Lumped Elements

The electrical element resistance, R, is described in the time domain based on 

In the frequency domain, its impedance has only a real part  

In Equation 4.2, co is the frequency of the AC signal. Resistance in electrochemical systems includes ionic resistance, electronic resistance, charge-transfer resistance, and mass transfer resistance. The ionic resistance is sometimes expressed as ionic conductivity, using the unit of siemens per centimetre (S/cm), which is the reciprocal of the resistivity  

Electronic resistance is normally used to describe the movement of electrons within a conducting media, such as metal wires or conducting polymers. In fuel 

Charge-transfer resistance is the resistance that occurs when electrons transfer at the electrode/electrolyte interface. The charge-transfer resistance is dependent on the reaction, the electrode surface, and the electrode potential. In general, an increase in overpotential leads to a decrease in charge-transfer resistance. 

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Figure 2-75. Lumped element models of transmission line electrical characteristics.

Figure 15.8 shows the thermal scheme of one detector there are six lumped elements with three thermal nodes at Tu T2, r3, i.e. the temperatures of the electrons of Ge sensor, Te02 absorber and PTFE crystal supports respectively. C), C2 and C3 are the heat capacity of absorber, PTFE and NTD Ge sensor respectively. The resistors Rx and R2 take into account the contact resistances at the surfaces of PTFE supports and R3 represents the series contribution of contact and the electron-phonon decoupling resistances in the Ge thermistor (see Section 15.2.1.3). 

Seven simulations were carried out at temperatures ranging between 7 and 16 mK. Data used at the various temperatures for the lumped elements are plausible values estimated from very low-temperature measurements. They are reported in Table 15.2. 

The suggested procedure to arrive at this goal is presented in Fig. 3.1. It starts with the transfer of a certain microhotplate layout into a geometry model for a complex FEM simulation. This step is shown in Fig. 3.2 and will be explained in more detail in one of the next sections. A complex 3-d FEM simulation is then performed. The results of this simulation are used to produce a lumped-element model. This model is translated into a hardware description language (HDL). Using the resistances of the device elements such as the heater resistance, Rheat> and the resistance of the temperature sensor, Rx. co-simulations with the circuitry can be performed. 

Using the thermal resistance and the total heat capacitance, the dynamic equation for a lumped-element model in the linear regime can be written as ... 

Figure 5.8 Typical planar resonators being used as building blocks for filters lumped element (a), microstrip (b), folded microstrip with integrated capacitors (c), coplanar (d), and 2-D microstrip resonator. Omitting the capacitive gap in the folded microstrip design (c) leads to a ring resonator (square if circular shaped), which also represents a quite commonly used microstrip resonator design.

In the case of viscoelastic loaded QCM two approaches have been followed one methodology is to treat the device as an acoustic transmission line with one driven piezo-electric quartz layer and one or more surface mechanical load (TLM) [50, 51]. A simpler approach is to use a lumped-element model (LEM) that represents mechanical inter-actions by their equivalent electrical BVD circuit components [52, 53]. 

Since the transverse shear wave may penetrate the damping surface layer and the viscous liquid, additivity of the equivalent electrical elements in the BVD circuit is only valid under certain particular conditions. Martin and Frye [53] studied the impedance near resonance of polymer film coated resonators in air with a lumped-element BVD model, modified to account for the viscoelastic properties of the film. In addition to the elements shown in Fig. 12.3 to describe the quartz crystal and the liquid, L/ and Rf were added to describe the viscoelastic film overlayer. For a small... 

In most electrochemical applications the lumped element model (LEM) is a good approximation within 1% of the transmission line model (TLM) provided the quartz and film impedance condition ZfIZQ < 1 is fulfilled [54]. 

One can show [42] that, when the surface mechanical impedance is not large, the distributed model in the vicinity of resonance (where we make measurements) can be reduced to the simpler lumped-element model of Fig. 13.8(b). This modified Butterworth-van Dyke (BVD) electrical equivalent circuit comprises parallel static and motional arms. The static... 

For the films and conditions we have used, the transmission line and lumped element models give indistinguishable results. Fitting of the data of Fig. 13.7 yields G as a function of time. These values increase at short times (due to nucleation phenomena) to long time limiting values of G = 1.9 x 106 dyne cm-2 and G" = 3.0 x 108 dyne cm-2. These values of the shear modulus components show that, in dichloromethane, the PVF film is a very rubbery polymer in which there is considerable viscoelastic loss when the film thickness exceeds 1 p.m. 

Figure 3.5 Equivalent-circuit models to describe the near-resonant electrical characteristics of the resonator (a) distributed model (b) lumped-element model. (Reprinted with permission. See Refs. [7 14J. (a) 1994 American Institute of Physics and (b) 1993 American Chemical Society.)...

The equivalent circuits (Figure 3.5) can be used to describe the electrical response of the perturbed device. The lumped-element model. Figure 3.Sb, is most convenient to use. When the resonator has a surface perturbation, the motional impedance increases, as represented by the equivalent-circuit model of Figure 3.7. This model contains the elements C , Li, C, and Ri corresponding to the unperturbed resonator. In addition, the surface perturbation causes an increase in the motional impedance Z(n as described by the complex electrical element Ze in Figure 3.7a. This element is given by [12]... 

Figure 3.7 Lumped-element equivalent-circuit models for die peituibed resonator [14] ...

The speed of electro-optic devices is greatly determined by the dielectric properties of the electro-optic material. For instance, the bandwidth per modulating power (A//P) of a guided-wave lumped-element modulator is given by ... 

The known load characteristics and the desirability of the lowest possible turn ratio for the pulse transformer suggest the lumped element Blumlein-pulse forming network (PFN) configuration (Fig. 5.1). Ordinarily, a Blumlein-pulse forming... 

The Detector Noise Module calculates the Noise Equivalent Power (NEP) and the 1 // noise of the selected detection system. This module is flexible and different types of detectors will require the computation of different parameters. The detector selected for further development is the Lumped Element Kinetic inductance Detector (Doyle et al. 2008), LeKID, as it presents the most promising solution high sensitivity spectro-spatial interferometry. For the current version of the simulator, a single pixel and single mode detector is assumed for simplicity and computational reasons. 

One way of solving the problem of optical coupling THz radiation to a KID device is to use a Lumped Element KID (LeKID), which unlike its distributed counterpart shows no current variation across the device. This means the device itself can act as the absorber as well as the sensing element in a detector system. The device is based on a series LC circuit inductively coupled to a microstrip feed line. 

S. Doyle, J. Naylon, P. Mauskopf, A. Porch, C. Dunscombe. Lumped Element Kinetic Inductance Detectors, ed. by A. Karpov. Eighteenth International Symposium on Space Teiahertz Technology, p. 170 (2007)... 

S. Doyle, P. Mauskopf, J. Naylon, A. Porch, C. Duncombe, Lumped element kinetic inductance detectors. J. Low Temp. Phys. 151(1-2), 530-536 (2008). ISSN 0022-2291. doi 10.1007/s10909-007-9685-2... 

M. Roesch, A. Benoit, A. Bideaud, N. Boudou, M. Calvo, A. Cruciani, S. Doyle, H.G. Leduc, A. Monfardini, L. Swenson, S. Leclercq, P. Mauskopf, K.F. Schuster, for the NIKA collaboration. Development of Lumped Element Kinetic Inductance Detectors for NIKA. ArXiv e-prints, December 2012... 

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