Agilent Technologies Impedance Measurement Handbook July 2006
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The Impedance Measurement Handbook A Guide to Measurement Technology and Techniques Copyright® 2000-2003 Agilent Technologies Co. Ltd All rights reserved. TABLE OF CONTENTS SECTION 1 Impedance measurement basics Paragraph 1-1 1-2 1-3 1-4 1-5 Impedance ...................................................................................... Measuring impedance .................................................................. Parasitics: there are no pure R, C or L ......................................
SECTION 3 Fixturing and cabling ––––––– LF impedance measurement ––––––– Paragraph 3-1 3-2 3-3 3-3-1 3-3-2 3-3-3 3-4 3-4-1 3-4-2 3-4-3 3-5 Terminal configuration ................................................................ Using test cables at high frequencies ......................................... Test fixtures ................................................................................... Agilent supplied test fixtures ......................................................
4-7-1 4-7-2 4-7-3 4-7-4 4-7-5 Variance in residual parameter value ........................................ A difference in contact condition ............................................... A difference in open and short compensation conditions ..... Electromagnetic coupling with a conductor near the DUT ................................................................................. Variance in environmental temperature ....................................
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SECTION 1 Impedance measurement basics 1-1. Impedance Impedance is an important parameter used to characterize electronic circuits, components, and the materials used to make components. Impedance (Z) is generally defined as the total opposition a device or circuit offers to the flow of an alternating current (AC) at a given frequency, and is represented as a complex quantity which is graphically shown on a vector plane.
Reactance takes two forms - inductive (X L) and capacitive (Xc). By definition, X L=2πfL and Xc=1/(2πfC), where f is the frequency of interest, L is inductance, and C is capacitance. 2πf can be substituted for by the angular frequency (ω:omega) to represent XL=ωL and Xc=1/(ωC). Refer to Figure 1-3. Figure 1-3. Reactance in two forms - inductive (XL) and capacitive (Xc) A similar reciprocal relationship applies to susceptance and admittance.
1-2. Measuring impedance To find the impedance, we need to measure at least two values because impedance is a complex quantity. Many modern impedance measuring instruments measure the real and the imaginary parts of an impedance vector and then convert them into the desired parameters such as |Z|, θ, |Y|, R, X, G, B. It is only necessary to connect the unknown component, circuit, or material to the instrument. However, sometimes the instrument will display an unexpected result (too high or too low).
1-4. True, effective, and indicated values A thorough understanding of true, effective, and indicated values of a component, as well as their significance to component measurements, is essential before you proceed with making practical measurements. ➣ A true value is the value of a circuit component (resistor, inductor or capacitor) that excludes the defects of its parasitics. In many cases, the true value can be defined by a mathematical relationship involving the component’s physical composition.
1-5. Component dependency factors The measured impedance value of a component depends on several measurement conditions, such as frequency, test signal level, and so on. Effects of these component dependency factors are different for different types of materials used in the component, and by the manufacturing process used. The following are typical dependency factors that affect measurement results.
Figure 1-9. Capacitor frequency response Test signal level: The test signal (AC) applied may affect the measurement result for some components. For example, ceramic capacitors are test signal voltage dependent as shown in Figure 1-10 (a). This dependency varies depending on the dielectric constant (K) of the material used to make the ceramic capacitor. Cored-inductors are test signal current dependent due to the electromagnetic hysteresis of the core material.
Figure 1-11. DC bias dependencies of ceramic capacitors and cored-inductors Temperature: Most types of components are temperature dependent. The temperature coefficient is an important specification for resistors, inductors and capacitors. Figure 1-12 shows some typical temperature dependencies that affect ceramic capacitors with different dielectrics. Other dependency factors: Other physical and electrical environments, e.g.
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SECTION 2 Impedance measurement instruments 2-1. Measurement methods There are many measurement methods to choose from when measuring impedance, each of which has advantages and disadvantages. You must consider your measurement requirements and conditions, and then choose the most appropriate method, while considering such factors as frequency coverage, measurement range, measurement accuracy, and ease of operation.
I-V method An unknown impedance Zx can be calculated from measured voltage and current values. Current is calculated using the voltage measurement across an accurately known low value resistor, R. In practice a low-loss transformer is used in place of R to prevent the effects caused by placing a low value resistor in the circuit. The transformer, however, limits the low end of the applicable frequency range.
Auto balancing bridge method The current, flowing through the DUT, also flows through resistor R. The potential at the “L” point is maintained at zero volts (thus called a “virtual ground”), because the current through R balances with the DUT current by operation of the I-V converter amplifier. The DUT impedance is calculated using voltage measurement at High terminal and that across R. Note: In practice, the configuration of the auto balancing bridge differs for each type of instrument.
Table 2-1. Common impedance measurement methods Advantages Disadvantages Applicable frequency range Typical Agilent products Common application Bridge method High accuracy (0.1%typ.). Wide frequency coverage by using different types of bridges. Low cost. Need to be manually balanced. Narrow frequency coverage with a single instrument. DC to 300 MHz None Standard lab Resonant method Good Q accuracy up to high Q. Need to be tuned to resonance. Low impedance measurement accuracy.
2-2. Operating theory of practical instruments The operating theory and key functions of the auto balancing bridge instrument are discussed in the paragraphs 2-3 through 2-4-8. A discussion of the RF I-V instrument is described in paragraphs 2-5 through 2-7-6. 2-3. Theory of auto balancing bridge method The auto balancing bridge method is commonly used in modern LF impedance measurement instruments. Its operational frequency range has been extended up to 110 MHz.
The measurement circuit is functionally divided into following three sections. The signal source section generates the test signal applied to the unknown device. The frequency of the test signal (fm) is variable from 40 Hz to 110 MHz, and the maximum frequency resolution is 1 mHz. A microprocessor controlled frequency synthesizer is employed to generate these high-resolution test signals. The output signal level, variable from 5 mV to 1 V, is adjusted using an attenuator.
Figure 2-4. Auto balancing bridge section block diagram Figure 2-5.
2-4. Key measurement functions The following discussion describes the key measurement functions for advanced impedance measurement instruments. Thoroughly understanding these measurement functions will eliminate the confusion sometimes caused by the measurement results obtained. 2-4-1. OSC level The oscillator output signal is output through the Hc terminal and can be varied to change the test signal level applied to the DUT.
2-4-2. DC bias In addition to the AC test signal, a DC voltage can be output through the Hc terminal and applied to the DUT. A simplified output circuit, with a DC bias source, is shown in Figure 2-7. Many of the conventional impedance measurement instruments have a voltage bias function, which assumes that almost no bias current flows (the DUT has a high resistance).
2-4-3. Ranging function To measure impedance from low values to high values, impedance measurement instruments have several measurement ranges. Generally, 7 to 10 measurement ranges are available and the instrument can automatically select the appropriate measurement range according to the DUT’s impedance. Range changes are generally accomplished by changing gain multiplier of the vector ratio detector, and by switching the range resistor (Figure 2-8 (a)).
2-4-4. Level monitor function Monitoring the test signal voltage or current applied to the DUT is important for maintaining accurate test conditions, especially when the DUT has a test signal level dependency. The level monitor function measures the actual signal level across the DUT. As shown in Figure 2-9, the test signal voltage is monitored at the High terminal and the test signal current is calculated using the value of range resistor Rr and the voltage across it.
Averaging function calculates the mean value of measured parameters from the desired number of measurements. Averaging has the same effect on random noise reduction as that by using a long measurement time. Figure 2-10. Relationship of measurement time and precision 2-4-6. Compensation function Impedance measurement instruments are calibrated at UNKNOWN terminals and, measurement accuracy is specified at the calibrated reference plane.
The induced errors are dependent upon test frequency, test fixture, test leads, DUT connection configuration, and surrounding conditions of the DUT. Hence, the procedure to perform compensation with actual measurement setup is a key technique to obtain accurate measurement results. The compensation theory and practice are discussed comprehensively in Section 4. 2-4-7.
Figure 2-11. Guarding techniques 2-4-8. Grounded device measurement capability Grounded devices such as the input/output of an amplifier can be measured directly using the I-V measurement method or the reflection coefficient measurement method (Figure 2-12 (a)). However, it is difficult for an auto balancing bridge to measure low-grounded devices because the measurement signal current bypasses the ammeter (Figure 2-12 (b)).
Figure 2-12.
2-5. Theory of RF I-V measurement method The RF I-V method featuring Agilent’s RF impedance analyzers and RF LCR meters is an advanced technique to measure impedance parameters in the high frequency range, beyond the frequency coverage of the auto balancing bridge method. It provides better accuracy and wider impedance range than the network analysis (reflection coefficient measurement) instruments can offer.
Figure 2-13.
2-6. Difference between RF I-V and network analysis measurement methods When testing components in the RF region, the RF I-V measurement method is often compared with network analysis. The difference in principle is highlighted as the clarifying reason why the RF I-V method has advantages over the reflection coefficient measurement method, commonly used with network analysis. The network analysis method measures the reflection coefficient value, Γx, of the unknown device.
Figure 2-14. Relationship of reflection coefficient to impedance Figure 2-15.
Figure 2-16. Comparison of typical Q accuracy 2-7. Key measurement functions 2-7-1. OSC level The oscillator output signal is output through the coaxial test port (coaxial connector) with source impedance of 50 Ω. The oscillator output level can be controlled to change the test signal level applied to the DUT. Specified test signal level is obtained when the connector is terminated with a 50 Ω load (The signal level for open or short condition is calculated from that for 50 Ω).
2-7-3. Calibration Most of the RF vector measurement instruments such as network analyzers need to be calibrated each time a measurement is initiated or a frequency setting is changed. The RF I-V measurement instrument requires calibration as well. At higher frequencies, a change in the instrument’s operating conditions, such as, environmental temperature, humidity, frequency setting, etc., have a greater effect on measurement accuracy.
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SECTION 3 Fixturing and cabling When interconnecting a device under test (DUT) to the measurement terminals of the auto balancing bridge instrument, there are several connection configurations to choose from. This section will introduce the basic theory and use of each connection configuration focussing on the auto balancing bridge instrument. In RF impedance measurements, the usable connection configuration is the two terminal method only.
The four-terminal pair (4TP) configuration solves the mutual coupling problem because it uses coaxial cable to isolate the voltage sensing cables from the signal current path (Figure 3-5). Since the return current flows through the outer conductor of the coaxial cable, the magnetic flux generated by the inner conductor is canceled by that of the outer conductor (shield). The measurement range for this configuration can be improved to below 1 Ω.
Figure 3-2. Three-terminal (3T) configuration Figure 3-3.
Figure 3-4. Five-terminal (5T) configuration Figure 3-5.
3-2. Using test cables at high frequencies The 4TP configuration is the best solution for wide-range impedance measurement. However, in basic 4TP measurement, its cable length is limited by the measurement frequency because the length of the cable must be much shorter than the wavelength.
Table 3-1.
3-3-3. User test fixture example Figure 3-7 shows an example of a user fabricated test fixture. It is equipped with alligator clips as the contact electrodes for flexibility in making a connection to DUTs. Also, this test fixture can be connected directly to 4TP instruments. The assembly procedure for this test fixture is shown in Figure 3-7. Figure 3-6. User fabricated test fixture open/short methods Figure 3-7.
3-4. Test cables When the DUT is tested apart from the instrument, it is necessary to extend the test ports (UNKNOWN terminals) using cables. If the cables are extended without regard to their length, it will cause not only an error, but will also result in bridge unbalance making measurement impossible. 3-4-1. Agilent supplied test cables Agilent Technologies supplies 1 m, 2 m and 4 m cables as listed in Table 3-2. The test cables from 16048A to 16048E are constructed using the same cable material.
Figure 3-8. Specifications of recommended cable (Agilent PN 8121-1218) 3-4-3. Test cable extension If the required test cable is longer than 1 m, 2 m, or 4 m, it is possible to extend the Agilent supplied test cable by using the following techniques. 4TP-4TP extension: As shown in Figure 3-9 (a), extension of the four coaxial cables should be connected together at the end of the extension. The actual connection is as shown in Figure 3-9 (b).
Figure 3-9. 4TP-4TP extension Figure 3-10.
Figure 3-11. Shielded 4T extension Table 3-2.
3-5. Eliminating the stray capacitance effects When the DUT has high impedance (e.g. Low Capacitance), the effects of stray capacitance are not negligible. Figure 3-12(a) shows an example of measuring a DUT using 4 terminal contacts. In this example, Cd is in parallel with the DUT. When a conductive plate is placed under the DUT, the combined capacitance (Ch//Cl) is also in parallel with the DUT, resulting in measurement error.
Figure 3-13. Coaxial test port circuit configuration 3-7. RF test fixtures RF test fixtures are designed so that the lead length (electrical path length) between the DUT and the test port is made as short as possible to minimize residuals. At frequencies typically below 100 MHz, measurement error due to test fixture residuals is small compared to instrument error and is normally negligible after compensation is made.
3-7-1. Agilent supplied RF test fixtures Agilent Technologies offers various types of RF test fixtures that meet the type of the DUT and required test frequency range. Consider measurable DUT size, electrode type, frequency, and bias condition to select a suitable test fixture. There are two types of RF test fixtures: coaxial and non-coaxial test fixtures, which are different from each other for both geometrical structures and electrical characteristics.
3-8. Test port extension in RF region In RF measurements, connect the DUT closely to the test port to minimize additional measurement errors. When there is an unavoidable need of extending the test port, such as in-circuit testing of devices and on-wafer device measurement using a prober, make the length of test port extension as short as possible.
Figure 3-15. Calibration plane extension Figure 3-16.
SECTION 4 Measurement error and compensation 4-1. Measurement error For real-world measurements, we have to assume that the measurement result always contains some error. Some typical error sources are: • Instrument inaccuracies (including DC bias inaccuracy and OSC level inaccuracy) • Residuals in the test fixture and cables • Noise The DUT’s parasitics were not listed because the DUT’s parasitics are a part of the DUT and we need to measure the DUT’s impedance including its parasitics.
4-2-1. Offset compensation When a measurement is affected by only a single component of the residuals, the effective value can be obtained by simply subtracting the error value from the measured value. For example, in the case of the low value capacitance measurement shown in Figure 4-2, the stray capacitance Co paralleled with the DUT’s capacitance Cx is significant to the measurement and can be compensated by subtracting the stray capacitance value from the measured capacitance value Cm.
Figure 4-3. Open/short compensation 4-2-3. Precautions for open and short measurements When an open measurement is made, it is important to accurately measure the stray capacitance. To do this, keep the distance between the test fixture terminals the same as when they are holding the DUT, set the integration time, averaging, and OSC level so that the instrument measures with maximum accuracy.
Figure 4-4. Example of shorting device. (Agilent PN: 5000-4226) 4-2-4. Open, short and load compensations There are numerous measurement conditions where complicated residual parameters cannot be modeled as the simple equivalent circuit in Figure 4-3. Open/short/load compensation is an advanced compensation technique that is applicable to complicated residual circuits.
Figure 4-5. Open/short/load compensation 4-2-5. What should be used as the load? The key point in open/short/load compensation is to select a load whose impedance value is accurately known. The criteria is as follows. Use a stable resistor or capacitor as the load device. The load device’s impedance value must be stable under conditions of varying temperature, magnetic flux, and other component dependency factors.
Figure 4-6. Electrode distance in load measurement Figure 4-7.
Step 1: Using a direct-connected test fixture, measure the load. Step 2: Measure load compensation data using fixture to be compensated. Figure 4-8. Actual open/short load measurement example 4-2-6. Application limit for open, short and load compensations When the residuals are too significant compared to the DUT’s impedance value, compensation may not work properly. For example, if the measured short impedance Zsm is about the same as DUT’s impedance, total measurement error will be doubled.
If RH = RL = Rhp = Rlc and Chp = Clp, D errors of 2-terminal and 4-terminal become the same when Cx = Chp This means that the 2-terminal connection is a better choice when the DUT capacitance is smaller than cable capacitance (Chp or Clc). Figure 4-9.
4-4. Measurement cable extension induced error Extending a 4TP measurement cable from the instrument will cause a magnitude error and phase shift of the measurement signal according to the extension cable length and measurement frequency.
Figure 4-11. Measurement error due to extended cable length The cable length compensation works for test cables whose length and propagation constants are known, such as the Agilent-supplied test cables of 1 m (2 m or 4 m). If different types of cable in different lengths are used, it may cause bridge unbalance in addition to measurement error.
k value is a decimal number mostly within the range of -1 to +1 and different for different instruments. As the above equation shows, the error rapidly increases in proportion to square of measurement frequency. Using open/short compensation will not reduce this error. Only open/short/load compensation can minimize this error.
Figure 4-12.
4-6. Calibration and compensation in RF region 4-6-1. Calibration Whether the RF I-V method or network analysis, the open, short and load calibration minimizes instrument inaccuracies. To perform calibration, open, short and load reference terminations are connected to the test port and, each of the terminations is measured. This calibration data is stored in instrument memory and used for calculation to remove the instrument errors.
When the test port is extended, calibration should be performed at the end of extension cable, as discussed in section 3. Thereby, the calibration plane is moved to the end of cable. To perform measurements met to specified accuracy, the instrument should be calibrated before measurement is initiated and each time the frequency setting is changed. The calibration defines the calibration reference plane at which measurement accuracy is optimized.
4-6-3. Compensation method As the error source model is different for the coaxial and non-coaxial sections of the test fixture, compensation method is also different for each of them. Electrical length compensation eliminates measurement errors induced by the phase shift in the coaxial section.
Accordingly, the residual parameters have greater effects on higher frequency measurements and become a primary factor of measurement errors. The accuracy of measurement results after compensation depends on how the open/short measurements have been performed properly. Figure 4-15. Relationship of residual parameter values to the typical impedance measurement range of the RF I-V method To perform optimum compensation, observe the precautions for open/short measurements as described in paragraph 4-2-3.
Conceptually, there are two methods of defining the short bar’s impedance: One is to assume the impedance to be zero. This has been a primordial method of defining the short impedance. In this definition method, measurement result is a relative value of the DUT to the short bar. The other method is to define the short bar’s inductance as xx H. (Residual resistance is negligible for small short bar.) In this method, the measurement result is deemed as the absolute value of the DUT.
4-6-7. Electrical length compensation In the lower frequency region, using the open/short compensation function can minimize most of test fixture residuals. In the RF region, however, this is not enough to reduce the effect of the test fixture residuals. The wavelength of RF frequencies is short and is not negligible compared to physical transmission line length of the test fixture.
4-6-8. Practical compensation technique The calibration and compensation methods suitable for measurement are different for how the test cable or fixture is connected to the test port. The following is a typical guideline for selecting appropriate calibration and compensation methods. (1) Measurements using Agilent test fixture without test port extension To make measurements using a test fixture connected directly to the test port, first perform calibration at the test port.
Figure 4-17. Difference in residual parameter values due to DUT positioning 4-7-2. A difference in contact condition Change in contact condition of the device also causes measurement discrepancies. When the device is contacted straightly across the measurement terminals, the distance of current flow between the contact points are minimum, thus providing the lowest impedance measurement value.
4-7-3. A difference in open/short compensation conditions Improper open/short measurements deteriorate accuracy of compensated measurement results. If the open/short measurement conditions are not always the same, inconsistent measurement values will result. Particularly, each short device has its inherent impedance (inductance) value and, if not defined as zero or an appropriate value, the difference of the short device used will produce resultant measurement discrepancies.
Figure 4-20. Eddy current effect and magnetic flux directivity of device 4-7-5. Variance in environmental temperature Temperature influences on the electrical properties of materials used for the test fixtures and cables. When the test port is extended using a coaxial cable, the dielectric constant of the insulation layer (between the inner and outer conductors) of the cable as well as physical cable length will vary depending on the temperature.
SECTION 5 Impedance measurement applications and enhancements Impedance measurement instruments are used for a wide variety of applications. In this section we present practical measurement examples based on real life applications. Also, special measurement techniques are covered to expand the range of impedance measurement applications. 5-1. Capacitor measurement Capacitors are one of the primary components used in electronic circuits.
Table 5-1. Capacitor types Type Application Advantage Disadvantage Film Blocking, buffering. bypass, coupling.
When we measure capacitors, we have to consider these parasitics. Impedance measurement instruments measure capacitance in either the series mode (Cs-D, Cs-Rs) or in the parallel mode (Cp-D, Cp-Rp). The displayed capacitance value, Cs or Cp, is not always equal to the real capacitance value C due to the presence of parasitic components.
Precautions for capacitor measurement depend on the capacitance value being measured. High-value capacitance measurement is a low impedance measurement. Therefore, contact resistance and residual impedance in the contact electrodes, test fixture, and cables must be minimized. Use a 4-terminal, 5-terminal or 4-terminal pair configuration to interconnect the DUT with the measurement instrument.
5-2. Inductor measurement An inductor consists of wire wound around a core and is characterized by the core material used. Air is the simplest core material for making inductors, but for volumetric efficiency of the inductor, magnetic materials such as iron, permalloy, and ferrites are commonly used. A typical equivalent circuit for an inductor is shown in Figure 5-8 (a). In this figure, Rp represents the iron loss of the core, and Rs represents copper loss of the wire.
±0.001, the maximum measurable Q value is 90.9. See Appendix E for Q accuracy calculation equation.) Except for resonant method, the impedance measurement instrument calculates the Q value by Q=X/R. Measured vector of the relatively high Q inductor is as shown in Figure 5-12. The impedance measurement error is represented by a small circle enclosing the error vector (∆). The R value of a high Q (low loss) inductor is very small relative to the X value.
Figure 5-11. Q measurement accuracy Figure 5-12. Q measurement error Furthermore, the following phenomena may occur when a cored inductor is measured using an auto balancing bridge type instrument. When a high level test signal is applied to an inductor, measurement may be impossible for a certain frequency range. This is because of the nonlinearity of the core material which causes harmonic distortion of the test signal current.
Figure 5-13.
5-3. Transformer measurement A transformer is one end-product of an inductor. So, the measurement techniques are the same as for inductor measurement. Figure 5-14 shows a schematic with the key measurement parameters of a transformer. A description of how to measure these parameters follows. Primary inductance (L1) and secondary inductance (L2) can be measured directly by connecting the instrument as shown in Figure 5-15. All other windings should be left open.
Inter-winding capacitance (C) between the primary and the secondary is measured by connecting one side of each winding to the instrument as shown in Figure 5-17. Mutual inductance (M) Obtain mutual inductance (M) by measuring the inductance in the series aiding and the series opposing configurations and then calculating the results using the equation given in Figure 5-18 (a). Mutual inductance can be measured directly if the transformer is connected as shown in Figure 5-18 (b).
Turns ratio (N) Approximate the turns ratio (N) by connecting a resistor in the secondary as shown in Figure 5-19 (a). From the impedance value measured at the primary, the approximate turns ratio can then be calculated. Direct turns ratio measurement can be made with a network analyzer or built-in transformer measurement function (option) of the 4263B LCR meter. Obtain the turns ratio from the voltage ratio measurements for the primary and the secondary, as shown in Figure 5-19 (b). Figure 5-19.
The 4263B’s transformer measurement function enables the measurement of the N, M, L1 and the DC resistance of the primary by changing measurement circuit connections with an internal switch. Figure 5-20 shows a simplified schematic block diagram of the 4263B. A test signal is applied to the primary and, L1 is calculated from the measured values of V1 and I1. M is calculated from V2 and I1. N is obtained from the ratio of V1 and V2.
5-4. Diode measurement The junction capacitance of a switching diode determines its switching speed and is dependent on the reverse DC voltage applied to it. An internal bias source of the measurement instrument is used to reverse-bias the diode. The junction capacitance is measured at the same time. Figure 5-22 shows the measurement setup.
5-5. MOS FET measurement Evaluating the capacitances between the source, drain, and gate of an MOS FET is important in design of high frequency and switching circuits. Generally, these capacitances are measured while a variable DC voltage source is connected to the drain terminal referenced to the source, and the gate held at zero DC potential (Figure 5-24). When an instrument is equipped with a guard terminal and an internal DC bias source, capacitances Cds, Cgd, and Cgs can be measured individually.
5-6. Silicon wafer C-V measurement The C-V (capacitance vs. DC bias voltage) characteristic of a MOS structure is an important measurement parameter for evaluating silicon wafers. To evaluate the capacitance that varies with applied DC bias voltage, capacitance is measured at a low AC signal level while sweeping a number of bias voltage points.
Figure 5-26.
As a result of extremely high integration of logic LSIs using MOS FETs, the thickness of the MOS FETs’ gate oxide is becoming thinner (less than 2.0 nm), and such MOS FETs have been produced recently. In evaluating these kinds of MOS FETs, leakage current becomes larger by the tunneling effect because the capacitance value of a thin gate oxide has high impedance, and most of the test signal flows as leakage current. Consequently, measurement of the thin gate oxide cannot be performed accurately.
5-7. High-frequency impedance measurement using the probe As shown in Table 5-3, an RF I-V instrument can be used for a wafer’s L, C, and R measurements, which are measurements in RF frequencies. Figure 5-28 shows an example measurement configuration when using the RF I-V instrument. This figure illustrates a measurement system configuration for using the E4991A RF impedance/material analyzer with a probe.
Figure. 5-28.
5-8. Resonator measurement The resonator is the key component in an oscillator circuit. Crystal and ceramic resonators are commonly used in the kHz and MHz range. Figure 5-29 (a) and (b) show typical equivalent circuit and frequency response for a resonator. A resonator has 4 primary elements; C, L, R, and Co. C and L determine the series resonant frequency, fr, and Co and L determine the parallel resonant frequency, fa.
2. It is important to properly set the oscillator output level; resonators are test signal dependent. The minimum impedance value and the series resonant frequency may vary depending on the applied test signal level. Decrease the test signal level while monitoring the test current (I-monitor function) until the specified test level is obtained. 3. Perform an open/short compensation. Use ALL POINT compensation mode instead of the interpolation mode because resonator measurements are narrowband.
(a) (b) Figure 5-31.
5-9. Cable measurements The characteristic impedance Z(Ω), capacitance per unit length C (pF/m) and the propagation constants α (dB/m) and β (rad/m) are parameters commonly measured when evaluating cables. Figure 5-32 shows a measurement setup for coaxial cable using an auto balancing bridge type impedance analyzer and the 16047E test fixture. Note that the High terminal of the test fixture is connected to the outer conductor of the cable.
Figure 5-33. Measurement result Balanced cable measurement A balun transformer is required for measuring balanced cable because the instrument’s UNKNOWN terminal is unbalanced. Refer to the next paragraph titled “Balanced device measurement” for details of measurement method. Figure 5-34 shows measurement setup for balanced cable. Agilent 16314A balanced/unbalanced 4-terminal converter can be used to measure balanced cables from 100 Hz to 10 MHz using an auto balancing bridge instrument.
5-10. Balanced device measurement When a balanced DUT (such as balanced cable or the balanced input impedance of a differential amplifier) is measured, it is necessary to connect a “balun” (balance-unbalance) transformer between the instrument and the DUT. Looking from the DUT side, the UNKNOWN terminals of the impedance measurement instrument are in an “unbalanced” configuration. Figure 5-35 (a) shows an example of an auto balancing bridge instrument.
Figure 5-36.
5-11. Battery measurement The internal resistance of a battery is generally measured using a 1 KHz AC signal. When a battery is connected directly to the auto balancing bridge type impedance measurement instrument, the instrument becomes the DC load, typically 100 Ω for the battery. Figure 5-37 shows the recommended setup for this measurement. C1 and C2 block DC current flowing into the instrument. The value of C1 should be calculated using the minimum measurement frequency.
5-12. Test signal voltage enhancement When measuring the impedance of test signal level dependent devices, such as liquid crystals, inductors and high value ceramic capacitors, it is necessary to vary the test signal voltage. Many of the auto balancing bridge instruments employ a test signal source whose output is variable typically from 5 mV to 1V rms.
Figure 5-39.
5-13. DC bias voltage enhancement DC biased impedance measurement is popularly used to evaluate the characteristics of the device under the conditions where the device actually operates in circuits. The internal DC bias function of the impedance measurement instruments is normally designed to apply a bias voltage to capacitor DUTs. It is suited to DC biased capacitor measurements. Maximum applicable bias voltage is different for instruments.
Figure 5-40. External DC bias measurement setup External DC voltage bias protection in 4TP configuration If the measurement frequency is above 2 MHz or the type of DUT is not suitable for these external bias fixtures, it is recommended to use the protective circuit shown in Figure 5-41. This circuit is usable with bias voltage up to ± 200 V. To reduce the effects of this additional circuit, perform the open/short compensation with no bias voltage applied. Figure 5-41.
5-14. DC bias current enhancement DC current biasing is used for inductor and transformer measurement. In low frequency region, the E4980A or 4284A precision LCR meter with the 42841A bias current source are both suitable for this application because they can apply up to 20 A of bias current. (This can be extended up to 40 A if two 42841As are connected in parallel.
Take caution of electrical shock hazards when using the external DC bias circuit. A large energy is charged in L1 and L2 as well as the DUT (Lx) by a bias current delivered from an external power supply and, when the DUT is disconnected from the measurement circuit, the DUT generates a very high spike voltage (kick-back voltage) to discharge the energy. To ensure operator safety, decrease the bias current to zero before disconnecting the DUT.
5-15. Equivalent circuit analysis and its application Agilent’s impedance analyzers are equipped with an equivalent circuit analysis function. The purpose of this function is to model the various kinds of components as three- of four-element circuits. The values of the component’s main elements and the dominant residuals can be individually determined with this function.
Figure 5-44. Equivalent circuit models If the simulated frequency response curve partially fits the measurement results, it can be said that the selected circuit mode is proper only for that part of the frequency range that it fits. Figure 5-45 (a) shows an example measurement for a low value inductor. As shown in Figures 5-45 (b) and (c), the measurement result does not agree with both the simulated curves over the full frequency range.
(a) (b) Circuit mode A (c) Circuit mode B Figure 5-45.
Measurement accuracy can be improved by taking advantage of the equivalent circuit analysis. Figure 5-47 (a) shows an Ls-Q measurement example for an inductor. In this example, an impedance analyzer measures the Q value at 10 MHz. Measured data read by MARKER is Ls=4.78 µH and Q=49.6. The Q measurement accuracy for this impedance at 10 MHz is calculated from the instrument’s specified D measurement accuracy of ± 0.011, and the true Q value will be between 32 and 109.
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APPENDIX A The concept of a test fixture’s additional error 1. System configuration for impedance measurement Very often, the system configured for impedance measurements utilizes the following components (See figure below as well). 1. 2. 3. Impedance measurement instrument Cables and adapter interfaces Test fixture System configuration for impedance measurement The Impedance measurement instrument’s characteristic measurement accuracy is defined at the measurement port of the instrument.
The equation for the test fixture’s additional error is shown below: Ze = ± { A + (Zs/Zx + Yo•Zx) × 100} (%) De = Ze/100 (D ≤ 0.
Open offset error: The term, Yo•Zx × 100 is called open offset error. If the same analysis is carried out with admittance, then it can be concluded that this term also affects the absolute admittance error, by adding an offset. Open repeatability (Yo) is determined from the variations in multiple measurements of the test fixture in open condition. As shown in the figure below, the maximum value of the admittance vector in the complex admittance plane is defined as open repeatability.
Terminal connection method: In order to make short repeatability small, there are test fixtures which utilize the 4-terminal connection method (for example 16044A). By employing this technique, the effect of contact resistance is reduced and short repeatability is drastically improved. As a result, the range of accurate low impedance measurements is vastly expanded. In the figure below, the difference between the 2-terminal connection and the 4-terminal connection is shown.
obtained. For open repeatability, measure the admittance of the test fixture’s open condition. In the same way, determine open repeatability by measuring at least 50 times.
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APPENDIX B Open and short compensation The open/short compensation used in Agilent’s instrument models the residuals as a linear network represented by the ABCD parameters, much like the open/short/load compensation techniques described previously in this document. The difference is that the open/short compensation assumes the unknown network as a “symmetrical network”. From this restriction, the open/short compensation does not require the load measurement to know each value of ABCD parameters.
Figure B-1.
APPENDIX C Open, short and load compensation The open/short/load compensation requires the measurement data of a standard DUT with known values in addition to the open/short measurement data. The residuals of a test fixture, cables or an additional circuit can be defined as a four-terminal network (a two-terminal pair network) expressed with A, B, C, D parameters as shown in Figure C-1. Figure C-1.
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APPENDIX D Electrical length compensation A test port extension can be modeled using a coaxial transmission line as shown in Figure D-1.
When a (virtual) transmission line in which the signal wavelength is equal to the wavelength in vacuum is assumed, the virtual line length ( e) that causes the same phase shift (β ) as in the actual line is given by the following equation: λo e = —— λ ( because β 2π 2π e = ——— = ————— ) λ λo Where, λo: wavelength in vacuum λ: actual wavelength in transmission line Therefore, the phase shift quantity, β , can also be expressed by using the phase constant βo in vacuum and the virtual line length e (because
APPENDIX E Q Measurement accuracy calculation Q measurement accuracy for auto balancing bridge type instruments is not specified directly as ±%. Q accuracy should be calculated using the following equation giving the possible Q value tolerance. Qt = 1 1 ± ∅D Qm Where: Qt is the possible Q value tolerance Qm is measured Q value ∆D is D measurement accuracy For example, when the unknown device is measured by an instrument which has D measurement accuracy of .
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