Some Methods to Calculate the Values of Passive Components from the - PowerPoint PPT Presentation

2nd IEEE International Workshop on Board Test Some Methods to Calculate the Values of Passive Components from the Measurements Made with an 1149.4 Compliant Device Teuvo Saikkonen, Juha-Veikko Voutilainen, and Markku Moilanen Department of Electrical and Information Engineering, University of Oulu, Oulu, Finland

Purpose • Describe and develop calculation methods alleviating the problems encountered when using low cost instruments • Study 1149.4 applications • Discuss the preconditions and limitations

Outline • Test circuits • Calculation methods • Experimental results • Discussion

Introduction • The first general purpose 1149.4 IC was introduced at ITC 2001 by Sunter et al. • Duzevik presented preliminary results of passive component measurement methods using that IC at BTW02 • The same IC is used also in our research • Goal: measure the component values with a low cost instrumentation without phase measuring capability

Simple Test Circuit ABM1 ABM1 ABM2 Function ~ generator R sense Z x ABM4 ABM3 AT1 To analog AT2 ground Voltmeter V AB1 AB2

Test Board • Adjustable gain LF bandpass filter • TAP, AT1, AT2, inputs for external signals and components • Access to selected nodes on the board • Sense resistor R sense • Several parallel RC circuits – resistances defined by DC measurement – capacitances defined by AC measurement when resistances are known

Delta Connection AT1 AT2 AT2 AT1 ABM ABM V2, V4 V1, V5 I 2 I 1 A01 A0 R 1 R 2 R 3 A23 A2 ABM ABM V6 V3

Equivalent Circuits U 1 R sense U 2 R sw U 3 Z x R x C x U 4 R G

Equivalent Circuits U 1 R sense U 2 R sw U 3 C x R x U 4 R G

Z x Purely Resistive U 1 R sense U 2 R sw U 3 − U U = 3 4 R R R x x sense − U U 1 2 U 4 R G

Z x Purely Capacitive = U 4 U RG+Rsw U RG+Rsw+Rsense U RG U Cx//Cin = U x U 2 U 1 U 3 Condition: 1) C in << C x or 2) 2 π fR G C x <<1 = − 2 2 2 = − 2 2 2 U U U U x U U + + R R R 1 x 3 4 G sw sense = − 2 2 2 U U U + R R 2 x G sw

Z x Purely Capacitive = U 4 U RG+Rsw U RG+Rsw+Rsense U RG U Cx//Cin = U x U 2 U 1 U 3 2 2 U U − − − 1 1 2 1 − − 2 2 2 2 U U U U = − 3 4 3 4 C C x in ω R sense

Z x a Parallel Connection of R and C U RG+ZR+Rsw+Rsense U RG+ZR+Rsw U RG+ZR U RG =U 4 U ZC =U x U 2 U 1 U 3 2 ω R R C R = − = ∠ − ω Z x j x x x arctan( R C ) x x x + ω + ω 2 2 1 ( R C ) 1 ( R C ) + ω 2 1 ( R C ) x x x x x x If R G << Z R or R G + Z R << Z C , U 4 can be neglected And if: 1) C in << C x or 2) 2 π fR G C x <<1, we get

Z x a Parallel Connection of R and C U RG+ZR+Rsw+Rsense U RG+ZR+Rsw U RG+ZR U RG =U 4 U ZC =U x U 2 U 1 U 3 2   2 2       U U   2   2 1 2     − − − sin A sin A A = arctan ω R x C x       U U   3 3 1 − 2 2 R R sense x ′ = − C C C = C x x in x ω

Delta Connection − − ( V V ) ( V V ) = = R 1 2 R 4 5 R 1 3 2 − − V V V V 2 3 5 6 − − − − − ( V V )( V V ) ( V V )( V V ) = R 1 3 4 6 2 3 5 6 2 − − − I ( V V ) I ( V V ) 1 4 6 2 2 3 − − − − − ( V V )( V V ) ( V V )( V V ) = R 1 3 4 6 2 3 5 6 3 − − − I ( V V ) I ( V V ) 2 1 3 1 5 6 − − V V V V s 1 s 2 s 3 s 4 = = I I 1 2 R R sense sense

Capacitance Measurement Results STA - LCR [%] 4,00 3,00 4.27 nF 2,00 19.6 nF 1,00 n 47.6 nF 0,00 226 nF -5 -4 -3 -2 -1 0 1 2 3 4 5 -1,00 453 nF -2,00 971 nF -3,00 -4,00 f = (2 π R sense C nom ) -1 ⋅ 10 (n/10)

Capacitance Measurement Results • Errors increase when measuring small capacitances – conditions C in << C x or 2 π fR G C x <<1 not completely fulfilled (C in = 100 pF) – inaccuracy of the voltmeter increases above 100 kHz – loading effect of the voltmeter – bandwidth limitations of the 1149.4 IC • Solution: use higher R sense ⇒ lower f

Capacitance Measurement Results • Errors increase also when measuring large capacitances – reasons still need more consideration

RC Circuit Measurement Results • R values: error 0.12 % or less (DC measurement) C Values: STA - LCR [%] 6,00 5,00 4,00 f = 5 kHz 3,00 f = 10 kHz f = 50 kHz 2,00 f = 100 kHz 1,00 0,00 0 1 2 3 4 -1,00 nF

RC Circuit Measurement Results • The accuracy of measurements deteriorates at low frequencies – Z x approaches a pure resistance ⇒ impossible to define the reactance accurately

Delta Network Measurement Results R Values: STA - REF. [%] R1 ≈ R2 ≈ R3 15,00 10,00 R1(R2) 5,00 R1(R3) 0,00 R2 1,E+01 1,E+02 1,E+03 1,E+04 1,E+05 1,E+06 1,E+07 R3 -5,00 R [ohm] -10,00 R sense = 1 k Ω

Delta Network Measurement Results • When R1, R2 and R3 differ significantly from each other (~2 orders of magnitude or more), quite large errors can be found (Table 9) – Analog ground (V3 and V6) values measured through AT2 erroneous – When voltages are probed directly from pins, results are more accurate

Discussion • Several conditions have to be fulfilled when selecting f meas and R sense – Based partly on the system under test – And partly on the measurement instruments and the 1149.4 IC – And also on the assumptions made to simplify the calculations • If there is no phase measuring capability prior knowledge of the nature of the reactance (L or C) is necessary

Conclusion • The lack of elaborate instruments can be compensated for by calculations • Familiarity with the system under test is a necessity – the consequences of choosing improper measurement conditions were shown • Calculation methods are worth development if considered cost-effective