# Analysis of AMI Communication Methods in Various Field Environments
## 2 Power Line Communication for AMI
### Measurement Methods for Power Line Communication  
In order to obtain SNR values at an MP, measuring the signal and noise powers is required. The signal and noise powers can be calculated with the signal and noise spectra measured by a spectrum analyzer, respectively. A measurement block diagram of the PLC system is shown in Figure 4a. \(H_{1}(f)\) and \(H_{2}(f)\) are the frequency responses of the couplers at the transmitter and the  
Figure 3: High-speed power line communication (HS PLC) modem connected to a smart meter (CNU Global Co. Ltd.). receiver, respectively. \(H_{p}(f)\) is the frequency response of the power line. \(x(t)\) is the signal source output and \(y(t)\) is the transmitter coupler output of \(x(t)\). The received signal through the power line is \(r(t)\) and \(z(t)\) is the output of the receiver coupler. We can notice that the spectrum of the PLC modem output \(y(t)\) is used for measurements because the PLC modem output is available only through a coupler. An example of a measured spectrum of \(y(t)\) for HS PLC is shown in Figure 4. Here, the resolution bandwidth (RBW) is set to 10 kHz. We first observe the frequency responses of a power line at different distances. To carry out the measurements for the observation, a low-voltage power line without power loads is deployed at a test site. The purpose of this observation is to examine the frequency response with respect to the distance. Thus, branches and loads are not connected to the power line. Two types of power lines are used for comparison: the overhead and underground power lines as shown in Figure 1. The measurements are obtained up to 200 m with 50 m intervals. The frequency responses are obtained with an RF signal generator and spectrum analyzer. A sinusoidal sweep is produced by the signal generator and this signal is provided to the power line. The magnitude spectrum of the power line is obtained by measuring the power spectrum of the received signal. The power spectrum is measured with the max-hold mode of the spectrum analyzer. We can notice that when the signal generator is used as a signal source as in Figure 4, the measured spectrum is the magnitude spectrum of \(z(t)\) through the power line and the coupler. We now describe the frequency responses in detail. Suppose that the measurement is performed at frequency \(f_{k}\), which is given as \(f_{k}=f_{b}+(k-1)\Delta f\), for \(k=1,\ldots,N\), where \(\Delta f=(f_{e}-f_{b})/N\). Here, \(f_{b}\) and \(f_{e}\) are the start and end frequencies, respectively, for the spectrum analyzer span, and the number of measurement points of the spectrum analyzer is denoted as \(N\). Let the measured power at frequency \(f_{k}\) of \(x(t)\) and \(z(t)\) be denoted as \(P_{x}(f_{k})\) and \(P_{z}(f_{k})\), respectively. Then the power spectral density (PSD) of \(x\), which is denoted as \(S_{x}\), can be approximated as  
\[S_{x}(f_{k})\approx P_{x}(f_{k})-10\log(B_{R})\ \ \ (\mathrm{dBm}/\mathrm{Hz}), \tag{1}\]  
where \(P_{x}\) is in dBm and \(B_{R}\) is the RBW of the spectrum analyzer. Let \(|H(f)|:=|H_{1}(f)|+|H_{p}(f)|+|H_{2}(f)|\) denote the total magnitude response of the power line and couplers. The magnitude response \(|H(f)|\) then satisfies  
\[|H(f_{k})|\approx P_{z}(f_{k})-P_{x}(f_{k})\ \ \ (\mathrm{dB}) \tag{2}\]  
from the relationship of \(S_{z}(f)=|H(f)|+S_{x}(f)\), and thus \(|H(f_{k})|\) can be obtained from (2). Figure 4: Model of the PLC system. (**a**) Measurement signals for the PLC system. (**b**) An example of the power spectrum of the HS PLC signal at the coupler output \(y(t)\). If the output power of the signal generator is 0 dBm at each frequency, then \(|H(f_{k})|\approx P_{z}(f_{k})\) holds from (2). Figure 5 shows measurement results at various distances for two types of the power lines for 0 dBm. The measurement is carried out at distances of 0 to 200 m with 50-m intervals. The x-axis (horizontal axis on the left) represents the distance between the transmitter and receiver.