Planar resonators

As an example, for copper with a room temperature conductivity of 5.8 x 107(O m) 1 the surface resistance at 10 GHz is 26 mil, the skin depth is 0.66 pm. Therefore, the Q of a cavity resonator with a geometric factor of several hundred is in the 104 range. However, for planar resonators like the ones shown in Figure 5.8 the G values are only a few Ohms leading to Q values of only a few hundred. This is too small for many filter and oscillator applications. 

For bulk dielectrics, a dielectric resonator can be formed by a cylindrically shaped piece of dielectric material. Dielectric thin films are more difficult to investigate, in particular when the loss tangent is very small. Planar resonator techniques as well as specially designed dielectric resonators can be used to examine their properties. For high-temperature superconductors both dielectric resonators and planar resonators represent an ideal tool to examine their surface impedance values. 

Planar resonators - Equation (5.11) is not only valid for dielectric resonators. Any other type of electromagnetic resonator employing dielectric parts, like metal ceramic coaxial-type resonators (e.g. used as filters in mobile phones) and microstrip or coplanar resonators (used in microwave integrated circuits) have a Q-contribution due to dielectric losses. For the latter type of resonator the dielectric losses are negligible in comparison to metallic losses, unless high temperature superconducting metallization layers are applied. 

Planar resonators and microstrip and coplanar transmission lines represent the passive elements in almost any integrated circuit technology at first, on chip integration in socalled mmics (monolithic microwave integrated circuits) with SiGe or m/v semiconducting active... 

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.

Apart from their use as devices, planar resonators are of common use for microwave characterization of high-temperature superconducting films in a device-specific configuration. 

Using the above argument, the substituent is thought to control the relative magnitude of the two rate constants and and hence the yield of ion pairs and radical pairs. Possibly, the planar resonance form depicted as 11 in Scheme 2... 

Particle Positions Under Gravity and Other Forces Yosioka and Kawasima also considered the direction in which an acoustic force will act on a particle in suspension. The equilibrium position of a particle within the field will be determined by the resolution of this acoustic force and any other forces acting on the particle. Typically this would be gravity, although it applies to any force. In the case of a planar resonant field in which the positive x-axis points vertically upwards, the particle will be in equilibrium when... 

The symmetrical trigonal planar, resonance-stabilised ylid derivative (6.445c) has been synthesised by the route indicated in (6.446). 

While most work has used planar resonators, it is also possible to manipulate particles in alternative geometries such as cylindrical tubes [6]. 

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