Omega Products CY670 User Manual

CY670 Series Silicon Diode Standard Curve CY670

Technical Data

M-4446/0307

Standard Curve CY670

Measurement Current = 10 µA ±0.05%

T Voltage dV/dT T Voltage dV/dT T Voltage dV/dT

(K) (V) (mV/K) (K) (V) (mV/K) (K) (V) (mV/K)

1.20 1.646540 -9.87 18.00 1.228300 -15.25 125.00 0.939242 -1.96

1.40 1.644290 -12.49 18.50 1.220700 -15.18 130.00 0.929390 -1.98

1.60 1.641570 -14.79 19.00 1.213110 -15.20 135.00 0.919446 -2.00

1.80 1.638370 -17.15 19.50 1.205480 -15.34 140.00 0.909416 -2.01

2.00 1.634720 -19.30 20.00 1.197748 -15.63 145.00 0.899304 -2.03

2.20 1.630670 -21.14 21.00 1.181548 -16.98 150.00 0.889114 -2.05

2.40 1.626290 -22.61 22.00 1.162797 -21.11 155.00 0.878851 -2.06

2.60 1.621660 -23.63 23.00 1.140817 -20.77 160.00 0.868518 -2.07

2.80 1.616870 -24.16 24.00 1.125923 -9.42 165.00 0.858120 -2.09

3.00 1.612000 -24.67 25.00 1.119448 -4.60 170.00 0.847659 -2.10

3.20 1.606970 -25.63 26.00 1.115658 -3.19 175.00 0.837138 -2.11

3.40 1.601730 -26.80 27.00 1.112810 -2.58 180.00 0.826560 -2.12

3.60 1.596260 -27.91 28.00 1.110421 -2.25 185.00 0.815928 -2.13

3.80 1.590570 -28.99 29.00 1.108261 -2.08 190.00 0.805242 -2.14

4.00 1.584650 -30.21 30.00 1.106244 -1.96 195.00 0.794505 -2.15

4.20 1.578480 -31.59 31.00 1.104324 -1.88 200.00 0.783720 -2.16

4.40 1.572020 -32.91 32.00 1.102476 -1.82 210.00 0.762007 -2.18

4.60 1.565330 -33.97 33.00 1.100681 -1.77 220.00 0.740115 -2.20

4.80 1.558450 -34.74 34.00 1.098930 -1.73 230.00 0.718054 -2.21

5.00 1.551450 -35.25 35.00 1.097216 -1.70 240.00 0.695834 -2.23

5.20 1.544360 -35.60 36.00 1.095534 -1.67 250.00 0.673462 -2.24

5.40 1.537210 -35.92 37.00 1.093878 -1.64 260.00 0.650949 -2.26

5.60 1.530000 -36.22 38.00 1.092244 -1.62 270.00 0.628302 -2.27

5.80 1.522730 -36.48 39.00 1.090627 -1.61 273.15 0.621141 -2.28

6.00 1.515410 -36.71 40.00 1.089024 -1.60 280.00 0.605528 -2.28

6.50 1.496980 -36.86 42.00 1.085842 -1.59 290.00 0.582637 -2.29

7.00 1.478680 -36.21 44.00 1.082669 -1.59 300.00 0.559639 -2.30

7.50 1.460860 -35.00 46.00 1.079492 -1.59 305.00 0.548102 -2.31

8.00 1.443740 -33.42 48.00 1.076303 -1.60 310.00 0.536542 -2.31

8.50 1.427470 -31.67 50.00 1.073099 -1.61 320.00 0.513361 -2.32

9.00 1.412070 -29.95 52.00 1.069881 -1.61 330.00 0.490106 -2.33

9.50 1.397510 -28.31 54.00 1.066650 -1.62 340.00 0.466760 -2.34

10.00 1.383730 -26.84 56.00 1.063403 -1.63 350.00 0.443371 -2.34

10.50 1.370650 -25.51 58.00 1.060141 -1.64 360.00 0.419960 -2.34

11.00 1.358200 -24.31 60.00 1.056862 -1.64 370.00 0.396503 -2.35

11.50 1.346320 -23.20 65.00 1.048584 -1.67 380.00 0.373002 -2.35

12.00 1.334990 -22.15 70.00 1.040183 -1.69 390.00 0.349453 -2.36

12.50 1.324160 -21.17 75.00 1.031651 -1.72 400.00 0.325839 -2.36

13.00 1.313810 -20.25 77.35 1.027594 -1.73 410.00 0.302161 -2.37

13.50 1.303900 -19.41 80.00 1.022984 -1.75 420.00 0.278416 -2.38

14.00 1.294390 -18.63 85.00 1.014181 -1.77 430.00 0.254592 -2.39

14.50 1.285260 -17.92 90.00 1.005244 -1.80 440.00 0.230697 -2.39

15.00 1.276450 -17.31 95.00 0.996174 -1.83 450.00 0.206758 -2.39

15.50 1.267940 -16.77 100.00 0.986974 -1.85 460.00 0.182832 -2.39

16.00 1.259670 -16.31 105.00 0.977650 -1.88 470.00 0.159010 -2.37

16.50 1.251610 -15.94 110.00 0.968209 -1.90 480.00 0.135480 -2.33

17.00 1.243720 -15.64 115.00 0.958657 -1.92 490.00 0.112553 -2.25

17.50 1.235960 -15.41 120.00 0.949000 -1.94 500.00 0.090681 -2.12

POLYNOMIAL REPRESENTATION

⎡⎤⎣

Curve CY670 can be expressed by a polynomial equation based on the Chebychev polynomials. Four separate ranges are required to accurately describe the curve. Table 1 lists the parameters for these ranges. The polynomials represent Curve CY670 on the preceding page with RMS deviations of 10 mK. The Chebychev equation is:

Tx atx

() ()

where T(x) = temperature in Kelvin, t

a normalized variable given by:

where Z = voltage and ZL and ZU = lower and upper limit of the voltage over the fit range. The Chebychev polynomials can

be generated from the recursion relation:

Alternately, these polynomials are given by: The use of Chebychev polynomials is no more complicated than the use of the regular power series and they offer significant advantages in the actual

fitting process. The first step is to transform the measured voltage into the normalized variable using Equation (2). Equation (1) is then used in combination with equations (3) and (4) to calculate the temperature. Programs 1 and 2 provide sample BASIC subroutines that will take the voltage and return the temperature T calculated from Chebychev fits. The subroutines assume the values ZL and ZU have been input along with the degree of the fit. The Chebychev coefficients are also assumed to be in any array A(0), A(1),..., A(i

An interesting property of the Chebychev fit is evident in the form of the Chebychev polynomial given in Equation (4). No term in Equation (1) will be greater than the absolute value of the coefficient. This property makes it easy to determine the contribution of each term to the temperature calculation and where to truncate the series if full accuracy is not required.

FUNCTION Chebychev (Z as double)as double REM Evaluation of Chebychev series X=((Z-ZL)-(ZU-Z))/(ZU-ZL) Tc(0)=1 Tc(1)=X T=A(0)+A(1)*X FOR I=2 to Ubound(A()) Tc(I)=2*X*Tc(I-1)-Tc(I-2) T=T+A(I)*Tc(I) NEXT I Chebychev=T END FUNCTION

Program 1. BASIC subroutine for evaluating the temperature T from the Chebychev series using Equations (1) and (3). An array Tc (i

) should be dimensioned. See text for details.

degree

(x) = a Chebychev polynomial, and ai = the Chebychev coefficient. The parameter x is

tx xtxtx

iii

+−

tx tx x

() ()

tx i x=

() ()

∑

ZL ZU Z

−− −

()( )

ZU ZL

()

=−

() () ()

cos • arccos

−

FUNCTION Chebychev (Z as double)as double REM Evaluation of Chebychev series X=((Z-ZL)-(ZU-Z))/(ZU-ZL) T=0 FOR I=0 to Ubound(A()) T=T+A(I)*COS(I*ARCCOS(X)) NEXT I Chebychev=T END FUNCTION

NOTE:

Program 2. BASIC subroutine for evaluating the temperature T

from the Chebychev series using Equations (1) and (4). Double precision calculations are recommended.

⎦

degree

arccos arctan

()

=−

(1)

(2)

(3)

(4)

⎡⎤

⎢⎥ ⎣⎦

−

Table 1.

2.0 K to 12.0 K 12.0 K to 24.5 K 24.5 K to 100.0 K 100 K to 500 K

ZL = 1.294390 ZU = 1.680000 A(0) = 6.429274 A(1) = -7.514262 A(2) = -0.725882 A(3) = -1.117846 A(4) = -0.562041 A(5) = -0.360239 A(6) = -0.229751 A(7) = -0.135713 A(8) = -0.068203 A(9) = -0.029755

ZL = 1.11230 ZU = 1.38373 A(0) = 17.244846 A(1) = -7.964373 A(2) = 0.625343 A(3) = -0.105068 A(4) = 0.292196 A(5) = -0.344492 A(6) = 0.271670 A(7) = -0.151722 A(8) = 0.121320 A(9) = -0.035566 A(10) = 0.045966

ZL = 0.909416 ZU = 1.122751 A(0) = 82.017868 A(1) = -59.064244 A(2) = -1.356615 A(3) = 1.055396 A(4) = 0.837341 A(5) = 0.431875 A(6) = 0.440840 A(7) = -0.061588 A(8) = 0.209414 A(9) = -0.120882 A(10) = 0.055734 A(11) = -0.035974

ZL = 0.07000 ZU = 0.99799 A(0) = 306.592351 A(1) = –205.393808 A(2) = -4.695680 A(3) = -2.031603 A(4) = -0.071792 A(5) = -0.437682 A(6) = 0.176352 A(7) = -0.182516 A(8) = 0.064687 A(9) = -0.027019 A(10) = 0.010019