Abstract:
A method includes measuring a magnetic field generated by an electrical wire using a three-axis magnetometer disposed within a portable electronic device. The device then determines a first magnetic field strength component aligned with a first direction and a second magnetic field strength component aligned with a second direction. The position of the electrical wire relative to the magnetometer is movable in the first direction, and wherein the position of the electrical wire is constrained in the second direction. The device then provides an instruction via a display to move the wire to a position where the first magnetic field strength component is equal to the second magnetic field strength component.

Description:
CROSS REFERENCE TO RELATED APPLICATIONS 
       [0001]    This application claims the benefit of U.S. Provisional Application No. 61/792,671, filed Mar. 15, 2013, which is hereby incorporated by reference in its entirety. 
     
    
     TECHNICAL FIELD 
       [0002]    The present invention relates to a portable digital power analyzer that uses a three-axis magnetometer to determine power consumption. 
       BACKGROUND 
       [0003]    Many systems exist to provide a user with the ability to monitor the power consumption of an entire dwelling or small business. These systems include “smart” electrical meters that are installed by utility companies, or systems that attach to a building&#39;s power distribution panel to provide detailed, minute by minute analytics. While this can be a useful tool to analyze electrical consumption, they are also very costly and require specially trained technicians to install. Additionally, such systems are not capable of identifying specific devices that may be contributing to a household&#39;s power use. Instead, this may require individual measurement of each device within the house. 
         [0004]    Individual device measurement has historically required either an intermediate measuring device that is placed (electrically) between the appliance and the wall outlet, or a current clamp that encircles a single conductor. The drawback to an intermediate device, is that the appliance must be separately plugged into the analyzer for testing. This creates an inconvenience for testing multiple devices, or a significant investment in hardware. Current clamps are impractical for residential use, as most residential electrical wiring includes multiple conductors that are bound together in a single cord. Additionally, meters that may utilize the current clamp readings are often expensive. 
       SUMMARY 
       [0005]    A method includes measuring a magnetic field generated by an electrical wire using a three-axis magnetometer disposed within a portable electronic device. The position of the electrical wire relative to the magnetometer is movable in a first direction, and is constrained in a second direction. The second direction may, for example, be normal to a surface of the device, and the electrical wire may be constrained in the second direction by placing the wire in contact with the surface. In one configuration the portable electronic device may be a cellular telephone. 
         [0006]    The device determines a first magnetic field strength component aligned with the first direction and a second magnetic field strength component aligned with the second direction. The device then provides an instruction via a display to move the wire to a position where the first magnetic field strength component is equal to the second magnetic field strength component. The instruction may include a visual alignment guide that is displayed via the display. 
         [0007]    The method may further include determining a current flowing through the electrical wire, or a power factor from the measured magnetic field. Once determined, the determined electrical parameters (e.g., the electrical current) may be uploaded to a database using a wireless radio provided in the portable electronic device. 
         [0008]    The above features and advantages and other features and advantages of the present invention are readily apparent from the following detailed description of the best modes for carrying out the invention when taken in connection with the accompanying drawings. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0009]      FIG. 1  is a schematic diagram of a portable digital computing device adjacent an electrical wire that connects a power source with a load. 
           [0010]      FIG. 2  is a schematic diagram of a smart phone-style portable digital computing device adjacent to a electrical wire. 
           [0011]      FIG. 3  is a schematic partial cross-sectional view of the portable digital computing device and wire of  FIG. 1 , taken along line  3 - 3   
           [0012]      FIG. 4  is a schematic diagram of a smart phone providing an indication to aid in aligning an electrical wire with a magnetometer of the phone to enable accurate detection of one or more electrical parameters. 
           [0013]      FIG. 5  is a schematic diagram of a method of prompting a user to position a wire relative to a smart phone to enable accurate estimation of one or more power parameters. 
           [0014]      FIG. 6  is a schematic plot illustrating a circular sampling technique to accumulate a highly sampled electrical cycle from a plurality of actual electrical cycles. 
           [0015]      FIG. 7  is a schematic diagram of a method of determining and displaying an electrical parameter from the output of a magnetometer in a portable digital computing device. 
           [0016]      FIG. 8  is a schematic plot of a validation strategy for determining whether there has been a change in a characteristic of an electrical load, or a movement of a wire relative to the portable digital computing device being used to monitor the wire. 
       
    
    
     DETAILED DESCRIPTION 
       [0017]    Referring to the drawings, wherein like reference numerals are used to identify like or identical components in the various views,  FIG. 1  schematically illustrates a portable computing device  10  that may be used to provide an estimate of various electrical usage characteristics of a load  12 , by monitoring an electrical supply wire  14  that couples the load  12  with a source S. 
         [0018]    An understanding of the characteristics of the current/power being consumed by the load  12  (i.e., through the wire  14 ), may allow a user to better understand their power consumption habits and alter behaviors where desired. The load  12  mentioned above may be any electrically operated device that is supplied with electrical power via a wire  14 . Examples of such devices/loads  12  include televisions, refrigerators, microwaves, fans, lights, desktop computers, portable equipment charging devices, window air conditioners, stereo systems, commercial equipment, and/or industrial equipment. The methods described herein are explained with reference to single-phase alternating current (AC) electricity, however, the methods may be similarly applicable to three-phase AC systems, and direct current (DC) systems. 
         [0019]    In one configuration, the portable computing device  10  may be a “smart phone”-style cellular telephone  16  (“smart phone  16 ”). As used herein, a smart phone  16  is a cellular telephone that permits a user to download and execute ancillary software and/or internet-based functionality in addition to placing and receiving telephone calls. As will be described below, the smart phone  16  may be specially configured to monitor an AC electrical wave in a wire  14  adjacent to the phone  16 , using only circuitry within the phone  16 . While the present description is made with respect to a smart phone  16 , in other configurations, the portable computing device  10  may resemble a tablet computer, a slate computer, a laptop computer, a personal digital assistant (PDA), a digital “smart watch”-style wrist watch, or other similar styles of general purpose portable computers. 
         [0020]    Referring to  FIG. 2 , the smart phone  16  may include a processor  20  that is configured to execute specialized power detection software  22  to determine one or more power parameters of the adjacent electrical wire  14  and the load  12  coupled thereto. The power parameters may be determined using specialized algorithms defined by the software  22 , together with magnetic field observations provided by a magnetometer  26  within the smart phone  16 . Examples of power parameters that may be calculated include, but are not limited to, current flow, real power flow, apparent power flow, a power factor, electrical line harmonics, harmonic distortion and/or phasor relationships. 
         [0021]    The included magnetometer  26  may be configured to monitor the strength of a magnetic field  28  surrounding the phone  16  in three-axes, and may provide a suitable indication of the strength of the field  28  to the processor  20  via an output  24 . In one configuration, the processor  20  may additionally include one or more mapping applications (not shown) that are configured to use the magnetometer  26  as a compass for determining an orientation of the phone  16  relative to a global magnetic-north. 
         [0022]    In addition to the processor  20  and magnetometer  26 , the smart phone  16  may include non-volatile memory  30  and a display device  32 , both in communication with the processor  20 , as well as a wireless radio  34  that may permit two-way radio communication between the phone  16  and a network  36  (e.g. the internet or a cellular telephone network). 
         [0023]    The processor  20  may be embodied as one or more distinct data processing devices, each having one or more microcontrollers or central processing units (CPU), read only memory (ROM), random access memory (RAM), electrically-erasable programmable read only memory (EEPROM), a high-speed clock, input/output (I/O) circuitry, and/or any other circuitry that may be required to perform the functions described herein. 
         [0024]    The non-volatile memory  30  may include solid-state flash memory, or any other similar form of long-term, non-volatile memory that may be used to store program data and/or software application algorithms. The processor  20  may be digitally interconnected with the non-volatile memory  30 , and may be configured to retrieve the program data and software application algorithms from the memory  30  and execute the algorithms in a manner that is known in the art. 
         [0025]    The display device  32  may include a liquid crystal display (LCD), a light emitting diode display (LED), an organic light emitting diode display (OLED) and/or any similar style display/monitor that may exist or that may be hereafter developed. The display device  32  may receive a visual data stream  38  from the processor  20 , and display it in a visual manner to a user. 
         [0026]      FIG. 3  illustrates a partial schematic cross-sectional view of the smart phone  16  and wire  14  of  FIG. 1 , taken along line  3 - 3 . As shown, the AC electrical wire  14  has at least two electrical conductors  40 ,  42  (e.g., metallic wires) that are separated by one or more layers of electrical insulation  44  (e.g., a polymeric insulator). Due to the nature of AC electricity, at any given time, the electrical current in the first conductor  40  flows in an opposite direction from the electrical current in the second conductor  42  (i.e., I 1 =−I 2 ), with a magnitude having a generally sinusoidal nature. 
         [0027]    Under normal conditions, the magnetic field of a single conductor is represented in Equation 1, 
         [0000]    
       
         
           
             
               
                 
                   B 
                   = 
                   
                     
                       
                         μ 
                         0 
                       
                        
                       I 
                     
                     
                       2 
                        
                       
                           
                       
                        
                       π 
                        
                       
                           
                       
                        
                       r 
                     
                   
                 
               
               
                 
                   Equation 
                    
                   
                       
                   
                    
                   1 
                 
               
             
           
         
       
     
         [0000]    where B is the magnetic field strength in Teslas; r is the radius from the center of the wire to a measuring point (generally ignoring the diameter of the wire); I is the current in amps; and μ 0  is the permeability of free space (i.e., approximately 4π×10 −7  T·m/A). 
         [0028]    As mentioned above, the magnetometer  26  may be a 3-axis magnetometer, which is capable of measuring magnetic field strength in three distinct coordinate directions that are generally orthogonal to each other (i.e., the “sensing axes”). In one configuration, the sensing axes may generally be aligned with the geometric axes of the smart phone  16 , where, the height of the phone  16  may define a Z-axis  50 , the width of the phone  16  may define an X-axis  52 , and the thickness of the phone  16  may define a Y-axis  54 . (the X and Z axes  52 ,  50  are best illustrated in  FIG. 1 , while the Z and Y axes  50 ,  54  are best illustrated in  FIG. 3 ). 
         [0029]    If a current-carrying wire  14  is parallel to both the X-axis  52  and the back surface  56  of the smart phone  16 , as shown in  FIG. 3 , the magnetic field components (B y1 , B z1 ) at a sensing location (y 1 ,z 1 ) relative to the first conductor  40  can be expressed as a function of the current I flowing through the wire  14 , as shown in Equation 2. Similarly, the magnetic field components (B y2 , B z2 ) at a sensing location (y 2 ,z 2 ) relative to the second conductor  42  are represented in Equation 3 
         [0000]    
       
         
           
             
               
                 
                   
                     ( 
                     
                       
                         B 
                         
                           y 
                           1 
                         
                       
                       , 
                       
                         B 
                         
                           z 
                           1 
                         
                       
                     
                     ) 
                   
                   = 
                   
                     ( 
                     
                       
                         
                           
                             z 
                             1 
                           
                            
                           
                             μ 
                             0 
                           
                            
                           I 
                         
                         
                           2 
                            
                           
                               
                           
                            
                           
                             π 
                              
                             
                               ( 
                               
                                 
                                   y 
                                   1 
                                   2 
                                 
                                 + 
                                 
                                   z 
                                   1 
                                   2 
                                 
                               
                               ) 
                             
                           
                         
                       
                       , 
                       
                         
                           
                             y 
                             1 
                           
                            
                           
                             μ 
                             0 
                           
                            
                           I 
                         
                         
                           2 
                            
                           
                               
                           
                            
                           
                             π 
                              
                             
                               ( 
                               
                                 
                                   y 
                                   1 
                                   2 
                                 
                                 + 
                                 
                                   z 
                                   1 
                                   2 
                                 
                               
                               ) 
                             
                           
                         
                       
                     
                     ) 
                   
                 
               
               
                 
                   Equation 
                    
                   
                       
                   
                    
                   2 
                 
               
             
             
               
                 
                   
                     ( 
                     
                       
                         B 
                         
                           y 
                           2 
                         
                       
                       , 
                       
                         B 
                         
                           z 
                           2 
                         
                       
                     
                     ) 
                   
                   = 
                   
                     ( 
                     
                       
                         
                           
                             - 
                             
                               z 
                               2 
                             
                           
                            
                           
                             μ 
                             0 
                           
                            
                           I 
                         
                         
                           2 
                            
                           
                               
                           
                            
                           
                             π 
                              
                             
                               ( 
                               
                                 
                                   y 
                                   2 
                                   2 
                                 
                                 + 
                                 
                                   z 
                                   2 
                                   2 
                                 
                               
                               ) 
                             
                           
                         
                       
                       , 
                       
                         
                           
                             - 
                             
                               y 
                               2 
                             
                           
                            
                           
                             μ 
                             0 
                           
                            
                           I 
                         
                         
                           2 
                            
                           
                               
                           
                            
                           
                             π 
                              
                             
                               ( 
                               
                                 
                                   y 
                                   2 
                                   2 
                                 
                                 + 
                                 
                                   z 
                                   2 
                                   2 
                                 
                               
                               ) 
                             
                           
                         
                       
                     
                     ) 
                   
                 
               
               
                 
                   Equation 
                    
                   
                       
                   
                    
                   3 
                 
               
             
           
         
       
     
         [0030]    Equations 2 and 3 may be combined using vector addition to represent the combined magnetic field in a global space (i.e. (B y , B z )) that is coincident with the sensed field measured by the magnetometer  26 . As evidenced by Equations 2 and 3, the position of the wire  14  with respect to the sensor/magnetometer  26  greatly affects the sensed magnetic field strength (B y , B z ). While the wire position along the Y-axis  54  may be constrained by requiring the user to establish physical contact between the wire and the back surface  56  of the phone  16 , the wire position along the Z-axis  50  may be highly variable. 
         [0031]    To aid the user in accurately and repeatably positioning the wire  14  along the Z-axis  50 , in one embodiment, as shown in  FIG. 4 , the phone  16  may use the integrated display  32  to provide a visual alignment indicator  57 , which may indicate proper wire placement to the user. By having a substantially constant wire position on the Z-axis  50 , the processor  20  may be calibrated to provide a consistent and accurate estimate of electrical current/power in the wire  14 . 
         [0032]    While a visual alignment indicator  57  may be a good open-loop indicator of a required wire position, it has also been found that a Z-axis position  50  where the magnetic field strength is equal in the Y and Z axes  54 ,  50  provides the most reliable computations/electrical estimates. Additionally, when at this position of magnetic equality, estimation errors attributable to variations in the thickness of the wire and/or distances between the wires are minimized. Said another way, an ideal wire location along the Z-axis  50  exists where |B y1 +B y2 |=|B z1 +B z2 | or where |B y |=|B z | (in a global frame). As generally illustrated in  FIG. 3 , these relationships have been found to be satisfied at least where the angle  58  between the wire vectors  60 ,  62  is approximately 30 degrees. This angle  58  generally results in the wire being slightly offset (e.g., by a distance |d|&gt;0) from the magnetometer  26  rather than being symmetrically disposed about it (e.g., d=0). 
         [0033]      FIG. 5  generally illustrates a method  70  of prompting a user to position a wire  14  relative to a smart phone  16  to enable accurate estimation of one or more power parameters of the wire  14  and/or an associated load  12 . The method  70  begins at step  72  when an energy monitoring application running on a smart phone  16  is initialized. Following the initialization, in step  74 , the processor  20  may provide an indication to the user, via the display  32 , to position the wire horizontally behind the phone  16  and firmly against the phone&#39;s back surface  56 . This indication may, for example, include providing an image of a wire or another visual reference indicator  57  on the display  32  as a guide for approximate placement (such as shown in  FIG. 4 ). In step  76 , the processor  20  may poll the magnetometer  26  for a magnetic field strength indication in a direction that is both transverse to the wire and parallel to the phone (i.e., B z  along the Z-axis  50 ), and in a direction that is transverse to both the wire and the phone (i.e., B y  along the Y-axis  54 ). In step  78 , the processor  20  may compare the relative magnitudes of B y and B   z . If B z  is greater than B y , in step  80 , the processor  20  may provide an indication to the user (via the display  32 ) to slide the wire down (i.e., in a negative Z direction), conversely if B z  is less than B y , in step  82 , the processor  20  may provide an indication  68  to the user (via the display  32 ) to slide the wire up (i.e., in a positive Z direction), such as shown in  FIG. 4 . Finally, if the wire  14  is positioned correctly such that the sensed magnitudes of B y  and B z  are equal, in step  84 , the processor  20  may provide an indication to the user (via the display  32 ) to maintain the position, where it will then proceed to determine the one or more power parameters of the wire in step  86 . 
         [0034]    Using Equations 2 and 3, the current I flowing through the wire  14  at any instant may be determined as a function of the sensed magnetic field (B y , B z ) by the magnetometer  26 . Additionally, the voltage V of the wire may be known (as it is generally regulated via the power distribution systems). From the known voltage and sensed current, the processor  20  may determine total real power (measured in Watts (W)). Additionally, by analyzing the current I in the frequency domain, total harmonic distortion (THD) may be computed, as well as a power factor (PF), a total apparent power (S) (measured in volt-amperes (VA)), and a total reactive power (Q) (measured in reactive volt-amperes (var)). 
         [0035]    To estimate the power factor, the processor  20  may need to derive the magnitude of at least the first and third harmonics of the AC electrical signal. For a 60 Hz AC signal (as is the case in the United States), the frequency of the first and third harmonics are respectively a 60 Hz, and 180 Hz. To avoid aliasing effects caused by the sampling frequency, the processor  20  needs to sample the wave at a rate that is greater than twice the fastest frequency (i.e., at the Nyquist rate). Therefore, to derive the magnitude of the third harmonic, the processor  20  would need to sample the magnetic field at a rate faster than 360 Hz. Presently, however, the magnetometers found in most consumer electronics (including smart phones  16 ) are polled devices that sample at a rate only up to approximately 100 Hz. This rate is more than three times slower than the required 360 Hz, and even too slow to determine the magnitude of the first harmonic (which would require a minimum sampling rate of 120 Hz). 
         [0036]    To solve this under-sampling problem, a circular sampling technique may be used to assemble a single detailed wave over a plurality of cycles. This technique may be possible in smart phones and other similar consumer electronics (as opposed to more sophisticated measuring devices) because the magnetometers in such consumer electronics generally lack anti-aliasing filters. More specifically, magnetometers in smart phones and other consumer electronics are generally intended to be used as a compass to measure an extremely stable magnetic field of the Earth. This field may only be perceived to change as a function of a physical yaw, pitch, or roll of the device, which is comparatively slow in view of the sampling frequency and/or speed of the processor. For this reason, these compass-style magnetometers generally do not require bandwidth limiting filters to prevent aliasing (as they are not required and perceived as added/unnecessary expense by the device manufacturers). 
         [0037]      FIG. 6  schematically illustrates a plot  100  of a circular sampling technique  102  as applied to an alternating magnetic field wave  104 , where magnetic field strength  106  is plotted against time  108 . In the presently used circular sampling technique  102 , the processor  20  polls the magnetometer  26  to receive a field strength reading  110  at a rate slightly slower than the frequency of the wave  104 . In this manner, the readings  110  may progressively advance through the wave  104  from cycle-to-cycle, across a plurality of cycles  112 . If the samples  110  are assembled into a single consolidated wave  114 , the consolidated readings  116  may collectively satisfy the Nyquist criteria, where the prior readings did not. For example, in one configuration, with a 60 Hz wave, the processor  20  may receive magnetic field strength readings  110  at a rate of approximately 50-59 Hz. In another configuration, the processor  20  may receive readings at a rate of approximately 53.24 Hz. 
         [0038]    A sampling method  120  is schematically illustrated in  FIG. 7 . Generally this method  120  may be performed after the wire  14  is accurately positioned, such as using the method  70  provided in  FIG. 4 . As shown, the processor  20  may begin sampling the ambient magnetic field strength at  122  by polling the magnetometer  26  at a predefined sampling frequency. In one configuration, the predefined sampling frequency may be slower than the expected frequency of the AC wave that the device is attempting to measure. In step  124 , the processor  20  may attempt to maintain the sampling at the predefined sampling frequency using a phased-locked-loop (PLL) that is referenced to an internal oscillator of the smart phone  16 . 
         [0039]    In most existing smart phones, the internal oscillator has been found to be somewhat unreliable. From phone to phone, the oscillator frequencies may deviate by up to approximately 2 Hz. Likewise, within a single device, there may be random phase noise, along with phase discontinuities of up to 2π radians (a complete cycle) due to random restarting of the sampling process after a random number of samples. While the PLL may be very consistent over a short period of time, due to the unreliable oscillator, it may be periodically unreliable and/or highly variable/irregular from device to device, particularly when compared with the extremely constant line frequency. 
         [0040]    Due to the variability between devices, and even the irregularities within a single device, it may be difficult or impossible to calibrate a particular sampling routine to be effective only using the PLL and requested sampling frequency. To more accurately assemble the consolidated wave  114 , the processor  20  may be required to treat the samples as being irregularly taken, and employ an absolute reference consolidation method  126  to generate a single, consolidated cycle. In one configuration the consolidation method  126  may be similar to a 1-dimensional lucky imaging processing technique. This consolidation method  126  may use an absolute reference, such as time, to coordinate the various samples, rather than attempting to use a known unreliable reference, such as requested sampling frequency or period. 
         [0041]    Certain embedded processors, such as RISC-based computer processors and/or CISC-based computer processors, such as those having an “ARM” architecture, are capable of providing accurate time stamps (e.g., within approximately 500 nS) to incoming signals. Regardless of the phase noise, actual sampling frequency, and/or phase discontinuities of the magnetometer  26 , in step  128 , the processor  20  may log the time each magnetic field strength reading arrives in such a manner. Using this accurate timestamp, together with an extremely reliable and known line frequency, in step  130 , the processor  20  may locate/position each recorded sample within a single 2π radian phase that is represented by a circular buffer. The highly accurate time stamps may allow the processor  20  to determine the absolute phase of each sample to within 1.47×10−4 radians, which may limit phase noise to less than 0.029% (i.e., a negligible effect). Once the phase is established, each sample may be stored in the sample buffer at an appropriate location given the size of the buffer. 
         [0042]    In one configuration, in step  132 , a second integer-buffer may be maintained concurrently with the sample buffer to determine whether the processor  20  has completed an entire cycle of samples (i.e., the sample buffer has been completely filled). In step  134 , if the integer buffer has not indicated that a complete cycle has been assembled, the processor  20  may continue sampling. If a complete sample has been acquired, however, then in step  136 , the processor  20  may compare the last logged sample with the most adjacent forward sample (e.g., from a previous iteration through the sample buffer). As generally illustrated in  FIG. 8 , if the most recent sample  150  deviates from the adjacent forward sample  152  by more than a predetermined amount  154 , then the processor may clear the sample buffer and begin assembling a new sample buffer in step  138 . While  FIG. 8  generally illustrates the samples being sequential, in practice, they may be interleaved. As such, in another configuration, the processor  20  may simply compare a recently acquired sample  150  to adjacent samples in the buffer. 
         [0043]    The practical interpretation of step  136  is to determine if there has been either a change in the powerflow through the wire, or a physical movement of the wire during the sampling period. In most appliances, over a several second period, the electrical characteristics of the appliance are generally stable. Therefore, a drastic discontinuity within the circular buffer between samples (e.g., greater than 10% of the maximum energy range) may suggest that either the load  12  has changed state (e.g. on to off), or an outside influence is affecting the sensed magnetic field (e.g., a proximate magnet, or movement of the wire). By clearing the sample buffer and restarting, the processor  20  is making the assumption that the transient power condition or outside influence has stabilized. If two errors occur in a sequential manner, then the processor  20  may display a “detection failed” message to the user and/or continue restarting until successful. 
         [0044]    In the above described method, the absolute-reference consolidation method  126  may establish a sample buffer that may be subdivided into a plurality of bins, with magnetic field strength samples being irregularly placed into the bins according to their respective timestamps. In one configuration, the sample buffer may include  192  discrete bins. In this manner, following the creation and validation of the sample buffer, in step  140 , the buffer may be smoothed by averaging groups of three adjacent samples to result in a 64 sample waveform. The smoothing reduces artifacts or noise that may be attributable to sensor interference, and/or random error in the magnetometer  26 . 
         [0045]    Following the smoothing in step  140 , the 64 bin smoothed waveform may be passed to a 64 sample Fast Fourier Transform (FFT) to determine the magnitude of the sensed magnetic field in the frequency domain (step  142 ). As may be appreciated the use of a 192 bin sample buffer and a 64 bin are provided merely as possible examples of buffer size to illustrate the above mentioned technique. Other buffer sizes may similarly be used without departing from the scope of the present disclosure. 
         [0046]    While the 64 sample buffer may be less sparse than the original 192 sample buffer, it still may contain discontinuities due to irregular sampling, or an insufficient amount of time to complete a full consolidated waveform. In one configuration, the discontinuities can be theorized as the original waveform, multiplied by a gating waveform. Since the waveform will be converted into a spectral representation by the Fourier transform, the gating waveform (i.e., the discontinuities) may generally have two effects. First, it/they may spread the higher frequency bands of the spectrum. These frequencies, however, may simply be ignored, as only low frequency bands (e.g., first and third) are necessary to estimate the power factor and/or other commonly requested usage-based parameters. 
         [0047]    As a second effect, the discontinuities may serve to generally lower the amplitudes of all frequency bins. In step  144 , however, this general decrease may be compensated by scaling the waveform up using the ratio of the buffer size to the actual number of samples successfully accumulated. For example, if the waveform has discontinuities in 3 of the 64 bins (i.e., magnetic field strength measurements only exist in 61 of the 64 bins), a scaling factor of 64/61 may be applied to the FFT output to correct the waveform amplitude. 
         [0048]    Once the power at each harmonic is scaled to compensate for the energy loss from missing samples, the fundamental (i.e. the first) and third harmonic amplitudes (i.e., M 1  and M 3 ) may be used to estimate the power factor (i.e., the phase difference between the current and the voltage of the device) in step  146 . 
         [0049]    In general, purely resistive loads have no harmonic content, so when the ratio of M 3 /M 1  is approximately equal to zero, the estimated power factor may be set to unity (1.0). Inductive loads are known to have some harmonic content, for example, due to magnetic core saturation. Therefore, when the ratio of M 3 /M 1  is between approximately 0.1 and 0.5, the power factor (PF) may be set according to Equation 4. 
         [0000]    
       
         
           
             
               
                 
                   PF 
                   = 
                   
                     1 
                     
                       1 
                       + 
                       
                         
                           M 
                           3 
                         
                         
                           M 
                           1 
                         
                       
                     
                   
                 
               
               
                 
                   Equation 
                    
                   
                       
                   
                    
                   4 
                 
               
             
           
         
       
     
         [0050]    Finally, in switching power supplies, such as in computers, televisions, and compact fluorescent bulbs, the AC wave is typically rectified and used to charge capacitors. This behavior causes the current signal to characteristically lead the voltage signal by a particular phase angle. When the processor  20  detects such a phase difference between M 1  and M 3 , it may use Equation 5 to determine the complex magnitude and solve for the power factor (PF) 
         [0000]    
       
         
           
             
               
                 
                   PF 
                   = 
                   
                     1 
                     
                       
                         
                           M 
                           1 
                           2 
                         
                         + 
                         
                           M 
                           3 
                           2 
                         
                       
                     
                   
                 
               
               
                 
                   Equation 
                    
                   
                       
                   
                    
                   5 
                 
               
             
           
         
       
     
         [0051]    Once the current, power factor, and various measures of real and apparent power are determined, the processor  20  may display the determined parameters to the user via the display  32  in step  148 . 
         [0052]    In another embodiment, the above-mentioned technique of sensing the magnetic field via the smart phone magnetometer  26  may be used to properly estimate and characterize the current flow through the wire. At the same time, an electrical field of the wire  14  may be sensed in a similar manner using audio circuitry of the device. Said another way, when a phone  16  is close enough to a wire  14  to measure the magnetic field  28  with the magnetometer  26 , the wire&#39;s electrical field induces interference in the phone&#39;s audio input circuitry. The electrical field is known to be proportional to the voltage signal of the wire, just like the magnetic field is proportional to the current signal. 
         [0053]    Therefore, by quantifying the current signal (using the sensed magnetic field) and the voltage signal (using the sensed electrical field), the power factor may be determined by directly measuring the phase difference between the two signals. This computation may be used to increase the accuracy of the power factor estimations derived from the harmonic signals, or may be used as a substitute for these estimations. 
         [0054]    As an additional capability, the smart phone  16  may utilize the wireless radio to upload the derived energy parameters to a central database, where they may be shared in social-media style with other users to establish a centralized database of typical power consumption for specific makes/models of home appliances. 
         [0055]    While the best modes for carrying out the invention have been described in detail, those familiar with the art to which this invention relates will recognize various alternative designs and embodiments for practicing the invention within the scope of the appended claims. It is intended that all matter contained in the above description or shown in the accompanying drawings shall be interpreted as illustrative only and not as limiting.