Coaxial line cell

In the overlapping range 1500-15000MHz the results were obtained using a coaxial line cell terminated by a movable short circuiting plunger( 7). 

Figure 5. Simplified drawings of sample cells, (a) Open coaxial line cell (b) lumped capacitance cell (c) open-ended coaxial cell. (Reproduced with permission from Ref. 113. Copyright 2000, Marcel Dekker, Inc.)...

Figure 5 Simplified drawings of sample cells (a) open coaxial line cell (b) lumped capacitance cell (c) end capacitance cell.

Figure 3. Simplified schematic drawings of dielectric sample cells for reflection measurements, (a) Lumped capacitance cell, (b) End capacitance cell, (c) Open coaxial line cell, (d) Coaxial line cell with 50 ohm termination. Bottom sections in all cases are 50 ohm 7 mm precision coaxial lines.

An alternative procedure for evaluating dielectric properties of conducting systems can be illustrated by considering the use of Equation 11 for the coaxial line cell. For frequencies such that f(Z) = 1 and using = c+o-g/iwk as in IV.C., Equation 11 gives... 

The sample termination section or cell can be so simple as the end of a coaxial line inner conductor in contact with liquid filling a volume bound by the outer conductor or placed between the end and a grounded plane terminating the outer conductor. These and other arrangements have, again from transmission line theory, an admittance y. (ito) related to... 

The admittance of the sample cell terminated by the coaxial line is then given by... 

Figure 9 Equivalent circuit accounting for the electrode-polarization effect. Fq(0 is a rapidly increasing voltage step I(i) is a current Zq is the coaxial line impedance Cp is the capacitance of electrode polarization Cq is an empty cell capacitance filled with a dielectric sample of permittivity e and conductivity 1/R Vp(t) and Fg(i) are the voltages at the appropriate parts of the circuit. (From Ref. 72. With permission from Elsevier Science B.V.)...

The voltage V(t) and the eurrent I(t) observed at the sample cell [plate or cylindrical capacity (72, 73)] at the end of a coaxial line are presented by Eqs (23) and (24), respectively. In the case of conduetive solutions, Eqs. (23) and (24) show that both the voltage and the current flow are influenced by electrode polarization. The observed voltage V(t) monotonically increases in the TDS time window of observation and the ciurent I(t) monotonically decays. The electrode polarization correction is then obtained by subtracting the function from V(t). The incident pulse VQ(t) generally is an approximation to a step function with zero long-time slope, and the monotonically increasing behavior of V(t), associated with the correction Bt, is a component of the reflected pulse R(t). Since this component is subtracted in Eq. (23) from R(t), it needs to be added (+5/ /Zq) to I(t) in Eq. (24) and only after this can the correction of conductivity contribution by relation (27) be taken into ac-eount. 

In this even simpler cell shown in Figure 3b, the volume beyond the end of the coaxial line center conductor (supported by a disk with dimensions to match the coaxial line admittance) is filled with dielectric. The sample is thus in the fringing field at the end of the line, or more generally can be regarded as filling a section of circular wave guide used at frequencies below cutoff for wave propagation. 

Another simple and more versatile cell consists of filling a length d of coaxial line with the sample of interest, as shown in Figure 3c. If fringing effects at the end of this length of line are neglected, the input admittance of the cell is given from transmission line theory by... 

Under the action of an alternating electric field, the electrical response of a system having dipolar interaction may be characterized by the complex permittivity e = s ((o) — ie"(ro) as discussed above. Methods to measure the frequency-dependent permittivity use coaxial lines. The cell of our... 

To derive Eq. 12.40 ideal coaxial lines have to be assumed which is not the case in practice. Therefore, calibration procedures have to be applied. First, the influence of the measuring cell has to be obtained and considered during the calculation of the sample impedance. Second, the direction-dependent resistance of the line has to be measured by a second calibration procedure because it cannot be obtained by an equivalent circuit diagram. 

Figure 6.10. (a) The comb electrode geometry (b) RF sample cell suitable for dielectric coaxial line reflectometry measurements in the frequency range from IMHz to 10 GHz. 

Coaxial line reflectometry (6.3.3) 1 MHz-1 GHz The sample capacitor is placed at the end of a low-loss precision coaxial impedance is determined from complex reflection factor, measured with a microwave reflectometer at analyzer end of coaxial line Special sample cells are available for sample thicknesses ranging from 1 pm (thin films) to 20 mm (liquids or solid samples) The turnkey BDS concept 70 system, available from Novocontrol, combines the Agilent HP E4991A RF impedance analyzer with the BDS 2200 RF sample cell the complex permeability of polymers can also be measured by using a magnetic sample cell... 

Two basically different kinds of cell arrangement can be distinguished those in which the dielectric filled section terminates the coaxial pulse generating and sampling line, and those in which this section is itself terminated by a further admittance. The former are usually simpler and more useful, but the latter can have advantages for some purposes. If the sample section is symmetrical with respect to interchange of its input and output connections, and is terminated by an arbitrary admittance yj, its input admittance is given from network theory by... 

The most recent version of the cell (Ho et al., 1994) consists of two coaxial 75% platinum-25% iridium electrodes coated with platinum black. As can be seen in Figure 4.1, one electrode is external platinum-iridium lined high-pressure vessel (6.35 cm long and 1 cm volume) and the other, a thin platinum wire, insulated by a non-porous sintered AI2O3 or Al203/Zr02 tube (for alkaline media), welded to a platinum-iridium cylinder located in the center. 

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