• Journal of electromagnetic engineering and science
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• v.2 no.1
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• pp.5-10
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• 2002

We have analized the inverse class-F and class-F amplifiers using their waveforms. From the analytic equations derived from the analysis, we have calculated tole efficiencies, output powers, DC power dissipations, and optimum fundamental load impedances of the inverse class-F and class-F amplifiers. We also have compared them for various operation conditions, which include the same peak current, saute DC power dissipation, same fundamental RF output power, and same fundamental load impedance with different Ron(on-resistance). These analyses have clearly shown the performance limitations, advantages, and guide to the optimized design of the inverse class-F amplifiers.

• Kyungpook Mathematical Journal
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• v.19 no.2
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• pp.205-211
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• 1979

In this paper we continue the study of formation radical (F-radical) classes initiated in [3]. Hereditary and stronger properties of F-radical classes are discussed by giving construction for lower hereditary, lower stronger and lower strongly hereditary F-radical classes containing a given class M. It is shown that the Baer F-radical B is the lower strongly hereditary F-radical class containing the class of all nilpotent ideals and it is the upper radical class with $\{(I,\;N){\mid}N{\in}C,\;N\;is\;prime\}{\subset}SB$ where SB denotes the semisimple F-radical class of B and C is an arbitrary but fixed class of homomorphically closed near-rings. The existence of a largest F-radical class contained in a given class is examined using the concept of complementary F-radical introduced by Scott [5].

• The Journal of Korean Institute of Electromagnetic Engineering and Science
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• v.22 no.12
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• pp.1060-1068
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• 2011

In this paper, Current-Mode Class-D(CMCD) RF Power Amplifier(PA) is designed and implemented at 900 MHz. Conventional CMCD PA has output parallel resonator to reconstruct a fundamental frequency component of the output signal. However the resonator can be removed by connecting inverse class-F PAs because even-harmonic components can be removed by CMCD PA's push-pull structure. Using load-pull, inverse class-F PA with GaN transistors is designed, and CMCD PA with the inverse class-F PA is implemented. The CMCD PA has 64.5 % drain efficiency, 34.2 dBm output power. Comparing with the drain efficiency of a CMCD PA with parallel resonator, the CMCD with the inverse class-F technology has 13.6 % improved drain efficiency.

• Journal of electromagnetic engineering and science
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• v.10 no.1
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• pp.6-12
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• 2010

In this paper, highly efficient class-F power amplifiers(PAs) with harmonic-controlling transmission lines(TLs) were built for cellular and WLAN applications at 840 MHz and 2.4 GHz each. Also, based on these single-band PAs, a dualband class-F PA was designed after a careful investigation into the harmonics of the two frequencies. The harmonic-controlling TL was designed for the class-F operation at dualband by switching the length of the shunt $\lambda$/4 TL part, while the series $\lambda$/4 TL is optimized for both frequencies. To verify the performance, two class-F PAs optimized at each frequency and a dualband class-F PA at the corresponding frequencies were built with the secondand the third-harmonic control circuits at each frequencies. As a result, the PA#1 at 840 MHz has a peak drain efficiency of 81.2 % with an output power of 24.4 dBm, while the PA#2 at 2.35 GHz shows a drain efficiency of 94.5 % with an output of 22.8 dBm. Finally, the dualband class-F PA#3 showed 60.5 % and 50.9 % drain efficiencies at 840 MHz and 2.4 GHz, with powers of 23.8 dBm and 19.62 dBm, respectively.

• Journal of the Institute of Electronics Engineers of Korea TC
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• v.44 no.7 s.361
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• pp.12-16
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• 2007

In this paper, The 3rd-IMD of class-F power amplifier is improved using CMRC structure in order to remove the parasitic End harmonic at the output load of class-F power amplifier. The total size is very small more than class-F power amplifier using PBG. (Photonicband Gap) structure during improved 3rd-IMD characteristic performance.

• Bulletin of the Korean Mathematical Society
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• v.52 no.5
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• pp.1559-1568
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• 2015

The relative class number $H_d(f)$ of a real quadratic field $K=\mathbb{Q}(\sqrt{m})$ of discriminant d is the ratio of class numbers of $O_f$ and $O_K$, where $O_K$ denotes the ring of integers of K and $O_f$ is the order of conductor f given by $\mathbb{Z}+fO_K$. In a recent paper of A. Furness and E. A. Parker the relative class number of $\mathbb{Q}(\sqrt{m})$ has been investigated using continued fraction in the special case when $(\sqrt{m})$ has a diagonal form. Here, we extend their result and show that there exists a conductor f of relative class number 1 when the continued fraction of $(\sqrt{m})$ is non-diagonal of period 4 or 5. We also show that there exist infinitely many real quadratic fields with any power of 2 as relative class number if there are infinitely many Mersenne primes.

• East Asian mathematical journal
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• v.37 no.5
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• pp.613-617
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• 2021

Abstract. For a positive square-free integer m, let K = ℚ($\sqrt{m}$) be a real quadratic field. The relative class number H_d(f) of K of discriminant d is the ratio of class numbers 𝒪_K and 𝒪_f, where 𝒪_K is the ring of integers of K and 𝒪_f is the order of conductor f given by ℤ + f𝒪_K. In 1856, Dirichlet showed that for certain m there exists an infinite number of f such that the relative class number H_d(f) is one. But it remained open as to whether there exists such an f for each m. In this paper, we give a result for existence of real quadratic field ℚ($\sqrt{m}$) with relative class number one where the period of continued fraction expansion of $\sqrt{m}$ is 6.

• Journal of the Institute of Electronics Engineers of Korea TC
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• v.46 no.2
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• pp.141-146
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• 2009

In this paper, a novel harmonic control circuit has been proposed for the design of high-efficiency power amplifier with Si LDMOSFET. The proposed harmonic control circuit haying the short impedances for the second- and third-harmonic components has been used to design the in/output matching network. The efficiency enhancement effect of the proposed harmonic control circuit is superior to the class-F or inverse class-F harmonic control circuit. Also, when the proposed harmonic control circuit has been adapted to the input matching network as well as the output matching network, the of ficiency enhancement effect of the proposed power amplifier has increased all the more. The measured maximum power added efficiency (PAE) of the proposed power amplifier is 82.68% at 1.71GHz band. Compared with class-F and inverse class-F amplifiers, the measured maximum PAE of the proposed power amplifier has increased in $5.08{\sim}9.91%$.

• Journal of the Institute of Electronics Engineers of Korea TC
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• v.45 no.9
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• pp.49-54
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• 2008

In this paper, the power added efficiency(PAE) of class F power amplifier is improved by applying a new Photonic Bandgap (PBG) structure on the output of amplifier. The proposed spiral PBG structure is a two-dimensional (2-D) periodic lattice patterned on a dielectric slab that does not require nonplanar fabrication process. This structure bas higher suppression performance at second harmonic. Also, It has a sharp skirt property. This new PBG structure can be applied with class F power amplifier for efficiency improvement. We obtained the PAE of 73.62 % for CDMA applications, and the PAE performance is improved as much as 6.2 % compared with that of a conventional class F power amplifier.

• Journal of the Korean Mathematical Society
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• v.32 no.4
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• pp.689-695
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• 1995

Let G be a finite group with k distinct conjugacy classes $C_1, C_2, \cdots, C_k$ and F an algebraically closed field such that char$(F){\dag}\left$\mid$ G \right$\mid$$. We denoted by $Irr_F$(G) the set of all irreducible F-characters of G and $Cf_F$(G) the set of all class functions of G into F. Then $Cf_F$(G) is a commutative F-algebra with an F-basis $Irr_F(G) = {\chi_1, \chi_2, \cdots, \chi_k}$.