Four-Terminal Parameter

The unknown coefficients Vf and in the general solution expressed as Equation 1.110 are determined from boimdary conditions. There are many approaches to obtain voltage and current solutions in a multiconductor system. The most well-known method is a four-terminal parameter (f-parameter) method of a two-port circuit theory. Also, an impedance parameter (Z-parameter) and an admittance parameter (Y-parameter) are well known. It should be noted that the F-parameter is not suitable for the application in a high-frequency region, while Z- and Y-parameter methods are not suitable to deal with low-frequency phenomena because of the nature of hyperbolic functions. 

are the voltage vectors at the sending and receiving ends in a multiconductor system 

The coefficients Fj to F4 in a multiconductor system are obtained in the same manner as those in Equation 1.87 taking care of a matrix form from Equations 1.110 and 1.111  

It should be noted that the order of the products in the earlier equation cannot be changed as has been done for a single conductor. Thai is, 

Equation 1.163 cannot be solved directly from a given boundary condition unless the coefficients in Equation 1.164 are calculated. By applying the modal transformation explained in the previous sections. Equation 1.163 is rewritten as 

---

Ametani, A. 2008. Four-terminal parameter formulation of solving induced voltages and currents on a pipeline system. lET Sci. Meas. 2. Technol. 2(2) 76-87. 

The four-terminal parameter (F-parameter) of a two-port circuit illustrated in Figure 1.18 is expressed in the following form ... 

This section describes an analytical method of calculating induced voltages and currents in a complex induced circuit, such as a cascaded pipeline with a few power lines, based on a conventional four-terminal parameter (f-parameter) formulation. The F-parameter formulation itself is well known, and it is straightforward to write a theoretical formula of the F-parameter for a multiphase circuit [38,45]. Thus, the calculation of the induced voltages and currents require a computer, that is, a software such as the EMTP. The method explained here replaces the multiphase F-parameter by a singlephase parameter by introducing an artificially induced current. The method is applied to a cascaded pipeline where the circuit parameters, the induced currents, and the boundary conditions are different in each part of the pipeline. The basic characteristic of the induced voltage and current distribution... 

The kinetic copolymerization models, which are more complex than the terminal one, involve as a rule no less than four kinetic parameters. So one has no hope to estimate their values reliably enough from a single experimental plot of the copolymer composition vs monomer feed composition. However, when in certain systems some of the elementary propagation reactions are forbidden due to the specificity of the corresponding monomers and radicals, the less number of the kinetic parameters is required. For example, when the copolymerization of two monomers, one of which cannot homopolymerize, is known to follow the penultimate model, the copolymer composition is found to be dependent only on two such parameters. It was proposed [26, 271] to use this feature to estimate the reactivity ratios in analogous systems by means of the procedures similar to ones outlined in this section. 

If the effect of the zones proximal to the current carrying electrodes and the polarization impedance of the electrodes themselves are to be reduced, the four-electrode system is preferred. Such four-electrode systems correspond to a two-port, four-terminal network equivalent (see Section 8.1). Because there are two ports, these systems actually measure transfer parameters between the ports. This means that if for instance impedance is measured to 0 O, this does not necessarily imply high-conductivity tissue, but rather no signal transfer from CC to PU electrodes. 

However, if we excite the same series RC-circuit with a controlled current step and record the voltage across the RC circuit, the voltage will increase linearly with time ad infinitum. The time constant is infinite. Clearly, the time constant is dependent not only on the network itself, but on how it is excited. The time constant of a network is not a parameter uniquely defined by the network itself. Just as immittance must be divided between impedance and admittance dependent on voltage or current driven excitation, there are two time constants dependent on how the circuit is driven. The network may also be a three-or four-terminal network. The time constant is then defined with a step excitation signal at the first port, and the possibly exponential response is recorded at the second port. 

The relationships are not particularly difficult, but they are cumbersome, partly because four different parameters are involved, as opposed to two parameters for the terminal model.Similar to the reduction from the terminal to the ideal model, when the following requirement is met... 

In a final section, we return to the lumped kinetics expressions discussed in Section 16.2. We will use them to analyze transient kinetics of the FT reaction as a function of the four main parameters that control activity and selectivity CO coverage, rate of CO dissociation, rate of chain growth, and rate of hydrocarbon chain termination. 

---