Lumped circuit

Multilayer technology is exploited just as for multilayer capacitors (see Section 5.4.3) to EIA size specifications, and inductor chips can be bandoliered ready for surface mounting, typical inductance values lying in the range 1 nH to about 20 /rH. They find important applications as EMI suppressors as well as for a wide range of applications as a lumped circuit component in equipment of all types -communications, entertainment , computers, etc. (see Fig. 9.17). 

Further lumped circuit options include circuits that allow accurate measurement of the current in, and voltage across, the unknown impedance (thus allowing calculation of that impedance), and the auto balancing bridge (Agilent Technologies, 2003). 

In considering the methods of measurement we must distinguish two basic types, namely lumped-circuit and distributed-circuit methods. The aim of... 

At high frequencies the electromagnetic wavelength inevitably becomes comparable with sample dimensions, and lumped-circuit methods must be abandoned in favour of distributed-circuit methods in which the sample becomes the medium for propagation of electromagnetic waves. Relative permittivity and loss must then be obtained from the observed wavelength and attenuation characteristics. 

There are some general principles concerning the design of specimen holders for lumped-circuit methods, which should be discussed before going on to... 

Experimental results for Debye lumped circuit with Tq = 10 s (a) using l-coefficient transform, (b) using 5-coefficient transform (Reproduce by permission from Proc. Inst. Electrical a Electronic Eng., 1970, 117,1891)... 

The change in rf voltage at the detector due to a change in the loaded Q may be calculated easily from the equivalent lumped circuit for the resonator, where the resonance absorption may be modeled as a small series resistance 8R. The detector voltage is... 

It is our thesis that the loop-gap lumped circuit resonator introduced recently by us will eventually supplant microwave cavity resonators in ESR spectroscopy except for a few specialized applications [53,291-293], Figure 24 (from Ref. 291) shows this resonator. In a sense, this is a hybrid structure midway between low-frequency lumped circuits where a capacitor and an inductor are connected by a transmission line, and high-frequency distributed circuit cavity resonators where the electric and magnetic... 

For relatively short lines, as might be of interest in interconnections on a microcircuit chip, a lumped circuit analysis is appropriate, and the performance can be estimated from an RC time constant. Here it is not sufficient to consider only the interconnect line resistance in the total resistance R. The effective output impedance of the CMOS device also contributes and is a key feature which limits the leverage of the superconductor. 

The methods listed in Table 7-1 for the frequency range above 108 Hz are referred to as distributed circuit methods. The analysis of the circuits in such methods is not so straightforward as in the case of the lumped circuit methods and the sample cell and geometry are considerably more complex also. 

Figure 2.7 Lumped circuit diagram for a reflection cavity...

Figure 2.9 Schematic lumped circuit diagram for a transmission cavity...

As already mentioned, the lumped-circuit technique is the most widely used by the research community [16]. The dielectric response is measured in parallel-plate or coaxial geometry as an association of resistances (R) and capacitances (C) in parallel or series. In a.c. measurements only, the parallel and series electrical circuits can be forced to be equivalent [20] giving for the admittance, T((d) and impedance Z(co), the following equations ... 

While in lumped-circuit methods the dielectric response is measured in the frequency domain, following the ajpplication of a sinusoidal alternating electrical field, for frequencies below 10 Hz it is advantageous to cany out the measurements in the time domain because it is less time consuming. The polarization or depolarization current following the application of a step-like electrical field is measured as a function of time. 

Time-resolved measurements on linear systems may be represented in many ways. For example, in the Nyquist representation, the transfer function H m) is plotted as a point in a two-dimensional plane having coordinates [Re(//) and Im(//)j, for each frequency measured. In specific cases, the transfer function may be represented also by an equivalent electrical circuit. This is a combination of lumped circuit elements (resistor, capacitor, etc.) having the same perturbation-response behavior as the system studied. 

Figure 33.5. Test circuit involviiig lumped circuit elements. Nominal values are the numbers on top, while those in parentheses are CNLS estimates. (Reprinted from J. R. Macdonald, J. Schoonman, and A. R Lehnen, Solid State Ionics 5, 137-140, 1981.)...

To examine the phenomena more closely a transformer circuit is shown schematically in Fig. 1. The primary winding is connected through the lumped circuit resistance to a voltage supply. The secondary winding, coupled to the same core, is connected to a lumped secondary circuit resistance and to an inductive load. This simplified transformer and load arrangement is sufficiently general to illustrate the desired principles of operation. The circuit equations for the primary and secondary circuits are as follows ... 

FIGURE 8.25 Lumped circuit model of a long polysilicon line. 

This model contains lumped circuit elements and one Warburg impedance, and its parameter set has six elements P= [ R2,R i,R, Ci,C, Q. In the Nyquist plot this model results in two symmetric semicircles and a -45° diffusion branch shifted on real axis with the value of the series resistance R. Figure 5 shows the electrical equivalent circuit and the impedance is given... 

Dielectric Analysis Based on Lumped Circuit Methods Frequency Response and Impedance Analysis... 

A biological material (a dielectric) can be exposed to electric or magnetic fields in frequencies from direct current (OHz) to x-rays (wlO Hz). From direct current to ac frequencies up to about 8 Hz, lumped circuits (composed of serial and parallel resistances and capacitance elements) are used to measure... 

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