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Microwave superconductivity

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					Microwave Superconductivity




1. Introduction
       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 Superconductivity 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.

      This topic describes the properties of superconductivity that can be exploited
in microwave and mm-wave technologies to yield components with appreciable
performance enhancement over conventional systems. Superconducting signal
transmission lines can yield low attenuation, zero-dispersion signal transmission
behavior for signals with frequency components less than about one tenth the
superconducting energy gap. No other known microwave device technology can
provide a similar behavior. Superconductors have also been used to make high
speed digital circuits, josephsons junction and RF and microwave filters for mobile
phone base stations.

2. Superconductivity
       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
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Heike Kamerlingh Onnes in 1911. Like ferromagnetism and atomic spectral lines
superconductivity is a quantum mechanical phenomenon. The electrical resistivity
of a metallic conductor decreases gradually as the temperature is lowered. The
temperature at which the transition to superconducting state occurs is known as the
critical temperature.




Fig1: zero resistance of super conductor




      However, in ordinary conductors such as copper and silver, impurities and
other defects impose a lower limit. Even near absolute zero a real sample of copper
shows a non-zero resistance. The resistance of a superconductor, despite these
imperfections, drops abruptly to zero when the material is cooled below its critical
temperature. Superconductivity occurs in a wide variety of materials, including
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simple elements like tin and aluminium, various metallic alloys and some heavily-
doped semiconductors. The common examples are niobium with Tc=9.2K.
however superconductivity doesnot occur noble metals like gold ,silver etc and
pure samples of ferromagnetic materials.

       The major properties shown by the super conductors are zero electrical
resistance and meissner effect.




2.1 Meissner effect:
        The Meissner effect (also known as the Meissner-Ochsenfeld effect) is the
expulsion of a magnetic field from a superconductor. Walther Meissner and Robert
Ochsenfeld discovered the phenomenon in 1933 by measuring the magnetic field
distribution outside tin and lead samples. The samples, in the presence of an
applied magnetic field, were cooled below what is called their superconducting
transition temperature. Below the transition temperature the samples cancelled all
magnetic field inside, which means they became perfectly diamagnetic. They
detected this effect only indirectly; because the magnetic flux is conserved by a
superconductor, when the interior field decreased the exterior field increased.




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          Fig2: meissner effect




      The meissner experiment demonstrated for the first time that
superconductors were more than just perfect conductors and provided a uniquely
defining property of the superconducting state. In fig2 shown the first one
represents the passing of magnetic field when T>Tc and second one shows
meissner effect at T <Tc.




2.2 High temperature superconductivity (HTS):
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      The major problem associated with superconductivity in earlier days was the
cryogenic burden or the difficulty in maintaining temperature below the critical
temperature. High-temperature superconductors (abbreviated high-Tc or HTS)
are materials that have a superconducting transition temperature (Tc) above 30 K,
which was thought (1960-1980) to be the highest theoretically allowed Tc. The first
high-Tc superconductor was discovered in 1986 by Karl Müller and Johannes
Bednorz, for which they were awarded the Nobel Prize in Physics in 1987.

      The interest towards superconductivity greatly increased after the discovery
in 1986 of a class of copper oxide material that shows superconductivity at
temperature near 40K.Rapid progress was made and the critical temperature
pushed to approximately 90-120K for these oxide-based high temperature
superconductors. Later hts was discovered in other materials like Lanthanum based
cuprate perovskite material with transition temperature of 35K, yttrium based
YBCO with transition temperature of 92K which was important because liquid
nitrogen could then be used as a refrigerant. Later highest temperature
superconductor was a ceramic material consisting of thallium, mercury, copper,
barium, calcium, and oxygen, with Tc=138 K ,iron based family of superconductor,
bismuth strontium calcium oxide or BSSCO with Tc=107K etc.




3. Theories of superconductivity:
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      Various theories have been developed to explain the principle of
superconductivity.



3.1 Ginzburg–Landau theory:
             In physics, Ginzburg–Landau theory is a mathematical theory used
to model superconductivity. It does not purport to explain the microscopic
mechanisms giving rise to superconductivity. Instead, it examines the macroscopic
properties of a superconductor with the aid of general thermodynamic arguments.
This theory is sometimes called phenomenological as it describes some of the
phenomena of superconductivity without explaining the underlying microscopic
mechanism.



3.2 BCS theory:
       In 1957 Bardeen, Cooper and Robert Schrieffer came up with theory called
the BCS theory of superconductivity. BCS theory is the first microscopic theory of
superconductivity. In the BCS framework, superconductivity is a macroscopic
effect which results from "condensation" of electron pairs, called Cooper pairs.
These nearly behave as bosons which, at sufficiently low temperature, form a large
Bose-Einstein condensate. At sufficiently low temperatures, electrons near the
Fermi surface become unstable against the formation of cooper pairs. Cooper
showed such binding will occur in the presence of an attractive potential, no matter
how weak. In conventional superconductors, such binding is generally attributed to
an electron-lattice interaction which is shown in fig 3(a) and 3(b)




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                    Fig 3(a)




                   Fig 3(b)

        Fig 3: The Electron-phonon interaction



       An electron moving through a conductor will attract nearby positive charges
in the lattice. This deformation of the lattice causes another electron, with opposite
"spin", to move into the region of higher positive charge density. The two electrons
are then held together with a certain binding energy. If this binding energy is
higher than the energy provided by kicks from oscillating atoms in the conductor
(which is true at low temperatures), then the electron pair will stick together and
resist all kicks, thus not experiencing resistance. Such a pair of electrons are known




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as Cooper pairs. Coupling and interaction between electrons can be represented by
Feynman diagram as in fig 4 shown below.

       For each superconducting material there is critical temperature (Tc) and
critical magnetic field (Hc) below which the material exhibits superconductivity or
the cooper pair exists. In addition to these there is critical current density (Jc)
which depends on metallurgy and physical condition of the specimen and it sets the
upper limit on the current that can be induced in specimen before the onset of the
generation of harmonic related signals that will degrade the performance of the
superconducting microwave device. The graphical representation of the statement
is shown in fig 5. The material shows superconductivity at points below the surface
shown in fig.




        Fig 4: Feynman dig.                       Fig 5: superconducting surface




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4. 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.




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                   Fig 6: band gap variation with temperature



        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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      As operating temperature closer to Tc the band gap also reduces. Hence the
superconductor will be more sensitive to temperature variations. So inorder to
avoid this operating temperature must be less than 2/3 of Tc. Thus for high
frequency application of superconducting materials the operating frequency of
device should be 10% or less of the frequency corresponding to energy gap of the
material and temperature must be less than 2/3Tc. For example in case of niobium
(Tc=9.2K) the band gap is about 670 GHz and can be operated at a maximum
frequency of 70GHz and temperature below 6K.




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5. Superconductor microwave device technology
      Superconducting materials are used for device fabrication since 1960. The
major advantage is in the field of attenuation and dispersion compared to the
copper transmission line. In case of copper transmission line the attenuation in the
frequency range from 10MHz to about 100THz varies smoothly. However for a
superconducting niobium-niobium oxide-niobium parallel plate transmission line
operating near 4K, the attenuation at low frequency is less than copper and rises as
frequency squared up to frequencies above 100GHz whereas magnitude remain
below that of copper transmission line. For further increasing frequency the
attenuation abruptly increases by about two order of magnitude at a frequency that
corresponds to energy gap of niobium, approximately 670GHz. At still frequency
attenuation follows square root frequency dependence for normal metal with
magnitude about a factor of ten larger than copper at room temperature.

      The phase velocity of signal increases with increasing frequency in a
monotonic fashion through out frequency region for copper. However for
superconducting transmission line the phase velocity is constant up to 100GHz.
For further increase in frequency the phase velocity dips goes through minimum
below 1000GHz and then increases with increase in frequency. Thus complex
signals with frequency components can propagate along superconducting
transmission line without dispersion.




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6. Superconducting communication filters
       The choice of resonator technology for microwave filter is influenced by the
insertion loss and the selectivity. To achieve higher selectivity more number of
resonators are required which increases the insertion loss. When conductor losses
are dominant it is possible to drastically reduce the resonator size by using
superconductors. Superconductivity can yield very high Q value resonator and
filter at reduced volume compared with that realized using conventional
technologies. The inherent advantage of the above property is that

     The volume of the entire system can be reduced.

     Due to low losses, highly complex filters with many poles can be built with
      low insertion loss.

     The cryogenic environment for the hts filter, Improves the performance of
      other components in the system like the low noise amplifier. Noise figure of
      the system is reduced.

     The interference problem can be minimized by the use of hts filter.

    These characteristics have made HTS technology attractive to the wireless
communications vendors, who frequently have strong interference problems,
which can be minimized by the use of an HTS filter and the lower noise figure of
the cryogenic system. The HTS filter system comprises a very high selectivity,
low-loss HTS filter followed by an extremely low noise, cryogenically cooled
semiconductor preamplifier. The hts filter circuit connects the base station antenna
to the input of the base station receiver. Its purpose is to minimize the
degradation of signal-to-noise ratio (SNR) that occurs in the base station receiver
as a natural consequence of detecting and extracting the information content of the
desired signals. The hts filter accomplishes this by performing two circuit
functions extremely well:

     Efficiently and effectively rejecting out-of-band interference and
     Amplifying in-band signals with extremely low added noise and high
      linearity.
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    6.1 Ultra selective HTS filter:
       For example an ultra-sharp skirt filter that has 22 poles and 10 transmission
zeros. The HTS filter is fabricated using thin film and microstrip technology. HTS
thin film for filter application requires homogeneous large area double sided sided
film with small surface resistance. HTS film is deposited on wafer substrate with
acceptable microwave properties like MgO. The substrate must have
            Suitable crystalline structure
            Low microwave loss tangent
            Non reactive with HTS material
            Tolerable thermal expansion match with HTS.
The YBCO deposition is done by sputtering or organometallic chemical vapour
deposition or pulsed laser deposition or thermal evaporation. Such a thin film is
shown in figure.




                      Fig 7: HTS thin film

        Advanced folded half wavelength resonator or clip resonators are used in the
design of filter inorder to reduce the area of filter and to increase performance of
filter. by clip resonator a reduction 54% area is obtained and 22 resonators can be
accommodated in 2-in wafer. Due to small loss of HTS such a close arrangement
of arms of resonator is possible and hence reduction in area. The clip resonator
structure and the arrangement in filter is shown in fig.


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                                   Fig 8: clip resonator




                              Fig 9: clip resonator arrangement



      Quadruplet coupling was used inorder to produce required number of
transmission zeros near band edge.it used inorder to maximize the number of zeros
while keeping the structure simple to design and tune. The coupling is shown in fig
below


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                         Fig 10: quadruplet coupling structure




      The performance of the filter is able to surpass the performance of a 50-pole
Chebyshev filter. The 22-pole filter is used to meet one of the existing 3G wireless
bands; a 1950-MHz center frequency and a 20-MHz bandwidth. The comparison
between the responses of the two filters, their insertion loss and group delays are
shown below




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           Fig 11: Responses of 22 pole HTS filter & 50 pole chebyshev filter




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        The roll off is same for both filters in the initial portion. But due to the
presence of zeros at transmission edge, the roll off become more steep up to 90dB
level. Due to low losses the insertion loss curve is close to zero in the pass band of
HTS filter. In HTS filter the curve is flat in wide region because of the distribution
of poles near the band edges. The group delay is depending on the pole density.
Since in HTS filter poles are distributed in band edges the group delay is low and
flat in the passband. This minimizes dispersion of signal.




7. Superconducting digital microwave technology

       Today the computers are operating at a speed of several GHz, so even the
digital technology is penetrating into microwave range. Eventhough the
conventional digital circuits are not able to operate in GHz range, the
superconducting circuits work in low GHz range. An active device in this field is
the two terminal Josephson junction, which has a trilayer SIS structure, where two
superconducting layers are the terminals of the device. The device can work either
in superconducting mode or in normal mode.

      Assume that the junction is cooled through the superconducting transition
temperature while there is no voltage applied to the device. If one now applies a
current to the device, a supercurrent will flow through the device, and as the
current is increased, the operating point will move vertical upward along the V=0
axis. When the current exceeds the critical current of the Josephson structure, the

device will switch into the normal state and a increase in voltage occurs.



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      If the applied current is then decreased, the operating point will move down
along the finite voltage branch until the zero voltage point is reached at the origin
of the current versus voltage curve, when the device will switch back into the
superconducting state.



       To produce digital circuit with josephson device one or more josephson
junctions are embedded in an otherwise superconducting circuit, and the circuit is
configured so that the Josephson junction(s) can be switched in and out of the
normal state by the action of a control current flowing through a control electrode.

       Because the Josephson device has zero resistance (and thus, zero loss) for a
good portion of the operating cycle, Josephson digital circuits exhibit very low
electrical losses. Josephson devices can switch at 770GHz range. Hence the
josephson digital devices has got high speed, low loss and low figure of merit.

    The superconductor digital technology is used in ADCs. The ADCs capable of
digitization of signals up to 21GHz. Application of microwave frequency ADC is
in microwave receiver with direct digitization at front end. So the amplifier and
down converters at the front end of receiver can be removed and ADC can be used
after LNA.




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8. Superconductivity in High-Energy Physics

      Microwave superconductivity is used in high energy particle accelerators
like cyclotron, it consist of electromagnets at edge of vacuum chamber. The
maximum speed of particle is limited by the magnetic field produced by magnet.
Superconducting magnets provide much higher magnetic field than air core iron
magnets. In order to increase the energy boost per transit superconducting cavities
were used which reduce the losses in walls of the cavity.

       The Large Hadron Collider by the European Organizations for Nuclear
Research (CERN) in Geneva, Switzerland, has about 20 superconducting RF
cavities along its 27-km circumference circular path. The next large particle
accelerator, which is currently under development, is called the International
Linear Collider (ILC), which will contain about 16,000 superconducting RF
cavities along its 31-km linear path.




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9. Conclusion


       Superconductivity is one of the most exotic phenomena observed in nature
and it can have an impressive impact on the performance of passive and active
devices operating throughout the microwave and mm wave region of the spectrum.
In these frequency ranges,
     The electrical losses are superconductors are significantly less than the
       losses for normal conducting metallization in device and component
       applications.
     Active superconducting Josephson device technology is inherently low loss
       and has demonstrated operation in excess of 700 GHz.

       There has been much progress in the recent years to exploit
superconductivity in selected microwave and mm-wave system. The HTS filters
having low loss, sharp roll off have been designed for wireless communication
systems to filter out of band interference and reduce noise. HTS found application
in high energy particle accelerators, ADC’s etc.
       In addition to advances in superconducting technology there have been gains
in cryogenic refrigeration community that can provide energy efficient, reliable
cryogenic refrigeration systems.




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10. References

             Martin Nisenoff and Jeffrey M.Pond, “superconductors and
              microwaves”, IEEE microwave magazine, may 2009

             G. Tsuzuki, S. Ye, and S. Berkowitz, “Ultra-sensitive 22-pole, 10
              transmission zero superconducting bandpass filter surpasses 50- pole
              Chebyhshev filter,” IEEE Trans. Microwave Theory Tech.


             Superconducting Microwave Filter Systems for Cellular Telephone
              Base Stations, IEEE Trans. Microwave Theory Tech., May 2004


             Superconductor Technologies, Inc., Santa Barbara, CA. [Online].
              Available: www.suptech.com

             L. A. Abelson and G. L. Kerber, “Superconductor integrated circuit
              fabrication technology,” Proc. IEEE, vol. 92, no. 10, pp. 1517–1531

             www.wikipedia.org




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11. Discussion:

     Why cooper pairs are having less energy than normal electrons?

           Cooper pair is the name given to two electrons (or other fermions) that
    are bound together at low temperatures in a certain manner. Arbitrarily small
    attraction between electrons in a metal can cause a paired state of electrons to
    have a lower energy than the Fermi energy. Some energy of electron is lost
    during interaction and it results in lattice vibrations called phonons. This causes
    reduction in energy of cooper pairs.

     Is super conductor different from perfect conductor?

             Superconductor is different from perfect conductor or ideal conductor.
    The meissner experiment demonstrated for the first time that superconductors
    were more than just perfect conductors and provided a uniquely defining
    property of the superconducting state.

     What are other cross-coupling structures?

             In addition to quadruplet coupling, various coupling structures present
    like Canonical structure, trisection structure, canonical asymmetric structure
    etc.




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