Propagation Constants and Characteristic Impedance

Where I, y and Zc are the length, the propagation constant and characteristic impedance of the cable, respectively. These quantities can be either estimated from measurement as done in section 3. 

This section discusses propagation constants and characteristic impedance and admittance matrices in the modal domain after reviewing modal theory. 

Propagation Constants and Characteristic Impedance 1.3.4.1 Propagation Constants... 

Most textiles that are used for acoustic purposes show open porosity due to many interconnected pores or voids inside. The acoustic performance of a porous textile is mainly determined by its (air) flow resistivity, which is an intrinsic property of the textile and is a measure of how easily air can enter and pass through a porous textile material (Cox and D Antonio, 2009). Flow resistivity, also known as static flow resistivity, is related to acoustical properties and plays a critical role in the calculation of many intrinsic acoustic properties of porous textiles, such as the characteristic impedance, the propagation constant, and the sound absorption coefficient. In the S.l. Unit system, flow resistivity is quoted in units of Nsm" and is defined as the unit-thickness specific flow resistance o (Morfey, 2001),... 

There are many acoustical methods proposed for measuring flow resistivity (Delany and Bazley, 1971 Smith and Parott, 1983). A method that uses a standard impedance tube directly to measure the static flow resistivity without any additional requirements to tube modification or sensor location change is described in ISO Standard, 10534-2 (1998) and by Tao et al. (2015). In the method, the specific acoustic impedance on the front surface of the test specimen is measured first by using the traditional transfer function method with the test specimen being placed against and with a known interval to the rigid termination, and then the characteristic impedance, the propagation constant, and the static flow resistivity are calculated based on the obtained impedance transfer functions. 

Explain why the modal propagation constants and the modal characteristic impedances for modes 1 and 2 (aerial modes) on a transposed three-phase line become identical. 

It is well known that current is distributed near a conductor s surface when its frequency is high. Under such a condition, the resistance (impedance) of the conductor becomes higher than that at a low frequency because the resistance is proportional to the cross section of the conductor. This is called frequency dependence of the conductor impedance. As a result, the propagation constant and the characteristic impedance are also frequency dependent. 

Propagation constant F and characteristic impedance Zq of a conductor are frequency dependent as they are functions of the impedance of the conductor, as explained in Section 1.2. It should be noted that a and p in Section 1.3.4.1 (see Figure 1.10) are not frequency dependent (in the sense discussed in this section). The frequency dependence of the attenuation constant a(co) and phase constant P(co) in Section 1.3.4.1 comes from the definition of impedance Z and admittance Fof a conductor ... 

Line impedance, admittance, and characteristic impedance matrices involve nonzero, off-diagonal elements or mutual coupling, although the propagation constant matrix is diagonal. If one needs to diagonalize these matrices, modal transformation is required. 

Modeling of High-Speed Interconnections. Modeling the electrical behavior of an interconnection involves two steps. First, the transmission line characteristics, such as the characteristic impedance, propagation constant, capacitance, resistance, dielectric conductance, and coupling parameters, must be calculated from the physical dimensions and material properties of the interconnection. In addition, structures, such as wire bonds, vias, and pins, must be represented by lumped resistance (R), inductance (L), and capacitance (C) elements. 

The dielectric layers should be thick to achieve low interconnect capacitance (or high characteristic impedance), which reduces the power consumption of driver circuits and the RC delay of the Interconnect. Finally, the dielectric material should have a low dielectric constant (e ) to minimize the propagation delay (which is limited by the speed of light in the dielectric), the interconnect capacitance and the crosstalk between signal lines. 

The dielectric constant of the substrate is the prime property because the propagation speed of the signal is inversely related to it. At these speeds the system has to be designed as a transmission line which must match the impedance of the devices used. Impedance mismatch can lead to reflected signals, and hence to signal distortion. The characteristic impedance of the line is also dependent on the dielectric constant, and for the devices now being used higher impedances are required and, therefore, low dielectric constant substrates. In addition, it is also important to have low-loss materials to prevent distortion of the pulses. 

Each type of transmission line has different characteristic impedance and propagation constant which are functions of the complex permittivity of the substrate and superstate. The complex permittivity of methanol is extracted in this method for the frequency up to 40 GHz using a hybrid method that combines experimental data with finite element analysis. 

We seek the input impedance Zi of a transmission line with length di, characteristic impedance Zi, and propagation constant Pi, and that terminates at an arbitrary load impedance Zl (as shown in the insert of Fig. A.l). 

Combining equations 6 and 7, the characteristic impedance and the propagation constant can deduced ... 

The transmission hnes are characterized by their characteristic impedances and propagation constants, which can also be expressed in terms of the associated distributed parameters R,L,G, and C per unit length of the hnes (Magnuson, Alexander, and Tripathi, 1992). In general, the characteristic parameters are expressed as... 

Figure 1.24 shows an example of the frequency dependence of attenuation constant a and propagation velocity c for the earth-return mode and the self-characteristic impedance Zq for a phase of a 500 kV overhead transmission line. 

For this, the definition and concept of a propagation constant (attenuation and propagation velocity) and a characteristic impedance are introduced. 

The three-element Windkessel model approximates the pulse propagation quahty of the arterial system as a combination of an infinitely long tube, which is represented by its characteristic impedance, Z , in series with a parallel arrangement of a peripheral flow resistance, R, and a total arterial compliance, C,. Within a single cardiac cycle, these three parameters are generally assumed to be constants (Toorop et al, 1987). Recent studies have scrutinized this assumption. For example, compliance has been shown to depend on the level of arterial pressure (Bergel, 1961). Other studies have called into question the accuracy of the various methods employed to experimentally determine their values (Stergiopulos et al.. 

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