Digital Subscriber Lines (xDSL) Twisted-pair channel modeling Heinz Koeppl Graz, 15.11.2001 [email protected] Digital Subscriber Lines (xDSL)Twisted-pair channel modeling – p.1/29 Talk overview • Introduction to DSL (digital subscriber line) • Twisted-pair channel modeling • Transceiver front-end noise • Channel capacity • Hybrid circuits Digital Subscriber Lines (xDSL)Twisted-pair channel modeling – p.2/29 Types of DSL • IDSN (integrated services digital networks) • Started 1985 at AT&T • Used bandwidth : 80 kHz • Basic rate ISDN transports 160 kb/s • loop length up to 18 kft (5.5 km) Digital Subscriber Lines (xDSL)Twisted-pair channel modeling – p.3/29 Types of DSL • HDSL (high bit-rate DSL) • Started 1988 at AT&T • Used bandwidth : 200 kHz • basic HDSL rate: 800 kb/s • loop length up to 12 kft (3.7 km) Digital Subscriber Lines (xDSL)Twisted-pair channel modeling – p.4/29 Types of DSL • ADSL (asymmetric DSL) • Started 1989 at Bellcore • Used bandwidth : 1 MHz • ADSL3: <9 Mb/s downstream, <1 Mb/s upstream • loop length up to 12 kft (3.7 km) Digital Subscriber Lines (xDSL)Twisted-pair channel modeling – p.5/29 Types of DSL • VDSL (Very-high-bit-rate DSL) • Started 1994 • Used bandwidth : 15 MHz • 52 Mb/s for <1 kft • 13 Mb/s for <12 kft Digital Subscriber Lines (xDSL)Twisted-pair channel modeling – p.6/29 Subscriber loop environment • connects central office (CO) and end user • designed for 4 kHz voice band • ringing voltage up to 140 volts • Plain Old Telephone Service (POTS), analog phones • different wire gauge, installations (aerial,: : :) Digital Subscriber Lines (xDSL)Twisted-pair channel modeling – p.7/29 Bridged taps • open wire connected in parallel to loop • used for reaching future customers unterminated reflections • ! signal loss, distortions • ! • 80% of US loops have bridged taps Digital Subscriber Lines (xDSL)Twisted-pair channel modeling – p.8/29 Loading coils • series inductor in twisted pair loop • used for extending beyond 18 kft • flattens frequency response across voice band • low pass filtering • blocks xDSL signals • 15% of US loops have loading coils Digital Subscriber Lines (xDSL)Twisted-pair channel modeling – p.9/29 Talk overview • Introduction to DSL (digital subscriber line) • Twisted-pair channel modeling • Transceiver front-end noise Digital Subscriber Lines (xDSL)Twisted-pair channel modeling – p.10/29 Two-port modeling • yields accurate results for DSL <20 MHz • loop consists of cascade of different wire types V1 A B V2 V2 (1) = = Φ " I1 # " C D # " I2 # " I2 # Digital Subscriber Lines (xDSL)Twisted-pair channel modeling – p.11/29 Two-port modeling with V2 1 (2) T (f) = = I2 V1 A + B V2 and V2=V1 = Z2 = ZL the load impedance yields ZL (3) T (f) = AZL + B Digital Subscriber Lines (xDSL)Twisted-pair channel modeling – p.12/29 Two-port modeling Transfer function H(f) VL(f) VL(f) V2(f) Z1 (4) = H(f) = = T (f) Vs(f) V2(f) VS(f) Z1 + ZS with Z1 = V1=I1, input impedance of two-port Digital Subscriber Lines (xDSL)Twisted-pair channel modeling – p.13/29 Equivalent circuit deriving the ABCD parameters Figure 1: The transmission line equivalent ciruit. Digital Subscriber Lines (xDSL)Twisted-pair channel modeling – p.14/29 Transmission line equation @v(z; t) @i(z; t) (5) = Ri(z; t) + L − @z @t @i(z; t) @v(z; t) (6) = Gv(z; t) + C − @z @t Digital Subscriber Lines (xDSL)Twisted-pair channel modeling – p.15/29 Time harmonic equations with (7)v(z; t) = V (z)ej!t ; i(z; t) = I(z)ej!t < < dV (z) dI(z) = (R+j!L)I(z); = (G+j!C)V (z) − dz − dz (8) Digital Subscriber Lines (xDSL)Twisted-pair channel modeling – p.16/29 Time harmonic equations combining gives 2 2 d V (z) 2 d I(z) 2 (9) = γ V (z); = γ I(z) dz2 dz2 with (10)γ = α + jβ = (R + j!L)(G + j!C) = pZY p • frequency dependent propagation constant γ • attenuation constant α • phase constant β Digital Subscriber Lines (xDSL)Twisted-pair channel modeling – p.17/29 Time harmonic equations Solutions are + γz γz + γz γz (11)V (z) = V0 e− + V0−e I(z) = I0 e− + I0−e : Characteristic impedance + V0 V0− R + j!L (12) Z0 = + = = I0 I0− sG + j!C Digital Subscriber Lines (xDSL)Twisted-pair channel modeling – p.18/29 Matrix form for a given wire length d V (0) cosh(γd) Z0 sinh(γd) V (d) = 1 sinh(γd) cosh(γd) " I(0) # " Z0 # " I(d) # (13) Digital Subscriber Lines (xDSL)Twisted-pair channel modeling – p.19/29 Characteristic functions with V (d)=I(d) = ZL 1 (14) T = cosh(γd) + Z0 sinh(γd) ZL and input impedance V (0)=I(0) ZL + Z0 tanh(γd) (15) Z1 = Z0 Z0 + ZL tanh(γd) Digital Subscriber Lines (xDSL)Twisted-pair channel modeling – p.20/29 Characteristic functions Z1 (16) H(f) = T (f) Z1 + ZS and therefore Z0= cosh(γd) H(f) = Z0 Z0 ZS + tanh(γd) + Z0 1 + tanh(γd) ZL ZL (17) h i h i Digital Subscriber Lines (xDSL)Twisted-pair channel modeling – p.21/29 Bridged taps 1 0 (18) Φ2 = " 1=Zbt 1 # when terminated with open circuit cosh(γd) (19) Z = Z0 bt t sinh(γd) Digital Subscriber Lines (xDSL)Twisted-pair channel modeling – p.22/29 Loading coils 1 j!Lcoil (20) Φcoil = " 0 1 # when terminated with open circuit cosh(γd) (21) Z = Z0 bt t sinh(γd) Digital Subscriber Lines (xDSL)Twisted-pair channel modeling – p.23/29 Overall two-port (22) Φ = Φ0Φ1 ΦN · · · and the source voltage divider is 1 ZS (23) Φ0 = " 0 1 # Digital Subscriber Lines (xDSL)Twisted-pair channel modeling – p.24/29 RCLG are frequency dependent Approximate measurement fittings valid up to 20 MHz: • resistance R(f) = a + bpf d • inductance L(f) = c + pf conductance G(f) f • / • Capacitance is approximately constant Digital Subscriber Lines (xDSL)Twisted-pair channel modeling – p.25/29 Talk overview • Introduction to DSL (digital subscriber line) • Twisted-pair channel modeling • Transceiver front-end noise Digital Subscriber Lines (xDSL)Twisted-pair channel modeling – p.26/29 Transceiver front-end noise • Near end Cosstalk (NEXT) • Far end Crosstalk (FEXT) • Impulse noise (CO switching,...) Digital Subscriber Lines (xDSL)Twisted-pair channel modeling – p.27/29 NEXT/FEXT • NEXT: Crosstalk between a receiving path and a transmitting path a DSL transceiver at the same end of two different subscriber loops • FEXT: crosstalk between a receiving path and a transmitting path a DSL transceiver at opposite ends of two different subscriber loops • can be modeled by Unger model Digital Subscriber Lines (xDSL)Twisted-pair channel modeling – p.28/29 Useful links • Online book about DSL at www.paradyne.com • ADSL - forum www.adsl.com • Html-bases documentation of the talk http://snape.inw.tu-graz.ac.at/talks/dsl/ Digital Subscriber Lines (xDSL)Twisted-pair channel modeling – p.29/29.