Transmissin Characteristics f Overhead M/PLC Channels Athanasis G. Lazarpuls and Panaytis G. Cttis Wrkshp n Applicatins fr Pwerline Cmmunicatins, Octber 28
Slide 2 Outline Intrductin and Review f t date Research Effrts Single Cnductr ver Lssy Earth MTL Analysis Mathematical Analysis Multicnductr Cnfiguratin Mdal Analysis Derivatin f the Prpagatin Matrix BPL Channel Mdel Numerical Cmputatin, Results and Discussin
Slide 3 Intrductin Typical Greek Overhead M cnfiguratin [] Basic Cnfiguratins Undergrund cables Overhead lines Adverse prperties f the verhead M grid when viewed as a cmmunicatins medium
Slide 4 Review f t date Research (/2) Single Cnductr ver Lssy Earth A Thin Wire ver Earth Quasi-transverse-electrmagnetic (TEM) mdes Transmissin Characteristics In 926, the earliest slutins, Carsn [2] Assumptins and Restrictins In 956, exact mdal equatins fr very thin verhead wires, Kikuchi [3-4] In 972, exact mdal equatin fr thin wire abve earth, Wait [5-6] In 997, D Amre s slutin [7]
Slide 5 Review f t date Research (2/2) MTL Analysis Traveling Waves in MTL Mdes Cmmn Mde (CM) Differential Mdes (DM) Line Cupling Wire-t-Wire (W-T-W) Wire-t-Grund (W-T-G) (Fig.) (Fig.2)
Slide 6 Mathematical Analysis (/4) Multicnductr Cnfiguratin i. and I (matrices n ) ii. P (matrix n n) iii. and Y (matrices n n) iv. Secnd-rder differential equatins gverning prpagatin via a cnductr 2 d 2 dz ( Y ) P 2 d I 2 dz t ( Y ) I P I () v. PY
Slide 7 Mathematical Analysis (2/4) Mdal Analysis Matrix Line ltages and Currents I (n ) Matrix Mdal ltages m and Currents I m (n ) Prpagatin cnstants γ ( f ) α ( f ) + j β ( f ) i T m m i i (2) when T v and T I matrices f similarity transfrmatin [7-8] γ i, α i, β i and λ i frm P i,,n I T I I (3)
Slide 8 Mathematical Analysis (3/4) Mdal Analysis Equatin fr Mdal ltages General Equatin fr Mdal ltages where + + m n m z z m n m z z m n m e e e e n n M L M O M L M L M O M L M γ γ γ γ (4) (5.) () ( ) m m m z F ( ) ( ) T m (5.2)
Slide 9 Mathematical Analysis (4/4) Prpagatin Matrix Derivatin Prpagatin Matrix P [7], [9] Internal, External, Grund Impedance Admittance P ( ) ( ) + + Y + Y i e g c g Mde Characteristic Impedance and Admittance Matrices [ ] [ { } ] c Y T e e I diag λ md md K λn I mde mde T, m (6) (7)
Slide BPL Channel Mdel (/5) A priri and Deterministic (Mdal) Transfer Functin [-] Mdal Frequency Respnse [2] Reflectin and Transmissin Cefficients Multipath Channel exhibiting Frequency Selectivity Multipath r Ech Mdel (L [3-5] r mdal M [6])
Slide BPL Channel Mdel (2/5) SM Methd, Meng [7] (Fig.) in in in2 L b + + + + L b tanh tanh tanh tanh ( γl3 ) ( γl ) 3 ( γl2 ) ( γl ) ( in // in2 ) + tanh( γl ) + ( // ) tanh( γl ) in in2 2 (2) (Fig.2) L ( in // in2 ) Γ Γ2 L in // in2 ( ) +
Slide 2 BPL Channel Mdel (3/5) S-parameters [8] S in in + 3 3 2 (8) S 2 2 2 (9) E g 2 E g Shifting in the reference planes [9] E g in in + g 3 2 2 ( + Γ ) e γ l γ l3 + Γ e ( + Γ ) e γ l 2 γ l + Γ2 e 3 () ()
Slide 3 BPL Channel Mdel (4/5) Step : Evaluatin f the scattering matrices f the netwrk mdules S k k,..,n Step 2: Evaluatin f transmissin matrices f the netwrk mdules T k k,..,n Step 3: Evaluatin f the endt-end transmissin matrix T Step 4: Evaluatin f the endt-end transfer functin H(f)S 2 (f)
Slide 4 BPL Channel Mdel (5/5) T and S matrices fr the whle netwrk S T S S 2 2 S 2 S22 S2 S S S 2 22 N (2) T (3) S (4) k T k T T T 2 T 22 T2T T T2 T 2
Slide 5 Results and Discussin (/5) Three mdes (CM and DM i,i,2) Separate Channels fr each mde Attenuatin Cnstants and Phase Delays Attenuatin cnstant α (db/km) 5 5 Cmmn Mde Differential Mde Differential Mde 2 2 35 4 6 8 Frequency (MHz) (Fig.) (Fig.2)
Slide 6 Results and Discussin (2/5) M/BPL Tplgies Tplgy : L 5m, L 2 5m, L b m Tplgy 2: L 5m, L 2 2m, L 3 m, L 4 2m, L b 6m, L b2 m, L b3 6m (urban case) Tplgy 3: L 5m, L 2 2m, L 3 m, L 4 2m, L b 3m, L b2 5m, L b3 2m (rural case) Tplgy 4, the same as Tplgy 3 but with n branches ( LOS case)
Slide 7 Results and Discussin (3/5) Channel attenuatin (db) Channel attenuatin (db) Channel attenuatin (db) Channel attenuatin (db) Tplgy 2 4 6 2 3 4 5 6 7 8 9 Tplgy 2 2 4 6 2 3 4 5 6 7 8 9 Tplgy 3 2 4 6 2 3 4 5 6 7 8 9 Tplgy 4 2 4 (Fig.3) 6 2 3 4 5 6 7 8 9 Frequency (MHz) Tplgy, 2, 3 and 4 Channel attenuatin (db) Channel attenuatin (db) Channel attenuatin (db) Channel attenuatin (db) Tplgy 2 4 6 2 3 4 5 6 7 8 9 Tplgy 2 2 4 6 2 3 4 5 6 7 8 9 Tplgy 3 2 4 6 2 3 4 5 6 7 8 9 Tplgy 4 2 4 6 2 3 4 5 6 7 8 9 Frequency (MHz) (Fig.4)
Slide 8 (Fig.5) Results and Discussin (4/5) Tplgy 3 and LOS case (Fig.6) Multipath Prpagatin Waste f Usable Bandwidth Number and Behavir f Ntches
Slide 9 Results and Discussin (5/5) (Fig.7) (Fig.8) Percentage Wasted Bandwidth
Slide 2 References (/3). T. A. Papadpuls, Ch. G. Kaludas and G. K. Papagiannis, A Multipath Channel Mdel fr PLC Systems based n Ndal Methd and Mdal Analysis, in Prc. 27 IEEE Internatinal Cnference n Pwer Line Cmmunicatins and Its Applicatins, ISPLC 7, Pisa, Italy. 2. J. R. Carsn, Wave prpagatin in verhead wires with grund return, Bell Syst. Tech. J., vl. 5, pp. 539 554, 926. 3. H. Kikuchi, Wave prpagatin alng an infinite wire abve grund at high frequencies, Prc. Electrtech. J., vl. 2, pp. 73 78, Dec. 956. 4. H. Kikuchi, On the transitin frm a grund return circuit t a surface waveguide, in Prc. Int. Cngr. Ultrahigh Frequency Circuits Antennas, Paris, France, Oct. 957, pp. 39 45. 5. J. R. Wait, Thery f wave prpagatin alng a thin wire parallel t an interface, Radi Sci., vl. 7, pp. 675 679, Jun. 972. 6. J. R. Wait and D. A. Hill, Prpagatin alng a braided caxial cable in a circular tunnel, IEEE Trans. Micrw. Thery Tech., vl. 23, pp. 4 45, May 975. 7. M. D Amre and M. S. Sart, A new frmulatin f lssy grund return parameters fr transient analysis f multi-cnductr dissipative lines, IEEE Trans. Pwer Del., vl. 2, n., pp. 33 34, Jan. 997.
Slide 2 References (2/3) 8. R. P. Claytn, Analysis f Multi-Cnductr Transmissin Lines. New Yrk: Wiley, 994. 9. P. Amirshahi and M. Kavehrad, High-Frequency Characteristics f Overhead Multicnductr Pwer Lines fr Bradband Cmmunicatins, IEEE Selected Areas in Cmmunicatins, vl. 24, issue 7, pp. 292 33, Jul. 26.. S. Galli, T. Banwell, "A Nvel Apprach t the Mdeling f the Indr Pwer Line Channel - Part II: Transfer Functin and Its Prperties," IEEE Transactins n Pwer Delivery, vl. 2, n. 3, July 25.. T. Banwell, S. Galli, "A Nvel Apprach t the Mdeling f the Indr Pwer Line Channel - Part I: Circuit Analysis and Cmpanin Mdel," IEEE Transactins n Pwer Delivery, vl. 2, n. 2, Apr. 25. 2. D. K. Cheng, Fundamentals f Engineering Electrmagnetic. New Yrk: Addisn-Wesley, 992. 3. H. Philipps, Mdeling f pwerline cmmunicatin channels, in Prc. Int. Symp. Pwer Line Cmmun. Appl., 2, pp. 4 25. 4. H. Philipps, Develpment f a statistical mdel fr pwer-line cmmunicatin channels, in Prc. Int. Symp. Pwer Line Cmmun. Appl., 2, pp. 53 6. 5. M. immerman and K. Dstert, A multipath mdel fr the pwerline channel, IEEE Trans. Cmmun., vl. 5, n. 4, pp. 553 559, Apr. 22.
Slide 22 References (3/3) 6. P. Amirshahi and M. Kavehrad, Transmissin channel mdel and capacity f verhead multi-cnductr medium-vltage pwer-lines fr bradband cmmunicatins, in Prc. CCNC, Las egas, N, Jan. 25, pp. 354 358. 7. Meng H., Chen S., Guan Y.L., Law C.L., S P.L., Gunawan E., Lie T.T, Mdeling f transfer Characteristics fr the bradband pwer line cmmunicatin channel, Pwer Delivery, IEEE Transactins n Publicatin, July 24, lume 9, Issue 3, pages 57-64. 8. G. Gnzalez, Micrwave Transistr Amplifiers. Englewd Cliffs, NJ: Prentice- Hall, 997. 9. D. M. Pzar, Micrwave Engineering. New Yrk: Wiley.
Slide 23 Transmissin Characteristics f Overhead M/PLC Channels Athanasis G. Lazarpuls and Panaytis G. Cttis e-mail: thlazar@mail.ntua.gr Wrkshp n Applicatins fr Pwerline Cmmunicatins, Octber 28