Patent Publication Number: US-2023139107-A1

Title: Component impedance measurement and characterization at high transient voltages

Description:
BACKGROUND OF THE INVENTION 
     Field of the Invention 
     Embodiments of the invention relate to electronics, and more particularly to electrical component characterization. 
     Description of the Related Art 
     High voltage transients are short duration surges of electrical energy which result from a sudden release of energy, such as by heavy inductive loads, lightning, or arising from charge released from an object or person to an electronic system. High voltage transients can also be referred to as electrical overstress (EOS) events. High voltage transient activity can lead to immediate failure in integrated circuits, or cause damage which is not readily apparent and results in erratic operation. In order to protect electronic devices from high voltage transient phenomena, transient protection circuits (for example, EOS protection circuits) are often included to suppress or redirect transient energy away from sensitive integrated circuits or other core circuitry. 
     When using an electrical component in a circuit exposed to electrical overstress (EOS), it is important to understand the behavior of the electrical component when exposed to high voltage transients. 
     SUMMARY OF THE INVENTION 
     Disclosed are apparatus and methods for characterizing electrical components for evaluating performance in a high voltage transient protection circuit. Impedance graphs provided by manufacturers for electrical components are typically low voltage measurements that do not necessarily accurately reflect component performance at high voltages above 150 volts. It is important to characterize and understand the behavior of these components at high voltages in order to ensure the components will protect circuitry as expected. In certain embodiments, a characterization method includes obtaining time domain voltage measurements from two terminals of a device under test (DUT) as it is exposed to high voltage transients from an electrical fast transient (EFT) generator. The time domain voltage data is transformed into frequency domain voltage data using a transform algorithm, and additional analysis is performed to derive scattering parameters, impedance, and other valuable metrics for component characterization. 
     In one aspect, a method of electrical characterization includes connecting a first terminal of an electrical component to a transient generator, connecting a second terminal of the electrical component to a load, obtaining a first plurality of voltage versus time measurements at the first terminal of the electrical component in response to an electrical transient from the transient generator, obtaining a second plurality of voltage versus time measurements at the second terminal of the electrical component in response to the electrical transient, processing the first plurality of voltage versus time measurements and the second plurality of voltage versus time measurements to generate frequency domain data, and determining at least one scattering parameter from the frequency domain data. 
     In another aspect, an electronic component characterization system includes a transient generator configured to provide an electrical transient to a first terminal of an electrical component undergoing characterization, a load configured to connect to a second terminal of the electrical component, one or more voltage probes configured to obtain a first plurality of voltage versus time measurements at the first terminal of the electrical component in response to the electrical transient, and to obtain a second plurality of voltage versus time measurements at the second terminal of the electrical component in response to the electrical transient, and a computer configured to process the first plurality of voltage versus time measurements and the second plurality of voltage versus time measurements to generate frequency domain data, and to determine at least one scattering parameter from the frequency domain data. 
     In yet another aspect, an electronic component characterization system includes a transient generator configured to provide an electrical transient to a first terminal of an electrical component undergoing characterization, a load configured to connect to a second terminal of the electrical component, one or more voltage probes configured to obtain a first plurality of voltage versus time measurements at the first terminal of the electrical component in response to the electrical transient, and to obtain a second plurality of voltage versus time measurements at the second terminal of the electrical component in response to the electrical transient, and means for processing the first plurality of voltage versus time measurements and the second plurality of voltage versus time measurements to generate frequency domain data and at least one scattering parameter. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG.  1    is a schematic of one embodiment of a test circuit setup for high voltage transient characterization of a component being evaluated. 
         FIG.  2 A  is one example of a time domain plot of transient voltage response measured from a first terminal of an electronic component. 
         FIG.  2 B  is one example of a time domain plot of transient voltage response measured from a second terminal of the electronic component. 
         FIG.  3 A  is one example of a frequency domain plot of the fast Fourier transform of the transient voltage responses of  FIG.  2 A  and  FIG.  2 B . 
         FIG.  3 B  is one example of a frequency domain plot of a scattering parameter S 21  for the transient voltage response of  FIG.  3 A . 
         FIG.  3 C  is a frequency domain plot of  FIG.  3 B  plotted on a logarithmic scale. 
         FIG.  4    is one example of a frequency domain plot of impedance curves for several transient responses of a wire-wound resistor. 
         FIG.  5    is a frequency domain plot of impedance curves for several transient responses of different amplitudes. 
         FIG.  6    is a block diagram illustrating one embodiment of a method of data acquisition and analysis for high voltage component characterization. 
         FIG.  7 A  is a schematic diagram of one embodiment of an electronic component characterization system in a first step of operation. 
         FIG.  7 B  is a schematic diagram of the electronic component characterization system of  FIG.  7 A  in a second step of operation. 
         FIG.  7 C  is a schematic diagram of the electronic component characterization system of  FIG.  7 A  in a third step of operation. 
         FIG.  7 D  is a schematic diagram of the electronic component characterization system of  FIG.  7 A  in a fourth step of operation. 
         FIG.  7 E  is a schematic diagram of the electronic component characterization system of  FIG.  7 A  in a fifth step of operation. 
         FIG.  8 A  is a schematic diagram of one example of a device suitable for electrical characterization. 
         FIG.  8 B  is a schematic diagram of another example of a device suitable for electrical characterization. 
         FIG.  8 C  is a schematic diagram of another example of a device suitable for electrical characterization. 
     
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT 
     The following detailed description of certain embodiments presents various descriptions of specific embodiments. However, the innovations described herein can be embodied in a multitude of different ways, for example, as defined and covered by the claims. In this description, reference is made to the drawings where like reference numerals can indicate identical or functionally similar elements. It will be understood that elements illustrated in the figures are not necessarily drawn to scale. Moreover, it will be understood that certain embodiments can include more elements than illustrated in a drawing and/or a subset of the elements illustrated in a drawing. Further, some embodiments can incorporate any suitable combination of features from two or more drawings. 
     Electrical components typically include datasheets providing performance information about the component. However, the performance information on datasheets is typically based on low voltage measurements. 
     When using an electrical component in a circuit exposed to electrical overstress (EOS), it is important to understand the behavior of the electrical component when exposed to high voltages, since the component&#39;s behavior can be significantly different under these conditions. 
     For example, during a design phase a circuit designer can face the issue of selecting a suitable transient voltage suppression (TVS) diode, common-mode choke, ferrite, or other suitable device(s) for providing protection against high voltage transient phenomenon. Although a manufacturer&#39;s impedance versus frequency graph can be used to select a component, such impedance graphs are either vector network analyzer (VNA) measurements or low voltage measurements that are not entirely accurate descriptions of the component&#39;s behavior at high voltages, such as 150 V or more. 
     It is desirable to characterize and understand the behavior of these components at high voltages in order to ensure that they provide circuit protection as expected at these high voltages. With the right information, correct and more robust electrical components can be chosen for better electromagnetic compatibility (EMC) performance. 
     In certain embodiments herein, a method of electrical characterization is provided in which a first terminal of an electrical component is connected to a transient generator (for instance, an electrical fast transient or EFT generator) and a second terminal of the electrical component is connected to a load. The method includes obtaining a first set of voltage versus time measurements at the first terminal of the electrical component in response to an electrical transient from the transient generator, obtaining a second set of voltage versus time measurements at the second terminal of the electrical component in response to the electrical transient, processing the first and second sets of voltage versus time measurements to generate frequency domain data (for example, using a fast Fourier transform or FFT), and determining at least one scattering parameter from the frequency domain data. 
     Such electrical characterization can be used to determine an S 21  parameter, an S 12  parameter, an S 11  parameter, and/or an S 22  parameter. Moreover, the scattering parameters can be used to generate data representing an impedance curve (for example, as an .s2p file or other suitable format) that characterizes the electrical component. 
     Accordingly, the measurement and analysis techniques provided herein can be used to obtain impedance versus frequency data (for instance, impedance graphs) at the transient voltages of interest, for example, at 500V, 1 kV, 2 kV and 4 kV. 
     Thus, the high voltage performance of various components can be analyzed and the one with the best performance over the applicable high voltage range can be chosen. Such characterization saves time and resources in going through unnecessary iterations on a test/evaluation board trying to figure out the best way to protect the circuitry against high voltage transients. 
     The electrical characterization techniques herein can advantageously use only voltage measurements to compute the characteristics of the component being tested. By providing electrical characterization in this manner, the use of any current probes can be avoided. For example, an added advantage of using only voltage measurements is that there are little to no restrictions based on the size or the gauge of wire connected to the component. In contrast, a current probe is constrained by a size of wire that can fit through the current probe. 
     To avoid the effects of probe loading, in certain implementations the same probe is used to obtain voltage versus time measurements at the first terminal and at the second terminal. For example, the probe can be positioned at the first terminal of the electrical component to obtain the first set of the voltage versus time measurements in response to the electrical transient from the transient generator. Additionally, the probe can be repositioned at the second terminal and the second set of voltage versus time measurements can be obtained in response to the transient generator regenerating the electrical transient. Such measurements can be repeated for multiple voltage levels of the electrical transient to gather further data. 
     Not only can such characterization techniques be used to characterize two terminal components, but components with additional terminals as well. In one example, an electrical component includes a pair of input terminals and a pair of output terminals. Additionally, the pair of input terminals are connected to one another to provide a first terminal for electrical characterization, and the pair of output terminals are connected to one another to provide a second terminal for electrical characterization. 
       FIG.  1    is a schematic of one embodiment of a test circuit setup  100  for high voltage transient characterization of a component being evaluated. 
     Referring initially to  FIG.  1   , an example circuit for impedance measurement and high voltage characterization of electronic components is shown generally by  100 . The setup  100  serves to measure a device under test (DUT)  160 , and includes a transient generator  110  (corresponding to an electrical fast transient (EFT) generator, in this example), a load  170  ( 50  Ω, in this example), and at least one voltage probe. 
     As shown in  FIG.  1   , the EFT generator  110  is represented or modeled as a voltage source  120  in series with an internal resistance  130  (about 50Ω, in this example), and thus is a Thevenin model of the EFT generator  110 . A first terminal of the EFT generator  110  drives the DUT  160 , while a second terminal of the EFT generator  110  is grounded (connected to a ground voltage or ground  101 ). 
     The EFT generator  110  is configured to supply the circuit  100  with short duration voltage transients having a selectable amplitude within a desired voltage range, for instance, at least about 200 volts to about 4 kilovolts. The EFT generator  110  can be programmed to generate the electrical transient with desired characteristics, such as amplitude and rise time. Moreover, the EFT generator  110  can be programmed to regenerate a particular electrical transient when needed, which can be used in configurations in which the same voltage probe is used to capture the voltage versus time measurements for each terminal of the DUT  160 . 
     With continuing reference to  FIG.  1   , an output of the EFT generator  110  is operably connected to a first terminal  161  of a device under test (DUT)  160 , which is the electrical component being characterized by the circuit  100 . Hereafter, “device under test”, “component under test”, “electrical device”, and “electrical component” are used interchangeably to refer to the DUT  160 . 
     In addition to the first terminal  161 , the DUT  160  has at least a second terminal  162 , although components with an arbitrary number of terminals may be characterized by substantially the same process as described herein. In a multi-terminal device, the first terminal  161  and second terminal  162  are not necessarily the numerical terminals  1  and  2  of the device. The second terminal  162  is connected to ground  101  by way of a known load  170 , which may be resistive and have a resistance selected to match the internal resistance  130  of the EFT generator  110  for impedance matching. 
     The circuit  100  further includes a first voltage measurement device or probe  140  electrically connected to the first terminal  161  and a second voltage measurement device or probe  150  electrically connected to the second terminal  162 . Such process can correspond to, for example, probes of an oscilloscope. However, any suitable probe or probes can be used. 
     Although shown as including two probes, a common or same probe can be used to capture voltage versus time measurements from the DUT  160 . For example, the EFT generator  110  can apply a pulse, and measurements of the DUT  160  at the first terminal  161  can be obtained by a probe. Thereafter, the EFT generator  110  can replicate the pulse, and measurements of the DUT  160  at the second terminal  162  can be obtained using the same probe. In certain implementations, measurements at the first terminal  161  and the second terminal  162  are obtained in response to multiple transient pulses associated with different characteristics (for example, different peak amplitudes). 
     As schematically depicted by the ground symbols adjacent to the first terminal  161  and the second terminal  162  of the DUT  160 , the voltage measurements are single-ended measurements referenced to ground, in this embodiment. 
     The voltage probe or probes can capture the voltage versus time measurements in any suitable manner. For example, such time domain voltage data can be captured at a preconfigured sampling rate and for a preconfigured record length. In certain embodiments, the sampling rate and record length may be configured automatically during signal capture. Signal capture may also occur synchronously or asynchronously depending on the configuration of the circuit  100  and the measurement probe(s). 
     An oscilloscope or other measurement device capable of interfacing with a computer may be selected for this purpose and to additionally store the time domain voltage measurements in a computer memory for analysis. In other embodiments, the time domain voltage measurements may be stored and analyzed onboard a capable measurement device that includes the computer. As described in detail herein, the data containing the time domain voltage measurements undergoes additional processing steps to analyze the data in the frequency domain. 
       FIG.  2 A  is one example of a time domain plot of transient voltage response measured from a first terminal of an electronic component.  FIG.  2 B  is one example of a time domain plot of transient voltage response measured from a second terminal of the electronic component. 
     Referring now to  FIG.  2 A  and  FIG.  2 B , an example plot of a voltage transient captured by the first voltage measurement device  140  over a span of 6 microseconds is indicated generally by  200 . A curve  210  of the voltage transient shows a brief peak  220  of approximately 500 volts representing a local maximum of the transient observed during a capture period. A corresponding plot of the transient of  FIG.  2 A  after it has passed through the device under test  160  is indicated generally at  230 , observed by the second voltage measurement device  150  during the same capture period. A second curve  240  representing the transient after substantial attenuation by the DUT  160  has a peak  250  of approximately 170 volts. Time domain data can be captured by the first and second voltage measurement devices  140 / 150  (or by a single measurement device) at a specified sampling rate and record length, given by Equation 1 below, where the duration of the capture period may also be referred to as acquired time. 
     
       
         
           
             
               
                 
                   
                     Sampling 
                     ⁢ 
                         
                     Rate 
                   
                   = 
                   
                     
                       Record 
                       ⁢ 
                           
                       Length 
                     
                     
                       Duration 
                       ⁢ 
                           
                       of 
                       ⁢ 
                           
                       Capture 
                       ⁢ 
                           
                       Period 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   1 
                 
               
             
           
         
       
     
     Although the plots of  FIGS.  2 A and  2 B  illustrate example time domain voltage measurements, the voltage peak of the transient, duration of the capture period, sampling rate, or any other parameter known to one skilled in the art may be adjusted for better characterization of the DUT  160 . In some embodiments, multiple iterations of voltage capture can be used in combination with signal processing techniques for broader characterization and impedance measurement. 
       FIG.  3 A  is one example of a frequency domain plot of the fast Fourier transform of the transient voltage responses of  FIG.  2 A  and  FIG.  2 B . 
       FIG.  3 A  is a plot of the transient function of  FIGS.  2 A and  2 B  transformed into the frequency domain for further analysis. In the preferred embodiment, a computer or digital storage oscilloscope (DSO) applies a fast Fourier transform (FFT) algorithm to transform the time domain voltage data captured by voltage measurement devices  140 / 150  into the frequency domain. 
     In various embodiments, other transforms including a Laplace transform, z-transform, or another Fourier transform algorithm may be used to acquire frequency domain voltage data. The resulting frequency domain transient curves  310  and  320  are stored in a computer memory and can be used to generate a frequency response curve  300  for further analysis. In one embodiment, the frequency domain transient data is converted by a LabVIEW program into a Microsoft Excel spreadsheet format. 
       FIG.  3 B  is one example of a frequency domain plot of a scattering parameter S 21  for the transient voltage response of  FIG.  3 A .  FIG.  3 C  is a frequency domain plot of  FIG.  3 B  plotted on a logarithmic scale. 
     As persons having ordinary skill in the art will appreciate, scattering parameters (S-parameters) describe electrical behavior of a network or device under test when subjected to steady state stimuli. 
     With reference to  FIGS.  3 B and  3 C , S 21  is one of several scattering parameters useful in characterizing the performance of the DUT  160 . S 21  is related to insertion loss because it represents the degree of attenuation of the voltage transient after passing through the DUT  160 . A unit-less plot of S 21  is shown generally by  330 , with a curve  340  illustrating the insertion loss of the DUT  160  over a frequency range of 100 kHz to 10 MHz. S 21  can be calculated from the frequency domain voltage data of  FIG.  3 A  by Equation 2 below, where V 1  and V 2  are the instantaneous voltages at a given frequency measured by voltage measurement devices  140  and  150 , respectively. 
     
       
         
           
             
               
                 
                   
                     S 
                     ⁢ 
                     21 
                   
                   = 
                   
                     
                       V 
                       ⁢ 
                       2 
                     
                     
                       V 
                       ⁢ 
                       1 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   2 
                 
               
             
           
         
       
     
     Scattering parameter S 21  may also be represented on a logarithmic scale using decibels, as in  FIG.  3 C , according to Equation 3 below. When on a logarithmic scale, S 21  is referred to as insertion loss (IL). 
         IL (dB)=−20 log 10   |S 21|  Equation 3
 
       FIG.  4    is one example of a frequency domain plot of impedance curves for several transient responses of a wire-wound resistor. 
     Referring now to  FIG.  4   , an example plot of impedance Z DUT  over a frequency range of 100 kHz to 100 MHz for a DUT  160  is indicated generally by  400 . The impedance can be calculated from the data of  FIGS.  3 B and  3 C , where Z 0  is an impedance of the known load  170  and S 21  is a value of the scattering parameter at a given frequency. Equation 4 and Equation 5 below provide example mathematic expressions for calculating impedance. 
     
       
         
           
             
               
                 
                   
                     Z 
                     1 
                   
                   = 
                   
                     
                       2 
                       * 
                       
                         
                           Z 
                           0 
                         
                         ( 
                         
                           1 
                           - 
                           
                             S 
                             ⁢ 
                             21 
                           
                         
                         ) 
                       
                     
                     
                       S 
                       ⁢ 
                       21 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   4 
                 
               
             
           
         
       
       
         
           
             
               
                 
                   
                     Z 
                     DUT 
                   
                   = 
                   
                     
                       Z 
                       1 
                     
                     2 
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   5 
                 
               
             
           
         
       
     
     In the pictured example, the DUT  160  is an approximately 100 ohm wire-wound resistor. The plot  400  includes a plurality of impedance curves  410  representing impedance of the DUT  160  when exposed to various transient voltages of interest. The EFT generator  110  can supply voltage transients to the DUT  160  having a peak voltage  220  ranging from approximately 200V to 4 kV, although the same method of characterizing the DUT  160  can be used with any high voltage transient. 
     In some cases the DUT  160  may exhibit nonlinearity, particularly at higher frequencies, which is valuable in understanding how the same component would perform when implemented into an EFT protection circuit. An impedance-frequency curve calculated by a vector network analyzer (VNA) shows how component characterization by the method of the present invention can yield a substantially different result compared to conventional methods. 
       FIG.  5    is a frequency domain plot of impedance curves for several transient responses of different amplitudes. 
     Likewise, in  FIG.  5    an example plot of impedance Z 0  over a frequency range of 100 kHz to 1 GHz for a DUT  160  is indicated generally by  500 . In the pictured example, the DUT  160  is a common-mode choke (CMC) by Wurth Elektronik having part number 744844470. Compared to the device of  FIG.  4   , the device of  FIG.  5    is nonlinear over the entire frequency range and performs substantially differently when exposed to various EFT voltages. 
     A VNA impedance-frequency curve  510  is provided as a rough approximation of the behavior of the DUT  160 . Additional impedance curves calculated from the measured response to 200 V, 2 kV, and 4 kV EFTs are indicated by  520 ,  530 , and  540  respectively. These various impedance curves reflect how the behavior of the DUT  160  deviates significantly from the VNA measurement above 200 V, particularly at frequencies in the 1 MHz to 10 MHz range. 
       FIG.  6    is a block diagram illustrating one embodiment of a method of data acquisition and analysis for high voltage component characterization. 
     Referring now generally to  FIGS.  1  to  6   , the method of characterizing components is shown generally by  600 . An EFT pulse  610  having a predetermined peak voltage  220  is delivered to the DUT  160  by the EFT generator  110 . The voltage measurement devices  140  and  150  (or a shared measurement device) acquire time domain voltage measurements  620  at a specified sampling rate and record length as configured by a technician. The time domain voltage measurement data is stored in a computer memory  630 . A computer coupled to the computer memory, uses a transform algorithm  640  (for example a fast Fourier transform) to transform the time domain voltage data into frequency domain voltage data. The computer may also use a Laplace transform, z-transform, discrete time Fourier transform, or any other transform algorithm known to one skilled in the art. 
     With continuing reference to  FIG.  6   , The frequency domain voltage data undergoes additional analysis  650  (for instance, using the computer), including calculating scattering parameters (including S 21 ), insertion loss, and impedance from the frequency domain data. Any or all of the results of the analysis can be graphically plotted as in  FIGS.  2 A through  5   . The steps of applying the transform algorithm  640  and analysis  650  may be performed by a LabVIEW program configured to transform and analyze the voltage data and store the results of the analysis in a Microsoft Excel format. The steps  610  through  650  can be repeated with varied EFT pulses for a more robust characterization of the device under test. 
       FIG.  7 A  is a schematic diagram of one embodiment of an electronic component characterization system in a first step of operation. The electronic component characterization system is characterizing an electronic component  710 , and includes a transient generator  701 , a load  702 , a voltage probe  703 , and a computer  704  that includes and/or is coupled to a memory  705 . The computer  704  can correspond to a processor, microcontroller, and/or any other suitable digital processing apparatus. 
     As shown in  FIG.  7 A , the transient generator  701  generates an electrical transient  706  that is provided to a first terminal T 1  of the electronic component  710 . Additionally, a second terminal T 2  of the electronic component  710  is connected to ground through the load  702 . The transient generator  701  is also grounded. The transient generator  701  is controlled by the computer  704 , in this example. 
     In the first step, the voltage probe  703  obtains a first set of voltage versus time measurements  711  of the first terminal T 1 . The first set of voltage versus time measurements  711  are stored in the memory  705 . 
       FIG.  7 B  is a schematic diagram of the electronic component characterization system of  FIG.  7 A  in a second step of operation. 
     In the second step, the voltage probe  703  has been repositioned to probe the second terminal T 2  of the electronic component  710  and the electrical transient  706  is regenerated and reapplied to the first terminal T 1  of the electronic component  710 . Additionally, the voltage probe  703  obtains a second set of voltage versus time measurements  712  of the second terminal T 2 , which are stored in memory  705 . 
     In certain implementations, the computer  704  directs (for example, by way of an application executed on the computer&#39;s processor) movement of the voltage probe  703  from the first terminal T 1  to the second terminal T 2  using a handler or other suitable repositioning mechanism. However, other implementations, are possible, such as configurations in which the voltage probe  703  is moved manually between steps. 
     Although  FIGS.  7 A and  7 B  depict a configuration using a single probe, the teachings herein are also applicable to configurations using multiple voltage probes. However, using a single voltage probe eliminates measurements inaccuracies arising from the probes loading one another. 
     Furthermore, although  FIGS.  7 A and  7 B  depict the measurements of the first terminal T 1  being obtained before the measurements of the second terminal T 2 , the order in which the measurements are obtained can be reversed (or performed concurrently in an implementation with two voltage probes). 
       FIG.  7 C  is a schematic diagram of the electronic component characterization system of  FIG.  7 A  in a third step of operation. 
     In the third step, the computer  704  processes the first set of voltage versus time measurements  711  and the second set of voltage versus time measurements  712  to generate frequency domain data  713 . For example, such frequency domain data  713  can include a first set of FFT coefficients obtained from performing an FFT of the first set of voltage versus time measurements  711 , and a second set of FFT coefficients obtained from performing an FFT of the second set of voltage versus time measurements  712 . 
     In certain embodiments, the first step, the second step, and the third step are repeated for multiple amplitude values of the electrical transient  706  such that the voltage versus time data and frequency domain data is captured for multiple transient amplitudes. Capturing such data for two or more transient amplitudes enhances the accuracy of the electrical characterization and resulting selection process of a suitable component. 
       FIG.  7 D  is a schematic diagram of the electronic component characterization system of  FIG.  7 A  in a fourth step of operation. 
     In the fourth step, the computer  704  processes the frequency domain data  713  to determine one or more scattering parameters  714 . For example, such scattering parameters or S-parameters can include S 11 , S 12 , S 21 , and S 22 . The scattering parameters are stored in the memory  705 . 
       FIG.  7 E  is a schematic diagram of the electronic component characterization system of  FIG.  7 A  in a fifth step of operation. 
     In the fourth step, the computer  704  processes the scattering parameters to determine impedance curve data  715 , which is stored in the memory  705 . In certain implementations, the impedance curve data  715  is processed and provided to a display  716  to thereby display impedance trajectories or graphs representing the behavior of the electrical component  710 . In certain implementations, the display  716  is used to display other data stored in the memory  705 , such as the first set of voltage versus time measurements  711 , the second set of voltage versus time measurements  712 , the frequency domain data  713 , and/or the scattering parameters  714 . 
       FIGS.  8 A to  8 C  represent example devices that can be characterized in accordance with the teachings herein. Although various examples of devices are shown, any suitable device can be characterized using the apparatus and methods for electrical characterization disclosed herein. 
       FIG.  8 A  is a schematic diagram of one example of a device suitable for electrical characterization. In this example, the device corresponds to a transient voltage suppression (TVS) diode having a cathode serving as a first terminal T 1  and an anode serving as a second terminal T 2 . 
       FIG.  8 B  is a schematic diagram of another example of a device suitable for electrical characterization. In this example, the device corresponds to an inductor or choke  802  having one end serving as a first terminal T 1  and another end serving as a second terminal T 2 . 
       FIG.  8 C  is a schematic diagram of another example of a device suitable for electrical characterization. In this example, the device corresponds to a common-mode choke  803  having four terminals. As shown in  FIG.  8 C , one pair of terminals are connected to one another to serve as the first terminal T 1  for characterization, while another pair of terminals are connected to one another to serve as the second terminal T 2  for characterization. 
     CONCLUSION 
     The foregoing description may refer to elements or features as being “connected” or “coupled” together. As used herein, unless expressly stated otherwise, “connected” means that one element/feature is directly or indirectly connected to another element/feature, and not necessarily mechanically. Likewise, unless expressly stated otherwise, “coupled” means that one element/feature is directly or indirectly coupled to another element/feature, and not necessarily mechanically. Thus, although the various schematics shown in the figures depict example arrangements of elements and components, additional intervening elements, devices, features, or components may be present in an actual embodiment (assuming that the functionality of the depicted circuits is not adversely affected). 
     The foregoing description may refer to elements or features as being “connected” or “coupled” together. As used herein, unless expressly stated otherwise, “connected” means that one element/feature is directly or indirectly connected to another element/feature, and not necessarily mechanically. Likewise, unless expressly stated otherwise, “coupled” means that one element/feature is directly or indirectly coupled to another element/feature, and not necessarily mechanically. Thus, although the various schematics shown in the figures depict example arrangements of elements and components, additional intervening elements, devices, features, or components may be present in an actual embodiment (assuming that the functionality of the depicted circuits is not adversely affected). 
     While certain embodiments have been described, these embodiments have been presented by way of example only, and are not intended to limit the scope of the disclosure. Indeed, the novel apparatus, methods, and systems described herein may be embodied in a variety of other forms; furthermore, various omissions, substitutions and changes in the form of the methods and systems described herein may be made without departing from the spirit of the disclosure. For example, while the disclosed embodiments are presented in a given arrangement, alternative embodiments may perform similar functionalities with different components and/or circuit topologies, and some elements may be deleted, moved, added, subdivided, combined, and/or modified. Each of these elements may be implemented in a variety of different ways. Any suitable combination of the elements and acts of the various embodiments described above can be combined to provide further embodiments.