Matick R.E., Transmission Lines for Digital and Communication Networks, IEEE Press, New York, 1995.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....skin depth of copper is 2m at 1GHz. Hence the resistance increases as the effective conductor cross section decreases due to skin effect. Similarly, since the flux inside the conductor decreases, the L int also decreases. The actual frequency dependent R and L expressions can be quite complicated [2,3,4]. For example, in the case of coaxial cables, these contain Bessel Functions and its derivatives. However, the high frequency behavior for a circular cross section conductor (of radius r 0 ) can easily be approximated as Even though R DC is small, because of skin effect the terms will vary as the ....

R. E. Matick, "Transmission Lines for Digital and Communication Network", 194-200

....= A2 = s2L,C s2LC, sRC, 4) R, L, and C are the line resistance, inductance, and capacitance per unit length, respectively. L, and C, are the coupling inductance and capacitance per unit length between line I and line 2. The minus sign in (3) and (4) occurs since C, is a positive value [11] [16]. V(x, s) and V2(x, s) are the Laplace transform of the voltages between line I and line 2, respectively, and ground. In order to simplify this analysis, a condition that the interconnect lines are loosely coupled is assumed, implying that Lm and Cm are small as compared to L and C such that the ....

R. E. Matick, Transmission Lines for Digital and Communication Networks, McGraw-Hill Book Company, 1969.

....These losses are often frequency dependent, which filters and limits the bandwidth of the signal. For example, at higher frequencies, current flows closer to the surface of the conductor hence reducing the area of current flow and increasing the resistive loss, a phenomenon known as skin effect [65]. The filtering effect varies with cable quality; with the high quality cables over the short distances used in this research, losses can be as low as 1dB m at 4GHz [18] 1. For lower loss on the line, a fiber optic cable, which is a channel that confines a propagating light wave, can be used to ....

R. Matick, Transmission lines for digital and communication networks 3rd ed., IEEE Press, 1997

....creating both signal integrity and timing uncertainty problems. When signal rise times are comparable to the round trip time of flight of the signal through the line, distributed transmission line characteristics become important and the line cannot be modeled as a single equipotential node [3] [23]. In this case, assuming the IC #1 IC #2 IC #N bus CLK Figure 2.1: Conventional bus block diagram conductor resistance is very small, the line can be modeled as a ladder network of infinitesimally small inductive and capacitive elements. The signal wave propagation velocity is then and the ....

R. Matick, Transmission lines for digital and communication networks, 3rd ed.,

....caused by the intrinsic bandwidth of the medium, and the desire to keep the latency through the link small. A. Cable Characteristics The bandwidth limitation of the cable depends on its physical characteristics: the size and construction of their conductor and shield, and the dielectric material [44]. The thickness of the conductor (wire gauge) determines the surface area in which the current can flow. Along with the conductivity of the metal, this area determines the conductor s resistance per meter. A signal current on the conductor requires a return path to close the circuit; the size of ....

Matick, Richard "Transmission lines for digital and communication networks" 3rd ed., IEEE Press, 1997

....From eq(A7) it is evident that a voltage gradient E t is supported by the flow of J t through the finite conductivity oe c of the conductor, being of the nature of an IR drop . The skin effect model allows calculation of an effective surface impedance which is, paraphrased from Matick [4], Z s = j p c =j oe c . In this model, eq(A7) takes the form J s = E s =2Z s where the transverse E s in the conducting skins can be represented as a voltage gradient Gammar t v s due to the IR drops in the two conductors. Accordingly, r t v s = Gamma2J s j p 0 c =j oe c : A15) Add ....

Matick, R.E., "Transmission Lines for Digital and Communications Networks", McGraw Hill, New York, 1969.

....of TL 1 and TL 2 .InTL 1 ,a V dd 2 wave propagates from NE 1 towards FE 1 , while in TL 2 ,aV dd 2 wave propagates from NE 2 towards FE 2 . Each one of these waves bounces back towards the near end point after it reaches the corresponding far end. This phenomenon is known as signal reflection [12]. For a higher magnitude of reflection, we ideally want the far ends to be an open circuit. Since the transmission lines have the same impedance both waves require the same time to travel back to the near end. If the switch opens exactly at the time when both waves travel back to the near end ....

Matick, R.E.: Transmission Lines for Digital and Communication Networks, IEEE

....in section 2.4.4. 2.4.1 Modeling Transmission Lines Transmission lines cannot be treated as lumped parameter circuits, so a distributed approach must be used. Distributed parameters are expressed as a function of length. A frequently used model for transmission lines is shown in Figure 6 ([17], ch.1) It consists of many small segments of length Dl containing lumped parameter elements. For this model to be valid, Dl must be much smaller than the wavelength of the applied signal. l c f = Background 17 L o is a distributed inductance in henries per meter, while C o is a distributed ....

.... L o Dl C o Dl Dl L o Dl C o Dl L o Dl C o Dl Background 18 One of the most important points that such an analysis can highlight is the fact that the impedance looking into a ladder network of inductive and capacitive elements, such as that shown in Figure 7, looks like a pure resistance ([17], p.7) This resistance is known as the characteristic impedance, Z o , of the transmission line, and it plays an important role in analyzing transients on transmission lines. The characteristic impedance is given by equation (2.2) Zo, equals a purely resistive impedance formed by the ....

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R.E. Matick, Transmission Lines For Digital And Communication Networks, New York: McGraw-Hill, 1995.

....this attenuation in more detail. 2.1 Skin depth determines line attenuation At high frequencies (above 100MHz) current is carried primarily on the surface of the conductor, dropping off to a value of e 1 at a depth of (1) where s is the conductivity of the material (5. 8E7 mhos m for copper) Matick 69] For a round conductor with radius r, this gives a resistance per unit length (ohms m) of dp fs ( 12 = Equalized 4Gb s Signalling Dally and Poulton (2) A thin strip guide with width w has a resistance per unit length of (3) In both cases the resistance is proportional to the square ....

Matick, Richard E. Transmission Lines for Digital and Communication Networks, McGraw-Hill, 1969.

....lines, mainly loss due to skin effect and to dielectric absorption. At high frequencies (above 100MHz) current is carried primarily on the surface of the conductor, dropping off to a value of e 1 at a depth of (1) where s is the conductivity of the material (5. 8x10 7 mhos m for copper) [6]. A thin strip guide with width w has a high frequency resistance per unit length of (2) However, the skin effect does not affect the conductor s resistance unless the frequency is above a frequency f s , where the skin depth is half the conductor thickness t, given by (3) Above this frequency, ....

Matick, R. E. Transmission Lines for Digital and Communication Networks, McGraw-Hill, 1969.

.... the routines for calculating the wave impedance and propagation constant of a transmission line, the input terminal admittance of the transmission line, given its length and load, and the complex output terminal voltage of the transmission line, given its length, load, and input terminal voltage [3]. line models is used to produce object code which is linked with the interpreter at compile time. It provides routines for calculating the transmission line parameters used by the xline routines from data read using the parser cable and microstrip commands. The cable command allows ....

R. E. Matick, "Transmission Lines for Digital and Communication Networks", New York, NY: McGraw-Hill, 1969, ch. 2.

....We assume that the change in the resistance of the line is negligible and focus on the extra capacitance caused by the coupling to the other line. The impedance due to the defect is Z d = R 1=j C d rather than the typical Z 0 = R 1=j C, and the reflection coefficient is (see for example, 8] [12], 16] Gamma d = Z 0 Gamma Z d Z 0 Z d which, for typical values of R and C, may be approximated as Gamma d C d =C Gamma 1 C d =C 1 and using the approximation for this extra capacitance in equation (3) above we obtain Gamma d (y; r) 8 : r S W Gammay if r y Gamma W 0 ....

R.E. Matick, Transmission Lines for Digital and Communication Networks, McGrawHill, New-York, 1969.

....this attenuation in more detail. 2.1 Skin depth determines line attenuation At high frequencies (above 100MHz) current is carried primarily on the surface of the conductor, dropping off to a value of e 1 at a depth of (1) where s is the conductivity of the material (5. 8E7 mhos m for copper) Matick 69] For a round conductor with radius r, this gives a resistance per unit length (ohms m) of dpf s( 12 = Equalized 4Gb s Signalling Dally and Poulton (2) A thin strip guide with width w has a resistance per unit length of (3) In both cases the resistance is proportional to the square ....

Matick, Richard E. Transmission Lines for Digital and Communication Networks, McGraw-Hill, 1969.

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Matick R.E., Transmission Lines for Digital and Communication Networks, IEEE Press, New York, 1995.

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R. Matick, Transmission Lines for Digital and Communication Networks, 3rd ed., IEEE Press, Piscataway, N.J., 1997.

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