MICROWAVE SUPER CONDUCTIVITY
      Superconductivity is a
phenomenon occurring in certain materials generally at very low
temperatures, characterized by exactly zero electrical resistance and
the exclusion of the interior magnetic field (the Meissner effect). It
was discovered by Heike Kamerlingh Onnes in 1911. Applying the principle
of S uper conductivity in microwave and millimeter-wave (mm-wave)
regions, components with superior performance can be fabricated. Major
problem during the earlier days was the that the cryogenic burden has
been perceived as too great compared to the performance advantage that
could be realized. There were very specialized applications, such as
low-noise microwave and mm-wave mixers and detectors, for the highly
demanding radio astronomy applications where the performance gained was
worth the effort and complexity. With the discovery of high temperature
superconductors like copper oxide, rapid progress was made in the field
of microwave superconductivity. 
Microwave Superconductivity 
According to BCS theory
cooper pairs are formed during superconducting state and it is having
energy slightly less than the normal electrons.so there exist a
superconducting energy gap between normal electrons and cooper pairs.
The band gap ‘E’ related to transition temperature by relation, 
E (at t=0K) =3.52*Kb*Tc
Where Kb – Boltzman’s constant
Tc – Critical temperature and
3.52 is a constant for ideal superconductor and may vary from 3.2 to 3.6 for most superconductors. 
       If a microwave or a
millimeter wave photon with energy greater than superconducting energy
gap incident on a sample and is absorbed by the cooper pair, it will be
broken with two normal electron created above the energy gap and zero
resistance property is lost by material. This property is shown in fig
below. For ideal with a transition temperature of Tc = 1K, the frequency
of the mm wave photon with energy equal to superconducting energy gap
at T=0K would be about 73GHz. For practical superconductors the photon
energy corresponding to energy gap would scale with Tc. For niobium
(Tc=9.2K) the most common material in LTS devices and circuits, the
frequency of radiation corresponding to energy gap is about 670GHz.
The zero resistance property of the superconductor is true for dc
(f=0). For finite frequencies there are finite but usually very small
electrical losses. The origin of these losses at non zero frequency is
due to the presence of two type of charge carriers in the
superconductor. Although cooper pairs move without resistance, the
carriers in normal state, those above energy gap behave as electrons in
normal conductor. As long as the operating frequency is below energy gap
the equivalent circuit for the superconductor is simply the parallel
combination of resistor and inductor, where resistor indicate normal
electrons and inductor the cooper pairs. These two carriers contribute
separately to the screening of fields.
          The characteristic decay
length of fields into a super conductor as determined by cooper pair
current is superconducting penetration depth. The penetration depth get
larger with increased temperature but only slightly close to Tc


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