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Figure 1 Simplified DUT Impedance Measurement with Grounded Current Meter. The calculated component impedance is the quotient of the complex voltage impressed. across the device divided by the complex device current Impedance is a complex value that. changes as a function of the applied test frequency. Again referring to Figure 1 if the op amp has negligible bias current IB 0 into the. negative input terminal then all of the current flowing through the unknown impedance I X. also will flow through the op amp feedback impedance ZF making IX equal to IF. Additionally the op amp differential input voltage V V is approximately equal to the. output voltage VO divided by the op amp open loop gain AVO which typically is a very large. number at lower frequencies, If the op amp output voltage is limited to 10 V and AVO 2 x 106 V V then the maximum. voltage across V V will be only 5 V thereby making the negative input terminal at a. virtual ground potential Finally the output voltage V O and the voltage across the feedback. impedance can be described as follows, Knowing the stimulus voltage amplitude VS the value of ZF and the voltage VZF across ZF. allows you to readily calculate the complex value of the unknown component. where Vs and VS the respective magnitude and phase. angle of the stimulus voltage, VZF and ZF the respective magnitude and phase angle. of the voltage across the feedback impedance, Calculating the real part of ZX will return the resistive component of the impedance while. calculating the imaginary component will yield the inductive or capacitive reactance value. To minimize measurement errors at higher test frequencies Z F also needs to be treated as a. complex number, If the DUT is purely resistive then the phase information is not required and Z can be.

replaced with R Equation 2 reduces to, Equation 3 can be used to calculate an unknown resistor value by using a DC source voltage. rather than an AC stimulus However when using DC rather than AC to measure a resistor. value care must be used to minimize any DC offsets and thermal EMFs from relays and. dissimilar metal junctions in the stimulus measurement and guard paths because they can. have a negative impact on the accuracy of the measurement. Two and Three Terminal Measurements, The circuit configuration in Figure 1 is called a two terminal or two wire measurement. because only source and measure connections are used This arrangement rarely occurs on. populated PCB assemblies because other components typically are connected to the device. being tested Guarding must be used to eliminate the negative effects of these other. components, Figure 2 shows a simplified circuit where the DUT R X is connected to other components. RA and RB and indicates how to connect guard terminals to isolate the DUT For simplicity. these complex impedances now are shown as simple resistances in the figure Wire terminal. resistances RS RM and RG also are shown With no passive guard in place at node G a. current divider would be created between RX and the series combination of RA and RB As a. result current would flow through both parallel paths and an error in the measurement. would occur, Figure 2 Basic Guarded DUT Impedance Measurement Configuration. With the passive grounded guard G in place R A now is shunted across the low output. impedance source and RB is placed across the op amp V and V input terminals With. virtually no voltage present across the V to V terminals there is negligible current flow. through RB Virtually all of the current flowing through R X also flows through RF where the. unknown device current is measured with meter M1,Four and Six Terminal Measurements.

Path resistances RS RM and RG can degrade the accuracy of the measurement and may. need to be compensated for with additional measurement terminals For example if R A is a. low impedance device then current will flow through it and through the non zero parasitic. guard resistance RG This current will create a voltage at node G that ultimately will force a. current through node M and introduce an error in the measurement of the DUT current. VRF RF The wire resistances RS and RM also will affect the measured value of RX The. calculated measurement value of RX that includes the error effects of residuals RS RM and. RG for Figure 2 is shown in Equation 4, where Rxcalc the calculated resistance value including measurement errors. RS the source lead resistance,RM the measurement lead resistance. RX the resistance being measured,RG the guard wire resistance. RA the Thevenin source side guarded resistance, RB the Thevenin measurement side guarded resistance2. Minimizing the guard error caused by the finite resistance RG can be achieved by allowing. the noninverting terminal of the op amp input to sense the voltage at node G remotely This. configuration shown in Figure 3 is what is commonly called a four wire guarded. measurement not to be confused with a four wire Kelvin measurement With the addition of. this fourth terminal there typically will be negligible voltage across R B and therefore. negligible error current through RM that would be injected into the transimpedance amplifier. from node G, Figure 3 Guarded Measurement Configuration with Guard Voltage Sense.

Adding another two terminals or wires can help to eliminate the errors caused by the source. and measure wire resistances RS and RM This six wire metrology is illustrated in Figure 4. Two possible options to connect the op amp s negative input terminal are represented by. the single pole double throw switch In position L the op amp current sense terminal is in. the local position while the R position denotes a remote sense position If there is no need. for guard terminal s or a guard sense terminal the configuration will reduce to a classic. four wire Kelvin connection scheme that still will help mitigate the source and measure wire. losses resulting from RS and RM, Figure 4 Guarded Configuration with Guard Voltage Sense and Remote or Local. Referring again to Figure 4 the digitizer measurements can be made with two individual. meters M1 and M2 that may have individual gain K 1 K2 and offset errors Voffset1 Voffset2. These gain and offset terms even if calibrated out may drift over time and temperature. negatively affecting the measured value of R X Equation 5. However if a single digitizer is used that is multiplexed between measuring the R X voltage. and the RF voltage the gain errors K1 and K2 tend to mathematically cancel because they. are nearly the same value Further if the real and imaginary terms of the measurement are. extracted through a single bin discrete Fourier transform then the DC offset terms can be. eliminated from the measurement bin Additionally the impedance instrument can be. designed to interleave alternating measurements of DUT voltage V RX and DUT current VRF RF. within a single or multiple AC cycles thereby adding no additional test time for the unit test. A plot of the percentage error as a function of the value of R X for 3 wire 4 wire and 6 wire. local and remote current sense measurements is illustrated in Figure 5 The conditions for. this plot are RS RM 0 8 RG 0 4 and RA RB 50 The error increase of the 3. and 4 wire measurements below about 200 is caused by the series resistances R S and RM. while the increase in the 3 wire plot above 200 is a result of the combination of the guard. voltage G and a low value of RB that continues to inject error current into the current meter. as the current from RX is diminishing with increasing RX values. Figure 5 Measurement Error vs Circuit Configuration. DUT Equivalent Circuits, Most in circuit testers can return series and parallel equivalent circuits involving CS CP LS. LP RS and RP for a given impedance measurement When measuring a capacitor with no. physical series or parallel resistors in the circuit it is sometimes not clear whether C S or CP. should be used The calculated values of CS and CP can be quite different because of the. quality of the component the measurement path resistance the component value and the. applied test frequency, As a general rule of thumb if the capacitor has a value less than 10 nF CP should be used. because the parallel resistance is likely to have a more significant effect on the. measurement than the series resistance Above about 1 to 10 F the parallel resistance is. likely to have less effect than the series resistance so CS should be used in these instances. Similarly low values of resistance generally should use R S while high values should use RP. Comparing the reactance of a capacitor or inductor to the parasitic resistance values can. help in determining whether to use a series or a parallel model. Other Test Considerations, When testing a component it may not be clear which pin should be the source node and. which pin should be the measurement node The key to determining the best connections. for the test is to consider what else is connected to the pins of the DUT For example if one. lead of the DUT is connected to a super node such as a power or ground node this lead. should be placed on the source side rather than on the current meter s measurement pin. With a super node many other nodes will need to be guarded and that will place a low. impedance and possibly highly capacitive load on the summing junction of the current. A low value resistive load will lower the available loop gain of the amplifier and create a. measurement error A capacitive load will create an open loop pole in the feedback network. and degrade the phase margin of the op amp and can cause excessive ringing and possible. oscillation In general any large value capacitors on a component lead or low value. resistors should be placed on the source node rather than the measure node. It is possible for a measurement to return a negative value The most common reason for. this is that a large capacitance is being guarded on the measurement node This guarded. capacitor when combined with the op amp feedback resistor creates an open loop pole in. the feedback network thereby degrading the phase margin of the op amp In the closed. loop response of the measurement amplifier there will be amplitude peaking and a large. phase change, If the test frequency is higher than the peaking frequency then the calculated capacitor or.

resistor value will likely be negative Operating at a test frequency below the peaking point. or lowering the feedback resistance value should rectify the problem at the expense of some. loss in overall measurement accuracy The approximate peaking frequency is given in. Equation 6 3,where FP1 open loop pole of op amp,AVO op amp DC open loop gain. ICT has been the workhorse of the manufacturing industry for more than 40 years and still. is the most economical way to identify the largest range of process and component defects. on the manufacturing line Analog testing of passive components is as important as ever. because of their increased usage Understanding the principles behind analog testing is. invaluable in generating stable tests that can hold up to high volume PCB manufacturing. References, 1 TestStation Testing Theory Teradyne Number 034 324 April 2006. 2 Khazam M Predicting Test Accuracy for Analog In Circuit Testing Proceedings of the. International Test Conference IEEE 1983 Paper 20 1. 3 Suto A J ACZ High Guard Calculations GenRad Application Note 1996. Acknowledgements, Hall H P Multi Terminal Impedance Measurements or Why Do those New Bridges Use So. Many Connections GenRad Application Note Form JN 4166A 1980. About the Author, Anthony Suto is a senior staff scientist at Teradyne and has more than 32 years of design. experience in the automatic test and inspection equipment industry Suto received his. electrical engineering degree from Union College in New York and has authored a variety of. patents and technical papers anthony suto teradyne com. Published in December 2012 issue of Evaluation Engineering. 1 Principles of Analog In Circuit Testing By Anthony J Suto Teradyne December 2012 In circuit test ICT has been instrumental in identifying manufacturing process

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