JIS Z803: (substitution method) 3 LCR LCR GPIB

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1 LCR NMIJ 003 Agilent 8A 500 ppm

2 JIS Z803: (substitution method) 3 LCR LCR GPIB

3 Taylor 5 LCR LCR meter (Agilent 8A: Basic accuracy 500 ppm) V D z o I V DUT Z 3 V 3 I A Z V = I V = 0 3 6

4 V, A LCR meter z o I V D A V V 3 3 I Z DUT 7 [Ω] 0 mh at 59 Hz 0 m ppm 3 (Lp) (Lc) (Hc) (Hp) [m] (LCR meter: Agilent 8A) 8

5 at 59 Hz 90 mv [ppm] Ω 00 Ω 0 Ω 80 Ω [mv] (LCR meter: Agilent 8A) Ω 0. Ω 0.5 ma 0.5 ma 00.9 Ω 0. Ω 00 mv ma ma 0 mv ma 0.50 ma LCR 00 Ω 0 ppm 0

6 LCR r x x = LCR y = fr ( rx, ) LCR y = f( x) = f ( rx, ) x = x+ ( y y) x x x 0 Taylor frr ( x0) frx ( x0) y = f( x ) ( ) ( ) ( ) ( ) 0 + x x0 + δ xx, 0 f x f x Xr 0 Xx 0 R X f R fr fx fx frr =, frx =, fxr =, fxx = r x r x X LCR f ( x ) f ( x ) Rr 0 Rx 0 y y F( x0 ) = fxr ( x0) fxx ( x0) y = f( x0) + F( x0) ( x x0) + δ( x, x ) ε 0 y = f( x0) + F( x0) ( x x0) + δ( x, x ) θ 0 δ x x+ ( y y) = x+ F( x0) ( x x) + δ( x, x0) δ( x, x0) = x + ( x ) ( x x ) + δ( x, x ) δ( x, x ) ( x0) f ( x0) ( x ) f ( x ) x frr Rx ε r θ x ( x0) = F( x0) E= = fxr 0 Xx 0 θr ε x E x 0

7 K. Suzuki et al., A Calibration Method for Four- Terminal-Pair High-Frequency Resistance Standards, IEEE Trans. Instrum. Meas., vol., no.3, pp ,993. e X x X θ x O e x x Ζ O O Impedance plane r y θ r R e r e R ε r, ε x θ r, θ x Z O δ = (δ r, δ x ) y Ax + ZO ( + εr) cosθr ( + εx) sinθx A ( + εr) sinθr ( + εx) cosθx ( ) δ = y Ax + Z O 3 x 0 ε r, ε x θ r, θ x δ x 0

8 ε x < C: µf ppm of µf C C Meas C - C [nf] [nf] Span Error of LCR meter (Agilent 8A, C = µf) Date: 00/May/30 Span 500 ppm C: 0 nf ( ~ C/ C = %) Hz Hz Span -500 ppm Increment Increment of Capacitance of capacitance C C [nf] [nf] 5 30 ppm H. Fujimoto et. al, Development of Four-Terminal Pair High Capacitance Standards and Calibration Method Using Resister Standards, 00 NCSL Japan Forum, in Japanese. tanδ Q or 6

9 ( ) δ = y Ax+ Z O r = X ( ) t t x= r x, y= ( R X) X = a x + a 0 σ (δ X ) X i X i δ X,i O x x i 7 I Z δ X / Z (0 mh, 00 mh) Improved Voltage Method () V V 3 V Z = I V 3 V3 = 0 Z = KZ V' ' KV Relative Error δ X/ Z [ppm] σ (δ X / Z ) =. ppm Ratio Z '/Z () K.Suzuki et al.: Non-Linearity Evaluation Method of Four-Terminal-Pair LCR Meter, NCSL International Conference Proceedings

10 δ X / Z < (0 mh, 00 mh) Improved Current Method () KV V σ(δ B / Y ) =.3 ppm Y V 3 Y p KVY p I = Y V V3 = 0 I V 3 I' ' KY Y = + p Y Y Relative Error δb / Y [ppm] Ratio (+ Y p K/Y ) () K.Suzuki et al.: Non-Linearity Evaluation Method of Four-Terminal-Pair LCR Meter, NCSL International Conference Proceedings X O x x x 0 ε, θ, δ No LCR Yes Taylor No Yes R 0

11 0 0-6 Improved Current Method (0 mh at Hz) Relative Error δb / Y [ppm] LCR meter: Agilent 8A S/N MY007, Voltage: 6 mv, Ratio LCR Agilent 8A 000 Hz

1 1 sin cos P (primary) S (secondly) 2 P S A sin(ω2πt + α) A ω 1 ω α V T m T m 1 100Hz m 2 36km 500Hz. 36km 1

1 1 sin cos P (primary) S (secondly) 2 P S A sin(ω2πt + α) A ω 1 ω α V T m T m 1 100Hz m 2 36km 500Hz. 36km 1 sin cos P (primary) S (secondly) 2 P S A sin(ω2πt + α) A ω ω α 3 3 2 2V 3 33+.6T m T 5 34m Hz. 34 3.4m 2 36km 5Hz. 36km m 34 m 5 34 + m 5 33 5 =.66m 34m 34 x =.66 55Hz, 35 5 =.7 485.7Hz 2 V 5Hz.5V.5V V

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