Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Variational theory of the tapered impedance transformer   Superconducting amplifiers are key components of modern quantum information
circuits. To minimize information loss and reduce oscillations a tapered
impedance transformer of new design is needed at the input/output for
compliance with other 50 $\Omega$ components. We show that an optimal tapered
transformer of length $\ell$, joining amplifier to input line, can be
constructed using a variational principle applied to the linearized Riccati
equation describing the voltage reflection coefficient of the taper. For an
incident signal of frequency $\omega_o$ the variational solution results in an
infinite set of equivalent optimal transformers, each with the same form for
the reflection coefficient, each able to eliminate input-line reflections. For
the special case of optimal lossless transformers, the group velocity $v_g$ is
shown to be constant, with characteristic impedance dependent on frequency
$\omega_c=\pi v_g / \ell$. While these solutions inhibit input-line reflections
only for frequency $\omega_o$, a subset of optimal lossless transformers with
$\omega_o$ significantly detuned from $\omega_c$ does exhibit a wide bandpass.
Specifically, by choosing $\omega_o\rightarrow 0$
($\omega_o\rightarrow\infty$), we obtain a subset of optimal low-pass
(high-pass) lossless tapers with bandwidth $(0,\sim\omega_c)$
($(\sim\omega_c,\infty)$). From the subset of solutions we derive both the
wide-band low-pass and high-pass transformers, and we discuss the extent to
which they can be realized given fabrication constraints. In particular, we
demonstrate the superior reflection response of our high-pass transformer when
compared to other taper designs. Our results have application to amplifier,
transceiver, and other components sensitive to impedance mismatch.

10
The categories of this paper are: q-bio
33
The categories of this paper are: plasm-ph
28
The categories of this paper are: alg-geom
8
The categories of this paper are: hep-ex
22
The categories of this paper are: chao-dyn
27
The categories of this paper are: comp-gas
32
The categories of this paper are: atom-ph
1
The categories of this paper are: cs
37
The categories of this paper are: supr-con
20
The categories of this paper are: acc-phys
34
The categories of this paper are: chem-ph
2
The categories of this paper are: math
14
The categories of this paper are: math-ph
18
The categories of this paper are: econ
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The categories of this paper are: dg-ga
13
The categories of this paper are: quant-ph