Automatic Test Equipment and Bench Test Correlation

AUTOMATIC TEST EQUIPMENT AND BENCH TEST CORRELATION

Alan Aragon, B.S.E.E.

A THESIS

ELECTRICAL ENGINEERING

Submitted to the Graduate Faculty of Texas Tech University in Partial Fulﬁllment of the Requirements for the Degree of

MASTER OF SCIENCE in ELECTRICAL ENGINEERING

Dr. Richard Gale Committee Chairman

Dr. Stephen Bayne

Dr. Ron Cox

Dr. Tim Dallas

Dr. Dominick Joseph Casadonte Jr.

Dean of the Graduate School

TABLE OF CONTENTS

ABSTRACT ...... iii LIST OF TABLES ...... iv LIST OF FIGURES ...... v I INTRODUCTION ...... 1 IIPART...... 2 III HARDWARE ...... 5 3.1 Bench Hardware Analysis Setup ...... 5 3.2 Bench Hardware Analysis ...... 5 3.3 ATE Hardware Analysis Setup ...... 10 3.4 ATE Hardware Analysis ...... 10 IV SOFTWARE ...... 15 4.1 Design Environment Considerations ...... 15 4.2 Software Considerations ...... 17 4.3 Software Implementation ...... 18 V STATISTICS AND MATH ...... 21 VI TEST IMPLEMENTATION ...... 27 VII CORRELATION DATA ...... 33 VIII CONCLUSION ...... 43 BIBLIOGRAPHY ...... 44 APPENDICES A ICHG AND VBREG DATA FULL TABLES ...... 46 B BASIC ANALYSIS OF ATE MEASUREMENT METHOD ...... 53 C BASIC ANALYSIS OF BENCH MEASUREMENT METHOD ...... 56

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ABSTRACT

The purpose of this research is to create an automated method to collect bench data for Automatic Test Equipment (ATE) tested parameters in order to identify correlation offsets if any on critical device parameters and to identify root causes of these correlation offsets. The devices under test are all single cell battery chargers that have stringent spec requirements over operating temperature range. In production tests these parameters are tested for on the ATE and parts not meeting spec are screened out. Hidden correlation offsets between ATE results and bench test results could mean that parts that actually lie outside speciﬁcations could be shipped to end customers.

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LIST OF TABLES

3.1 List of hardware...... 6

4.1 Comparison between LabVIEW graphical, LabVIEW CVI, and C# design environments...... 15

5.1 Standard deviation population percentages...... 22

7.1 ILIM data from the ATE...... 33 7.2 ILIM data from the bench...... 34 7.3 ILIM data percentage difference between ATE and bench...... 34 7.4 ICHG data from the ATE...... 35 7.5 ICHG data from the bench test...... 35 7.6 ICHG data percentage difference...... 36 7.7 ICHG data percentage difference after correlation factor is applied..... 37 7.8 VBREG data from the ATE...... 40 7.9 VBREG data from the bench test...... 41 7.10 VBREG data percentage difference...... 42

A.1 ICHG data from the ATE...... 46 A.2 ICHG data from the bench test...... 47 A.3 ICHG data percentage difference...... 48 A.4 ICHG data percentage difference after correlation factor is applied..... 49 A.5 VBREG data from the ATE...... 50 A.6 VBREG data from the bench test...... 51 A.7 VBREG data percentage difference...... 52

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LIST OF FIGURES

2.1 BQ2425x datasheet pg. 1. [1]...... 3 2.2 BQ2425x block diagram. [1]...... 4

3.1 Hardware block diagram...... 5 3.2 Voltage measurement setup. VIN = 7.5V...... 6 3.3 Current measurement setup. VIN = 1.5V. RAGI=1 kΩ±1% RKEI=12.5 kΩ± 1%...... 7 3.4 Agilent 34401a voltage measurement zoomed in. Sample number is of each sample taken. σ = 1.75048×10−5, µ = 4.97165...... 8 3.5 Agilent 34401a voltage measurement with KA7805 specifications...... 9 3.6 Agilent 34401a current measurements zoomed in. σ = 1.44356×10−7, µ = 1.49095×10−3...... 10 3.7 Agilent 34401a current measurements with possible current values of the resistor...... 11 3.8 Keithley 2440 voltage measurement zoomed in. σ = 1.79594×10−5, µ = 4.97163...... 12 3.9 Keithley 2440 voltage measurement with KA7805 specifications...... 12 3.10 Keithley 2440 current measurement zoomed in. σ = 1.0908×10−8, µ = 1.19352×10−4...... 13 3.11 Keithley 2440 current measurement with KA7805 specifications...... 13 3.12 ATE voltage measurements...... 14 3.13 ATE current measurements...... 14

4.1 Input Current Limit test tab...... 19 4.2 Charge Current test tab...... 20 4.3 Battery Voltage Regulation test tab...... 20

5.1 A normal distribution...... 21 5.2 Visual example of the standard deviation population percentages...... 22 5.3 Cp and Cpk visualization.[2]...... 25 6.1 BQ2425x typical charging proﬁle. [1]...... 30 6.2 Example battery. [3]...... 31

7.1 ICHG correlation graph...... 36 7.2 VBREG correlation graph...... 39

B.1 Forcing voltage, measuring current. [4]...... 53 B.2 Forcing current, measuring voltage. [4]...... 55

C.1 Dual-slope circuit. [5]...... 56 C.2 Multi-slope run-up circuit. [5]...... 57

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CHAPTER 1 INTRODUCTION

The motivation behind this thesis is to create an additional method of testing that would identify correlation offsets in a simple and effective manner. The ATE is the primary machine to test parameters for units in development. While these machines are excellent for testing, an additional method of testing is needed to identify if there are any correlation offsets. This additional method will be bench testing. It allows for the testing of a small number of parts without the complexity of the ATE. The bench tests can also be automated to allow a sample size that is large enough to see a correlation offset if any exists. To automate the bench tests, software would be created to control the bench equipment and gather the data. It would also allow any engineer to quickly setup the bench test because it would be created to be simplistic. The automated tests would also allow start-and-forget testing of the units to permit the engineer to perform other tasks while the data is gathered for later analysis. The correlation offsets are usually hidden and are unknown until the correlation is completed. With the automated bench test these hidden offsets, if any, will be found quickly.

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CHAPTER 2 PART

The part that will be used in the development of the bench test software will be the BQ24250 developed by Texas Instruments. The BQ24250 (250) is a single cell Li-Ion battery charger. The 250 can be programmed to change a variation of parameters such as; input current limit, charge voltage, and charge current. It also has built in self protection. The ﬁgures above show the ﬁrst page of the BQ2425x datasheet (see Fig. 2.1) and the block diagram of the BQ2425x (see Fig. 2.2). The 250 typically charges batteries that are in the 3.5 to 4.4 V range. Some applications that the 250 can be used in are cellular devices, cameras, MP3 players and portable equipment. Three critical parameters of the 250 are input current, charge current, and charge voltage. Since the input to the 250 varies, it is essential that the input current be correct. The input current also must not exceed the current of the source. Charge current management for the 250 is also crucial. It determines the duration it takes for the battery cell to be charged. Too slow and the patience of the user is exceeded. Too fast and the battery can be damaged. The charge current should be the maximum it can be without damaging the battery. The charge voltage parameter is important because it determines if the battery is charged properly. It prevents overcharging and undercharging of the battery. If the battery is overcharged, then it can be damaged. If the battery is undercharged, then it will not have the expected life expectancy and the product using the battery will run out of charge quicker than expected.

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Figure 2.1: BQ2425x datasheet pg. 1. [1]

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Figure 2.2: BQ2425x block diagram. [1]

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CHAPTER 3 HARDWARE

3.1 Bench Hardware Analysis Setup The software is connected to a simple hardware setup. To perform the tests that are being considered there are several pieces of bench equipment needed. The equipment used with this software is a power supply, a source meter, and three digital multi-meters. To talk to the EVM, a USB interface adaptor developed by Texas Instruments is used. To talk to the bench equipment, a USB to GPIB connected developed by National Instruments is used. These adaptors are connected to a computer where the software will be run. A simple block diagram of how the hardware is connected is shown in Figure 3.1. Table 3.1 shows which instruments were speciﬁcally used in this thesis.

Figure 3.1: Hardware block diagram.

3.2 Bench Hardware Analysis It is important that the hardware being used to perform these test be accurate and pre- cise. If the instruments are not measuring how they should be, then it cannot be conclusive if the device is passing or failing the tests. Understanding that the measurements gathered from these instruments can be assumed to be correct. Measurements were gathered from the Agilent 34401a and the Keithley 2440 Source Meter. The Keithley 2440 Source Meter was used instead of the 2420 that is described in the thesis because it is in the same family

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Table 3.1: List of hardware.

Equipment Model Power supply Agilent 3632A Source meter Keithly 2420 Digital multi-meter Agilent 34401A GPIB National Instruments USB interface adaptor Texas Instruments was the one that was available. The setups used to measure voltage and current from the two instruments are shown in Figure 3.2 and 3.3.

Figure 3.2: Voltage measurement setup. VIN = 7.5V.

LabVIEW was used to automate the gathering of the data from the Agilent 34401a and the Keithley 2440 Source Meter. The Agilent code was reworked a couple of times due to discomfort about the results that it was producing. Although the results were well

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Figure 3.3: Current measurement setup. VIN = 1.5V. RAGI=1 kΩ±1% RKEI=12.5 kΩ± 1% within the limits that are needed for the measurements in this thesis, it was still reworked to achieve the best results as possible. There are many error factors that could contribute to the Agilents gathering of the data and so there was a delay introduced to the code to try to combat some of these factors. A couple of the factors that were thought of were ramp-up time, ramp-down time, heating, and cooling. The results from the Keithley 2440 were a lot more consistent and did not need a delay to minimize these error factors. In the figures below, the data from the Agilent 34401 are shown. The first figure shows voltage measurements from the KA7805 5V regulator. Figure 3.4 shows the voltage readings that are zoomed in to show a six sigma spread. The figures have 250 samples taken over a 20.83 minute time frame. Some noise and drift can be noticed in the figure. The cause for the drift is unknown, but when viewing the data in Figure 3.5, the drift does not affect the measurements. Figure 3.5 shows the gathered data within the limits described in the KA7805s datasheet. When the data is placed within these limits, it shows that the Agilent is measuring properly. It can be assured with 95% confidence that the Agilent will measure the voltage level between 4.91764 V and 4.91766 V. Five decimal points are used because that is what the display on the Agilent 34401a uses. The current measurements for the Agilent 34401a are show in Figure 3.6 and 3.7. The current was measured by applying 1.5 V across a 1000 Ω ± 1% resistor and 250 samples were taken. The same type of affect was happening with the current measurement of the

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Figure 3.4: Agilent 34401a voltage measurement zoomed in. Sample number is of each sample taken. σ = 1.75048×10−5, µ = 4.97165.

Agilent just like in the voltage measurement. Although it was a bit more scattered, the data was still within a six sigma spread. Figure 3.6 shows a zoomed in view of the data with the six sigma spread around the mean. Figure 3.7 shows the data in potential current values of the resistor. The upper being current if the resistor was 1010 Ω and the lower being the current if the resistor was 990 Ω. From the current measurements that the Agilent 34401a made, it can be said that with 95% conﬁdence that the value will lie between 1.49089E-03 to 1.49101E-03 A. The data gathered from the Keithley 2440 are shown in Figures 3.8, 3.9, 3.10, 3.11. The key difference noticed from the Keithley 2440 and the Agilent 34401a is how the data is spread across the mean. Because of this distribution only 100 samples were taken with the Keithley 2440. Figure 3.8 shows the data in a six sigma spread around the mean. The Keithley exhibits a more random set of data that hovers closely to the mean of the measurements. Figure 3.9 shows the same data with the limits of the KA7805 5V regulator. Just like the Agilent, the Keithley shows a nice ﬂat line when these limits are considered.

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Figure 3.5: Agilent 34401a voltage measurement with KA7805 speciﬁcations.

It can be said with 95% conﬁdence that the Keithley will measure between 4.97162 V and 4.97163 V. The current measurements from the Keithley showed the same trend as the voltage measurements. The resistor value used in the current measurements for the Keithley was a 12.5k Ω ±1. This resistor can be in-between a range of 12375 Ω and 12625 Ω. Figure 3.10 shows the data distribution within a six sigma spread. Like the voltage measurements, the current measurements exhibit a random spread around the mean of the measurements but packed a little more tightly. There is an outlier in the data gathered, but it can be dismissed because it is more than six sigma away from the mean and it is the only value like this. Figure 3.11 shows the current limits with the minimum and maximum possible resistor values. The conﬁdence that the value will lie between 1.19350E-04 and 1.19354E-04 is 95%. In conclusion, from the shown graphs and gathered data, the Agilent 34401a and Keith- ley 2440 are well within the limits needed to acquire measurements for data that is needed in this thesis. The drift and measurement variation is on orders of magnitude smaller than

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Figure 3.6: Agilent 34401a current measurements zoomed in. σ = 1.44356×10−7, µ = 1.49095×10−3. the process variation. The measurements that are being made for the thesis are in the milli- volt and milliamp range and the change is in the microvolt and microamp range. If the data gathered appears to be incorrect, then the bench instruments can be ruled out as a problem and the cause of the problem can be approached from a different angle.

3.3 ATE Hardware Analysis Setup The ATE also needs to be veriﬁed that the measurements gathered by it are correct. To verify the voltage measure of the ATE, the ATE was set to force 5V on no load and the voltage forced was measured by the ATE. Current measurements were made by forcing 3V from the ATE across a resistor with a value of about 2k Ω.

3.4 ATE Hardware Analysis Figure 3.12 and 3.13 show the data that was gathered from the ATE. Although the data gathered shows that the measurements from the ATE are accurate there is some quantization

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Figure 3.7: Agilent 34401a current measurements with possible current values of the resistor. error in the measurements. In the voltage measurements it can be seen that the quantization error is about 0.3 mV. The quantization errors in the measurement are on orders of magnitude smaller than the process variation and therefore can be ignored. As with the bench measurements, the ATE measurements are well within the process variation of the device. Both ATE and bench instruments gathered measurements lie within the process variation of device, it can be concluded that the measurements gathered from the instruments can be ruled out as being incorrect while performing tests on the device.

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Figure 3.8: Keithley 2440 voltage measurement zoomed in. σ = 1.79594×10−5, µ = 4.97163.

Figure 3.9: Keithley 2440 voltage measurement with KA7805 speciﬁcations.

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Figure 3.10: Keithley 2440 current measurement zoomed in. σ = 1.0908×10−8, µ = 1.19352×10−4.

Figure 3.11: Keithley 2440 current measurement with KA7805 speciﬁcations.

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Figure 3.12: ATE voltage measurements.

Figure 3.13: ATE current measurements.

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CHAPTER 4 SOFTWARE

4.1 Design Environment Considerations To develop the software, three design environments were taken into consideration. The environments looked at to develop the software were: LabVIEW Graphical, LabVIEW CVI, and C#. While any of these programs could accomplish the needed task, one had to be determined that would yield the most beneﬁts. Table 4.1 shows a feature table of all three environments. These features were chosen based on need to be in the software. The features listed in Table 4.1 were all weighted differently. The features that were weighed the most were: device driver abundance, readability, and iterative loops.

Table 4.1: Comparison between LabVIEW graphical, LabVIEW CVI, and C# design environments.

LabVIEW Graphical LabVIEW CVI C#

Integrated environment XXX Device driver abundance XX X Debugging ability (breakpoints) X XX Iterative loops XXX Ease of use changing instrument parameters) X XX Small software foot print package) XX X Ease of readability X XX Open licensing X X X

All three environments had iterative loops, but LabVIEW CVI and C# had a more intuitive way of creating loops as they are text based coding and not graphical. Though, LabVIEW Graphical demonstrated an easier way of stopping the loops. It was easier to create a loop that could be followed systematically in LabVIEW CVI and C#. This leads into the next feature chosen, ease of readability. The software will need to be able to

15 Texas Tech University, Alan Aragon, August 2013 be read by another engineer to interpret the code and modify it if necessary. LabVIEW Graphical was proven to be difficult to quickly interpret the organized flow of the tests. It was difficult to tell which virtual instruments (VIs) lead to where and the way loops are made in LabVIEW Graphical, it was not easy to quickly tell what was going through which aspect of the loop. Since LabVIEW CVI and C# are text based coding, the code flows systematically and can be read by another engineer easily. The third main deciding feature between the three design environments was the device driver abundance. C# was lacking in this aspect due to the sheer amount of support LabVIEW has on instruments. While C# did have device driver support, it was nowhere near the amount that the LabVIEW family has. Bringing instruments into the LabVIEW environments was also a lot simpler seeing as they were natively created for LabVIEW. This kind of driver support is a must have when creating the software for the bench testing. It allows the user to implement a new instrument without much hassle if the default instruments are not available for use. After taking all these features into consideration, LabVIEW CVI was chosen as the design environment that would be used to develop the bench test software. LabVIEW CVI was chosen because it is a hybrid between LabVIEW Graphical and C# design environments. LabVIEW CVI has the three main features that were looked for in the design environments. Because it is developed by the same company that makes LabVIEW Graph- ical, LabVIEW CVI has the same support for device drivers. This allows the usage of the large database of drivers that National Instruments has. Because LabVIEW CVI is text based coding, the code can be read systematically. By this, it is meant that the code can be read from top to bottom and the different functions of the software can be found quickly and easily. By having this feature, an engineer that is not familiar with the source code of the software can go in and begin to understand the process by which the software functions will very little hassle. LabVIEW CVI also has the ability to create iterative loops with ease since it is text based coding. Loops are necessary for this software because the tests may have several different parameters that need to be tested. By allowing the software to loop through all the parameters, it frees up the engineer that is performing the tests to do other

16 Texas Tech University, Alan Aragon, August 2013 tasks. LabVIEW CVI also has built in GUI development. This allows for quick and easy creation of a GUI for the user to interact with and change desired parameters.

4.2 Software Considerations After the design environment was decided, the next task was to develop the user interface for the bench test software. The interface for the software will need to allow the engineer performing the tests to change specific parameters for the part and the bench equipment. The interface also needs to be simple and easy to understand with minimal training. These considerations went into the process of designing the back-end and front- end for the ATE to bench correlation software. The instruments are connected to the PC via a GPIB (General Purpose Interface Bus) to USB adaptor developed by National Instruments. The GPIB protocol allows for automated control over bench equipment by a PC. The software will need to automatically detect that there are instruments connected to the PC in use and with a press of a button it detect each instruments respected GPIB address. This keeps the engineer from having to manually set each instruments GPIB address in the code itself. With the software automatically grabbing the GPIB addresses for each piece of bench equipment, there also needs to be a way for the user to select the appropriate GPIB address for each piece of equipment so the software knows how to control each one correctly. Another consideration as mentioned before was allowing the user to adjust parameters for both the bench equipment and the part itself. Such parameters for the bench equipment would be voltage levels and compliance levels. For the part, it would be parameters that pertain to the test that is being performed. Adding an ability to loop through all the options for a specific parameter related to the test is also needed so that the user can run the test for each parameter without having to start the test each time. The ability to loop through a specific parameter was also carried over to allowing the software to perform all the tests one after another with a single press of a button. With a loop all tests procedure implemented, there was also a consideration that the user may not want all the tests performed but still wanted a couple of them performed. So there would need to be a way for the user to decide

17 Texas Tech University, Alan Aragon, August 2013 if a test would be performed during the loop all tests procedure. It was also considered that it would be essential to see the registers of the part. This would allow the user to make sure that the correct registers is being written and that they are being written with the correct value. To further help debug any potential problems it was decided that the user be able to manually change a register. By doing so, certain problems such as the USB interface adaptor not working, could easily be determined or dismissed. Each test having its own individual tab was another design consideration for the bench test software. This will avoid confusion on which parameters belong to which test. Having each test in their own tab, the user will know with full confidence that the parameters they are changing are for that test only. A couple of other considerations accounted for were declaring a test number for each test and allowing the user to input the number of the part they are testing. With the software controlling the bench equipment and the user adjusting the parameters to their needs, there needs to be a way to collect all the data. This would be done simply by creating a text file that contains all the measurements and set parameter values for a test. This text file then could be taken into software such as Microsoft Excel to perform data analysis on. If the data were to be processed in Microsoft Excel, then it would need to be organized in such a way that it can easily be imported into Microsoft Excel. A simple format to the text file would solve this problem. With the data being collected in a text file the software will have to organize the files so that the user can quickly find the ones that they are looking for. A naming and dating scheme would be need to be implemented to tackle this problem. With having the text file with the data gather for a test it was also noted that the file should contain a test number and the number of the part that is being tested. This would be for the engineer to know which test was performed and for which part out of all the sample parts with just looking at the data itself.

4.3 Software Implementation Taking all the necessary features into consideration, the software was built. The GUI design is shown in Figure 4.1 below.

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Figure 4.1: Input Current Limit test tab.

Every design consideration was implemented into the software to allow the user to have full control over the tests. The layout for GUI was designed to have a simple step by step flow for the user to setup everything properly. The first step to setting up the test is the acquiring the addresses for each piece of equipment. So, the Get Addresses is set at the top of the GUI to indicate that that is the first step. Afterwards, the addresses need to be assigned to the correct form of use. Below the Get Addresses button is the bar that the user uses to set the addresses to their indicated use. Setting these parameters is global for all the tests and is essential to the software correctly performing the tests. The next step is adjusting the parameters for each test. These have been laid out with the bench equipment parameters on the left side of the box and the part parameters on the right side of the box. Each test has its own tab in the software. In Figure 4.1, the parameters are shown for the Input Current Limit test. Figure 4.2 and Figure 4.3 show the parameters for the Charge Current Test and the Battery Regulation Voltage respectively. The software was also designed to be customizable. It is required to be this way because the ability to edit the code to be used for other devices is a large benefit. If the code were to only be for one device and had to be rewritten every time for a new device, the time spent rewriting the code would be wasted. By having the code customizable, other devices can

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Figure 4.2: Charge Current test tab. use the same software to perform the bench tests on. Due to the nature of text based coding, these parameters were defined as variables to allow the parameter value be changed in all the necessary places without having to go through all the code and manually change the value. In the code the device specific parameters are defined at the start of the code to allow the user change the software to their device needs.

Figure 4.3: Battery Voltage Regulation test tab.

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CHAPTER 5 STATISTICS AND MATH

The data gathered from the tests usually fall into a normal distribution with some parameters such as trimmed exhibiting rectangular distributions. A normal distribution is the most important and the most frequently used distribution in both the theory and application of statistics [6]. The distribution is given by the formula shown below, where is the mean of the distribution and is the standard deviation.

2 1 − (x−µ) f (x) = √ e 2σ2 (5.1) σ 2π The normal distribution is shaped as a Gaussian curve. A Gaussian function is sym- metric along the mean of the function. Figure 5.1 below demonstrates an example of a Gaussian curve.

Figure 5.1: A normal distribution.

The standard deviation relates to the normal curve by showing where the population falls in the deﬁned deviation. As the level of standard deviation is increased, the percentage of the population increases. Table 5.1 below shows the percentage of the population that is related to the level of standard deviation chosen.

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Table 5.1: Standard deviation population percentages

Standard Deviation Percentage of Population 1σ 68.27% 2σ 95.45% 3σ 99.73%

A visual representation of the standard deviation percentages on a Gaussian curve is shown below.

Figure 5.2: Visual example of the standard deviation population percentages.

These different levels of standard deviation are essential in determining if the parameter being tested meets the expectations of the designers. The more of the population that fits within the limits described by the designer, the more devices can be distributed with certainty. Therefore an appropriate level of standard deviation is needed to declare if the measured parameter is good. The level of standard deviation will need to be just enough to not be too specific and not too little to include too many failures. The industry leading standard for an appropriate level of standard deviation is a level of Six Sigma. This standard was developed by Motorola in 1986 [7]. The central idea behind Six Sigma is that if you can measure how many ”defects” you have in a process, you can systematically figure out how to eliminate them and get as close to ”zero defects”

22 Texas Tech University, Alan Aragon, August 2013 as possible [8]. Six Sigma signifies that the tested product will have no more than 3.4 defects per million. Six Sigma allows the manufacture to have confidence that the product they are shipping will meet customer expectations. Six Sigma is proven to give process capability indices that the tested product does fall within the designed specifications. Process capability indices are a key role in the development of a product. The process capability indices signify that the process performed on the product produces an accept- able outcome within the specific limits. This is very important in the manufacturing and development process of a product. The process capability indices are Cp,Cpu,Cpl,Cpk, and Cpkm. These indices all assume that the data is normally distributed. In a practical application, the process standard deviation is almost always unknown and must be replaced by an estimate σˆ [2]. The mean of the data will also be estimated by µˆ .

The process capability ratio Cˆp estimates the success of the product if the mean is centered between the given speciﬁcations limits. The formula for Cˆp is given below.

USL − LSL Cˆp = (5.2) 6σˆ

The designed upper and lower limits are given by USL and LSL. While Cp deals with data that has upper and lower limits, there may be instances where there are only one-sided speciﬁcations that need to be met. To calculate these, one-sided process capability ratios are used. The two formulas for one-sided process capability ratios are shown below.

USL − µˆ Cˆpu = (5.3) 3σˆ

µˆ − LSL Cˆ = (5.4) pl 3σˆ

Cˆpu is the estimated upper speciﬁcation and Cˆpl is the estimated lower speciﬁcation.

While Cp denotes if the data gathered lies within the design speciﬁcations, it has the large assumption that the mean of the data lies in the center of the limits. Unfortunately, this does not necessarily happen and that a different method to determine the success of the product is needed. Cpk does just this.

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Cˆpk estimates the success of the product if the mean is not necessarily located between the speciﬁcation limits. Generally, if Cˆp = Cˆpk, the process is centered at the midpoint of the speciﬁcations, and when Cˆpk < Cˆp the process is off-center [2]. Below is the formula for Cˆpk.

USL − µˆ µˆ − LSL Cˆ = min[ ] (5.5) pk 3σˆ 3σˆ

While Cpk does a good job of estimating whether or not the data falls in-between the designed limits it can be fooled by two sets of data that have the same Cpk, but are actually centered differently. Cpkm was developed to overcome errors like this. Cpkmˆ is similar to

Cˆpk, but it estimates the success around a given target, T. The formula for Cpkmˆ is given below.

Cˆ ˆ pk Cpkm = q (5.6) µˆ −T 2 1 + ( σˆ ) By using Six Sigma as the level of quality, it can be expect that the Cpk will turn out to be 2.0 if the data lies within the designed limits. A visual representation of how Cp and

Cpk affect a distribution is shown below in Figure 5.3. To find the number of devices that pass specifications according to a criterion that is defined, the cumulative distribution function (CDF) is calculated. The CDF of a function, in this case a Gaussian distribution, is the probability that a randomly selected X will be less than a particular value x [9]. Due to the Gaussian distribution the variable X is a continuous random variable. X in this case is the devices that were tested. The equation for the CDF is shown below.

Z x F(x) = P(X < x) = P(−∞ < X < x) = f (t)dt (5.7) −∞ Where f(t) is the equation for a Gaussian distribution. Plugging the Gaussian distribution equation into the CDF equation shown above F(x) is equal to

x 2 Z 1 − (t−µ) F(x) = √ e 2σ2 dt (5.8) −∞ σ 2π

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Figure 5.3: Cp and Cpk visualization.[2]

To calculate the probability that X will lie in the range a to b, the CDF function can be expressed as the different of two CDF functions evaluated at x = a and x = b show below [2]

P(a < X < b) = F(b) − F(a) (5.9)

Using these equations allows the calculation of how many devices pass according to previously defined specifications. The devices that do not pass the criteria can then be put aside and dealt with accordingly. In order to obtain a reasonable set of data, a sample size of the product needs to be determined. It has been said that the statistically significant sample size is 30. It is more of a rule of thumb than an actual calculated sample size. The idea of the sample size being 30 is reinforced by the central limit theorem (CLT). As you increase the sample size in com- puting the CLT the curve begins to look like a Gaussian distribution. At around 30 samples, the graph resembles the Gaussian distribution very closely and increasing the sample size

25 Texas Tech University, Alan Aragon, August 2013 past that still shows the distribution. Because the formulas that are used to calculate how well a set of data fits in the designed specifications, we can use the assumption that 30 samples will be a Gaussian distribution. Using more samples will increase our confidence in the part, but it will also increase the time needed to test the data and therefore the cost of testing the product.

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CHAPTER 6 TEST IMPLEMENTATION

The tests chosen to be performed in this thesis were chosen based on the importance they have with customers of the BQ24250. Because the 250 is a battery charger integrated circuit (IC), there are specific parameters that the customer wants to see. Meeting and even exceeding the customers expectations for a battery charger IC is a key goal. The parameters that the customer looks for in the 250 are the performances of the high Z leakage, the input current limit, the charge current, and the battery voltage regulation. These parameters are crucial to test because these parameters are able to be trimmed. Trimming parameters allows the engineer to shift the population of the data in increments of ±0.5σ. If the data is close to the design limits, but just shy, trimming will save time and production costs by allowing the product to meet specifications with just a simple trim. While trimming is very helpful in meeting the target specifications, it has to be used cautiously. This is where the bench tests come in. These tests are performed to find the offsets of the data if there are any. If there is an offset and the trim is performed, then it could actually send the product out of the target specifications. This needs to be avoided at all costs because trimming a chip that is actually meeting specifications loses money due to the chip now being out of specifications and thus a failed chip. High Z leakage is an important parameter for a battery charger IC. The high Z leakage is there to prevent the charger from drawing a lot of current and discharging the battery. This is important to the customer because they do not want the battery to be discharging when its not charging. The discharging of the battery will also reduce the time that the user will have battery life for their device. To minimize the leakage current from the battery the high Z parameter needs to meet the designers specifications. This parameter can be trimmed to meet the target, but it needs to be tested first to make sure there are no offsets. If there is an offset, then trimming may not even been needed. Because of how important it is that the battery not discharge while not charging, this parameter has to be very accurate. That is why the bench testing needs to be performed to find the offsets before any trimming

27 Texas Tech University, Alan Aragon, August 2013 is performed. Although this test is not specifically performed in the software developed for this thesis, it still is an important parameter that needs to be tested. Currently it is done by hand, but most likely in the future it will be added the automated tests due to its value. The input current limit parameter on the battery charger is another important parameter. This parameter regulates the current from the power source that is charging the battery. It is used to achieve the correct current level to charge the battery to its maximum potential. The input current limit parameter makes sure that the charge is not exceeding the capabilities of the power source. If the current capability of the power source is exceeded, then the voltage level of the source will drop. This parameter is important to the customer not only because the charge needs to use the power source to fully charge the battery, but because they do not want their end users plugging in the device and it destroying the source. For example, the specifications for USB 2.0 range from 100 mA to 1.5 A [10]. If the power source is a USB supply that is at 500 mA the charger needs to be set at 500 mA so it does not draw too little current and so that it does not draw too much current from the USB source. So making sure that this parameter has the correct design specifications is very important. To prevent this from happening, correlation is performed to find any possible offsets so that any trimming of these parameters leads the device to meet the specifications. The input current limit test is included in the software. In the software, the input current limit test is the first test shown. It is also the first test performed if the user selects that all the tests be ran. The layout of the parameters for the input current limit test is shown in Figure 4.1. The parameters for the input current limit are in the drop down selector named “Input Current”. Once all the parameters are set to the users choice and the hardware is setup, the test is then run. To begin the test, the software first gathers all the parameters and addresses of the bench equipment that were set by the user. It then sets the correct power levels and compliance levels for the bench equipment. The bench equipment is setup first, because the power supply on the bench equipment is powering the EVM that contains the device. After the bench equipment is setup up, the device is then configured to the specifications of the user. When the registers of the device are set, they are then read to visually show the user what the settings are. This is for the

28 Texas Tech University, Alan Aragon, August 2013 user to check if the registers are writing correctly. The test is then performed by automating the bench equipment. At first, the software makes sure that the voltage at the device is the correct voltage that the user defined. If it is not, the software performs a compensation function to achieve the correct voltage. This compensation function is performed by reading the voltage at the device, comparing it to the voltage of the user defined voltage and if it is off by a predetermined value, then it tells the power supply to increase in voltage. This is repeated until the voltage level at the device is within a certain accuracy of the user defined value. After the compensation is performed, the software then reads the current at the battery to make sure that it is getting the correct current. The input current is then measured ten times and then averaged. This test is performed in a loop by default to measure the input current for different levels of voltage from the power supply. For this particular test, the initial voltage level is to turn on the EVM; afterwards, it then uses the values of “Vin Start”. It then increments the voltage level by the value defined in “Vin Step” until the voltage level reaches the defined “Vin Stop”. In this test, there is also an option to run through each of the input current limit parameters. The values are stored in a text file with all the information on the values of the parameters that the user set after the test is completed. Another important parameter that the battery charger has is the charge current parameter. This parameter regulates the current that flows into the battery. In Figure 6.1 below, the typical 250 charging profile is shown. The charge current parameter that is being tested is noted by the orange square on Figure 6.1. It is important because it needs to be set correctly to make sure the charge is using the correct current rating for the battery. It is also essential that the charge current not exceed the ratings for battery, but instead come as close to it as possible. Therefore, it is crucial to find the possible offsets of this parameter. The customer wants this parameter to be the max possible without degrading the life of the battery being used. It also cannot be too little or else it will not charge fast enough. If it does not charge fast enough, then the end user will be disappointed with the product and thus the customer will be disappointed as well.

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Figure 6.1: BQ2425x typical charging proﬁle. [1]

The charge current parameter is the second test in the software. The test is located in the second tab of the software. It is the second test performed if all the tests are being run. Figure 4.2 shows the layout of all the parameters for this test. The parameters for the charge current are in the drop down selector labeled “IBAT REG”. Similar to the input current limit test, after all the parameters are set by the user, the test is then run. The software takes the parameters set by the user and first sets the bench equipment accordingly. The bench equipment is also configured first because just like the input current limit test, the power supply powers the EVM. The device is then configured to prepare it for the charge current test. The registers are also read for the user to see if they are correct. The test begins with the compensation function as described before. The source meter is then set to the defined starting battery voltage. The current and voltage is then read from the source meter. Then the charge current of the device is measured ten times and averaged. The charge current test, like the input current test, is also performed in a loop by default. The battery begins with the voltage defined in “Vbat Start”. The software then increments the voltage by “Vbat Step” until it reaches the defined value in “Vbat Stop”. This test also has an option to run

30 Texas Tech University, Alan Aragon, August 2013 through all the available parameters for the charge current. The gathered data is stored in a text file with all the information on the values of the parameters that the user set after the test is completed. The last important parameter discussed in this thesis is the battery voltage regulation parameter. This parameter use to be a separate device, but with technology going forward, it was integrated into the battery charger IC. This parameter on the 250 is very programmable. The 250 can be set to charge a multitude of Li-Ion batteries that range from 3.5 to 4.4 V. Since there is such a large range of Li-Ion batteries with different voltage ratings, it is important that the charger be able to be programmed to fulfill the voltage requirement on the specific battery. For example, the battery shown in the Figure 6.2 has a voltage rating of 3.7 V. To charge this battery to the full capacity, the battery voltage regulation parameter on the 250 would need to be programmed to 3.7 V. It is important to have the charger charge the battery to fully capacity because that is what the customer is expecting. If the battery is not charged to its rated voltage then the battery will not last as long. The end-user needs to have a fully charged battery so they can have more use from the product. This is why it is important that the parameter for the battery voltage regulation is meeting the designed specification.

Figure 6.2: Example battery. [3]

The third test that the software performs is the battery voltage regulation test. This test is in the third tab of the software. It is the last test to be performed if all the tests are ran. The tab for this test is shown in Figure 4.3. The parameters for the battery regulation voltage are

31 Texas Tech University, Alan Aragon, August 2013 in the drop down selector labeled “VBAT REG”. Like the other two tests, the user defines all the parameters that are necessary to perform the test. The software then takes these defined parameters and begins with configuring the bench equipment. Exactly like the previous tests, the power supply is first configured to power the EVM. The register values are then written to the device to configure it for the battery voltage regulation test. Similar to the other tests, the registers are displayed for the user. The compensation function is then performed to start the test. Then the source meter is then set to the user defined value. The source meter current and voltage is then read by the software. The digital multi-meter (DMM) that is connected to the BAT pin of the EVM is then read ten times and averaged for the voltage level. Then input power, output power, efficiency, and error percentage are calculated. Unlike the other tests, this test does not have a default loop and only runs once unless the user selects to test all the parameters. The data gathered during the test is stored in a text file with all the information on the values of the parameters that the user set like the previous tests.

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CHAPTER 7 CORRELATION DATA

After the data is gathered from the bench tests and the ATE, it needs to be correlated to find any offsets. The data alone does not show what the offsets between the ATE and the bench test are. To find the correlation between the tests, some calculations will be needed. Mathematical models will be computed using the data to find best fit lines to then correlate the ATE and bench tests together. A few scenarios of data correlation will be discussed in this chapter. The ICHG and VBREG tables in this chapter have been reduced in size for brevity. The full tables can be viewed in Appendix A. The data gathered from the ATE and the bench tests is put into an excel document. The tests are separated from each other to allow for easy reading of the data. The data is also sectioned off according to how the tested was performed, either via ATE or bench. The first scenario that will be looked at is the input current limit (ILIM) test. Tables 7.1 and 7.2 are the data sets for the input current limit test from the ATE and bench test.

Table 7.1: ILIM data from the ATE

ILIM(ATE) 1 2 3 4 5 100MA INT Tr mAMPS 95.121 95.124 94.944 95.659 95.302 150MA ILIM mAMPS 141.788 141.069 141.424 142.326 142.507 500MA INT Tr mAMPS 472.798 475.787 475.195 475.163 477.593 900MA ILIM mAMPS 863.186 868.375 865.748 865.781 865.781 1500MA ILIM mAMPS 1456.593 1464.376 1457.841 1461.716 1457.841 2000MA ILIM mAMPS 1949.696 1958.792 1945.755 1958.760 1947.068

Table 7.3 shows the percentage difference between the ATE and the bench test data. These percentages signify that there is a possible offset between the two tests. The cells highlighted yellow show that the difference between the two tests is ±2% or more. The ±2% threshold does not have a scientiﬁc basis; it has just been chosen to quickly highlight diverse offsets. The data that relates to these cells is then looked at to determine the type of offset that there is between the two tests.

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Table 7.2: ILIM data from the bench

ILIM(ATE) 1 2 3 4 5 100MA INT Tr mAMPS 92.85 92.7 92.52 93.9 93.2 150MA ILIM mAMPS 138.2 137.2 137.12 139.4 139.3 500MA INT Tr mAMPS 469.2 473.1 472.66 471.6 472.6 900MA ILIM mAMPS 869.3 879.7 873.73 869.4 867.4 1500MA ILIM mAMPS 1444.7 1475.8 1477.78 1474.9 1457.1 2000MA ILIM mAMPS 1980 1979.6 1964.2 1973.7 1954.9

Table 7.3: ILIM data percentage difference between ATE and bench

ILIM 1 2 3 4 5 100MA INT Tr mAMPS -2.45% -2.62% -2.62% -1.87% -2.25% 150MA ILIM mAMPS -2.60% -2.82% -3.14% -2.10% -2.30% 500MA INT Tr mAMPS -0.77% -0.57% -0.54% -0.76% -1.06% 900MA ILIM mAMPS 0.70% 1.29% 0.91% 0.42% 0.19% 1500MA ILIM mAMPS -0.82% 0.77% 1.35% 0.89% -0.05% 2000MA ILIM mAMPS 1.53% 1.05% 0.94% 0.76% 0.40%

To calculate the offset from the ILIM data, the highlighted cells are looked at. The correlation factor is then calculated by subtracting the bench value from the ATE value. This is repeated for each device and data value. An average of the correlation factor is then taken. After the average is found, the error is the recalculated by adding the averaged correlation factor to the ATE data and that is then subtracted from the bench data. The percent error is now lower and thus signiﬁes that if this offset is applied to the ATE data, then the bench data and the ATE data correlation will improve. As an example, the correlation factor for the 100 mA parameter will be calculated. To calculate the correlation factor, the each ATE value is subtracted from each bench test value. The resulting correlation factors are then averaged and a single value is determined. The value for the 100 mA parameter came out to be -2.1961. This is applied to the ATE by moving the trim target. To calculate the new error percentage between the ATE and bench test values, the correlation factor is applied to the ATE values and then subtracted from the bench test value and then the value is divided by the bench value. After applying the correlation factor to each value, the error is now lower and the correlation between the ATE and bench test is reasonable.

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The next test that had an offset was the charge current (ICHG) test. The data from the ATE and the bench test is shown below in the respective tables.

Table 7.4: ICHG data from the ATE ICHG (Bench) 1 2 3 4 5 ICHG Customer **1 AMPS 0.5465 0.5570 0.5515 0.5439 0.5563 ICHG Customer **2 AMPS 0.5962 0.6069 0.6009 0.5934 0.6063 ICHG Customer **3 AMPS 0.6455 0.6571 0.6502 0.6432 0.6563 ICHG Customer **4 AMPS 0.6946 0.7071 0.6999 0.6928 0.7062 ICHG Customer **5 AMPS 0.7439 0.7571 0.7492 0.7423 0.7568 ICHG Customer **6 AMPS 0.7932 0.8070 0.7987 0.7920 0.8068 ICHG Customer **7 AMPS 0.8429 0.8570 0.8485 0.8421 0.8574 ICHG Customer **8 AMPS 0.8921 0.9069 0.8980 0.8920 0.9075 ICHG Customer **9 AMPS 0.9418 0.9567 0.9476 0.9418 0.9577 ICHG Customer **10 AMPS 0.9912 1.0066 0.9968 0.9914 1.0076 ICHG Customer **11 AMPS 1.0409 1.0566 1.0466 1.0412 1.0580 ICHG Customer **12 AMPS 1.0904 1.1073 1.0964 1.0908 1.1084 ICHG Customer **13 AMPS 1.1401 1.1572 1.1459 1.1403 1.1588 ICHG Customer **14 AMPS 1.1895 1.2078 1.1956 1.1901 1.2093 ICHG Customer **15 AMPS 1.2393 1.2581 1.2454 1.2397 1.2597

Table 7.5: ICHG data from the bench test ICHG (Bench) 1 2 3 4 5 ICHG Customer **0 AMPS 0.496 0.4923 0.4945 0.4795 0.4928 ICHG Customer **1 AMPS 0.547 0.5429 0.5454 0.5298 0.5439 ICHG Customer **2 AMPS 0.599 0.5936 0.5958 0.5802 0.5946 ICHG Customer **3 AMPS 0.65 0.6444 0.6465 0.6307 0.6454 ICHG Customer **4 AMPS 0.696 0.6952 0.6976 0.6812 0.6961 ICHG Customer **5 AMPS 0.743 0.7459 0.7485 0.7316 0.7474 ICHG Customer **6 AMPS 0.793 0.7965 0.8002 0.7822 0.7984 ICHG Customer **7 AMPS 0.845 0.8473 0.8519 0.8333 0.8495 ICHG Customer **8 AMPS 0.896 0.8981 0.9033 0.8841 0.9006 ICHG Customer **9 AMPS 0.95 0.9488 0.9547 0.9349 0.9518 ICHG Customer **10 AMPS 1.002 0.9995 1.0057 0.9856 1.0026 ICHG Customer **11 AMPS 1.055 1.0513 1.0565 1.0362 1.0547 ICHG Customer **12 AMPS 1.106 1.1029 1.0949 1.0878 1.1061 ICHG Customer **13 AMPS 1.159 1.1538 1.1467 1.1383 1.1575 ICHG Customer **14 AMPS 1.208 1.2053 1.1972 1.1892 1.209 ICHG Customer **15 AMPS 1.258 1.2567 1.2428 1.2398 1.2604

Just like the input current limit test, the highlighted percentages in the table above show which values signify that there is an offset between the ATE and the bench test data. As seen by the data in Table 7.6, the ICHG data has some correlation error. The data from the

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Table 7.6: ICHG data percentage difference

ICHG parameter is plotted in Figure 7.1. As calculated by the graph, the trend line between the two testers is: y = 1.017x − 0.018 (7.1)

Figure 7.1: ICHG correlation graph.

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Applying this equation to the ICHG data, the data can be scaled and offset to try to make the ATE and bench test correlate well. Typically it is wanted that the scaling factor be close to 1 and the DC offset be close to 0. The equation of the line looks close to these requirements for a good correlation, but according to Table 7.3, there are differences greater that 2%, therefore the data needs to be adjusted to correlate well. To apply the equation to the data, the ATE value is multiplied by 1.017 and then .018 is subtracted from that value. The bench value is then subtracted by this newly calculated value. After all the values are calculated, the percentage difference is then recalculated. The resulting calculations are shown in Table ??.

Table 7.7: ICHG data percentage difference after correlation factor is applied

From Table ??, it is seen that the highest percentage difference is now 1.91%. Though the new percentages look like an improvement over the old data, it is not a significant improvement. Columns containing the percentage difference for device 1 and 3 shows that there is not a reasonable spread. This could be because the standard deviation between the parts is pretty high on the ATE. So when the correlation factor is applied, it still wont give a reasonable value. If this correlation factor were to be used, the specifications would become tighter. The ICHG parameter is typically specified at ±7% at room temperature. Since after applying the correlation factor the max percent difference is 1.91%, that value

37 Texas Tech University, Alan Aragon, August 2013 will tighten the specifications and make it around ±5%. Unless there is work done to reduce the standard deviation, the correlation factor will not help. This kind of data signifies that the way the data is being gathered for this parameter on the ATE needs to be more robust. Therefore, the how and the way that the ATE is gathering measurements needs to be revised and adjusted to give better results to reflect system performance. The third test that was performed was the battery voltage regulation (VBREG) test. Shown below is the data gathered from the ATE and the bench for the voltage battery regulation parameter respectively. The difference between the two tests is shown in the data below. Looking at this data shows that there is no significant offset between the ATE and the bench test. This result is really good. Not having an offset between two tests signifies that the ATE measurements correlate strongly with the bench measurements, no further action is required. After plotting the data for the battery voltage regulation parameter, it enforces the notion that the correlation between the ATE and the bench tests is good. The plot of the gathered data is displayed in Figure 7.2. The equation for the trend line on Figure 7.2 is: y = 0.9977x − 0.0105 (7.2)

To have a set of data that correlates well, it is needed that the scaling factor be 1 and the DC offset be close to 0. As seen from the equation for the VBREG correlation, the scaling factor is 0.9977 which is very close to 1 and the DC offset is 0.0105 which is very close to 0. These signify that the data between the ATE and the bench test is a very good correlation. If the offset were to be applied, the DC offset would be 10.5 mV and the gain factor would be 0.23%. While applying these values would increase the correlation between the ATE and the bench test, they would not have a signiﬁcant value. Therefore the correlation between the ATE and the bench test for the VBREG parameter can be considered a good correlation.

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Figure 7.2: VBREG correlation graph.

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Table 7.8: VBREG data from the ATE VBAT REG(ATE) 1 2 3 4 5 VBREG Set *0 V 3.4932 3.4988 3.5037 3.4961 3.4987 VBREG Set *1 V 3.5133 3.5188 3.5235 3.5162 3.5184 VBREG Set *2 V 3.5332 3.5387 3.5434 3.5365 3.5387 VBREG Set *3 V 3.5533 3.5588 3.5633 3.5567 3.5585 VBREG Set *4 V 3.5731 3.5788 3.5832 3.5768 3.5787 VBREG Set *5 V 3.5931 3.5986 3.6032 3.5970 3.5987 VBREG Set *6 V 3.6132 3.6187 3.6232 3.6171 3.6188 VBREG Set *7 V 3.6333 3.6390 3.6432 3.6374 3.6388 VBREG Set *8 V 3.6533 3.6588 3.6633 3.6575 3.6588 VBREG Set *9 V 3.6734 3.6790 3.6834 3.6776 3.6793 VBREG Set *10 V 3.6935 3.6992 3.7034 3.6976 3.6992 VBREG Set *11 V 3.7132 3.7193 3.7237 3.7180 3.7193 VBREG Set *12 V 3.7333 3.7396 3.7434 3.7381 3.7392 VBREG Set *13 V 3.7532 3.7594 3.7635 3.7581 3.7592 VBREG Set *14 V 3.7734 3.7795 3.7836 3.7783 3.7792 VBREG Set *15 V 3.7935 3.7996 3.8035 3.7985 3.7995 VBREG Set *16 V 3.8136 3.8195 3.8235 3.8186 3.8195 VBREG Set *17 V 3.8335 3.8395 3.8436 3.8388 3.8395 VBREG Set *18 V 3.8533 3.8597 3.8637 3.8589 3.8596 VBREG Set *19 V 3.8733 3.8798 3.8838 3.8790 3.8794 VBREG Set *20 V 3.8933 3.8999 3.9038 3.8990 3.8996 VBREG Set *21 V 3.9132 3.9199 3.9239 3.9191 3.9197 VBREG Set *22 V 3.9333 3.9400 3.9440 3.9391 3.9396 VBREG Set *23 V 3.9533 3.9599 3.9641 3.9592 3.9596 VBREG Set *24 V 3.9733 3.9799 3.9840 3.9794 3.9797

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Table 7.9: VBREG data from the bench test VBAT REG(Bench) 1 2 3 4 5 VBREG Set *0 V 3.493 3.5 3.5055 3.4993 3.504 VBREG Set *1 V 3.513 3.5204 3.5254 3.5196 3.524 VBREG Set *2 V 3.533 3.5403 3.5454 3.5398 3.544 VBREG Set *3 V 3.553 3.5602 3.5654 3.56 3.564 VBREG Set *4 V 3.573 3.5801 3.5854 3.5801 3.584 VBREG Set *5 V 3.593 3.6001 3.6054 3.6002 3.604 VBREG Set *6 V 3.613 3.6202 3.6254 3.6201 3.624 VBREG Set *7 V 3.633 3.6403 3.6454 3.6402 3.644 VBREG Set *8 V 3.653 3.6602 3.6652 3.6601 3.664 VBREG Set *9 V 3.673 3.6801 3.6854 3.6803 3.684 VBREG Set *10 V 3.693 3.7002 3.7054 3.7005 3.704 VBREG Set *11 V 3.713 3.7207 3.7254 3.7207 3.724 VBREG Set *12 V 3.733 3.7408 3.7451 3.7405 3.744 VBREG Set *13 V 3.753 3.7605 3.7653 3.7607 3.764 VBREG Set *14 V 3.773 3.7807 3.7854 3.7805 3.784 VBREG Set *15 V 3.793 3.8007 3.8054 3.8007 3.804 VBREG Set *16 V 3.813 3.8209 3.8253 3.821 3.824 VBREG Set *17 V 3.833 3.8407 3.8454 3.8411 3.844 VBREG Set *18 V 3.853 3.8605 3.8654 3.8609 3.864 VBREG Set *19 V 3.873 3.8807 3.8854 3.8812 3.884 VBREG Set *20 V 3.893 3.9008 3.9054 3.9012 3.904 VBREG Set *21 V 3.913 3.9207 3.9254 3.9213 3.924 VBREG Set *22 V 3.933 3.9407 3.9454 3.941 3.944 VBREG Set *23 V 3.953 3.9607 3.9654 3.9613 3.964 VBREG Set *24 V 3.9725 3.9807 3.9854 3.9811 3.984

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Table 7.10: VBREG data percentage difference

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CHAPTER 8 CONCLUSION

Finding correlation offsets is very important. These offsets help determine if a part is actually doing what it is supposed to despite the numbers looking wrong on the test and it helps determine if a trim is needed or not. When the offsets are found, the tests can be adjusted accordingly so that the devices being tested are accurately measured and determined if they are good. The offsets can sometimes be hidden, so using two separate testing methods can find these hidden offsets. The software developed in this paper to automate bench testing of devices greatly contributes to the necessity of finding the offsets. The software was also created to be easily customizable to allow it to be used for other devices. By automating the data acquisition, it allows for gathering data from larger sample sizes and allows time to be freed up for other priorities. After the offsets are recognized they are then assessed to determine how to compensate for the offset. Although the sample size used for this thesis was five, it is typical to use a lot larger sample size such as 30. For the purpose of data collection for this thesis only five units were made available. The larger sample sized is used because based on the evidence gathered from the formulas previously described. As seen with the data gathered from the tests, there will be situations where the offset is a simple DC offset, other situations where applying the offset will not help the data, and others where the parameter actually correlates well without the need of any correcting offset. There are many different scenarios that the parameters can have, so having a method to determine these scenarios is very helpful.

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BIBLIOGRAPHY

[1] Texas Instruments. 2.0 A Single Input I2C/Standalone Switch-Mode Li-Ion Battery Charger with Power-Path Management, 2013. [Datasheet].

[2] Douglas C Montgomery. Introduction to Statistical Quality Control. John Wiley & Sons, Inc., 6th edition, 2009.

[3] 3.7 V Lithium Ion Battery. http://www.amazon.com/ LG-LGIP-520B-BATTERY-HELIX-VX5400/dp/B003ATJ23O/ref=sr 1 1?ie= UTF8&qid=1361312008&sr=8-1&keywords=4.2v+li-ion+cell+phone+battery, 2013. [Online Image; accessed 19-Feb-2013].

[4] Analog Devices. Quad Parametric Measurement Unit with Integrated 16-Bit Level Setting DACs, 2013. [Datasheet].

[5] Wayne C. Goeke. An 8 1/2- Digit Integrating Analog-to-Digital Converter with 16- Bit, 100,000-Sample-per-Second Performance. Hewlett-Packard Journal, 40:8, 1989.

[6] NIST/SEMATECH. NIST/SEMATECH e-Handbook of Statistical Methods. http: //www.itl.nist.gov/div898/handbook/, 2013. [Online; accessed 11-Feb-2013].

[7] Internet Archive: Wayback Machine. About Motorola University: The Inventors of Six Sigma. http://web.archive.org/web/20051106025733/http://www.motorola.com/ content/0,,3079,00.html, 2013. [Online; accessed 11-Feb-2013].

[8] GE.com. What is Six Sigma. http://www.ge.com/en/company/companyinfo/quality/ whatis.htm, 2013. [Online; accessed 11-Feb-2013].

[9] Mark Burns and Gordon W. Roberts. An Introduction to Mixed-Signal IC Test and Measurement. Oxford University Press, Inc., 2001.

[10] Intel Lucent Microsoft NEC Philips Compaq, Hewlett-Packard. Universal Serial Bus Speciﬁcation, April 2000. [Online; accessed 19-Feb-2013].

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[11] Wayne C. Goeke. Continuously integrating high-resolution analog-to-digital converter. Patent US5117227 A, 1992.

[12] Ronald J. Riedel. Integrating analog to digital converter. Patent US5101206 A, 1992.

45 Texas Tech University, Alan Aragon, August 2013

APPENDIX A ICHG AND VBREG DATA FULL TABLES

Table A.1: ICHG data from the ATE ICHG (Bench) 1 2 3 4 5 ICHG Customer **1 AMPS 0.5465 0.5570 0.5515 0.5439 0.5563 ICHG Customer **2 AMPS 0.5962 0.6069 0.6009 0.5934 0.6063 ICHG Customer **3 AMPS 0.6455 0.6571 0.6502 0.6432 0.6563 ICHG Customer **4 AMPS 0.6946 0.7071 0.6999 0.6928 0.7062 ICHG Customer **5 AMPS 0.7439 0.7571 0.7492 0.7423 0.7568 ICHG Customer **6 AMPS 0.7932 0.8070 0.7987 0.7920 0.8068 ICHG Customer **7 AMPS 0.8429 0.8570 0.8485 0.8421 0.8574 ICHG Customer **8 AMPS 0.8921 0.9069 0.8980 0.8920 0.9075 ICHG Customer **9 AMPS 0.9418 0.9567 0.9476 0.9418 0.9577 ICHG Customer **10 AMPS 0.9912 1.0066 0.9968 0.9914 1.0076 ICHG Customer **11 AMPS 1.0409 1.0566 1.0466 1.0412 1.0580 ICHG Customer **12 AMPS 1.0904 1.1073 1.0964 1.0908 1.1084 ICHG Customer **13 AMPS 1.1401 1.1572 1.1459 1.1403 1.1588 ICHG Customer **14 AMPS 1.1895 1.2078 1.1956 1.1901 1.2093 ICHG Customer **15 AMPS 1.2393 1.2581 1.2454 1.2397 1.2597 ICHG Customer **16 AMPS 1.2888 1.3085 1.2953 1.2895 1.3102 ICHG Customer **17 AMPS 1.3382 1.3585 1.3449 1.3394 1.3603 ICHG Customer **18 AMPS 1.3880 1.4089 1.3949 1.3892 1.4106 ICHG Customer **19 AMPS 1.4377 1.4596 1.4445 1.4392 1.4609 ICHG Customer **20 AMPS 1.4872 1.5098 1.4944 1.4890 1.5118 ICHG Customer **21 AMPS 1.5361 1.5601 1.5443 1.5383 1.5624 ICHG Customer **22 AMPS 1.5860 1.6104 1.5944 1.5881 1.6128 ICHG Customer **23 AMPS 1.6355 1.6605 1.6435 1.6380 1.6637 ICHG Customer **24 AMPS 1.6851 1.7106 1.6937 1.6880 1.7141 ICHG Customer **25 AMPS 1.7351 1.7610 1.7434 1.7375 1.7648 ICHG Customer **26 AMPS 1.7846 1.8112 1.7933 1.7873 1.8155 ICHG Customer **27 AMPS 1.8341 1.8615 1.8432 1.8368 1.8660 ICHG Customer **28 AMPS 1.8844 1.9121 1.8931 1.8875 1.9171 ICHG Customer **29 AMPS 1.9341 1.9627 1.9431 1.9378 1.9671 ICHG Customer **30 AMPS 1.9837 2.0126 1.9930 1.9877 2.0175

46 Texas Tech University, Alan Aragon, August 2013

Table A.2: ICHG data from the bench test ICHG (Bench) 1 2 3 4 5 ICHG Customer **0 AMPS 0.496 0.4923 0.4945 0.4795 0.4928 ICHG Customer **1 AMPS 0.547 0.5429 0.5454 0.5298 0.5439 ICHG Customer **2 AMPS 0.599 0.5936 0.5958 0.5802 0.5946 ICHG Customer **3 AMPS 0.65 0.6444 0.6465 0.6307 0.6454 ICHG Customer **4 AMPS 0.696 0.6952 0.6976 0.6812 0.6961 ICHG Customer **5 AMPS 0.743 0.7459 0.7485 0.7316 0.7474 ICHG Customer **6 AMPS 0.793 0.7965 0.8002 0.7822 0.7984 ICHG Customer **7 AMPS 0.845 0.8473 0.8519 0.8333 0.8495 ICHG Customer **8 AMPS 0.896 0.8981 0.9033 0.8841 0.9006 ICHG Customer **9 AMPS 0.95 0.9488 0.9547 0.9349 0.9518 ICHG Customer **10 AMPS 1.002 0.9995 1.0057 0.9856 1.0026 ICHG Customer **11 AMPS 1.055 1.0513 1.0565 1.0362 1.0547 ICHG Customer **12 AMPS 1.106 1.1029 1.0949 1.0878 1.1061 ICHG Customer **13 AMPS 1.159 1.1538 1.1467 1.1383 1.1575 ICHG Customer **14 AMPS 1.208 1.2053 1.1972 1.1892 1.209 ICHG Customer **15 AMPS 1.258 1.2567 1.2428 1.2398 1.2604 ICHG Customer **16 AMPS 1.309 1.3081 1.2951 1.2907 1.3119 ICHG Customer **17 AMPS 1.36 1.3592 1.3408 1.3418 1.363 ICHG Customer **18 AMPS 1.412 1.4109 1.3944 1.3926 1.4147 ICHG Customer **19 AMPS 1.464 1.4626 1.4442 1.444 1.4662 ICHG Customer **20 AMPS 1.513 1.5142 1.4927 1.4949 1.5181 ICHG Customer **21 AMPS 1.545 1.5661 1.5435 1.5456 1.5701 ICHG Customer **22 AMPS 1.615 1.6174 1.5937 1.5965 1.6219 ICHG Customer **23 AMPS 1.665 1.6689 1.642 1.6479 1.6741 ICHG Customer **24 AMPS 1.717 1.7203 1.6916 1.6991 1.7255 ICHG Customer **25 AMPS 1.77 1.7732 1.7398 1.7506 1.7778 ICHG Customer **26 AMPS 1.806 1.8246 1.7878 1.8016 1.83 ICHG Customer **27 AMPS 1.867 1.8769 1.8346 1.8529 1.8818 ICHG Customer **28 AMPS 1.914 1.9291 1.8825 1.9053 1.9346 ICHG Customer **29 AMPS 1.956 1.9811 1.9285 1.9571 1.9866 ICHG Customer **30 AMPS 2.012 2.0325 1.9707 2.0083 2.0381

47 Texas Tech University, Alan Aragon, August 2013

Table A.3: ICHG data percentage difference

ICHG 1 2 3 4 5 ICHG Customer **0 AMPS -0.23% -2.99% -1.46% -3.10% -2.66% ICHG Customer **1 AMPS 0.08% -2.59% -1.12% -2.66% -2.28% ICHG Customer **2 AMPS 0.46% -2.23% -0.86% -2.28% -1.97% ICHG Customer **3 AMPS 0.69% -1.96% -0.58% -1.98% -1.69% ICHG Customer **4 AMPS 0.20% -1.72% -0.33% -1.70% -1.46% ICHG Customer **5 AMPS -0.12% -1.51% -0.10% -1.47% -1.26% ICHG Customer **6 AMPS -0.03% -1.32% 0.19% -1.25% -1.06% ICHG Customer **7 AMPS 0.25% -1.14% 0.40% -1.06% -0.92% ICHG Customer **8 AMPS 0.43% -0.98% 0.58% -0.89% -0.76% ICHG Customer **9 AMPS 0.86% -0.84% 0.75% -0.74% -0.62% ICHG Customer **10 AMPS 1.08% -0.71% 0.88% -0.59% -0.50% ICHG Customer **11 AMPS 1.34% -0.50% 0.94% -0.48% -0.31% ICHG Customer **12 AMPS 1.41% -0.40% -0.13% -0.28% -0.21% ICHG Customer **13 AMPS 1.63% -0.30% 0.07% -0.17% -0.11% ICHG Customer **14 AMPS 1.53% -0.20% 0.13% -0.07% -0.02% ICHG Customer **15 AMPS 1.49% -0.11% -0.21% 0.00% 0.06% ICHG Customer **16 AMPS 1.54% -0.03% -0.01% 0.09% 0.13% ICHG Customer **17 AMPS 1.60% 0.05% -0.31% 0.18% 0.20% ICHG Customer **18 AMPS 1.70% 0.14% -0.03% 0.24% 0.29% ICHG Customer **19 AMPS 1.80% 0.21% -0.02% 0.33% 0.36% ICHG Customer **20 AMPS 1.71% 0.29% -0.11% 0.40% 0.41% ICHG Customer **21 AMPS 0.58% 0.38% -0.05% 0.48% 0.49% ICHG Customer **22 AMPS 1.80% 0.43% -0.04% 0.52% 0.56% ICHG Customer **23 AMPS 1.77% 0.50% -0.09% 0.60% 0.62% ICHG Customer **24 AMPS 1.86% 0.56% -0.12% 0.65% 0.66% ICHG Customer **25 AMPS 1.97% 0.69% -0.21% 0.75% 0.73% ICHG Customer **26 AMPS 1.19% 0.73% -0.31% 0.80% 0.79% ICHG Customer **27 AMPS 1.76% 0.82% -0.47% 0.87% 0.84% ICHG Customer **28 AMPS 1.55% 0.88% -0.56% 0.93% 0.91% ICHG Customer **29 AMPS 1.12% 0.93% -0.76% 0.99% 0.98% ICHG Customer **30 AMPS 1.41% 0.98% -1.13% 1.02% 1.01%

48 Texas Tech University, Alan Aragon, August 2013

Table A.4: ICHG data percentage difference after correlation factor is applied

ICHG 1 2 3 4 5 ICHG Customer **0 AMPS 1.68% -1.07% 0.45% -1.05% -0.74% ICHG Customer **1 AMPS 1.67% -1.01% 0.45% -0.97% -0.70% ICHG Customer **2 AMPS 1.77% -0.93% 0.45% -0.89% -0.67% ICHG Customer **3 AMPS 1.77% -0.90% 0.50% -0.84% -0.62% ICHG Customer **4 AMPS 1.09% -0.85% 0.55% -0.76% -0.59% ICHG Customer **5 AMPS 0.60% -0.82% 0.60% -0.71% -0.57% ICHG Customer **6 AMPS 0.54% -0.78% 0.74% -0.65% -0.52% ICHG Customer **7 AMPS 0.68% -0.73% 0.82% -0.60% -0.52% ICHG Customer **8 AMPS 0.74% -0.69% 0.89% -0.56% -0.48% ICHG Customer **9 AMPS 1.07% -0.65% 0.95% -0.52% -0.44% ICHG Customer **10 AMPS 1.20% -0.62% 0.99% -0.46% -0.42% ICHG Customer **11 AMPS 1.37% -0.50% 0.96% -0.45% -0.31% ICHG Customer **12 AMPS 1.37% -0.48% -0.19% -0.32% -0.29% ICHG Customer **13 AMPS 1.52% -0.44% -0.06% -0.29% -0.26% ICHG Customer **14 AMPS 1.36% -0.42% -0.06% -0.26% -0.24% ICHG Customer **15 AMPS 1.25% -0.39% -0.46% -0.24% -0.22% ICHG Customer **16 AMPS 1.25% -0.36% -0.32% -0.21% -0.20% ICHG Customer **17 AMPS 1.26% -0.32% -0.67% -0.17% -0.18% ICHG Customer **18 AMPS 1.31% -0.28% -0.44% -0.16% -0.13% ICHG Customer **19 AMPS 1.37% -0.26% -0.47% -0.12% -0.10% ICHG Customer **20 AMPS 1.24% -0.22% -0.61% -0.09% -0.09% ICHG Customer **21 AMPS 0.05% -0.16% -0.58% -0.05% -0.06% ICHG Customer **22 AMPS 1.25% -0.15% -0.61% -0.04% -0.02% ICHG Customer **23 AMPS 1.19% -0.11% -0.70% 0.00% 0.01% ICHG Customer **24 AMPS 1.25% -0.08% -0.76% 0.02% 0.02% ICHG Customer **25 AMPS 1.34% 0.02% -0.87% 0.09% 0.06% ICHG Customer **26 AMPS 0.50% 0.03% -1.00% 0.11% 0.09% ICHG Customer **27 AMPS 1.06% 0.09% -1.19% 0.15% 0.11% ICHG Customer **28 AMPS 0.82% 0.13% -1.31% 0.20% 0.15% ICHG Customer **29 AMPS 0.36% 0.16% -1.52% 0.22% 0.21% ICHG Customer **30 AMPS 0.63% 0.18% -1.91% 0.24% 0.22%

49 Texas Tech University, Alan Aragon, August 2013

Table A.5: VBREG data from the ATE VBAT REG(ATE) 1 2 3 4 5 VBREG Set *0 V 3.4932 3.4988 3.5037 3.4961 3.4987 VBREG Set *1 V 3.5133 3.5188 3.5235 3.5162 3.5184 VBREG Set *2 V 3.5332 3.5387 3.5434 3.5365 3.5387 VBREG Set *3 V 3.5533 3.5588 3.5633 3.5567 3.5585 VBREG Set *4 V 3.5731 3.5788 3.5832 3.5768 3.5787 VBREG Set *5 V 3.5931 3.5986 3.6032 3.5970 3.5987 VBREG Set *6 V 3.6132 3.6187 3.6232 3.6171 3.6188 VBREG Set *7 V 3.6333 3.6390 3.6432 3.6374 3.6388 VBREG Set *8 V 3.6533 3.6588 3.6633 3.6575 3.6588 VBREG Set *9 V 3.6734 3.6790 3.6834 3.6776 3.6793 VBREG Set *10 V 3.6935 3.6992 3.7034 3.6976 3.6992 VBREG Set *11 V 3.7132 3.7193 3.7237 3.7180 3.7193 VBREG Set *12 V 3.7333 3.7396 3.7434 3.7381 3.7392 VBREG Set *13 V 3.7532 3.7594 3.7635 3.7581 3.7592 VBREG Set *14 V 3.7734 3.7795 3.7836 3.7783 3.7792 VBREG Set *15 V 3.7935 3.7996 3.8035 3.7985 3.7995 VBREG Set *16 V 3.8136 3.8195 3.8235 3.8186 3.8195 VBREG Set *17 V 3.8335 3.8395 3.8436 3.8388 3.8395 VBREG Set *18 V 3.8533 3.8597 3.8637 3.8589 3.8596 VBREG Set *19 V 3.8733 3.8798 3.8838 3.8790 3.8794 VBREG Set *20 V 3.8933 3.8999 3.9038 3.8990 3.8996 VBREG Set *21 V 3.9132 3.9199 3.9239 3.9191 3.9197 VBREG Set *22 V 3.9333 3.9400 3.9440 3.9391 3.9396 VBREG Set *23 V 3.9533 3.9599 3.9641 3.9592 3.9596 VBREG Set *24 V 3.9733 3.9799 3.9840 3.9794 3.9797 VBREG Set *25 V 3.9933 4.0000 4.0040 3.9995 3.9998 VBREG Set *26 V 4.0131 4.0200 4.0241 4.0195 4.0198 VBREG Set *27 V 4.0330 4.0400 4.0442 4.0396 4.0398 VBREG Set *28 V 4.0528 4.0602 4.0643 4.0597 4.0599 VBREG Set *29 V 4.0728 4.0802 4.0844 4.0798 4.0799 VBREG Set *30 V 4.0927 4.1002 4.1043 4.0999 4.1000 VBREG Set *31 V 4.1126 4.1203 4.1243 4.1200 4.1202 VBREG Set *32 V 4.1326 4.1403 4.1444 4.1403 4.1403 VBREG Set *33 V 4.1525 4.1605 4.1645 4.1603 4.1604 VBREG Set *34 V 4.1723 4.1807 4.1844 4.1806 4.1803 VBREG Set *35 V 4.1923 4.2006 4.2047 4.2006 4.2004 VBREG Set *36 V 4.2124 4.2207 4.2247 4.2207 4.2204 VBREG Set *37 V 4.2323 4.2407 4.2449 4.2408 4.2405 VBREG Set *38 V 4.2523 4.2608 4.2650 4.2609 4.2605 VBREG Set *39 V 4.2722 4.2808 4.2851 4.2807 4.2805 VBREG Set *40 V 4.2919 4.3010 4.3051 4.3009 4.3007 VBREG Set *41 V 4.3120 4.3211 4.3253 4.3211 4.3205 VBREG Set *42 V 4.3322 4.3412 4.3454 4.3411 4.3406 VBREG Set *43 V 4.3520 4.3613 4.3653 4.3612 4.3604 VBREG Set *44 V 4.3720 4.3813 4.3855 4.3812 4.3804 VBREG Set *45 V 4.3918 4.4014 4.4058 4.4014 4.4002 VBREG Set *46 V 4.4118 4.4214 4.4259 4.4214 4.4202 VBREG Set *47 V 4.4318 4.4413 4.4459 4.4415 4.4405

50 Texas Tech University, Alan Aragon, August 2013

Table A.6: VBREG data from the bench test VBAT REG(Bench) 1 2 3 4 5 VBREG Set *0 V 3.493 3.5 3.5055 3.4993 3.504 VBREG Set *1 V 3.513 3.5204 3.5254 3.5196 3.524 VBREG Set *2 V 3.533 3.5403 3.5454 3.5398 3.544 VBREG Set *3 V 3.553 3.5602 3.5654 3.56 3.564 VBREG Set *4 V 3.573 3.5801 3.5854 3.5801 3.584 VBREG Set *5 V 3.593 3.6001 3.6054 3.6002 3.604 VBREG Set *6 V 3.613 3.6202 3.6254 3.6201 3.624 VBREG Set *7 V 3.633 3.6403 3.6454 3.6402 3.644 VBREG Set *8 V 3.653 3.6602 3.6652 3.6601 3.664 VBREG Set *9 V 3.673 3.6801 3.6854 3.6803 3.684 VBREG Set *10 V 3.693 3.7002 3.7054 3.7005 3.704 VBREG Set *11 V 3.713 3.7207 3.7254 3.7207 3.724 VBREG Set *12 V 3.733 3.7408 3.7451 3.7405 3.744 VBREG Set *13 V 3.753 3.7605 3.7653 3.7607 3.764 VBREG Set *14 V 3.773 3.7807 3.7854 3.7805 3.784 VBREG Set *15 V 3.793 3.8007 3.8054 3.8007 3.804 VBREG Set *16 V 3.813 3.8209 3.8253 3.821 3.824 VBREG Set *17 V 3.833 3.8407 3.8454 3.8411 3.844 VBREG Set *18 V 3.853 3.8605 3.8654 3.8609 3.864 VBREG Set *19 V 3.873 3.8807 3.8854 3.8812 3.884 VBREG Set *20 V 3.893 3.9008 3.9054 3.9012 3.904 VBREG Set *21 V 3.913 3.9207 3.9254 3.9213 3.924 VBREG Set *22 V 3.933 3.9407 3.9454 3.941 3.944 VBREG Set *23 V 3.953 3.9607 3.9654 3.9613 3.964 VBREG Set *24 V 3.9725 3.9807 3.9854 3.9811 3.984 VBREG Set *25 V 3.9924 4.0007 4.0054 4.0014 4.004 VBREG Set *26 V 4.0122 4.0207 4.0252 4.0213 4.024 VBREG Set *27 V 4.032 4.0407 4.0453 4.0412 4.044 VBREG Set *28 V 4.0522 4.0607 4.0652 4.0613 4.064 VBREG Set *29 V 4.072 4.0807 4.0851 4.0815 4.084 VBREG Set *30 V 4.092 4.1007 4.1051 4.1017 4.104 VBREG Set *31 V 4.1118 4.1209 4.1249 4.1218 4.124 VBREG Set *32 V 4.1315 4.1409 4.1451 4.1416 4.144 VBREG Set *33 V 4.1514 4.1609 4.165 4.162 4.164 VBREG Set *34 V 4.1713 4.181 4.185 4.1821 4.184 VBREG Set *35 V 4.1912 4.2011 4.205 4.2023 4.204 VBREG Set *36 V 4.2111 4.221 4.225 4.2221 4.224 VBREG Set *37 V 4.2311 4.2409 4.245 4.2423 4.244 VBREG Set *38 V 4.251 4.261 4.265 4.2622 4.264 VBREG Set *39 V 4.2708 4.2812 4.285 4.2825 4.284 VBREG Set *40 V 4.2905 4.3012 4.305 4.3024 4.304 VBREG Set *41 V 4.3107 4.3214 4.325 4.3222 4.324 VBREG Set *42 V 4.3307 4.3414 4.345 4.3422 4.344 VBREG Set *43 V 4.3505 4.3615 4.365 4.3623 4.364 VBREG Set *44 V 4.37 4.3815 4.385 4.3824 4.384 VBREG Set *45 V 4.39 4.4015 4.405 4.4028 4.404 VBREG Set *46 V 4.41 4.4215 4.425 4.4226 4.424 VBREG Set *47 V 4.43 4.4415 4.445 4.4426 4.4424

51 Texas Tech University, Alan Aragon, August 2013

Table A.7: VBREG data percentage difference

VBAT REG 1 2 3 4 5 VBREG Set *0 V -0.01% 0.04% 0.05% 0.09% 0.15% VBREG Set *1 V -0.01% 0.05% 0.05% 0.10% 0.16% VBREG Set *2 V -0.01% 0.04% 0.06% 0.09% 0.15% VBREG Set *3 V -0.01% 0.04% 0.06% 0.09% 0.15% VBREG Set *4 V 0.00% 0.04% 0.06% 0.09% 0.15% VBREG Set *5 V 0.00% 0.04% 0.06% 0.09% 0.15% VBREG Set *6 V 0.00% 0.04% 0.06% 0.08% 0.14% VBREG Set *7 V -0.01% 0.04% 0.06% 0.08% 0.14% VBREG Set *8 V -0.01% 0.04% 0.05% 0.07% 0.14% VBREG Set *9 V -0.01% 0.03% 0.05% 0.07% 0.13% VBREG Set *10 V -0.01% 0.03% 0.05% 0.08% 0.13% VBREG Set *11 V -0.01% 0.04% 0.05% 0.07% 0.13% VBREG Set *12 V -0.01% 0.03% 0.04% 0.06% 0.13% VBREG Set *13 V -0.01% 0.03% 0.05% 0.07% 0.13% VBREG Set *14 V -0.01% 0.03% 0.05% 0.06% 0.13% VBREG Set *15 V -0.01% 0.03% 0.05% 0.06% 0.12% VBREG Set *16 V -0.02% 0.04% 0.05% 0.06% 0.12% VBREG Set *17 V -0.01% 0.03% 0.05% 0.06% 0.12% VBREG Set *18 V -0.01% 0.02% 0.04% 0.05% 0.11% VBREG Set *19 V -0.01% 0.02% 0.04% 0.06% 0.12% VBREG Set *20 V -0.01% 0.02% 0.04% 0.06% 0.11% VBREG Set *21 V -0.01% 0.02% 0.04% 0.06% 0.11% VBREG Set *22 V -0.01% 0.02% 0.04% 0.05% 0.11% VBREG Set *23 V -0.01% 0.02% 0.03% 0.05% 0.11% VBREG Set *24 V -0.02% 0.02% 0.03% 0.04% 0.11% VBREG Set *25 V -0.02% 0.02% 0.03% 0.05% 0.10% VBREG Set *26 V -0.02% 0.02% 0.03% 0.05% 0.11% VBREG Set *27 V -0.02% 0.02% 0.03% 0.04% 0.10% VBREG Set *28 V -0.02% 0.01% 0.02% 0.04% 0.10% VBREG Set *29 V -0.02% 0.01% 0.02% 0.04% 0.10% VBREG Set *30 V -0.02% 0.01% 0.02% 0.04% 0.10% VBREG Set *31 V -0.02% 0.01% 0.01% 0.04% 0.09% VBREG Set *32 V -0.03% 0.01% 0.02% 0.03% 0.09% VBREG Set *33 V -0.03% 0.01% 0.01% 0.04% 0.09% VBREG Set *34 V -0.02% 0.01% 0.01% 0.04% 0.09% VBREG Set *35 V -0.03% 0.01% 0.01% 0.04% 0.09% VBREG Set *36 V -0.03% 0.01% 0.01% 0.03% 0.09% VBREG Set *37 V -0.03% 0.00% 0.00% 0.04% 0.08% VBREG Set *38 V -0.03% 0.00% 0.00% 0.03% 0.08% VBREG Set *39 V -0.03% 0.01% 0.00% 0.04% 0.08% VBREG Set *40 V -0.03% 0.01% 0.00% 0.03% 0.08% VBREG Set *41 V -0.03% 0.01% -0.01% 0.03% 0.08% VBREG Set *42 V -0.03% 0.00% -0.01% 0.03% 0.08% VBREG Set *43 V -0.03% 0.00% -0.01% 0.03% 0.08% VBREG Set *44 V -0.05% 0.00% -0.01% 0.03% 0.08% VBREG Set *45 V -0.04% 0.00% -0.02% 0.03% 0.09% VBREG Set *46 V -0.04% 0.00% -0.02% 0.03% 0.09% VBREG Set *47 V -0.04% 0.00% -0.02% 0.02% 0.04%

52 Texas Tech University, Alan Aragon, August 2013

APPENDIX B BASIC ANALYSIS OF ATE MEASUREMENT METHOD

The PMU in the ATE uses the force and measure method to make its measurements. To measure voltage, the PMU forces a current and reads the voltage. To measure current, the PMU forces a voltage and reads the current. Figure B.1 shows the block diagram of how the PMU is setup to force voltage and measure current at the same time. The DUT is connected to MEASVHx and DUTGND. The external RSENSE is an optional feature that the user includes to increase the current range to 80mA. The internal RSENSE is changed by the user depending on the current range they are using.

Figure B.1: Forcing voltage, measuring current. [4]

The DAC at the positive input of the FORCE AMPLIFIER is set to a known voltage. This voltage is applied to the DUT. The voltage applied to the DUT is seen via MEASVHx. The DUTGND is the reference point of the DUT so that the voltage can be seen according to what the DUT sees. These two inputs are sent through buffers and then put in a differ-

53 Texas Tech University, Alan Aragon, August 2013 ential amplifier of a gain of one to see the voltage drop across the DUT. The output of the differential amplifier is sent back up to the FORCE AMPLIFIER to compare it with the DAC to make sure that the applied voltage to the DUT is what the user wants it to be. The current is measured via the RSENSE. Because the RSENSE is a known resistance and the voltages drop is measured across it, the current can be computed. The voltages taken before and after the RSENSE resistor are sent through buffers and then to a differential amplifier that has a gain of five or ten. This gain is there to maximize the range of the ADC. This is then output to MEASOUTx and an ADC is there to take the voltage to calculate the current. Figure B.2 shows the block diagram of how the PMU is setup to force current and measure voltage at the same time. To just measure voltage the user would force 0 A of current. It uses the same pieces as the current measurement setup. The output to MEASOUTx is now from the bottom differential amplifier and the feedback loop into the FORCE AMPLI- FIER is now from dotted line section area called MEASURE CURRENT AMPLIFIER. The DAC is converted to output a current. This current is sent through the FORCE AM- PLIFIER to be sent to the DUT. The MEASURE CURRENT AMPLIFIER section is the feedback to the FORCE AMPLIFIER to make sure the current being output is correct. The voltage on the DUT with reference to the DUTGND is measured via the differential amplifier that MEASVHx and DUTGND are connected to. The output of the differential amplifier is then output to MEASOUTx and sent through an ADC to acquire the digital code for the measure voltage.

54 Texas Tech University, Alan Aragon, August 2013

Figure B.2: Forcing current, measuring voltage. [4]

55 Texas Tech University, Alan Aragon, August 2013

APPENDIX C BASIC ANALYSIS OF BENCH MEASUREMENT METHOD

The Agilent 34401a and Keithley 2440 use a continuously integrating, multi-slope A/D converter measurement method. A continuously integrating converter is typically a multi- slope run-up with a residue ADC combination. Figure C.1 shows the basic design of a dual- slope method integrating ADC. The basic idea of the circuit is that the system is measuring how long the charge up of the unknown voltage is compared to the known reference voltage. This design has a run-up and run-down phase. The algorithm begins with the integrator at zero, this is achieved by shorting the integrator capacitor [5]. A capacitor is charged using the unknown voltage during the run-up phase. The run-up phase is set for a ﬁxed period of time, while the run-down phase is run until the output of the integrator is zero.

Figure C.1: Dual-slope circuit. [5]

The time allowed for run-up and the time it takes to bring the voltage to zero are used in the calculation of the unknown voltage. The equation below is used to calculate the unknown for the basic circuit is shown, where tu is the run-up time and td is the run-down time [5]. Because the output of the integrator needs to be zero, the reference voltage will needed to be switched between negative and positive based on the sign of the output of the ampliﬁer after the run-up phase.

56 Texas Tech University, Alan Aragon, August 2013

td VIN = −VREF (C.1) tu

Figure C.2: Multi-slope run-up circuit. [5]

The multi-slope run-up method is an enhanced version of the run-up phase. It is a method that is used to improve the resolution of the converter. Figure C.2 shows an example circuit of a multi-slope run-up converter. The dual-slope techniques resolution is limited by the maximum voltage swing of the integrator and the wideband circuit noise [5]. The idea behind the multi-slope run-up method is that the system is applying the negative and positive voltage references so that the output of the circuit stays within the voltage swing of the integrator ampliﬁer. The positive and negative reference voltages are selected based on the result of a comparator at the output of the integrator ampliﬁer. The duration of how long the positive or negative reference was applied to the circuit is noted by the system. This is repeated for the duration of a set sampling period. To increase the accuracy of the algorithm, a residual ADC is added to the system. Typically the method requires a run-down phase to calculate the voltage, but adding an additional ADC can remove the necessity of the run-down phase. This is accomplished by converting the residual analog signal remaining at the end of run-up into a fractional slope count which can be added to the slope count determined during run-up so that the resulting total slope count is directly proportional to the input voltage [11]. The unknown voltage is calculated by adding the voltage from the second ADC to the voltage measured by the run-up phase.

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When combining the multi-slop run-up method and the residual ADC method, it cre- ates a ”high resolution and high speed analog-to-digital conversion without the need for a run-down interval” [12] known as a continuously integrating converter. With a continuous integrator, many readings can be performed without having to remove the unknown voltage from the system. Using this method also allows for quicker readings at the increased resolution that the multi-slope phase allows.