# Compensation for Group Velocity of Polychromatic Wave Measurement in Dispersive Medium
## 4 Experimental Results  
Figure 2 shows the illustration of the proposed system. The system is composed of (1) digital phosphor oscilloscope (DPO); (2) arbitrary waveform generator (AWG); and (3) inductive couplers. AWG generates the reference signal and apply the signal to target cable though the inductive coupler. The inductive coupler uses the electromagnetic induction phenomenon to apply a signal to the cable without connection between the cable core and signal line. In this paper, we use three inductive couplers and coupler 1 is used to apply a signal to cable, couplers 2 and 3 acquire the signal. An incident signal propagates along the cable and was acquired in the oscilloscope through the couplers 2 and 3. For ease of understanding, the signals were numbered according to the order in which they were acquired. The transmitted signals acquired through the couplers 2 and 3, before the signal being reflected, were numbered 1 and 2 and located at 0 m and 40 m, respectively. The distance propagated based on the first acquired signal though coupler 2 becomes the position of the signal. The signals reflected from the cable termination were in turn acquired via couplers 3 and 2, which were located at 80 m and 120 m. In order to verify the variation of group velocity due to the dispersion, we converted the experimental system into an equivalent circuit model using the simulation tool. Through the tuning of loss factor in the simulation tool, we conducted the simulation to compare the signal passing through the lossy medium with lossless medium. The comparison results are shown in Figure 3. The results consist of 3 types simulations: (a) lossless cable: 40 m; (b) lossy cable: 40 m; (c) lossy cable: 80 m. To verify the effect of loss factor, we compared the transmitted signal in lossy medium with that in lossless medium (simulations: (a) and (b)). Also, simulations were conducted with different cable lengths in order to analyze whether the group velocity of the signal varies due to the reflection (simulations: (b) and (c)). As shown in Figure 3a, the incident signals of each simulation are identical, but the reflected signals of each did not match. Figure 3b shows an enlarged view of the reflected signals. The highest peak in the time domain of the signal can be thought of as the highest energy point, and the group velocity of the signal can be determined by the time delay between these peak points, and this time delay is called the time of arrival of group velocity. Comparing the waveforms of (a) and (b), the time delay between the peak points of the reflected signal generated at 40 m and 80 m are \(0.102\cdot 10^{-6}\) s and \(0.207\cdot 10^{-6}\) s, respectively. If there was no change in group velocity depending on the travel distance, the time of arrival of group velocity of the reflected signal generated at 80 m  
Figure 1: Illustration of compensation method based on IF curves. had to be \(0.204\times 10^{-6}\) m. More time delays mean slower group velocity. These results show that the group velocity is decreasing as the signal propagates. Since the incident signal is a positive chirp signal, the rear part of the signal in time domain contains a high frequency component. As shown in the reflected signals of red and black line of Figure 3b, in the front part, the zero-crossing points of each signal are matched, but the zero-crossing points in the rear part do not coincide with each other. These results indicate that the higher frequency components of the signal are attenuated as the signal propagates in the lossy medium. Comparing the reflected signals generated at 80 m, we verified that the reflection only affect the magnitude of signal, not group velocity. Figure 4a shows the total acquired signal from the inductive couplers after signal restoration process [9; 10]. As seen in the fourth signal in Figure 4a, because the signal is difficult to distinguish from the noise, TFCC is used to roughly find the position of the transmitted signal.