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#### The Transactions of the Korean Institute of Electrical Engineers

##### ISO Journal TitleTrans. Korean. Inst. Elect. Eng.

1. (Department of Electrical Engineering, Hanbat National University, Korea)

Reflectometry, Propagation constant, Instantaneous frequency estimation Algorithm, Simulator, Time-Frequency domain Reflectometry

## 1. ์ ๋ก

์ ๋ ฅ ์์คํ์ ๊ด๋ฆฌ๋ฅผ ์ํด ์ผ์ด๋ธ ๊ณ ์ฅ์  ํ์ง ๋ฐ ๋ธํ ์ธก์ ์ ๋ํ ๋ฐฉ๋ฒ ๊ฐ๋ฐ์ด ํ์ํ๋ค. ์ต๊ทผ ์ฅ๊ฑฐ๋ฆฌ ์ก์ ์ ํ์์ฑ์ด ์ฆ๊ฐํ๋ฉด์ HVDC(High Voltage Direct Current)์ ์์ฅ๊ท๋ชจ๊ฐ ์ฑ์ฅํ๊ณ  ์๋ค. HVDC ์ผ์ด๋ธ์ ์ฉ๋์ฑ ์ถฉ์ ์ ๋ฅ๊ฐ ์์ด ์ฅ๊ฑฐ๋ฆฌ ์ก์ ์ ์ ๋ฆฌํ๊ณ  ์ ์ ์ฒด, ์์ค ์์ค์ด ์์ด ๋์ฉ๋ ์ก์ ์ด ๊ฐ๋ฅํ๋ค. ๋ํ ๋์ฒด ์ ํญ์ด ๋ฎ์ ์ก์  ์์ค์ด ์ ๊ณ , ์ ๋ ฅ์กฐ๋ฅ ๋ฐ ๋ถํ ์ ์ด๊ฐ ์์ํ์ฌ ์ ๋ก ์ด์ฉ๋ฅ ์ ๋์ผ ์ ์๋ ์ฅ์ ์ด ์๋ค (1). ์ด์ ๋ฐ๋ผ ์ฅ๊ฑฐ๋ฆฌ ์ ๋ก์ ์ ์ฉ ๊ฐ๋ฅํ ์ง๋จ ๋ฐฉ๋ฒ์ ๊ฐ๋ฐ์ด ์๊ตฌ๋๊ณ  ์๋ค.

ํ์ฌ ์ผ์ด๋ธ์ ๊ณ ์ฅ์  ํ์ง ๋ฐ ๊ฑด์ ์ฑ ํ๊ฐ์ ์ ๊ธฐ์ ์ธ ๋ฐฉ๋ฒ์ผ๋ก๋ VLF(Very Low frequency) tan delta ์ธก์ ๋ฒ, PD(Partial Discharge)์ง๋จ๋ฒ์ด ๋ํ์ ์ผ๋ก ์ ์ฉ๋๊ณ  ์๋ค (2). VLF tan delta๋ ๊ทน์ ์ฃผํ ์ ์ ์์ค๋ฅผ ์ธ๊ฐํ ํ์ tan delta๋ฅผ ์ธก์ ํ๋ ์ง๋จ๋ฒ์ผ๋ก, tan delta๋ ์ ์ฐ์ฒด์ ์์ค์ ์ํ ์์ค์ ๋ฅ์ ์ปคํจ์ํฐ์ ์ ๋ฅ์ ๋น๋ฅผ ๋ํ๋ด๊ณ , tan delta๊ฐ ํด์๋ก ๋์ค์ ๋ฅ๊ฐ ์ฆ๊ฐํ๋ ๊ฒ์ ์๋ฏธํ๋ค. tan delta๋ ๋ธ์ด์ฆ์ ์ํฅ์ ๊ฐ์ธํด ์ ๋ฐํ ํ์ฅ ์ง๋จ์ด ๊ฐ๋ฅํ๊ณ  ์ผ์ด๋ธ์ ์ ์ฒด์ ์ธ ์ดํ ์ํ๋ฅผ ์ง๋จํ  ์ ์์ผ๋ฉฐ IEEE std, 400.2 ์ง์นจ์์ ํ์  ๊ธฐ์ค์ด ์ ์๋์ด ์๋ค (3). ๊ทธ๋ฌ๋ ์ผ์ด๋ธ ๊ธธ์ด์ ๋ฐ๋ผ ์ฆ๊ฐํ๋ ์ปคํจ์ํฐ ์ถฉ์ ์ฉ๋์ผ๋ก ์ธํด 1.2 km ์ด์์ ์ฅ๊ฑฐ๋ฆฌ ์ ๋ก์๋ ์ ์ฉ์ด ์ด๋ ต๋ค (4). PD๋ ๊ตญ๋ถ์  ๋ฐฉ์ ํ์์ผ๋ก ์ ์ฐ์ฒด ํ๋ฉด์ด๋ ๋ด๋ถ์ ๊ณต๊ทน์ ์ํด ๋ฐ์ํ๋ค. ์ด๋ ์ ์ฐ์ฒด์ ์ดํ๋ฅผ ์ผ์ผํค๋ ํ๊ดด์ ์ฃผ์์ธ์ด๋ค. PD ์ง๋จ๋ฒ์ ๋ถ๋ถ ๋ฐฉ์  ์ ๋ฐ์ํ๋ ํ์ค๋ฅผ ํตํด ๊ณ ์ฅ์ ์ ์ธก์ ํ  ์ ์๋ค. ๊ทธ๋ฌ๋ ๋ถ๋ถ๋ฐฉ์ ์ด ์ผ์ด๋ ์ง์ ์์์ ๋ฐ์ํ ํ์ค๋ ์ผ์ด๋ธ์ ๋ฐ๋ผ ์ด๋ํ๋ฉฐ ๊ฐ์ ์ ๋ถ์ฐ์ ๋น ๋ฅด๊ฒ ๊ฒช๊ฒ ๋๋ค. ๋ฐ๋ผ์ ์ฅ๊ฑฐ๋ฆฌ ์ ๋ก์ ๊ณ ์ฅ์  ํ์ง๋ฅผ ์ํด์๋ ์ถ๊ฐ์ ์ธ ์ ํธ ์ฒ๋ฆฌ ๊ธฐ์  ๊ฐ๋ฐ์ด ํ์ํ๋ค.

๊ณ ์ฅ์  ํ์ง์ ์๋กญ๊ฒ ๋์๋๊ณ  ์๋ ๋ฐ์ฌํ ๊ณ์ธก๋ฒ์ ์ํผ๋์ค ๋ถ์ผ์น ์ง์ ์์ ๋ฐ์ฌ๋ ์ ํธ๋ฅผ ๋ถ์ํ์ฌ ๊ณ ์ฅ์ ์ ํ์งํ๋ ๊ธฐ์ ์ด๋ค. ๋ฐ์ฌํ ๊ณ์ธก๋ฒ์ PLC ํต์ ์ฉ์ผ๋ก ๊ฐ๋ฐ๋ ๋น์ ์ด์ ์ปคํ๋ฌ๋ฅผ ์ด์ฉํ์ฌ ํ์  ์ํ์ ์ง๋จ์ด ๊ฐ๋ฅํ๋ฉฐ ์ธ๊ฐํ ์ ํธ์ ๋ฐ๋ผ ํฌ๊ฒ ์๊ฐ ์์ญ, ์ฃผํ์ ์์ญ, ์๊ฐ-์ฃผํ์ ์์ญ์ ๋ฐ์ฌํ ๊ณ์ธก๋ฒ์ผ๋ก ๋ถ๋ฅํ  ์ ์๋ค (5).

TDR(Time Domain Reflectometry)์ ์๊ฐ ์์ญ ๋ฐ์ฌํ ๊ณ์ธก๋ฒ์ผ๋ก ๊ณ๋จ ์ ํธ ๋๋ ํ์ค ์ ํธ๋ฅผ ๊ธฐ์ค ์ ํธ๋ก ์ฌ์ฉํ๋ค (6). ์ํผ๋์ค ๋ถ์ผ์น ์ง์ ์์ ๊ธ๊ฒฉํ ์ ์์ ๋ณํ๊ฐ ์๊ธด ๋ฐ์ฌ ์ ํธ ๋ฐ์์ง์ ์ ๊ณ ์ฅ์ ์ผ๋ก ํ๋จํ๋ค.

FDR(Frequency Domain Reflectometry)์ ์ฃผํ์ ์์ญ ๋ฐ์ฌํ ๊ณ์ธก๋ฒ์ผ๋ก ์์์ ๊ฒ์ถํ๋ PD-FDR์ ์ฃผ๋ก ์ฌ์ฉํ๋ค (7). ์ ํํ๋ฅผ ๊ธฐ์ค ์ ํธ๋ก ์ฌ์ฉํ๋ฉฐ ์ฃผํ์๋ฅผ ์ฆ๊ฐ์ํค๋ฉฐ ์ผ์ด๋ธ์ ์ธ๊ฐํ๋ค. ์ด๋ ์ ์ฃผํ ํต๊ณผ ํํฐ๋ฅผ ํตํด DC ์ฑ๋ถ๋ง ์ถ์ถํ ์ ํธ์ ์์์ ๊ฒ์ถํ๋ค. ์ํผ๋์ค ๋ถ์ผ์น ์ง์ ์์ ์์ ์ฐจ์ด๋ฅผ ๊ณ์ฐํ์ฌ ๊ณ ์ฅ์  ๊ฑฐ๋ฆฌ๋ฅผ ์ธก์ ํ๋ค (7).

TFDR(Time-Frequency Domain Reflectometry)๋ ์๊ฐ-์ฃผํ์ ์์ญ์ ๋ฐ์ฌํ ๊ณ์ธก๋ฒ์ผ๋ก ์๊ฐ์ ๋ฐ๋ผ ์ฃผํ์๊ฐ ์ ํ์ ์ผ๋ก ์ฆ๊ฐํ๋ ์ฒฉ ์ ํธ๋ฅผ ๊ธฐ์ค ์ ํธ๋ก ์ฌ์ฉํ๊ณ  ์๊ฐ ํญ(Time Duration, TD), ์ฃผํ์ ๋์ญํญ(Frequency Band width, BW), ์ค์ฌ ์ฃผํ์(Center Frequency, CF)๋ฅผ ์กฐ์ ํ์ฌ ์ ํธ๋ฅผ ์ค๊ณํ  ์ ์๋ค. ์ธ๊ฐ ์ ํธ์ ์ทจ๋ํ ๋ฐ์ฌ ์ ํธ๋ฅผ ์๊ฐ-์ฃผํ์ ์ํธ์๊ดํจ์(Time-Frequency Cross Correlation, TFCC)๋ฅผ ํตํด ๊ณ ์ฅ์ ์ ํ์งํ  ์ ์์ผ๋ฉฐ, ์๊ฐ-์ฃผํ์ ์์ญ์์ ์๊ทธ๋-๋น ๋ถํฌ๋ฅผ ํตํด ์ ํธ ํด์์ด ๊ฐ๋ฅํ๋ค.

์ ๊ธฐ์  ์ ํธ ํด์์ ๊ธฐ๋ฐ์ผ๋ก ํ ์ง๋จ๋ฒ์ ๊ณตํต์ผ๋ก ์ฅ๊ฑฐ๋ฆฌ ์ ๋ก ์ง๋จ์ ์ํด ์ ํธ์ ๊ฐ์ ๋ฅผ ํด๊ฒฐํด์ผ ํ๋ค. TFDR์ ์ธ๊ฐ ์ ํธ์ ๋ฐ์ฌ ์ ํธ์ ์ ์ฌ๋๋ฅผ ์ด์ฉํ TFCC๋ฅผ ํตํด ๊ณ ์ฅ์ ์ ํ์ธํ๋ค. ๋ฐ๋ผ์ ์ ํธ์ ํฌ๊ธฐ๋ฅผ ์ด์ฉํ๋ ๋ค๋ฅธ ๋ฐ์ฌํ ๊ณ์ธก๋ฒ๊ณผ๋ ๋ค๋ฅด๊ฒ ์ ํธ๊ฐ ๊ฐ์ ๋ฅผ ๊ฒช๋๋ผ๋ ์ฅ๊ฑฐ๋ฆฌ ์ ๋ก์์ ๊ณ ์ฅ์  ํ์ง๊ฐ ๊ฐ๋ฅํ๋ค. ์ด๋ ์ค์  ์ ์ฃผ-ํด๋จ HVDC ์ ๋ก์ ์ ์ฉ๋๊ณ  ์์ด ์ฅ๊ฑฐ๋ฆฌ ์ ๋ก์ ๊ณ ์ฅ์  ํ์ง ๊ธฐ์ ๋ก ์ฃผ๋ชฉ๋ฐ๊ณ  ์๋ค (1). ๊ทธ๋ฌ๋ ์ค๊ณ๋๋ ๊ธฐ์ค ์ ํธ๋ ๋ค์ํ ์ฃผํ์๊ฐ ํฌํจ๋ ์ ํธ์ด๊ธฐ ๋๋ฌธ์ ์ ํ ์ ์ฃผํ์์ ๋ฐ๋ฅธ ์๋์ ์ฐจ์ด๊ฐ ๋ฐ์ํ๋ค. ๋ํ ์ ํ ๊ฑฐ๋ฆฌ๊ฐ ์ฆ๊ฐํ ์๋ก ์ ํธ๋ ์ฃผํ์์ ์์กดํ ๊ฐ์ ๋ก ์ ํธ๊ฐ ํฌํจํ๊ณ  ์๋ ์ฃผํ์ ์ฑ๋ถ๋ค์ ์๋๊ฐ ๋ฌ๋ผ์ง๋ฉฐ, ๊ฐ์ ๊ฐ ์ผ์ด๋๋ ๋ถ์ฐ์ด ๋ฐ์ํ๋ค. ์ ํ ์ ํธ์ ์ฃผํ์ ๋ณ ์ฑ๋ถ์ด ์ ํ ๊ฑฐ๋ฆฌ์ ๋ฐ๋ผ ์๊ณก์ด ๋ฐ์ํ๊ฒ ๋๋ฉด ๊ฒฐํจ์์ ์์ฑ๋ ๋ฐ์ฌ ์ ํธ์ ์ธ๊ฐ ์ ํธ์ TFCC ๊ฐ์ด ๊ฐ์๋์ด ์ธ๊ฐ ์ ํธ์ ์ ์ฌ์ฑ์ด ๋จ์ด์ง๊ณ  ์ฅ๊ฑฐ๋ฆฌ ์ ๋ก์์ ๊ณ ์ฅ์  ํ์ง์ ์ฑ๋ฅ์ด ์ ํ๋๋ค.

๋ณธ ๋ผ๋ฌธ์์๋ ๋ฐ์ฌํ ๊ณ์ธก ์ ์ ํ ๊ฑฐ๋ฆฌ์ ๋ฐ๋ผ ์ฆ๊ฐํ๋ ๊ฐ์  ๋ฐ ๋ถ์ฐ์ ๊ณ ๋ คํ์ฌ, ์ฃผํ์์ ์ ํ ๊ฑฐ๋ฆฌ์ ๋ฐ๋ฅธ ์ ํ ์๋์ ๊ฒฝํฅ์ฑ์ ๋ถ์ํ๊ณ ์ ์ ํ ์ ํธ์ ์๊ทธ๋-๋น ๋ถํฌ๋ฅผ ํตํด ์๊ฐ-์ฃผํ์ ์์ญ์์ ์์ ์ฃผํ์๋ฅผ ๋ถ์ ์๊ณ ๋ฆฌ์ฆ์ ๊ตฌํํ๊ณ  ์ฅ๊ฑฐ๋ฆฌ ์ ๋ก์ ์ ์ฉํ๊ธฐ ์ํด ์๋ฎฌ๋ ์ดํฐ๋ฅผ ๊ฐ๋ฐํ๊ณ  ์ ์ํ ์๊ณ ๋ฆฌ์ฆ ์ฑ๋ฅ์ ๊ฒ์ฆํ์๋ค.

## 2. ๋ณธ ๋ก

### 2.1 ์๊ฐ-์ฃผํ์ ์์ญ ๋ฐ์ฌํ ๊ณ์ธก๋ฒ

๋ฐ์ฌํ ๊ณ์ธก๋ฒ์ด๋ ์ํผ๋์ค ๋ถ์ผ์น ์ง์ ์์ ๋์์ค๋ ๋ฐ์ฌํ๋ฅผ ์ธก์ ํ์ฌ ๊ณ ์ฅ์ ์ ํ์งํ๋ ๊ธฐ๋ฒ์ด๋ค. ์๊ฐ-์ฃผํ์ ์์ญ ๋ฐ์ฌํ ๊ณ์ธก๋ฒ์์ ์ฌ์ฉํ๋ ๊ธฐ์ค ์ ํธ๋ ๊ฐ์ฐ์์ ํฌ๋ฝ์  ์ ํ ์ฒฉ ์ ํธ์ด๋ฉฐ, ์๊ฐ์ ๋ฐ๋ผ ์ฃผํ์๊ฐ ์ ํ์ ์ผ๋ก ๋ณํํ๋ค. ์ ํธ๋ ๋ค์ ์ (1)๊ณผ ๊ฐ๋ค (8).

##### (1)
$s(t)=e^{-\dfrac{A(t-t_{0})^{2}}{2}+\dfrac{j B(t-t_{0})^{2}}{2}+j\omega_{0}(t-t_{0})}$

($A=\dfrac{1}{2\tau_{0}^{2}}$, $B=\sqrt{(2\pi BW)^{2}2A-A^{2}}$, $w_{0}=2\pi f_{0}$ )

$\tau_{0}$๋ ์๊ฐ ํญ(Time Duration)์ ์ํฅ์ ๋ฐ์ผ๋ฉฐ ์ ํธ ๋ ์ก์๋น์ ๋น๋กํ๋ค. $f_{0}$, $t_{0}$๋ ์ค์ฌ ์ฃผํ์(Center Frequency), ์ค์ฌ ์๊ฐ์ ์๋ฏธํ๋ค. BW๋ ์ฃผํ์ ๋์ญํญ(Bandwidth)๋ฅผ ์๋ฏธํ๋ฉฐ, ์ ํธ์ ๋ถํด๋ฅ(Resolution)์ ๋์ดํด์คํธ ์ด๋ก (Nyquist theorem)์ ๋ฐ๋ผ ์ฃผํ์ ๋์ญํญ์ ๋น๋กํ๋ฉฐ ๋ค์ ์ (2)์ ๊ฐ๋ค (9).

##### (2)
$\Delta R=\dfrac{v_{p}}{2BW}$

๊ฐ์ฐ์์ ํฌ๋ฝ์  ์ ํ ์ฒฉ ์ ํธ๋ ์๊ฐ ํญ๊ณผ ์ฃผํ์ ๋์ญํญ์ด ๋์์ ์ฆ๊ฐํ  ์ ์๋ ๋ถํ์ ์ฑ ์๋ฆฌ๋ฅผ ๊ณ ๋ คํ์ฌ ์ ์ ํ ์ ํธ๋ฅผ ์ค๊ณํด์ผ ํ๋ฉฐ ๋ถํ์ ์ฑ ์๋ฆฌ ํ๋ณ์์ ๋ค์๊ณผ ๊ฐ๋ค (10).

##### (3)
$TB=\dfrac{2\piยท\dfrac{BW}{\sqrt{2}}}{6}ยท\dfrac{\dfrac{TD}{\sqrt{2}}}{6}\ge 0.5$

์ (2), (3)์ ๋ฐ๋ผ ๊ธฐ์ค ์ ํธ ์ค๊ณ ์ ๋ถํด๋ฅ๊ณผ ๋ถํ์ ์ฑ์ ์๋ฆฌ๋ฅผ ๋์์ ๊ณ ๋ คํ์ฌ ์ ํธ๋ฅผ ์ค๊ณํด์ผ ํ๋ค. ์ค๊ณ๋ ์ ํธ๋ ๋ค์ํ ์ฃผํ์ ์ฑ๋ถ์ผ๋ก ๊ตฌ์ฑ๋๊ณ , ์ฃผํ์์ ๋ฐ๋ฅธ ์ ํ ์๋๊ฐ ์ฐจ์ด๊ฐ ์์ด ์ ํ ๊ฑฐ๋ฆฌ๊ฐ ๋ฉ์ด์ง์๋ก ์ ํธ๋ ๋ถ์ฐ ๋ฐ ์๊ณก๋๋ค. ๋ฐ๋ผ์ ์ ํ ์์ ๋ฐ ๊ฑฐ๋ฆฌ์ ๋ฐ๋ผ ์ํฅ์ ๋ฐ๋ ์ ํธ ๋ถ์์ด ํ์ํ๋ค.

์ ํ๋ ์ ํธ๋ ์ ํ ๋งค์ง์ ์ ํ ์์๋ฅผ ๊ณ ๋ คํ ์ฃผํ์ ์ข์ ํํฐ $G(z,\:w)= e^{-jk(w)z}$์ ์ํด ์ ํธ๊ฐ ์๊ณก๋๋ฉฐ, ์ด๋ ๋ค์ ์ (4)์ ๊ฐ๋ค. ์ฃผํ์ ์์ญ์ ์ (4)๋ฅผ ํธ๋ฆฌ์ ์ญ๋ณํํ์ฌ ์๊ฐ ์์ญ์์ ์ ํ ๊ฑฐ๋ฆฌ $z$ ๋งํผ ์ ํ๋ ์ ํธ๋ฅผ ํ์ธํ  ์ ์๊ณ  ์ด๋ ๋ค์ ์ (5)์ ๊ฐ๋ค (11).

##### (4)
$S(z,\:w)=e^{-jk(w)z}S(0,\:w)$

##### (5)
$s(z,\:t)=\dfrac{1}{2\pi}\int_{-\infty}^{\infty}e^{j(wt-k(w)z)}S(0,\:w)dw$

์ ํ ์์ $k$๋ $\beta -j\alpha$๋ก ๊ตฌ์ฑ๋๋ฉฐ ์ค์๋ถ $\beta$๋ ์์ ์์, ํ์๋ถ $\alpha$๋ ๊ฐ์  ์์์ด๋ค. ์ ํธ๊ฐ ์ข์ ์ฃผํ์ ๋์ญ์ ๊ฐ๋ ํ๋์ญ ์ ํธ(narrow band signal)์ผ ๋, $\omega_{0}$์ ๋ํด ํ์ผ๋ฌ ๊ธ์๋ก ์ด๊ณ๋ํจ์๊น์ง ํ์ฅํ์ฌ ์ถ์ ํ๋ฉด ๋ค์ ์ (6)๊ณผ ๊ฐ๋ค (12).

##### (6)
$\left .\left . k_{0}=k(\omega_{0}),\:\dot k_{0}=\dfrac{dk}{d\omega}\right |_{w_{0}},\:\ddot k_{0}=\dfrac{d^{2}k}{d\omega^{2}}\right |_{w_{0}}$

##### (7)
$k(\omega)=k_{0}+\dot k_{0}(\omega -\omega_{0})+\dfrac{1}{2}\ddot k_{0}(\omega -\omega_{0})^{2}+\cdots$

์ฌ๊ธฐ์ $\dot k_{0}=\dot\beta_{0}-j\dot\alpha_{0}$์ด๋ฉฐ $\dot\beta_{0}$์ ์ ํ ์๋์ ์ญ์๋ฅผ ๋ํ๋ธ๋ค. $k(\omega)$๋ฅผ ๊ณ ๊ณ๋ก ์ถ์ ํ ์๋ก ์ ๋ฐํ ํํ์ด ๊ฐ๋ฅํ์ง๋ง ๋ณธ ๋ผ๋ฌธ์์๋ ๊ฐ์  ๋ฐ ๋ถ์ฐ์ ์์ธ์ด ๋๋ ์ด๊ณ๋ํจ์ $\ddot k_{0}=\ddot\beta_{0}-j\ddot\alpha_{0}$๊น์ง ๋ํ๋๋ค. ์ ํ ์์๋ฅผ ์ด๊ณ๋ํจ์๊น์ง ๊ณ ๋ คํ์ฌ ๊ธฐ์ค ์ ํธ๋ฅผ ๋ํ๋ด๋ฉด ๋ค์ ์ (8)๊ณผ ๊ฐ๋ค.

##### (8)
$s(z,\:t)=\dfrac{1}{2\pi}\int_{-\infty}^{\infty}e^{jw(t-k_{0}'z)-jk_{0}''zw/2}S(0,\:w)dw$

์ ํ ์์์ ์ด๊ณ๋ํจ์์ ๋ฐ๋ผ ์ ํธ์ ์๊ฐ์ ๋ฐ๋ฅธ ์ฃผํ์ ์ฆ๋ถ $\dot\omega_{0}$๋ ๋ค์ ์ (9)์ ๊ฐ๋ค.

##### (9)
$\dot\omega_{0}=\dfrac{\ddot\beta_{0}z}{(\tau_{0}^{2}+\ddot\alpha_{0})^{2}+(\ddot\beta_{0}z)^{2}}$

์ ํ ๊ฑฐ๋ฆฌ๊ฐ ์ฆ๊ฐํจ์ ๋ฐ๋ผ TD์ ์ํฅ์ ๋ฐ๋ $\tau_{0}$์๋ ๋ณ์กฐ๊ฐ ์ ์ฉ๋๋ฉฐ, ์ด๋ $\tau_{c hi rp}$์ผ๋ก ํํํ  ์ ์๋ค. $\tau_{ch i rp}^{2}$์ $\tau_{0}$์ ์ฃผํ์ ์ฆ๋ถ $\dot\omega_{0}$์ ๋ณต์์ ํํ๋ก ๋ค์ ์ (10)๊ณผ ๊ฐ๋ค.

##### (10)
$\tau_{ch i rp}^{2}=\dfrac{\tau_{0}^{2}(1+j\dot\omega_{0}\tau_{0}^{2})}{1+j\dot\omega_{0}\tau_{0}^{4}}$

์ ์์ ๋ฐ๋ผ ์ฒํ์ด ์ ์ฉ๋ ์ ํ ์ ํธ์ ์คํํธ๋ผ์ ์์ ๋ค์๊ณผ ๊ฐ๋ค.

##### (11)
$S(z,\:\omega)=\sqrt{2\pi\tau_{ch i rp}^{2}}e^{-j\dot k_{0}z\omega}e^{-(\tau_{ch i rp}^{2}+ j\ddot k_{0}z)\omega^{2}/2}$

##### (12)
$S(z,\:t)=\sqrt{\dfrac{\tau_{ch i rp}^{2}}{\tau_{ch i rp}^{2}+ j\ddot k_{0}z}}\exp\left[-(t-\dot k_{0}z)^{2}\dfrac{}{2(\tau_{ch i rp}^{2}+j\ddot k_{0}z)}\right]$

์ ํธ์ ๋ถ์ฐ์ ๊ณ ๋ คํ  ๊ฒฝ์ฐ ๋ถ์ฐ์ ๋ํ๋ด๋ ์ด๊ณ ์ ํ ์์ ๊ฐ์ ๊ณ ๋ คํ ๊ทธ๋ฃน ์๊ฐ ์ง์ฐ ์์ ์ด์ฉํ์ฌ ๊ทธ๋ฃน ์๋๋ฅผ ๊ตฌํ๋ฉฐ ๋ค์ ์ (13)๊ณผ ๊ฐ๋ค.

##### (13)
$t_{g}=\dot\beta_{0}z-\dfrac{\dot\alpha_{0}\ddot\beta_{0}z^{2}}{\tau_{0}^{2}+\ddot\alpha_{0}z}$

๊ทธ๋ฌ๋ ์ด๋ ์ ํ ๊ฑฐ๋ฆฌ๊ฐ ์ถฉ๋ถํ ์ฆ๊ฐํ  ๊ฒฝ์ฐ ๊ณ ์ฃผํ ๋ถ๋ถ์ด ์๋ฉธ๋๋ ๊ฒ์ ๊ณ ๋ คํ์ง ์์๊ธฐ ๋๋ฌธ์ ์ ํ ์ ํธ์ ๋ถ์ฐ์ ๋ณด์ ํ๋ ํํฐ ์ค๊ณ ๊ฐ๋ฐ์ด ํ์ํ๋ค.

### 2.2 ์์ ์ฃผํ์ ์ถ์  ์๊ณ ๋ฆฌ์ฆ

์์ ์ฃผํ์(Instantaneous Frequency, IF)๋ ์ฃผํ์๊ฐ ์๊ฐ์ ๋ฐ๋ผ ๋ณํํ  ๋ ํน์  ์๊ฐ์์์ ์ฃผํ์๋ก ์ ์๋๋ฉฐ ์ ํธ์ ์๊ฐ์ ๋ํ ๋ณํ ํน์ฑ์ ์ค๋ช์ ์ํด ๋ง์ด ์ฌ์ฉ๋๋ค (13). ์์ ์ฃผํ์๋ ํ๋ฒํธ ๋ณํ์ ์ด์ฉํ์ฌ ์ ํธ์ ์ค์๋ถ $s(t)$์ ํ์๋ถ $\hat s(t)$๋ฅผ ๊ฐ๋ ํด์์  ์ ํธ๋ก ๋ง๋  ๋ค IF๋ฅผ ๋ค์ ์ (15)๋ก ํํํ  ์ ์๋ค.

##### (14)
$\varphi(t)=\arg(s(t)+j\hat s(t))$

##### (15)
$f_{s}=\dfrac{1}{2\pi}\dfrac{d\varphi}{dt}$

์ ํ๋ ์ ํธ๋ ์๊ทธ๋-๋น ๋ถํฌ(Wigner-Ville Distribution)๋ก ๋ณํํ์ฌ ์๊ฐ-์ฃผํ์ ์์ญ์ ํน์ง์ ๋์์ ๊ด์ฐฐํ  ์ ์๋ค. ์๊ทธ๋-๋น ๋ถํฌ๋ ์ ํธ์ ์๋์ง ๋ถํฌ๋ฅผ ๋ํ๋ด๋ฉฐ ๋ค์ ์ (16)๊ณผ ๊ฐ๋ค (14).

##### (16)
$W_{s}(t,\:\omega)=\dfrac{1}{2\pi}\int_{-\infty}^{\infty}s(t+\dfrac{1}{2}\tau)s^{*}(t-\dfrac{1}{2}\tau)e^{-j\tau\omega}d\tau$

์ ํ ์ ํธ์์ ๋ฐ์ํ ์๊ณก์ ์๊ทธ๋-๋น ๋ถํฌ์์ ๋ํ๋ ๊ฐ ์ ํธ์ IF ์ถ์ ์ ํตํด ํ์ธํ  ์ ์์ง๋ง, ์ฅ๊ฑฐ๋ฆฌ ์ ํ๋ ์ ํธ๋ ๊ฐ์ ๊ฐ ์ฌํด ์ ํธ์ ์กด์ฌ๋ฅผ ์๊ทธ๋-๋น ๋ถํฌ์์ ํ์ํ๊ธฐ ์ด๋ ต๋ค (15).

IF ์ถ์ ์ ์ด๋ ต์ง๋ง TFCC๋ฅผ ํตํด ๊ธฐ์ค ์ ํธ์ ์ ์ฌํ ์ ํ ์ ํธ์ ์์น๋ฅผ ํ์งํ  ์ ์์ผ๋ฉฐ ๊ธฐ์ค ์ ํธ์ ๋ฐ์ฌ ์ ํธ์ ํฌ๊ธฐ๋ก ๋๋ ์ฃผ๊ธฐ ๋๋ฌธ์ ์ ํธ์ ํฌ๊ธฐ์ ์๊ด์์ด ๊ฒฐ๊ณผ๋ฅผ ๋์ถํ  ์ ์๋ค. ์ ๊ทํ๋ ๊ธฐ์ค ์ ํธ์ ์ ํ ์ ํธ์ TFCC๋ ์ (17)๊ณผ ๊ฐ๋ค (16).

##### (17)
$C_{sr}(t)=\dfrac{1}{E_{s}E_{r}(t)}\iint W_{r}(t',\:w)W_{s}(t'-t,\:w)dwdt'$

##### (18)
$E_{r}(t)=\iint W_{r}(t',\:w)dwdt'$

##### (19)
$E_{s}(t)=\iint W_{s}(t ,\:w)dwdt$

์ฌ๊ธฐ์, $E_{s}(t)$, $E_{r}(t)$๋ ๊ธฐ์ค ์ ํธ์ ๋ฐ์ฌ ์ ํธ์ ์๋์ง๋ฅผ ๋ํ๋ด๋ฉฐ, TFCC๋ ๋ ์ ํธ์ ์๋์ง๋ฅผ ๋๋์ด ์ ๊ทํํ๊ธฐ ๋๋ฌธ์ ๋ฐ์ฌ ์ ํธ์ ํฌ๊ธฐ์ ๊ด๊ณ์์ด 0๊ณผ 1 ์ฌ์ด์ ์ ์ฌ๋๋ฅผ ๊ฐ๊ฒ ๋๋ค.

ํ๋์ญ ์ ํธ์ ๊ฐ๊น์ธ์๋ก ํ๋ฒํธ ๋ณํ๋ ์ ํธ๋ ์ง๊ต ์ ํธ์ ๊ฐ๊น์ ์ ํธ์ ์๊ทธ๋-๋น ๋ถํฌ์์ ๊ฐ์ฅ ๋์ ์๋์ง์์ IF๋ฅผ ํจ๊ณผ์ ์ผ๋ก ์ถ์ ํ  ์ ์๋ค. ๋ํ ์๊ทธ๋-๋น ๋ถํฌ์ ํผํฌ ๊ธฐ๋ฐ IF ์ถ์ ์ ์ ํ FM ์ ํธ์ ์ต์ ํ๋ ๋ฐฉ๋ฒ์ด๋ค (17). ์๊ฐ-์ฃผํ์ ์์ญ ๋ฐ์ฌํ ๊ณ์ธก๋ฒ์์๋ ์๊ฐ์ ๋ฐ๋ผ ์ฃผํ์๊ฐ ์ ํ์ ์ผ๋ก ์ฆ๊ฐํ๋ ์ ํธ๋ฅผ ์ฌ์ฉํ๋ฏ๋ก ์ฃผํ์ ์์ญ์์ IF๋ ์ ํ ์ ํธ์ ์๊ทธ๋-๋น ๋ถํฌ์์ ๊ฐ์ฅ ๋์ ์๋์ง๋ฅผ ๊ฐ๋ ์ ์ ์๋ฏธํ๋ค.

๊ทธ๋ฆผ. 1. ์๋ฎฌ๋ ์ดํฐ ๋ฉ์ธ ํ๋ฉด

Fig. 1. Simulator main screen

ํ์ง๋ง ์ ํธ๋ ๊ฐ์ ๊ฐ ์ฌํด ์๊ทธ๋-๋น ๋ถํฌ๋ฅผ ํตํ IF ์ธก์ ์ด ์ด๋ ค์ ์ ํธ ๋ณต์ ์๊ณ ๋ฆฌ์ฆ์ด ํ์ํ๋ค. ์ด์ ๋ฐ๋ผ min-max ์ ๊ทํ๋ฅผ ์ด์ฉํ์ฌ ์ ํ ์ ํธ์ ํฌ๊ธฐ๋ฅผ ๊ธฐ์ค ์ ํธ์ ๋์ผํ๊ฒ 0๊ณผ 1 ์ฌ์ด ๊ฐ์ผ๋ก ๋ณต์ํ์์ผ๋ฉฐ ๋ค์ ์ (20)์ ๊ฐ๋ค.

##### (20)
$x_{no}{al}=\dfrac{{x}-{x}_{\min}}{{x}_{\max}-{x}_{\min}}$

๋ณต์๋ ์๊ทธ๋-๋น ๋ถํฌ์ ํผํฌ์ ์ ํตํด IF ์ถ์  ์๊ณ ๋ฆฌ์ฆ์ ๊ตฌํํ์๋ค, IF๋ฅผ 1์ฐจ ํจ์๋ก ์ถ์ ํ๊ณ  ์ ํ ์ต์์ ๊ณฑ๋ฒ(Linear Least Squares Estimation, LLS)์ผ๋ก ํํํ์์ผ๋ฉฐ ๋ค์ ์(21)๊ณผ ๊ฐ๋ค.

##### (21)
$J=\sum_{i=1}^{m}(y_{i}-x_{i}^{T}w)^{2}=(Y-Xw)^{T}(Y-Xw)$

##### (22)
$Y=Xw$, $Y=\begin{bmatrix}y_{1}\\y_{2}\\โค\\โค\\โค\\y_{n}\end{bmatrix}$, $X=\begin{bmatrix}x_{1}&1\\x_{2}&1\\โค&.\\โค&.\\โค&.\\x_{n}&1\end{bmatrix}$, $w=\begin{bmatrix}a\\b\end{bmatrix}$

์ฌ๊ธฐ์ Y๋ ์์ ์ฃผํ์๋ฅผ 1์ฐจ ํจ์๋ก ํํํ๊ธฐ ์ํด ์๊ทธ๋-๋น ๋ถํฌ์ ์ ์ผ ํฐ ๊ฐ๋ค์ ๋จ๊ฒจ๋์ ์๊ฐ-์ฃผํ์ ํ๋ฉด์ ์ฃผํ์๋ฅผ ๋ํ๋ด๋ฉฐ, X๋ ์๊ฐ ์ถ์ ๋ฐ์ดํฐ์ ์๋ ฅ ๋ฒกํฐ์ ๊ฐ๋ค๊ณผ ํฌ๊ธฐ๊ฐ n์ด๊ณ  ๋ชจ๋  ์์๊ฐ 1์ธ ์ด๋ฒกํฐ๋ฅผ ๋๋ํ ๋์ ๊ฒ์ด๋ค. $w$๋ ๊ฐ์ค์น ๋ฒกํฐ๋ฅผ ์๋ฏธํ๋ฉฐ ์ฌ๊ธฐ์ $w$๋ ์์ ์ฃผํ์์ 1์ฐจ ํจ์ํํ $y=ax+b$์ ๊ธฐ์ธ๊ธฐ์ $y$์ ํธ์ ๋ํ๋ธ๋ค. J๋ ๋น์ฉํจ์๋ฅผ ๋ํ๋ด๋ฉฐ J๋ฅผ $w$์ ๋ํด ๋ฏธ๋ถํ์ฌ ๊ฐ์ค์น $w$ ๊ตฌํ  ์ ์์ผ๋ฉฐ ๋ค์ ์ (24)์ ๊ฐ๋ค.

##### (23)
$\dfrac{\partial J}{\partial w}=2X^{T}Xw-X^{T}Y=0$

##### (24)
$w=(X^{T}X)^{-1}X^{T}Y$

๊ธฐ์ค ์ ํธ์ ์ ํ ์ ํธ์ ์๊ทธ๋-๋น ๋ถํฌ์ LLS์ ํตํด ์ถ์ ํ 1์ฐจ ํจ์์ ๊ธฐ์ธ๊ธฐ๋ฅผ ๋ฐ์ํ์๋ค. TFCC ๊ธฐ๋ฐ์ ์ ํธ ๋ณต์ ์๊ณ ๋ฆฌ์ฆ์ ํ์ฉํ์ฌ ์ ํธ๋ฅผ ๋ณต์ํ๊ณ  LLS๋ฅผ ํตํด IF๋ฅผ ์ถ์ ํ  ์ ์๋ ์๊ณ ๋ฆฌ์ฆ์ ๊ตฌํํ์๋ค.

## 3. ์คํ ๊ฒฐ๊ณผ ๋ฐ ๊ณ ์ฐฐ

### 3.1 ์๋ฎฌ๋ ์ดํฐ ๊ฐ๋ฐ

HVDC ์์ฅ ๊ท๋ชจ์ ํ๋์ ๋ฐ๋ผ ์ฅ๊ฑฐ๋ฆฌ ์ก์ ์ ํ์์ฑ์ด ์ฆ๊ฐํ๊ณ  ์๋ค. ํ์ง๋ง HVDC ์ผ์ด๋ธ ๊ณ ์ฅ์  ํ์ง๋ ์ ๋ฌธ๊ฐ์ ์๋ จ๋ ๋ฐ ๊ฒฝํ์ ์์กด๋๋ฉฐ, ์ ํํ ์ง๋จ์ด ๋ถ๊ฐ๋ฅํ ์ฌ๋ก๊ฐ ๋ง๋ค (1). ์ด์ ๋ฐ๋ผ ์ฅ๊ฑฐ๋ฆฌ ์ ๋ก์ ์ ์ฉ ๊ฐ๋ฅํ ๋ฐ์ฌํ ๊ณ์ธก๋ฒ ์๋ฎฌ๋ ์ดํฐ๋ฅผ ๊ฐ๋ฐํ์๋ค. ์ฅ๊ฑฐ๋ฆฌ ์ ๋ก์ ๊ฒฝ์ฐ ์ ํ ๊ฑฐ๋ฆฌ๊ฐ ์ฆ๊ฐํ ์๋ก ์ ํธ์ ๊ฐ์ ์ ๋ถ์ฐ์ด ์ฌํด์ ธ ๊ณ ์ฅ์  ํ์ง ์ฑ๋ฅ ์ ํ๋๋ฉฐ, IF ์ถ์ ์ ํตํ ์ฃผํ์ ์ฑ๋ถ์ ๊ฐ์  ํน์ฑ ๊ธฐ๋ฐ ๋ณด์  ํํฐ ์ค๊ณ๊ฐ ํ์ํ๋ค. ์ด๋ฅผ ์ํด์ IF ์ถ์ ์ด ํ์ํ์ง๋ง, ์ฅ๊ฑฐ๋ฆฌ ์ ํ ์ ํธ๋ ์๊ทธ๋-๋น ๋ถํฌ์์ ํ์ง๊ฐ ์ด๋ ต๋ค. ์ ํธ์ ์กด์ฌ ์ฌ๋ถ๋ TFCC๊ฐ ํด๊ฒฐํด์ค ์ ์์ง๋ง, ์ ํธ ์๋์ง ์์ฒด๊ฐ ์์์ ธ ์๋ ์ํฉ์์ IF ์ถ์ ์ ๋ถ๊ฐ๋ฅํ๋ค. ๋ฐ๋ผ์ ๋ณธ ๋ผ๋ฌธ์์ ์ ํ ๊ฑฐ๋ฆฌ์ ๋ฐ๋ฅธ ์๊ณก์ ๋ฐ์ํ ์ ํ ์ ํธ์ ๋ฐ์ฌ ์ ํธ๋ฅผ ๋ถ์ ๊ฐ๋ฅํ ์๋ฎฌ๋ ์ดํฐ๋ฅผ ๊ฐ๋ฐํ์๊ณ , ์ ์ํ ์ ํธ ๋ณต์ ์๊ณ ๋ฆฌ์ฆ์ ํตํด ์ ํ ์ ํธ๋ฅผ ๊ธฐ์ค ์ ํธ์ ํฌ๊ธฐ์ ๋ง๊ฒ ๋ณต์ํ๊ณ  IF ์ถ์  ์๊ณ ๋ฆฌ์ฆ์ ์ฑ๋ฅ์ ์๋ฎฌ๋ ์ดํฐ๋ฅผ ํตํด ๊ฒ์ฆํ์๋ค.

์๋ฎฌ๋ ์ดํฐ๋ ์ ํธ ์ธ๊ฐ๋ถ, ์ ํธ ๊ณ์ธก๋ถ, ์๊ทธ๋-๋น ๋ถํฌํ๋ฉด ๋ฐ ์ ํ ์์ ์๋ ฅ๋ถ, IF ๊ณ์ธก๋ถ๋ก ๊ตฌ์ฑ๋๋ค. ์๋ฎฌ๋ ์ดํฐ์ ๋ฉ์ธ ํ๋ฉด์ ๊ทธ๋ฆผ 1๊ณผ ๊ฐ๋ค.

(1) ์ ํธ ์ธ๊ฐ๋ถ

โ ์์ญ ์ค์ (Domain) : ๊ณ์ธก๋ฒ ์ ํ์์ญ์ผ๋ก ์๊ฐ ์์ญ, ์ฃผํ์ ์์ญ, ์๊ฐ-์ฃผํ์ ์์ญ์ ๊ฒฐ์ ํ๋ค.

โ ๊ธฐ๋ณธ๊ฐ(Default) : ์์๋ก ์ค์ ํ ์ ํธ ์์ฑ์ ํ์ํ ๊ฐ์ ๋ถ๋ฌ์จ๋ค. ์ค์  ๋ฐ์ฌํ ๊ณ์ธก ์ ์ฌ์ฉ๋๋ ์ฅ๋น๋ฅผ ๊ณ ๋ คํ์ฌ ์ค์ ํ์๋ค.

โ ๋ถํ์ ์ฑ ์๋ฆฌ ํ์ธ(Check) : ๋ถํ์ ์ฑ์ ์๋ฆฌ์ ๋ฐ๋ผ ์๊ฐ ํญ๊ณผ ์ฃผํ์ ๋์ญํญ์ ๊ณฑ์ ๋ฐ๋์ 0.5์ด์์ ๊ฐ์ ๋ง์กฑํด์ผ ํ๋ค. ์ด์ ๋ฐ๋ผ ์ค์ฌ ์ฃผํ์๋ฅผ ๊ธฐ์ค์ผ๋ก ์ํ๋ง ๋ ์ดํธ(Sampling Rate)๊ฐ, ์ฃผํ์ ๋์ญํญ์ ๊ธฐ์ค์ผ๋ก ์๊ฐ ํญ์ด ๋ณ๊ฒฝ๋๋ค.

โ ์ ํธ ์์ฑ(Signal Generation) : ์ค์ ๋ TD, BW, CF ๊ฐ์ ๋ฐ์ํ์ฌ ๊ธฐ์ค ์ ํธ๋ฅผ ์์ฑํ๋ค.

(2) ์ ํธ ๊ณ์ธก๋ถ

โ ๊ธฐ๋ณธ๊ฐ(Default) : ์ ํ ์ ํธ์ ๊ณ์ธก์ง์ ๊ณผ ๋ฐ์ดํฐ ์ทจ๋์ ์ํ ์ค์ ๊ฐ์ ๋ถ๋ฌ์จ๋ค.

โ ๋ฐ์ดํฐ ๊ณ์ธก ๋ฐ ์ทจ๋(Data Acquisition) : ์ ํธ๋ฅผ ๊ณ์ธกํ ํ ๋ฐ์ดํฐ๋ฅผ ์ทจ๋ํ์ฌ ์ธ๊ฐ ์ ํธ ๋ฐ ์ ํ ์ ํธ๋ฅผ ๋ํ๋ด๊ณ , ์ด์ ๋ฐ๋ฅธ ์๊ทธ๋-๋น ๋ถํฌ ๊ฐ์ ์ทจ๋ํ๋ค.

โ ์ ํ ์์ : ๋งค์ง์ ํน์ฑ์ธ ์ ํ ์์๋ฅผ ์๋ ฅํ  ์ ์์ผ๋ฉฐ, ์ค์ ๋ถ๋ถ๊ณผ ํ์ ๋ถ๋ถ์ผ๋ก ๋๋์ด์ ธ ์๋ค. ์ ํ ์๋๋ $\dot\beta_{0}$์ ์ญ์๋ก ํํํ๋ค.

โ ์๊ทธ๋-๋น ๋ถํฌ : ์ธ๊ฐ ์ ํธ์ ์ ํ ์ ํธ์ ์๊ทธ๋-๋น ๋ถํฌ๋ฅผ ๋ํ๋ธ๋ค.

โ ์์ ์ฃผํ์ : ์ธ๊ฐ ์ ํธ์ ์ ํ ์ ํธ์ ์์ ์ฃผํ์ ๊ธฐ์ธ๊ธฐ๋ฅผ on/off๋ก ํ์ํ  ์ ์๋ค. ์ ํธ๊ฐ ์ ํ ๋ ์๋ก ๊ฐ์  ๋ฐ ๋ถ์ฐ์ ๊ฒช์ด ์๊ทธ๋-๋น ๋ถํฌ์์ IF ์ถ์ ์ด ์ด๋ ค์ ์ ํธ ๋ณต์ ์๊ณ ๋ฆฌ์ฆ์ ํตํด ๊ธฐ์ค ์ ํธ์ ๊ฐ์ ์๋์ง ๋ถํฌ๋ก ์กฐ์ ํ๊ณ  ์์ ์ฃผํ์๋ฅผ ํ์ํ์๋ค.

### 3.2 ์คํ ๊ตฌ์ฑ ๋ฐ ๊ฒฐ๊ณผ

๋ณธ ๋ผ๋ฌธ์์ ์ ์ํ ์๊ณ ๋ฆฌ์ฆ์ ์ฑ๋ฅ์ ๊ฒ์ฆํ๊ธฐ ์ํด ๋ฐ์ฌํ ๊ณ์ธก๋ฒ ์์คํ ์ค๊ณ๋ฅผ ๊ณ ๋ คํ์ฌ ์๋ฎฌ๋ ์ดํฐ๋ฅผ ๊ฐ๋ฐํ์๊ณ  ๋ฐ์ฌํ ๊ณ์ธก๋ฒ ์์คํ ๊ตฌ์ฑ๋๋ ๊ทธ๋ฆผ 2์ ๊ฐ๋ค. ์ ํธ๋ ๋น์ ์ด์ ์ปคํ๋ฌ๋ฅผ ํตํด ์ธ๊ฐํ๊ณ  ๊ณ์ธกํ๋ฉฐ, ๋์ผ ์์น์์ ์ ํธ ์ธ๊ฐ ๋ฐ ์ทจ๋์ ๊ฐ์ ํ์ฌ ๊ฐ๋ฐํ์๋ค. ์ ํธ๋ฐ์๊ธฐ์์ ์์ฑ๋ ๊ธฐ์ค ์ ํธ๋ T-์ปค๋ฅํฐ๋ฅผ ํตํด ๋์งํธ ์ค์ค๋ก์ค์ฝํ์ ์ทจ๋๋๊ณ  ์ ํธ์ฒ๋ฆฌ ์์คํ์ ์ ์ก๋๋ค. ๋ค๋ฅธ ์ฑ๋์ ํตํด ์ค๊ณ๋ ๊ธฐ์ค ์ ํธ๋ ์ผ์ด๋ธ์ ์ธ๊ฐ๋๊ณ  ์ํผ๋์ค ๋ถ์ผ์น ์ง์ ์์ ๋ฐ์ํ ์ ํธ๋ ๋ฐ์ฌ๋์ด ๋์์จ๋ค. ๋ณธ ๋ผ๋ฌธ์์๋ ์ ํ์ ๋ํ ์ ํธ ๊ฐ์  ๋ฐ ๋ถ์ฐ์ ๋ถ์ํ๊ธฐ ์ํด์ ์๋ฎฌ๋ ์ดํฐ๋ฅผ ๊ฐ๋ฐํ์๊ณ , ์๋ฎฌ๋ ์ด์์ ์ ํ ์ ํธ ์ธก์ ๊ณผ ๋ฐ์ฌ ์ ํธ ์ธก์  ๋ ์ํฉ์ผ๋ก ์ ํธ ๋ถ์์ด ๊ฐ๋ฅํ๋ค. ๋ฐ์ฌ ์ ํธ ์ธก์  ์ ์ผ์  ์ง์ ์ ๋ก๋ ์ํผ๋์ค๋ฅผ ๋ฌดํ๋๋ก ์๋ ฅํ์ฌ ์ข๋จ์ ๋ชจ์ํ  ์ ์๋ค.

์ทจ๋ํ ๊ธฐ์ค ์ ํธ์ ๋ฐ์ฌ ์ ํธ์ TFCC๋ฅผ ํตํด ์ํผ๋์ค ๋ถ์ผ์น ์ง์ ์ ํ์ธํ  ์ ์๊ณ  ์๊ทธ๋-๋น ๋ถํฌ๋ฅผ ํตํด ์๊ฐ-์ฃผํ์ ์์ญ์์ ์์ ์ฃผํ์๋ฅผ ์ถ์ ํ  ์ ์๋ค. ๊ธฐ์ค ์ ํธ์ TD๋ 150 $ns$, BW๋ 40 MHz, CF๋ 20 MHz๋ก ์ค์ ํ์๊ณ , ์ค์ฌ ์๊ฐ์ 500 $ns$๋ก ์ค์ ํ์ฌ ์คํ์ ์งํํ์๋ค. ๋ก๋ ์ํผ๋์ค์ ๋ฐ๋ฅธ IF ์ธก์  ์ ์ค๊ณ๋๋ ๊ธฐ์ค ์ ํธ๋ ๋ชจ๋ ๋์ผํ๋ค. ์ค๊ณํ ์๊ฐ ์์ญ์์ ๊ธฐ์ค ์ ํธ์ ์๊ทธ๋-๋น ๋ถํฌ๋ ๊ทธ๋ฆผ 3๊ณผ ๊ฐ๋ค.

์ ํ ์์๋ ์ ๋ก ์ ์์ ์ํฅ์ ๋ฐ๊ธฐ ๋๋ฌธ์ ์ผ์ด๋ธ ์ข๋จ์ ๋ก๋ ์ํผ๋์ค์ ๋ฐ๋ผ ์ ํ ์์๊ฐ ๋ฌ๋ผ์ง๋ค. ์ผ์ด๋ธ์ ์ดํ์ ๋ ๋ฐ ๊ณ ์ฅ์ ์ ์ ๋ฌด ๋ฑ ์ ๋ก ์ ์์ ์ํฅ์ ์ฃผ๋ ๋ค์ํ ์์ธ์ ๋ฐ๋ผ ์ ํ ์์๋ ๋ณํํ๋ค. ๋ณธ ์คํ์์๋ ๋ก๋ ์ํผ๋์ค๊ฐ ๊ฐ๋ฐฉ ์ํ์ผ ๋ ์๋ฎฌ๋ ์ด์์ ์งํํ์๋ค. ์ ํ ์์ ํ๋ผ๋ฏธํฐ๋ ํ 1๊ณผ ๊ฐ๋ค (18). ์ธ๊ฐ ์ ํธ์ ๋ํ ์ ํ ์ ํธ๋ 150 m, 300 m, 450 m, 600 m ๊ฐ๊ฒฉ์ผ๋ก ์ทจ๋ํ๋ค.

๊ทธ๋ฆผ. 2. Pxie๋ฅผ ์ด์ฉํ ๋ฐ์ฌํ ๊ณ์ธก๋ฒ ์์คํ

Fig. 2. Refletometry system using Pxie

๊ทธ๋ฆผ. 3. ์๊ฐ ์์ญ์์ ๊ธฐ์ค ์ ํธ์ ์๊ทธ๋-๋น ๋ถํฌ

Fig. 3. Reference signal and Wigner-Ville Distribution

ํ 1. ์ ํ ์์ ํ๋ผ๋ฏธํฐ

Table 1. Propagation constant parameters

 ํ๋ผ๋ฏธํฐ ๊ฐ $\dot\alpha_{0}$ $1.1216\times 10^{-10}$ $\dot\beta_{0}$ $5.5690\times 10^{-9}$ $\ddot\alpha_{0}$ $-2.1787\times 10^{-19}$ $\ddot\beta_{0}$ $-2.0324\times 10^{-19}$

๊ทธ๋ฆผ. 4. ์๊ฐ ์์ญ์์ ์ ํ ์ ํธ

Fig. 4. Propagation signal in time domain

์ธ๊ฐ ์ ํธ์ ์ ํ์ ๋ฐ๋ฅธ ์๊ฐ ์์ญ์์์ ๋ณํ๋ ๊ทธ๋ฆผ 4์ ๊ฐ์ผ๋ฉฐ ์๊ฐ ์์ญ์์ ์ ํ ๊ฑฐ๋ฆฌ๊ฐ ์ฆ๊ฐํจ์ ๋ฐ๋ผ ์ ํธ์ ๊ฐ์ ๊ฐ ์ปค์ ธ ์ ํธ์ ํผํฌ ๊ฐ์ด ๊ฐ์ํ๋ ๊ฒ์ ํ์ธํ  ์ ์๋ค.

์ ํธ๊ฐ ๋งค์ฐ ์์์ ธ ํํ์ผ๋ก๋ ๋ถ์ฐ์ ํ์ธํ  ์ ์์ด ์ ํ ์์๋ฅผ ์ด๊ณ๋ํจ์๊น์ง ๊ณ ๋ คํ ์ฃผํ์ ์ข์ ํํฐ $G(z,\:w)= e^{-jk(w)z}$์ ํ 1์ ์ฌ์ฉํ์ฌ ๊ฒฐ๊ณผ๋ฅผ ๋ํ๋๋ค. ์ ํ ๊ฑฐ๋ฆฌ์ ๋ฐ๋ฅธ ์ฃผํ์ ๋ถ์ฐ์ ํ์ธํ๊ธฐ ์ํด ๊ณ ์ ํธ๋ฆฌ์ ๋ณํ์ ์งํํ์ฌ ๊ธฐ์ค ์ ํธ๋ฅผ ์ฃผํ์ ์์ญ์์ ํ์ธํ์๊ณ  ๊ฒฐ๊ณผ๋ ๊ทธ๋ฆผ 5์ ๊ฐ๋ค. ๊ทธ๋ฆผ 5๋ ์ ํ ๊ฑฐ๋ฆฌ๊ฐ ์ฆ๊ฐํ ์๋ก ๊ณ ์ฃผํ ์ฑ๋ถ์ด ์ ์ฃผํ ์ฑ๋ถ๋ณด๋ค ๊ฐ์๊ฐ ์ฌํ๊ณ  ์ด๋ก ์ธํด ์ค์ฌ ์ฃผํ์๊ฐ ๋ณํ๋ฅผ ํ์ธํ  ์ ์๋ค. ์ด๋ก ์ธํด ๊ฑฐ๋ฆฌ๊ฐ ์ ํ๋๋ ๋์์ ์ ํ ์๋์ ๋ณํ๋ฅผ ์ ์ถํ  ์ ์๋ค.

๋ก๋ ์ํผ๋์ค๊ฐ ๊ฐ๋ฐฉ๋ ์ํ์ผ ๋ ์ ํ๋ ์ ํธ์ ์๊ทธ๋-๋น ๋ถํฌ๋ ๊ทธ๋ฆผ 6๊ณผ ๊ฐ๋ค. ๊ทธ๋ฆผ 6์์ ์ฅ๊ฑฐ๋ฆฌ๋ก ์ ํ๋ ์๋ก ๊ฐ์ ๋ฅผ ๊ฒช์ด 150 m ์ง์  ์ดํ๋ก๋ ์๊ทธ๋-๋น ๋ถํฌ๋ฅผ ํตํด ์์ ์ฃผํ์๋ฅผ ์ถ์ ํ  ์ ์๋ค. ์ด์ ๋ฐ๋ผ ๋ณธ ๋ผ๋ฌธ์์ ์ ์ํ ์ ํธ ๋ณต์ ์๊ณ ๋ฆฌ์ฆ์ ์ ์ฉํ์ฌ ์๊ทธ๋-๋น ๋ถํฌ์ ํฌ๊ธฐ๋ฅผ ์ธ๊ฐ ์ ํธ์ ๋์ผํ๊ฒ ์กฐ์ ํ ํ IF๋ฅผ ์ถ์ ํ์๋ค. IF ์ถ์  ์๊ณ ๋ฆฌ์ฆ์ด ์ ์ฉ๋ ์ ํ ์ ํธ์ ์๊ทธ๋-๋น ๋ถํฌ๋ ๊ทธ๋ฆผ 7๊ณผ ๊ฐ๋ค.

์๊ทธ๋-๋น ๋ถํฌ์ ๋ฐ๋ผ ์ธ๊ฐ ์ ํธ๊ฐ ์ฅ๊ฑฐ๋ฆฌ๋ก ์ ํ๋ ์๋ก ์ ์ฃผํ ๋ถ๋ถ๋ณด๋ค ๊ณ ์ฃผํ ๋ถ๋ถ์์ ๋ถ์ฐ์ด ํฌ๊ฒ ์ผ์ด๋จ์ ํ์ธํ  ์ ์๋ค.

๊ทธ๋ฆผ. 5. ์ ํ ์ ํธ์ ์ฃผํ์ ์๋ต

Fig. 5. Frequency response of propagation signal

๊ทธ๋ฆผ. 6. ์ ํ๋ ๊ธฐ์ค ์ ํธ์ ์๊ทธ๋-๋น ๋ถํฌ

Fig. 6. Wigner-Ville Distribution of propagated signal

๊ทธ๋ฆผ. 7. ์๊ทธ๋-๋น ๋ถํฌ์์ ์ถ์ ํ IF

Fig. 7. IF estimation in Wigner-Vllie Distribution

๋ก๋ ์ํผ๋์ค๊ฐ ๊ฐ๋ฐฉ๋ ์ํ์์ ์ ํ ๊ฑฐ๋ฆฌ๊ฐ ์ฆ๊ฐํ ์๋ก ์์ ์ฃผํ์์ ๊ธฐ์ธ๊ธฐ๊ฐ ๊ฐ์ํ๊ฒ ๋๋๋ฐ ์ด๋ ์ ํ ์์์ ๋ฐ๋ผ ์ ํธ๊ฐ ์ ํ๋ ์๋ก ๊ณ ์ฃผํ์ ๋ถ์ฐ์ด ์ฌํด ์ ์ฃผํ๋ณด๋ค ๋์ฐฉ ์๊ฐ์ด ๋ฆ์ด์ ธ ๊ธฐ์ธ๊ธฐ๊ฐ ๊ฐ์ํ๊ฒ ๋๋ค. ๋ก๋ ์ํผ๋์ค๊ฐ ๊ฐ๋ฐฉ ์ํ์ผ ๋ ์์ ์ฃผํ์์ ๊ธฐ์ธ๊ธฐ๋ ํ 2๊ณผ ๊ฐ๋ค.

ํ 2. ์ ํ ๊ฑฐ๋ฆฌ์ ๋ฐ๋ฅธ IF์ ๊ธฐ์ธ๊ธฐ

Table 2. Slope of IF along propagation distance

 ์ ํ ๊ฑฐ๋ฆฌ ์์ ์ฃผํ์์ ๊ธฐ์ธ๊ธฐ 0 [ $m$ ] $1.061\times 10^{15}$ 150 [ $m$ ] $1.390\times 10^{15}$ 300 [ $m$ ] $2.924\times 10^{15}$ 450 [ $m$ ] $-3.455\times 10^{16}$ 600 [ $m$] $-5.326\times 10^{15}$

## 4. ๊ฒฐ ๋ก

๋ณธ ๋ผ๋ฌธ์์๋ ์ฅ๊ฑฐ๋ฆฌ ์ ํ์ ๋ฐ๋ฅธ ์ ํธ์ ๊ฐ์์ ๋ถ์ฐ์ด ๊ณ ๋ ค๋ ์์ ์ฃผํ์ ์ถ์  ์๊ณ ๋ฆฌ์ฆ์ ๊ฐ๋ฐํ์์ผ๋ฉฐ ์ ํ ์๋์ ๊ฒฝํฅ์ฑ์ ํ์ํ๊ณ  ์ฅ๊ฑฐ๋ฆฌ ์ ๋ก์ ์ ์ฉ ๊ฐ๋ฅํ ์๋ฎฌ๋ ์ดํฐ๋ฅผ ๊ฐ๋ฐํ์๋ค. ๊ฐ์๊ฐ ์ผ์ด๋ ์ ํธ์ ์ ํธ ๋ณต์ ์๊ณ ๋ฆฌ์ฆ์ ์ ์ฉํ์ฌ ์๊ทธ๋-๋น ๋ถํฌ์ ํฌ๊ธฐ๋ฅผ ์กฐ์ ํ ํ ์๊ทธ๋-๋น ๋ถํฌ๋ฅผ ํตํด ์๊ฐ-์ฃผํ์ ์์ญ์์ ์์ ์ฃผํ์๋ฅผ ์ถ์ ํ์๋ค. ์ ํ ์๋๋ ์์ ์์์ ์ํด ๋ณํํ๋ฉฐ ์ ํ ๊ฑฐ๋ฆฌ๊ฐ ์ฆ๊ฐํ ์๋ก ๊ฐ์ ๋ฐ ๋ถ์ฐ์ด ์ฌํด์ง๋ฉฐ ๊ณ ์ฃผํ ์ฑ๋ถ์ด ์ ์ฃผํ๋ณด๋ค ๋ง์ด ์๊ณก๋๋ฉฐ, ์ด์ ๋ฐ๋ผ ์ฃผํ์ ์ฑ๋ถ ๋ณ ์ ํ ์๋๊ฐ ๋ณํํ๋ค. ์ด๋ ๊ณ ์ฅ์  ํ์ง ์ฑ๋ฅ์ ์ ํ๋ก ์ด์ด์ง๋ฉฐ ์ด๋ฅผ ํด๊ฒฐํ๊ณ ์ ์ฃผํ์์ ๋ฐ๋ฅธ ์ ํ ์๋๋ฅผ ๋ณด์ ํ๋ ์๊ณ ๋ฆฌ์ฆ์ ๊ฐ๋ฐ์ด ํ์ํ๋ค. ๋ํ ์ ํธ ๋ณต์ ์๊ณ ๋ฆฌ์ฆ์ ๊ธฐ๋ฐ์ผ๋ก ๋ณด์ ํํฐ์ค๊ณ๋ฅผ ํ  ์์ ์ด๋ค.

### Acknowledgements

This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) : 2021R1A2C1095779. This research was supported by Korea Electric Power Corporation.(Grant number: R22XO05-03)

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## ์ ์์๊ฐ

##### ์ฑํ๋ชจ (Hyun-Mo Seong)

he was born in Daejeon, South Korea.

He has been receiving the B.S. degrees from the Department of Electrical Engineering, Hanbat National University, Daejeon, South Korea, since 2018.

His general research interests include condition monitoring based on machine/ deep learning, diagnosis and prognostics of power equipment, signal processing techniques, and time-frequency analysis.

##### ์ฌ์ฐ์ญ (Yeon-Sub Sim)

He was born in Daejeon, South Korea.

He received the B.S. degrees from the Department of Electrical Engineering, Hanbat National University, Daejeon, South Korea, in 2022, where he is currently pursuing the M.S. degrees.

His general research interests include asset management systems based on machine/deep learning and efficient data analysis for complex data and the related applications.

##### ์ฅ์น์ง (Seung Jin Chang)

He was born in Seoul, South Korea.

He received the B.S. and Ph.D. degrees from the Department of Electrical and Electronic Engineering, Yonsei University, Seoul, in 2010 and 2017, respectively.

In 2018, he joined the School of Electrical and Computer Engineering, Seoul National University, Seoul, as a Post-Doctoral Researcher.

In 2018, he also joined the Department of Electrical Engineering, Hanbat National University, Daejeon South Korea, as an Assistant Professor, where he is currently an Associate Professor.

His current research interests are characterized by condition monitoring based on machine/deep learning, diagnosis and prognostics of power equipment, including cables and batteries, applied signal processing techniques, and timeโfrequency analysis.