RF measurements I: signal receiving techniques

For the characterization of components, systems and signals in the RF and microwave range, several dedicated instruments are in use. In this paper the fundamentals of the RF-signal sampling technique, which has found widespread applications in 'digital' oscilloscopes and sampling scopes, are discussed. The key element in these front-ends is the Schottky diode which can be used either as an RF mixer or as a single sampler. The spectrum analyser has become an absolutely indispensable tool for RF signal analysis. Here the front-end is the RF mixer as the RF section of modern spectrum analysers has a rather complex architecture. The reasons for this complexity and certain working principles as well as limitations are discussed. In addition, an overview of the development of scalar and vector signal analysers is given. For the determination of the noise temperature of a one-port and the noise figure of a two-port, basic concepts and relations are shown. A brief discussion of commonly used noise measurement techniques concludes the paper.Comment: 24 pages, contribution to the CAS - CERN Accelerator School: Specialised Course on RF for Accelerators; 8 - 17 Jun 2010, Ebeltoft, Denmar

Spherical Fourier Transforms on Locally Compact Quantum Gelfand Pairs

We study Gelfand pairs for locally compact quantum groups. We give an operator algebraic interpretation and show that the quantum Plancherel transformation restricts to a spherical Plancherel transformation. As an example, we turn the quantum group analogue of the normaliser of SU(1,1) in $SL(2,\mathbb{C}$) together with its diagonal subgroup into a pair for which every irreducible corepresentation admits at most two vectors that are invariant with respect to the quantum subgroup. Using a $\mathbb{Z}_2$-grading, we obtain product formulae for little $q$-Jacobi functions

Unconventional Ideas for Axion and Dark Matter Experiments

In this contribution an entirely different way compared to conventional approaches for axion, hidden photon and dark matter (DM) detection is proposed for discussion. The idea is to use living plants which are known to be very sensitive to all kind of environmental parameters, as detectors. A possible observable in such living plants could be the natural bio-photon level, a kind of metabolism related chemoluminescence. Another observable might be morphological changes or systematic leave movements. However a big problem for such kind of experiment would be the availability of a known, controllable and calibrated DM source. The objective of this small paper is primarily to trigger a debate and not so much to present a well-defined and clearly structured proposal.Comment: Contributed to the 11th Patras Workshop on Axions, WIMPs and WISPs, Zaragoza, June 22 to 26, 201

RF engineering basic concepts: the Smith chart

The Smith chart is a very valuable and important tool that facilitates interpretation of S-parameter measurements. This paper will give a brief overview on why and more importantly on how to use the chart. Its definition as well as an introduction on how to navigate inside the chart are illustrated. Useful examples show the broad possibilities for use of the chart in a variety of applications.Comment: 22 pages, contribution to the CAS - CERN Accelerator School: Specialised Course on RF for Accelerators; 8 - 17 Jun 2010, Ebeltoft, Denmar

The L^p-Fourier transform on locally compact quantum groups

Using interpolation properties of non-commutative L^p-spaces associated with an arbitrary von Neumann algebra, we define a L^p-Fourier transform 1 <= p <= 2 on locally compact quantum groups. We show that the Fourier transform determines a distinguished choice for the interpolation parameter as introduced by Izumi. We define a convolution product in the L^p-setting and show that the Fourier transform turns the convolution product into a product.Comment: 29 pages, to appear in the Journal of Operator Theor

Completeness of singlet pair states for quantum spin systems

It is shown that for an arbitrary subdivision of an antiferromagnetic spin- lattice into two subsystems every singlet state can be expressed as a linear combination of single pair states (SPS). These SPS states are products of singlet states for a pair of representatives of either subsystem