Fundamentals of DC Testing
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1 Fundamentals of DC Testing Aether Lee erigy Japan Abstract n the beginning of this lecture, Ohm s la, hich is the most important electric la regarding DC testing, ill be revieed. Then, in the second section, e ill discuss resistance measurement.. Ohm s La Probably no one ill disagree that DC testing is all about ohm s la hich can be expressed in a simple form: Literally, as shon in Figure, the current floing through a resistor is proportional to the voltage across it and reverse proportional to the resistance of it. Figure. Ohm s la. n another ay of expression, for an ideal resistor, vary the voltage across it and note the value of correspondent current, e can have a straight line passing through origin, as shon in Figure 2. Aether, Fundamentals of DC Testing May09
2 2 2 Figure 2. curve of an ideal resistor. The slope of the line is the reverse of the resistance from Ohm s la. The slope can be derived by 2 2 No, consider that hat has been put in Figure is not an ideal resistor so that the curve in Figure 2 is no longer a straight line Figure. curve of an electric component. As shon in Figure, calculated resistance from equation 2 does not represent the component. Hoever, if e take derivative at, i.e. push 2 as close as possible in equation 2, e have Aether, Fundamentals of DC Testing 2 May09
3 d d The reverse of the resistance is no the tangent of the curve at. Equation 2 in a fact is an rough estimation of equation in the range of [, 2]. The derivative form of Ohm s la reminds us about the equations of capacitance and inductance. dv i C dt di v L 5 dt f Laplace Transform is performed on both sides of equation and 5, e have folloing equations hich are similar to Ohm s la. sc 6 sl 7 n other ords, e can express the relationship of time varying current and voltage by treating capacitance and inductance as resistance like quantity, hich is called impedance and usually denoted by Z, in sdomain. Z 8 sc Z sl 9 By replacing capacitors and inductors ith impedance expression derived from equations 8 and 9 in Kirchhoff s circuit la, Ohm s la and its extended version can be applied to analyze complex netork containing resistors, capacitors and inductors.. esistance Measurement Before e go too far, let s dra back to consider the fundamental question: ho to measure the resistance. A straight forard setup to do so is to connect a resistor ith a voltage source along ith an ampere meter. The resistance is then determined by simply dividing the forced voltage ith the current reading from the meter. Aether, Fundamentals of DC Testing May09
4 A Figure. A straight forard setup. Hoever, in the real orld, the ires have resistance as ell so the calculated value is the sum of all resistance in the loop. A Figure 5. The resistance of ires. 2 forced 2 0 As shon in equation 0, the value of resistance contains error terms introduced by the ires. Conceptually, error terms can be eliminated by measuring the voltage across the resistor at the same time. Aether, Fundamentals of DC Testing May09
5 A 2 Figure 6. Take the voltage across the resistor. With the modified setup above, the readings are exactly the current floing through the resistor and the voltage across it. Hoever, there is also resistance on the ires connecting the voltage meter to the resistor. A 2 Figure 7. The resistance on the ires ith ampere and voltage meters. The error terms can be analyzed as folloing. Aether, Fundamentals of DC Testing 5 May09
6 oltagemeter oltagemeter oltagemeter oltagemeter oltagemeter oltagemeter oltagemeter oltagemeter oltagemeter As shon in equation, the value of resistance of the resistor under test is not related to the resistance of the ires connecting the voltage source to it. Furthermore, if the current floing through voltage meter is kept infinitesimal, the error terms get eliminated. t can be done by simply having a high impedance voltage meter or ires. Consider to implement Figure 7 as a voltage or current source ith force and sense lines. t then makes a socalled fourired connection. Aether, Fundamentals of DC Testing 6 May09
7 Force Sense M M Sense dut dut Figure 8. Fourired connection. Force Suppose no e have this connection on a printed circuit board. Based on equation and the previous discussion, the bigger the impedance along the sense loop is, the better accuracy is. t can be done by separating force and sense lines and narroing the line idth. DUT DUT S F ired S F Figure 9. ncrease sense impedance by separating force and sense lines and narroing the line idth. Aether, Fundamentals of DC Testing 7 May09
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