Patent Document

BACKGROUND 
     1. Technical Field 
     The present invention relates to a single (reflected) or a two port (transmission) distance to fault analyzer configured to measure passive intermodulation (PIM) created by two separate signal sources as well as to measure distance to a fault creating PIM. 
     2. Related Art 
       FIG. 1  shows a block diagram of components of a prior art test system setup for measuring PIM. The test system utilizes two signal sources  2  and  4 , with a first signal source  2  producing a signal at frequency F1 and the second signal source  4  producing a signal at frequency F2. When these multiple signals are allowed to share the same signal path in a nonlinear transmission medium, unwanted additional signals occur. The 3 rd  order response is particularly troublesome as it produces signals at 2F1−F2as well as 2F2−F1. The term widely uses for this phenomenon is Passive Intermodulation or PIM. The PIM test system of  FIG. 1  measures this phenomenon. 
     In the system of  FIG. 1 , the signal sources  2  and  4  are provided through high power amplifiers (HPAs)  6  and  8  and isolators  10  and  12  to a hybrid combiner  14  to create a combined signal with frequencies F1 and F2 at the hybrid combiner  14  output. The duplexer  16  sends the signals F1 and F2 to the test port P 1 . A reverse or reflected signal from port P 1  is then produced at frequency 2F1−F2, and forwarded through duplexer  16  to switch  18 . The switch  18  in the receive (R) position provides the signal 2F1−F2 through an amplifier  20  to a digital receiver or spectrum analyzer  22  for measurement. The port P 1  can be connected by cable to port P 2  and switch  18  switched over to make a transmission (T) measurement. With the transmission measurement, signals are provided at F1 and F2 with mixing products at 2F1−F2 to port P 2 . The duplexer  26  provides the signals F1 and F2 to termination  24 , while the signal 2F1−F2 is provided from duplexer  26  through switch  18  and amplifier  20  to the digital receiver or spectrum analyzer  22  for measurement. 
       FIG. 2  shows an example of actual frequencies used when measuring a load with the test system setup of  FIG. 1 . Components carried over from  FIG. 1  to  FIG. 2  are similarly labeled, as will be components carried over in subsequent figures. The two signals F1 and F2 and how they create a third interfering signal can be explained using an example measurement setup with two distinct transmitters, a Personal Communication Service or PCS Band transmitter  2  transmitting at F1=1930 MHz and an Advanced Wireless Service or AWS Band transmitter  4  transmitting at F2=2127.5 MHz. The PIM produced signal, which can be the result of reflection from a corroded connector or antenna in the transmission path, is simulated by PIM source  30  attached to port P 1 . It is unknown where an actual PIM or multiple PIM sources may be located. This can be especially troubling when multiple connectors are involved as can be present in a PCS/AWS site tower. But, the PIM source  30  in combination with its connecting cable and load can be designed to simulate reflection from at least one connector. 
     The PIM source  30  generates a signal at 2×1930−2127.5=1732.5 MHz that is in the receive Band of the AWS system  4 . A signal is produced at 2F2−F1=2325 MHz, as also shown in  FIG. 2 , but since that signal is outside the transmit or receive band of either transmitter  2  and  4 , it is not relevant to the present measurement. The two signals transmitted from sources  2  and  4  produce about 40 watts of power for each carrier or +46 dBm each. The resulting PIM signal is on the order of −100 dBm. 
     The receive channel of the AWS source  4  in an actual operating environment can be desensitized by this interfering signal due to the broadband noncorrelated characteristic of the modulation present on both transmit carriers spreading the power over the entire receive channel. DIN 7-16 coax cable connectors typically have PIM values on the order of −140 to −168 dBc. The PIM measurement, thus, must detect signals that are &lt;−146 dBc. Since the desired PIM signal to be measured is the 1732.5 MHz signal, the bandpass filter  32  with center frequency of 1732.5 is used to filter out other signal components and provide the PIM signal for measurement to the digital receiver or spectrum analyzer  22 . An exemplary digital receiver or spectrum analyzer  22  used to perform the test can be a Summitek Instruments Model S12000D Passive Intermodulation Analyzer in the D configuration or a Telstra PIMT2V2 low power PIM Tester. 
     SUMMARY 
     Embodiments of the present invention enable making through and reflected PIM measurements on any one port or two-port device with the ability to determine, in distance, where the individual PIM impairments are located. The one port measurements can be typical reflection measurements made using a vector network analyzer and the two port measurements can similarly be conventional transmission measurements made using a VNA. The difference between the VNA measurement and the PIM measurement is the VNA measurement separates the forward signal and the reverse signal using a directional coupler. The PIM measurement separates the forward signal and the reverse signal using a frequency selective duplexer 
     In embodiments of the invention, a PIM measurement circuit includes two frequency sources that are provided through a combiner for a CW characterization of the PIM circuit. To enable distance determination, an FM measurement is created by using a saw tooth offset sweep generator attached to one of the two frequency sources operating at a significantly lower frequency than the frequency source. With downconversion and processing of the signal from the PIM circuit, the FM signal provides a frequency variation that is converted using a Fourier transform to time domain, enabling determination of the distance and magnitude of the PIM source. Multiple PIM sources separated in distance translate to multiple FM signals separated in frequency. Spectrum analysis can also be used to determine distance to each of the multiple PIM sources as well as signal magnitude from each PIM source. 
     To create a 2F1−F2 signal used for downconversion of the PIM source signal, in one embodiment a 2× frequency converter is connected to the signal source providing the signal of frequency F1. The signal source providing F2 for downconversion can be either the same as that provided to the PIM, or a separate signal source providing a frequency F2 minus the saw tooth offset sweep signal to allow a forward (ramp up) trace signal while eliminating a reverse (ramp down) trace generated with the saw tooth offset sweep. 
     In some embodiments to determine distance only, phase shift rather than frequency shift can be used. To determine distance using phase shift, in one embodiment instead of downconverting the 2F1−F2 signal directly using a mixer to determine a frequency shift, a phase detector is used to measure the phase shift. In an alternative embodiment, a 0/90 degree phase splitter can be used to produce a quadrature signal with the Real and Imaginary components to enable measuring the 2F1−F2 PIM signal using linear quadrature detection circuitry. The magnitude and phase are retained in this arrangement. In yet another embodiment, down conversion to a fixed base band signal is used to determine distance as well as to measure both amplitude and phase to fully characterize the PIM signal. 
     In some embodiments of the present invention to enable precise distance measurements, circuitry is further provided to enable calibration to be performed. Calibration can be performed using a load, a calibrated PIM, and a quarter wave length section of cable to identify a 180 degree phase rotation at the frequency of the PIM. A cable can also be connected to make a through measurement. Internal switches and duplexers are included in various embodiments to enable calibration with the two separate signal sources. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       Further details of the present invention are explained with the help of the attached drawings in which: 
         FIG. 1  shows a block diagram of components of a prior art test system setup for measuring passive intermodulation (PIM); 
         FIG. 2  shows an example of actual frequencies used when measuring a load with the test system setup of  FIG. 1 ; 
         FIG. 3  shows the block diagram of components of a first embodiment of the present invention using FM-CW as a means of determining distance with a PIM measurement device; 
         FIG. 4  shows an alternative to the circuitry to  FIG. 3  for determining distance to fault using FM-CW in a PIM measurement device that will transpose the reverse sweep to the same frequency as the forward sweep; 
         FIG. 5  shows a block diagram of a PIM measurement device using CW signals, but using phase shift, as opposed to frequency shift as in  FIGS. 3-4 , as a means of determining distance to fault; 
         FIG. 6  shows modification to the block diagram in  FIG. 5  with a linear quadrature detector circuitry added allowing both amplitude and phase measurements of the PIM signal; 
         FIG. 7  shows modification to the block diagram of  FIG. 5  that downconverts the varying frequency PIM signals to fixed 200 KHz offset baseband signals while still retaining the amplitude and phase of the original signals; 
         FIG. 8  shows the PIM measurement circuit of  FIG. 7  with calibration components added to enable calibrating the distance and amplitude of the reflected PIM measurement; 
         FIG. 9  is a block diagram showing modification of the circuit of  FIG. 7  to make a through PIM measurement; 
         FIG. 10  shows modification to the measurement circuit of  FIG. 9  that allows for a through calibration to enable characterization of the signal output of mixer  42 ; 
         FIG. 11  shows a full implementation of embodiments of the present invention as shown in  FIG. 7  through  FIG. 10 ; and 
         FIG. 12  provides a graph of a stimulus signal and a delayed response signal caused by a PIM reflection to illustrate variables used to calculate a difference frequency, ΔF. 
     
    
    
     DETAILED DESCRIPTION 
       FIG. 3  shows the block diagram of components of a first embodiment of the present invention using FM-CW as a means of determining distance in a PIM measurement device. The FM sweep is introduced using sweep generator  40 . The sweep generator  40  is connected to F1 source  2 . For purpose of illustration, the sweep generator  40  is shown creating a 1.4844 uS period saw tooth causing a +/−11.25 MHz modulation (ranging 22.5 MHz as shown) that is added to F1 of source  2 . The FM sweep signal F1 and the fixed signal F2 when modified by the PIM source will produce the additional signals 2*(F1+FM)−F2 and 2*F2−(F1+FM). The delayed in time (distance) signal 2*(F1+FM)−F2 will be mixed with an internally generated non delayed in time (distance) signal 2*(F1+FM)−F2 to produce the desired measurement signal ΔF. The ΔF signal represents 68597× distance in feet. The distance to fault from P 1  can, thus, be determined by distance in feet=ΔF/68597 
     The circuitry of  FIG. 3  has components added to accomplish addition of the sweep generator frequency and then downconversion of the output signal for analysis. To provide a signal source for downconversion, the circuitry includes a ×2 frequency multiplier  44  connected to the F1 source  1930  to provide a 3860 MHz output with a +/−22.5 MHz sweep. The output of the ×2 frequency multiplier  44  is provided to a first input of a newly added mixer  42 . The second input of mixer  42  is provided from the F2 signal generator  4 , so that the output of mixer  42  provides a frequency 3680−2127.5=1732.5 MHz. Bandpass filter  46  centered at 1732.5 MHz eliminates other mixing products from mixer  42  to provide a first input to downconverting mixer  48 . A second input of mixer  48  provides the reflected test signal at 1732.5 MHz from bandpass filter  32 . With both inputs of mixer  48  at 1732.5 MHz, they are downconverted at the output of mixer  48 , leaving substantially only the frequency deviation ΔF due to reflection of a test signal created by the PIM source  30 . A lowpass filter  49  removes mixing products higher than 50 MHz, leaving only the forward trace sweep ΔF and retrace sweep signal 45 MHz−ΔF. Measurement of ΔF with a digital receiver using Fourier transform to time domain or a spectrum analyzer gives a measurement of total distance from port P 1  to the PIM source using the formula Distance in feet=ΔF/68597, with post processing to account for the both the forward sweep ΔF and retrace 45 MHz−ΔF. 
     Exemplary signal frequencies are shown in  FIG. 3 , as well as subsequent drawings, to illustrate operation of the circuitry and are not intended to limit the operation frequencies that can be used with the circuitry. Further in  FIG. 3  and in subsequent drawings included with the specific frequency number a signal type indicator. As shown, a 1 unit thickness indicator represents a non-modulated signal, a 2 unit thickness indicator represents a modulated signal, and a 4 unit thickness indicator indicates a signal that is both modulated and doubled in frequency. Also illustrated in  FIG. 3  are the forward sweep ΔF signal lobes and the retrace signal (45−ΔF) signal lobe illustrating the difference in these signals as generated by the circuitry of  FIG. 3 . 
       FIG. 4  shows an alternative to the circuitry to  FIG. 3  for determining distance to fault that will eliminate the retrace (45 MHz−ΔF) from the output frequency. The result will be a detected frequency of ΔF=distance×68597 for both the forward sweep and the retrace sweep. This eases the post processing burden as well as increases the signal to noise ratio of the measurement. 
     The circuit of  FIG. 4  includes an additional oscillator  50  operating at F2 minus the sweep frequency of sweep generator  40  (2127.5−=2105 MHz in the example shown). The output of oscillator  50  is applied to the second input of mixer  42  instead of the output of the F2 oscillator  4  that is connected in  FIG. 3 . Thus, the output of the mixer  42  is now a signal at frequency 3860−2105=1755 MHz. The bandpass filter  46 , thus, has a center frequency adjusted to 1755 MHz. The output of bandpass filter  46  at 1755 MHz mixes in mixer  48  with the output of bandpass filter  32  to provide a signal at ΔF−22.5 MHz for the forward sweep and 45 MHz−ΔF−22.5 MHz=22.5 MHz−ΔF for the retrace. These signals when mixed in mixer  51  with a fixed 22.5 MHz signal from oscillator  52  and provided through filter  53  will produce ΔF−22.5 MHz+22.5 MHz=ΔF for the forward sweep and 22.5 MHz−ΔF−22.5 MHz=−ΔF for the retrace. The distance to fault from the port P 1  can, thus, be measured using the formula Distance in feet=ΔF/68597 without significant post processing. 
       FIG. 5  shows a block diagram of a PIM measurement device using CW signals, but using a change in phase, as opposed to frequency shift as in  FIGS. 3-4 , as a means of determining distance to fault. The sweep generator  40  uses a step frequency of 674 KHz over 33.4 steps causing a +/−11.25 MHz frequency change on F1. The reflected PIM signal will produce a phase change at phase detector  56  equal to distance in feet=Δφ degrees/1.097 
     The circuit of  FIG. 5  substitutes a phase detector  56  for the mixer  48  and lowpass filter  49  of  FIG. 3 . The inputs of the phase detector are provided from the outputs of bandpass filters  32  and  46 . The filters  32  and  46  provide equal frequency outputs, both shown as 1732.5 MHz, so that the phase detector  56  then provides the phase change measurement signal Δφ. Distance in feet from the port P 1  to the PIM source can be determined in feet using the formula distance in feet=Δφ degrees/1.097. No amplitude measurement of the PIM signal, however, will be available from the output of phase detector  56 . 
       FIG. 6  shows modification to the block diagram in  FIG. 5  with a linear quadrature detector circuitry added allowing both amplitude and phase measurements of the PIM signal. The circuitry includes a 0/90 degree phase splitter  64  with both a 0 degree and a 90 degree phase shifted output to provide Imaginary and Real signal components to first inputs of mixers  60  and  62 . The phase splitter  64  receives an input from bandpass filter  46 . A 0 degree power splitter  58  receives the output from bandpass filter  32  and provides second inputs to the two mixers  60  and  62 . The output of the mixer  60  is provided through low pass filter (LPF)  66  to provide an imaginary signal (I). The output of mixer  62  is provided through low pass filter (LPF)  68  to provide a real signal (R). 
     As indicated in the  FIG. 6  the value for Δφ=arctangent (I/R) with I being the Imaginary component from mixer  60  and R being the real component signal from mixer  68 . The value of the PIM magnitude can be calculated by A=squareroot(I 2 +R 2 ). 
       FIG. 7  shows modification to the block diagram of  FIG. 5  that downconverts the varying frequency PIM signals to fixed 200 KHz offset baseband signals to allow measurement of distance to a PIM source as well as magnitude of the PIM source using low frequency A/D conversion. In  FIG. 7  an oscillator  70  is added operating at the frequency 2(F1+FM)−F2 plus the desired fixed offset intermediate frequency (Fif) to serve as a local oscillator for downconversion to baseband. Here with the desired offset of Fif being 200 KHz, F1 being 1930 MHz and F2 being 2127.5 MHz, the frequency of oscillator  70  is shown at 1732.7 MHz. A connection from step sweep generator  40  is made to oscillator  70  to provide the sweep offset FM. Also added in place of the phase detector  56  of  FIG. 5  are 0 degree splitter  58  mixers  60  and  62  and output bandpass filters  66  and  68 . 
     In the circuitry of  FIG. 7 , the mixer  60  has an input receiving the reflected signal from the PIM source through bandpass filter  32 . The mixer  62  has an input receiving a reference signal from the output of bandpass filter  46 . A second input of the mixers  60  and  62  receive the output of local oscillator  70  as provided through splitter  58 . The output of filter  68 , thus provides a reference signal downconverted to 200 KHz, while the output of the filter  66  provides the reflected signal for measurement downconverted to 200 KHz. The fixed 200 KHz signals from filters  66  and  68  can be processed to measure PIM amplitude as well as distance to fault using phase angle. 
       FIG. 8  shows the PIM measurement circuit of  FIG. 7  with calibration components added to enable calibrating the distance, phase and amplitude for a one port PIM reflection measurement. A non PIM producing load  81  provides a first calibration component used to provide a phase and amplitude reference to measure the system&#39;s inherent PIM for cancellation. A known PIM standard with a series load  82  is connected and measured relative to the standard load  81  as a second calibration component. Finally, a PIM source with a ¼ wavelength section of line length (L) at the frequency of 2F1−F2 is attached as a third standard  83 , enabling the different length line to produce a 180 degree phase shift on the returned PIM measurement for comparison. The resulting calibration will yield a full scale measurement of the known PIM standards down to the system noise floor. 
       FIG. 9  is a block diagram showing modification of the circuit of  FIG. 7  to make a through PIM measurement. The circuit includes both a port P 1  and port P 2 . The return path through bandpass filter  32  is disconnected from its connection to port P 1  in  FIG. 8 , and connected through a duplexer  84  to port P 2  in  FIG. 9 . An unknown PIM source with cable  86  is connected between ports P 1  and P 2  for the through measurement. As illustrated, the two signals F1=1930 MHz and F2=2127.5 MHz are provided to port P 1 , while those signals along with signals of 2F1−F2=1732 MHz and 2F1+F2=2325 MHz generated by the PIM source proceeds through port P 2  and duplexer  84 . The duplexer  84  sends the signals at 1930 MHz and 2127.5 MHz to a load, while the remaining signals are provided through bandpass filter  32  centered at 1732.5 MHz. Thus, the 1732.5 MHz forward unknown PIM signal is provided to mixer  62 , while the 1732.5 frequency reference signal is provided through mixer  60  for downconversion and subsequent measurement. 
       FIG. 10  shows modification to the measurement circuit of  FIG. 9  that allows for a through calibration of a known PIM signal. The circuit of  FIG. 10  modifies the circuitry of  FIG. 9  to include an internal calibration switch  90 , a 0 degree splitter  91  a precision attenuator  93  and duplexer  92 . The calibration switch  90  allows connection of the precision calibrated 1732.5 MHz output of filter  46  to duplexer  92  when calibration is desired. The 0 degree splitter  91  enables the signal from filter  46  to be provided to the calibration switch  90  as well as to the mixer  62  for downconversion to provide a reference signal. The duplexer  92  connects to the calibration switch  90  and allows forward transmission of the reference PIM signal level through switch  90  to port P 1 , as well as the signal from combiner  14  to pass to test port P 1 . The duplexer  92  prevents any signals other than the 2*(F1+FM)−F reference signal and F1+FM and F2 from leaving port P 1  while preventing F1+FM and F2 from entering the switch  90 . The thru line  94  is used during calibration along with calibration switch  90  so that the calibration signal from attenuator  93  is provided through test ports P 1  and P 2  and is then downconverted to a thru signal using mixer  60 . The thru signal is compared with the reference signal output from mixer  62  to enable the thru calibration. 
       FIG. 11  shows a full implementation of embodiments of the present invention as shown in  FIG. 7  through  FIG. 10 . The circuit of  FIG. 11  modifies the circuitry of  FIG. 10  to substitute calibration switch  90  with switches  102  and  104 . Switch  102  provides the same function of switch  90  to connect or disconnect the output of 0 degree splitter  91  and attenuator  93  to duplexer  92  during through calibration. Switch  102  in combination with switch  104  further allows the test port P 1  to be connected to the mixer  60  to provide a downconverted reflected signal for comparison to the reference signal measurement from mixer  62 . The switch  104  alternatively allows the test port P 2  to be connected to mixer  60  to provide a downconverted through (T) measurement, or to allow the switch  102  to connect test port P 1  to mixer  60 . The calibration components as well as PIM measurement devices are combined as a PIM calibration kit  106  and can be connected for test measurements as described with respect to  FIGS. 8 through 10 . 
       FIG. 11  further shows that the frequency domain can be converted to time or distance calculation using a DSP  110 . The DSP  110  can be simply programmed to perform the distance calculation from measurements taken using the test setup of  FIG. 11 . The DSP  110  for determining distance can be a single device that also does processing of the, reflected and through signals for a test measurement. Although shown as a DSP  110 , it is understood that a microprocessor, field programmable gate array (FPGA), or a general application specific integrated circuit (ASIC) can be used to provide frequency to time domain conversion to determine distance to a PIM either together or separate from other measurement circuitry. The DSP  110  is provided in combination with a dual A/D converter  108 . The dual converter  108  converts the analog forward signal from one analog port to digital, and converts the analog reverse signal or through signal at the other port to a digital signal for processing in the DSP  110 . Although shown with a dual A/D converter  108 , separate simultaneously triggered converters can be used. As indicated previously, the system of  FIG. 11  provides PIM measurements and differs from a standard VNA by separating forward and reverse signals using duplexer  92  rather than a directional coupler. 
     In one illustrative example, a PCS device is used along with an AWS device to illustrate how frequencies can create passive intermodulation (PIM). In the example, the PCS transmit operation frequency is 1930 MHz and the AWS transmit frequency is 2127.5 MHz. The AWS receive channel operates in the range of 1710 MHz to 1755 MHz. A ΔF of +/−11.25 MHz centered at the PCS frequency of 1930 will produce an intermodulation frequency at 2*1930−2127.5 or 1732.5 MHz with a ΔF of +/−22.5 MHz due to the 2× multiplier in the intermodulation equation, or 1732.5+/−22.5 MHz. This will interfere with the AWS receive channel range of 1710-1755 MHz, and the distance to PIM measurement will indicate the amplitude of the interference as well as the distance to any defective component causing the PIM. 
     The minimum distance that can be measured to a fault in a distance to PIM causing defect according to embodiments of the present invention can be easily calculated using the formula below. The minimum distance is related to the velocity of propagation for the cable. For a typical low loss cable having a propagation of 0.9 and using a sweep frequency Fswp of 45 MHz, due to the 2F1 doubling of sweep frequency, can be calculated as follows: 
     
       
         
           
             
               dist 
               min 
             
             = 
             
               
                 
                   C 
                   * 
                   Vp 
                 
                 
                   2 
                   * 
                   Fswp 
                 
               
               = 
               
                 
                   
                     186 
                     , 
                     000 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     mi 
                     ⁢ 
                     
                       / 
                     
                     ⁢ 
                     S 
                     * 
                     5280 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     Ft 
                     ⁢ 
                     
                       / 
                     
                     ⁢ 
                     mi 
                     * 
                     0.9 
                   
                   
                     2 
                     * 
                     45 
                     * 
                     
                       10 
                       6 
                     
                   
                 
                 = 
                 
                   9.82 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   Ft 
                 
               
             
           
         
       
     
     Determination of distance from frequency caused by delay ΔF can similarly be easily calculated as described below with reference to  FIG. 12 .  FIG. 12  provides a graph of a stimulus signal and a delayed response signal caused by a PIM reflection. The graph of  FIG. 12  plots change of frequency versus change in time. The difference frequency caused by delay ΔF shows the frequency change from the stimulus to the delayed response signal. Similarly, the change of time Δt shows a time delay between the stimulus and the response. An initial time TA and initial frequency FA are shown for the plots. Further a frequency FB is shown illustrating the maximum frequency difference between the minimum frequency FA and maximum frequency of both the stimulus and delayed response signal. 
     With reference to  FIG. 12 , the formula for difference frequency ΔF is as follows: 
     
       
         
           
             
               Δ 
               ⁢ 
               
                   
               
               ⁢ 
               F 
             
             = 
             
               
                 Δ 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 t 
                 ⁢ 
                 
                   
                     FB 
                     - 
                     FA 
                   
                   
                     TB 
                     - 
                     TA 
                   
                 
               
               = 
               
                 Δ 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 t 
                 ⁢ 
                 
                   Fswp 
                   tswp 
                 
               
             
           
         
       
     
     The formula for Δt can further be calculated as follows: 
     
       
         
           
             
               Δ 
               ⁢ 
               
                   
               
               ⁢ 
               t 
             
             = 
             
               
                 2 
                 * 
                 dist 
               
               
                 C 
                 * 
                 Vp 
               
             
           
         
       
     
     Substituting the formula for Δt, the formula for ΔF becomes: 
     
       
         
           
             
               Δ 
               ⁢ 
               
                   
               
               ⁢ 
               F 
             
             = 
             
               
                 2 
                 * 
                 dist 
                 * 
                 Fswp 
               
               
                 C 
                 * 
                 Vp 
                 * 
                 tswp 
               
             
           
         
       
     
     For an FM CW linear saw tooth ramp, and assuming a non-aliased cable to PIM distance of 100 m or 328 Ft and Vp of 0.9, sweep time, tswp, is as follows: 
     
       
         
           
             tswp 
             = 
             
               
                 
                   4 
                   * 
                   dist 
                 
                 
                   C 
                   * 
                   Vp 
                 
               
               = 
               
                 
                   
                     4 
                     * 
                     328 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     ft 
                   
                   
                     186 
                     , 
                     000 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     mi 
                     ⁢ 
                     
                       / 
                     
                     ⁢ 
                     S 
                     * 
                     5280 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     Ft 
                     ⁢ 
                     
                       / 
                     
                     ⁢ 
                     mi 
                     * 
                     0.9 
                   
                 
                 = 
                 
                   1.4844 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   uS 
                 
               
             
           
         
       
     
     Providing this value for tswp into the formula for ΔF and using the sweep frequency Fswp of 45 MHz and Vp of 0.9, we obtain ΔF as follows: 
     
       
         
           
             
               Δ 
               ⁢ 
               
                   
               
               ⁢ 
               F 
             
             = 
             
               
                 dist 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 in 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 feet 
                 * 
                 
                   
                     2 
                     * 
                     45 
                     * 
                     
                       10 
                       6 
                     
                   
                   
                     
                       
                         
                           186 
                           , 
                           000 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           mi 
                           ⁢ 
                           
                             / 
                           
                           ⁢ 
                           S 
                           * 
                           5280 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           Ft 
                           ⁢ 
                           
                             / 
                           
                           ⁢ 
                           mi 
                           * 
                         
                       
                     
                     
                       
                         
                           0.9 
                           * 
                           1.488 
                           * 
                           
                             10 
                             
                               - 
                               6 
                             
                           
                         
                       
                     
                   
                 
               
               = 
               
                 dist 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 in 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 feet 
                 * 
                 0.68597 
               
             
           
         
       
     
     Although the present invention has been described above with particularity, this was merely to teach one of ordinary skill in the art how to make and use the invention. Many additional modifications will fall within the scope of the invention, as that scope is defined by the following claims.

Technology Category: h