Method of compensating loss and dispersion of transmission line for time domain reflectometry
A system and method compensates distortions in transmission line measurement by obtaining a frequency response of a transmission line responsive to a test signal; approximating the frequency response as a function of a complex valued variable; and applying an analytic continuation to extend the function of the complex valued variable to a modified frequency response corresponding to a lossless frequency response, to compensate for loss in the transmission line. The modified frequency response may be further sampled at linearly spaced points in a wave number domain to compensate for dispersion of the transmission line.
1. A measurement apparatus comprising:
a transmitter configured to launch a test signal into a transmission line;
a receiver configured to receive a signal from the transmission line responsive to the test signal; and
a controller configured to obtain a frequency response of the transmission line responsive to the received signal, approximate the frequency response as a function of a complex valued variable, and apply an analytic continuation to extend the function of the complex valued variable to a modified frequency response corresponding to a lossless frequency response, to compensate for loss in the transmission line, wherein the controller is further configured to sample the modified frequency response at linearly spaced points in a wave number domain to compensate for dispersion of the transmission line.
2. The measurement apparatus of claim 1 , wherein applying the analytic continuation comprises expanding the function of the complex valued variable by Laurent series.
3. The measurement apparatus of claim 1 , wherein the controller is further configured to transform the modified frequency response by inverse Fourier transform,
the measurement apparatus further comprising a display configured to display the transformed modified frequency response.
4. The measurement apparatus of claim 1 , wherein the analytic continuation is made by a Laurent Series.
5. A measurement apparatus comprising:
a transmitter configured to launch a test signal into a transmission line;
a receiver configured to receive a signal from the transmission line responsive to the test signal; and
a controller configured to obtain a frequency response of the transmission line responsive to the received signal, approximate the frequency response as a function of a complex valued variable, and apply an analytic continuation to extend the function of the complex valued variable to a modified frequency response corresponding to a lossless frequency response, to compensate for loss in the transmission line, wherein the controller is configured to obtain the frequency response by measuring amplitude and phase of either one of a signal reflected from the transmission line, and a signal reaching a remote end of the transmission line.
6. The measurement apparatus of claim 5 , wherein applying the analytic continuation comprises expanding the function of the complex valued variable by Laurent series.
7. The measurement apparatus of claim 5 , wherein the controller is further configured to transform the modified frequency response by inverse Fourier transform, the measurement apparatus further comprising a display configured to display the transformed modified frequency response.
8. The measurement apparatus of claim 5 , wherein the analytic continuation is made by a Laurent Series.
9. A measurement apparatus comprising:
a transmitter configured to launch a test signal into a transmission line;
a receiver configured to receive a signal from the transmission line responsive to the test signal; and
a controller configured to obtain a frequency response of the transmission line responsive to the received signal, approximate the frequency response as a function of a complex valued variable, and apply an analytic continuation to extend the function of the complex valued variable to a modified frequency response corresponding to a lossless frequency response, to compensate for loss in the transmission line, wherein the received signal is a time domain impulse response provided from the transmission line responsive to the test signal, and the controller is configured to obtain the frequency response by transforming the time domain impulse response into the frequency response by Fourier transform.
10. The measurement apparatus of claim 9 , wherein applying the analytic continuation comprises expanding the function of the complex valued variable by Laurent series.
11. The measurement apparatus of claim 9 , wherein the controller is further configured to transform the modified frequency response by inverse Fourier transform,
the measurement apparatus further comprising a display configured to display the transformed modified frequency response.
12. The measurement apparatus of claim 9 , wherein the analytic continuation is made by a Laurent Series.