invention;

(4) FIG. 3A shows a curve of the series resistor in FIG. 2 varying with the temperature;

(5) FIG. 3B shows a curve of the parallel resistor in FIG. 2 varying with the temperature;

(6) FIG. 3C shows a curve of a total resistor varying with the temperature, with the total resistor composed of the resistors in FIG. 2 interconnected in series and parallel;

(7) FIG. 4A is a test curve of the resistor circuit of the example of the present invention and the existing resistor circuit at the first process corner; and

(8) FIG. 4B is a test curve of the resistor circuit of the example of the present invention and the existing resistor circuit at the second and third process corners.

DETAILED DESCRIPTION OF THE EMBODIMENTS

(9) As shown in FIG. 2, there is a resistor circuit with temperature coefficient compensation of the example of the present invention. The resistor circuit with temperature coefficient compensation of the example of the present invention comprises a first series resistor R1 composed of a first resistor Rp1 and a second resistor Rn1 interconnected in series, and a second parallel resistor R2 composed of a third resistor Rp2 and a fourth resistor Rn2 interconnected in series, with the first series resistor R1 and the second parallel resistor R2 interconnected in series.

(10) The first resistor Rp1 has a first positive temperature coefficient, and the second resistor Rn1 has a first negative temperature coefficient, with the first resistor Rp1, the second resistor Rn1, the first positive temperature coefficient and the first negative temperature coefficient set to make the positive and negative temperature coefficients of the first series resistor R1 offset each other.

(11) The third resistor Rp2 has a second positive temperature coefficient, and the fourth resistor Rn2 has a second negative temperature coefficient, with the third resistor Rp2, the fourth resistor Rn2, the second positive temperature coefficient and the second negative temperature coefficient set to make the positive and negative temperature coefficients of the second parallel resistor R2 offset each other.

(12) The temperature coefficient of the resistor can include a first-order coefficient, a second-order coefficient and so on; when considering a multiple-order coefficient, there is the following Formula (I):
R=R.sub.0×(1+α.sub.1×T+α.sub.2×T.sup.2+ . . . )  (1)

(13) In Formula (I), R represents resistance having a temperature coefficient, R0 represents a constant term of the resistance, T represents the difference between the actual temperature and the ambient temperature (with the ambient temperature in the example of the present invention being 25° C.), α.sub.1 represents a first-order coefficient, and α.sub.2 represents a second-order coefficient. A higher-order coefficient than α.sub.2 can be generally ignored. Therefore, it is preferred that the first positive temperature coefficient, the first negative temperature coefficient, the second positive temperature coefficient, and the second negative temperature coefficient are all a first-order coefficient.

(14) The temperature coefficient of the first series resistor R1 can be deduced as follows:
R1=Rp1+Rn1=Rp1.sub.0×(1+α.sub.11×T)+Rn1.sub.0×(1+α.sub.12×T)=Rp1.sub.0+Rn1.sub.0+(Rp1.sub.0×α.sub.11+Rn1.sub.0×α.sub.12)T  (2)

(15) In Formula (2), R1 represents the value of the first series resistor R1, Rp1 represents the value of the first resistor Rp1, Rn1 represents the value of the second resistor Rn1, Rp1.sub.0 represents the constant term of Rp1, Rn1.sub.0 represents the constant term of Rn1, α.sub.11 represents the first positive temperature coefficient, and α.sub.12 represents the first negative temperature coefficient. It can be known that, in order to make R1 irrelevant to the temperature, the coefficient (Rp1.sub.0×α.sub.11+Rn1.sub.0×α.sub.12) needs to be set as zero, that is, the absolute value of the product of the first positive temperature coefficient α.sub.11 and the constant term of the first resistor Rp1 is equal to the absolute value of the product of the first negative temperature coefficient α.sub.12 and the constant term of the second resistor Rn1. In a preferred example, the absolute value of the first positive temperature coefficient is set to be equal to that of the first negative temperature coefficient, and the constant term of the first resistor Rp1 is also set to be equal to that of the second resistor Rn1.

(16) The temperature coefficient of the second series resistor R2 can be deduced as follows:

(17) $\begin{array}{cc}R2=\frac{\mathrm{Rp}2\times \mathrm{Rn}2}{\mathrm{Rp}2+\mathrm{Rn}2}=\frac{\mathrm{Rp}{2}_0\times \mathrm{Rn}{2}_0\left[1+{\alpha }_{13}+{\alpha }_{14}\right)T+\left({\alpha }_{13}\times {\alpha }_{14}\right)T^2]}{\mathrm{Rp}{2}_0+\mathrm{Rn}{2}_0+\left(\mathrm{Rp}{2}_0\times {\alpha }_{13}+\mathrm{Rn}{2}_0\times {\alpha }_{14}\right)T}& \left(3\right)\end{array}$

(18) Performing the Taylor expansion on Formula (3) and omitting the second-order term to get the following equation:

(19) $\begin{array}{cc}\hspace{1em}R2=\frac{\mathrm{Rp}{2}_0\times \mathrm{Rn}{2}_0}{Rp{2}_0+Rn{2}_0}\times \left\{1+\left[{\alpha }_{13}+{\alpha }_{14}-\frac{\mathrm{Rp}{2}_0\times {\alpha }_{13}+\mathrm{Rn}{2}_0\times {\alpha }_{14}}{Rp{2}_0+Rn{2}_0}\right]\times T\right\}& \left(4\right)\end{array}$

(20) R2 in Formulas (3) and (4) represents the value of the second parallel resistor R2, Rp2 represents the value of the third resistor Rp2, Rn2 represents the value of the fourth resistor Rn2, Rp2.sub.0 represents the constant term of Rp2, Rn2.sub.0 represents the constant term of Rn2, α.sub.13 represents the second positive temperature coefficient, and α.sub.14 represents the second negative temperature coefficient. It can be known that, in order to make R2 irrelevant to temperature, the coefficient

(21) $\left[{\alpha }_{13}+{\alpha }_{14}-\frac{\mathrm{Rp}{2}_0\times {\alpha }_{13}+\mathrm{Rn}{2}_0\times {\alpha }_{14}}{\mathrm{Rp}{2}_0+Rn{2}_0}\right]$
needs to be set as zero. When the absolute value of the second positive temperature coefficient α.sub.13 is set to be equal to that of the second negative temperature coefficient α.sub.14, the constant term of the third resistor Rp2 is also set to be equal to that of the fourth resistor Rn2. When the absolute value of the second positive temperature coefficient α.sub.13 is set to be unequal to that of the second negative temperature coefficient α.sub.14, the constant terms of the third resistor Rp2 and the fourth resistor Rn2 are such set as to meet the above Formula (4), thus making the first-order temperature coefficient of the second parallel resistor R2 be zero.

(22) In a preferred example, the first positive temperature coefficient is equal to the second positive temperature coefficient, and the first negative temperature coefficient is equal to the second negative temperature coefficient.

(23) In the example of the present invention, the first resistor Rp1, the second resistor Rn1, the third resistor Rp2 and the fourth resistor Rn1 are formed with the CMOS process and integrated on one and the same silicon chip. The first resistor Rp1 is a polysilicon resistor, a diffusion resistor or an N-well resistor in the CMOS process; the third resistor Rp2 is a polysilicon resistor, a diffusion resistor or an N-well resistor in the CMOS process; the second resistor Rn1 is a polysilicon resistor; and the fourth resistor Rn2 is a polysilicon resistor. Thus, the resistor circuit with temperature coefficient compensation of the example of the present invention can be used in the on-chip RC oscillator.

(24) As shown in FIG. 3A, there is a curve of the series resistor R1 in FIG. 2 varying with the temperature. As shown in FIG. 3B, there is a curve of the parallel resistor in FIG. 2 varying with the temperature, and specifically a curve of four times the value of the parallel resistor R2, i.e. R2′, varying with the temperature. As shown in FIG. 3C, there is a curve of a total resistor R3 varying with the temperature, with the total resistor R3 composed of the resistors in FIG. 2 interconnected in series and parallel. The example of the present invention, by interconnecting in series the first series resistor R1 and the second parallel resistor R2 having temperature coefficient compensation, respectively, can provide the secondary temperature coefficient compensation function between the first series resistor R1 and the second parallel resistor R2 of the present invention; that is, when the process corners of the resistors having a positive and negative temperature coefficient are changed oppositely in direction, the temperature coefficient of the second parallel resistor R2 will deteriorate in the other direction while the temperature coefficient of the first series resistor R1 deteriorates in one direction, with both just achieving compensation, thereby able to keep the temperature coefficient compensation function in any combination of process corner variations and achieve the high-precision resistance at any process corners.

(25) As shown in FIG. 4A, there is a test curve of the resistor circuit of the example of the present invention and an existing resistor circuit at the first process corner, wherein the abscissa of the curve is T, i.e. the difference between the actual temperature and the ambient temperature, and the ordinate is unit resistance (Unite res.). As shown in FIG. 4B, there are test curves of the resistor circuit of the example of the present invention and an existing resistor circuit at the second and third process corners. Both of the first resistor Rp1 and the third resistor Rp2 of the resistor circuit tested in FIGS. 4A and 4B are of the p-type diffusion resistor B with a positive temperature coefficient in the CMOS process, and both of the second resistor Rn1 and the fourth resistor Rn2 are of the n-type polysilicon resistor A with a negative temperature coefficient in the CMOS process. To have a comparison, the resistor Rp101 of the existing resistor circuit shown in FIG. 1 is of the p-type diffusion resistor B with a positive temperature coefficient in the CMOS process, and the resistor Rn101 is of the n-type polysilicon resistor A with a negative temperature coefficient in the CMOS process. The first process corner is TypA&B, the second process corner is MAX A and MIN B, and the third process corner is MIN A and MAX B. The curve 201a is a test curve of the existing resistor circuit at the first process corner, the curve 201b is a test curve of the resistor circuit of the example of the present invention at the first process corner, the curve 202a is a test curve of the existing resistor circuit at the second process corner, the curve 202b is a test curve of the resistor circuit of the example of the present invention at the second process corner, the curve 203a is a test curve of the existing resistor circuit at the third process corner, and the curve 203b is a test curve of the resistor circuit of the example of the present invention at the third process corner. It can be known from the above comparison that the resistor of the example of the present invention can really make the resistor circuit keep the temperature coefficient compensation function in any combination of process corner variations, and achieve the high-precision resistance at any process corners. Besides, as shown in Table I, there are measurement values of the resistor circuit of the example of the present invention and an existing resistor circuit at the third process corner, respectively, with the measurement values in Table I obtained by dividing the difference between the greatest value and the minimum value of the unit resistance by the minimum value.

(26) TABLE-US-00001 TABLE I Measurement value of the Measurement resistor circuit of the value of the example of the present existing resistor Process invention circuit Multiples corner (MAX/MIN − 1%) (MAX/MIN − 1%) increased TypA&B 0.125% 0.625%  about 5 MAX A,  0.15% 4.35% about 29 MIN B MIN A, 0.255% 4.35% about 17 MAX B

(27) The present invention has been described in detail above through specific examples, which do not restrict the present invention. However, without departing from the principle of the present invention, those skilled in the art can also make a lot of deformation and improvement, which should be also regarded as within the scope of protection of the present invention.