Impedance characteristic

For a single-phase lossless overhead line in the air, the characteristic impedance is found from Equations 1.49 and 1.69  

The earlier equation shows that the characteristic impedance becomes independent of frequency for a lossless line and if is called surge impedance as defined in Equation 1.58. 

For a line with losses, the characteristic impedance is foimd as 

The real parf r and fhe imaginary parf x of fhe characferisfic impedance are found in fhe same way as we found a and p  

---

With appropriate caUbration the complex characteristic impedance at each resonance frequency can be calculated and related to the complex shear modulus, G, of the solution. Extrapolations to 2ero concentration yield the intrinsic storage and loss moduH [G ] and [G"], respectively, which are molecular properties. In the viscosity range of 0.5-50 mPa-s, the instmment provides valuable experimental data on dilute solutions of random coil (291), branched (292), and rod-like (293) polymers. The upper limit for shearing frequency for the MLR is 800 H2. High frequency (20 to 500 K H2) viscoelastic properties can be measured with another instmment, the high frequency torsional rod apparatus (HFTRA) (294). 

Generally the material response stress versus particle velocity curves in Fig. 8.6 are nonlinear and either a graphical or more complicated analytic method is needed to extract a spall strength, Oj, from the velocity or stress profile. When behavior is nominally linear in the region of interest a characteristic impedance (Z for the window and for the sample) specify material... 

The transfer coefficient yand the characteristic impedance Z are important parameters of the pipeline and consist of complex quantities, in contrast to the analogous data in Section 24.4. Substituting Z and Y from Eqs. (23-1) to (23-4) leads to ... 

If the pipeline ends within a close proximity region or if the pipeline is electrically cut off by an insulating unit, a ground must be connected at this point, whose grounding resistance corresponds roughly to the characteristic impedance, Z, according to Eq. (23-16) or with in Fig. 23-9. 

Reflection of acoustic waves incident on a planar interface between two isotropic media is most easily considered in terms of impedances. Acoustic characteristic impedance is defined as minus the ratio of traction to particle displacement velocity,... 

The MCP significantly enhances the speed and reduces the power consumption of the system. Because the ICs are spaced closely together, the interconnection length and propagation delay are greatly reduced, and faster clock speeds are possible. The short interconnections also reduce the need for line termination to prevent reflections. Characteristic impedance is better controlled within the MCP, and fewer signal reflection points exist. Finally, the power dissipation of output drivers can be reduced because of the lower resistive losses and capacitive load of the interconnection. 

A variety of transmission line structures can be fabricated in planar layers of conductor and dielectric (Figure 9). The stripline and offset stripline are best suited for multilayer structures. The offset stripline, with two orthogonal signal layers between a pair of reference voltage planes, eliminates one intermediate plane and achieves higher characteristic impedance for a given dielectric thickness than do two stripline layers but increases the possibility for crosstalk between layers. 

A closed-form expression for the characteristic impedance of a lossless stripline illustrates its dependence on the geometry and material properties of the interconnection (51)... 

The optimum characteristic impedance is dictated by a combination of factors. Interconnections with low characteristic impedance (<40 fl) cause high power dissipation and delay in driver circuits, increased switching noise, and reduced receiver noise tolerance (35). High characteristic impedance causes increased coupling noise and usually has higher loss. Generally, a characteristic impedance of 50-100 fl is optimal for most systems (35), and a ZQ of 50 fl has become standard for a variety of cables, connectors, and PWBs. For a polyimide dielectric with er = 3.5, a 50-fl stripline can be obtained with b = 50 xm, tv = 25 xm, and t = 5 xm. 

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. 

In general Z is complex and can be divided into a real and imaginary part Z = R+iX, where R is the resistive component and X is the reactive component. For materials where the attenuation of ultrasound is small the imaginary part can be ignored, so Z = R = pc, which is called the characteristic impedance. 

CDC 6000, 210 COPAS, 217 Caruso, 134 Cepstral distance, 30 Chaos measure, 61 Characteristic impedance, 433 Chipmunk effect, 322 Cholesky decomposition, 148 Chorusing, 298, 303 Circulant matrix, 126 Clarinet synthesis, 455 Clarity index, 98 Clicks (See Restoration)... 

Several quantities characterize the behavior of power lines as far as transient response is concerned. One important quantity is the characteristic impedance, expressed as ... 

In a power line that has no losses, the voltage and the current are linked by the characteristic impedance Z0. 

The other important consideration concerns the transmission of ultrasound (and other forms of energy) from one medium to another and the importance of impedance matching . When wave energy is transferred from one medium to another then a part is transmitted and the rest reflected. The ratio of reflected to transmitted energies depends on the characteristic impedances of the two media and the transmission is total if these are matched. In the case of acoustic waves the specific impedance (Z) of a medium is given by the product of the density p and the velocity of sound v. that is... 

EIS data analysis is commonly carried out by fitting it to an equivalent electric circuit model. An equivalent circuit model is a combination of resistances, capacitances, and/or inductances, as well as a few specialized electrochemical elements (such as Warburg diffusion elements and constant phase elements), which produces the same response as the electrochemical system does when the same excitation signal is imposed. Equivalent circuit models can be partially or completely empirical. In the model, each circuit component comes from a physical process in the electrochemical cell and has a characteristic impedance behaviour. The shape of the model s impedance spectrum is controlled by the style of electrical elements in the model and the interconnections between them (series or parallel combinations). The size of each feature in the spectrum is controlled by the circuit elements parameters. 

---