Theory of a Negative-Resistance Transmission Line Amplifier with Distributed Noise Generators

Chang, K. K. N.

doi:10.1063/1.1735710

Cited by 10 publications

(3 citation statements)

References 4 publications

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“…Puzzlingly, however, this argument overlooks the fact that the amplifier would also boost the signal. Indeed, according to transmission-line theory—a mathematical framework successfully used to represent cochlear wave propagation in 1, 2, and 3 dimensions [ 61 , 77 , 79 , 81 ]—spatially distributed (cascaded) wave amplification boosts the input signal, which is spatially coherent, more than the internal noise, which is not [ 82 , 83 ]. Passive transmission lines, in which the spatial gradient of wave power is negative, manifest the opposite behavior: input signals are attenuated more than the internal noise.…”

Section: Discussionmentioning

confidence: 99%

The Long Outer-Hair-Cell RC Time Constant: A Feature, Not a Bug, of the Mammalian Cochlea

Altoè

Shera

2023

JARO

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The cochlea of the mammalian inner ear includes an active, hydromechanical amplifier thought to arise via the piezoelectric action of the outer hair cells (OHCs). A classic problem of cochlear biophysics is that the RC (resistance-capacitance) time constant of the hair-cell membrane appears inconveniently long, producing an effective cut-off frequency much lower than that of most audible sounds. The long RC time constant implies that the OHC receptor potential—and hence its electromotile response—decreases by roughly two orders of magnitude over the frequency range of mammalian hearing, casting doubt on the hypothesized role of cycle-by-cycle OHC-based amplification in mammalian hearing. Here, we review published data and basic physics to show that the “RC problem” has been magnified by viewing it through the wrong lens. Our analysis finds no appreciable mismatch between the expected magnitude of high-frequency electromotility and the sound-evoked displacements of the organ of Corti. Rather than precluding significant OHC-based boosts to auditory sensitivity, the long RC time constant appears beneficial for hearing, reducing the effects of internal noise and distortion while increasing the fidelity of cochlear amplification.

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Section: Discussionmentioning

confidence: 99%

The Long Outer-Hair-Cell RC Time Constant: A Feature, Not a Bug, of the Mammalian Cochlea

Altoè

Shera

2023

JARO

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“…Classically, the thermal noise generated by a lossy transmission line is modelled through the use of distributed noise generators [47][48][49]. In this section, we first describe the evolution of frequency modes in the presence of distributed sources, and then we relate the distributed sources to thermal noise.…”

Section: Thermal Noisementioning

confidence: 99%

Quantum analysis of second-order effects in superconducting travelling-wave parametric amplifiers

Zhao

Withington

2021

J. Phys. D: Appl. Phys.

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We have performed a quantum mechanical analysis of travelling-wave parametric amplifiers (TWPAs) in order to investigate five experimental phenomena related to their operations, namely the effect of impedance mismatch, the presence of upper idler modes, the presence of quantum and thermal noise, the generation of squeezed states, and the preservation of pre-squeezed states during amplification. Our analysis uses momentum operators to describe the spatial evolution of quantised modes along a TWPA. We calculate the restriction placed on pump amplitude as well as amplifier gain as a result of impedance mismatch between a TWPA and its external system. We apply our analysis to upper idler modes and demonstrate that they will result in suppressed gain. We show that an ideal TWPA is indeed quantum-limited—i.e. it introduces a half-quantum of zero-point fluctuation which is the minimum possible noise contribution for a phase-preserving linear amplifier. We analyse the thermal noise associated with a TWPA by considering the effect of distributed sources along an amplifier transmission line. Our analysis predicts a doubling of thermal noise in the high gain limit as a result of wave-mixing between signal and idler modes. We study the operation of a TWPA in the presence of a DC bias current, and have shown that highly squeezed states can in principle be generated. However, amplifying a pre-squeezed state using a non-degenerate TWPA generally reduces the squeezing advantage.

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“…Classically, the thermal noise generated by a lossy transmission line is modelled through the use of distributed noise generators [42][43][44]. In this section, we first describe the evolution of frequency modes in the presence of distributed sources, and then we relate the distributed sources to thermal noise.…”

Section: Thermal Noisementioning

confidence: 99%

Quantum analysis of second-order effects in superconducting travelling-wave parametric amplifiers

Zhao,

Withington

2021

Preprint

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We have performed a quantum mechanical analysis of travelling-wave parametric amplifiers (TW-PAs) in order to investigate five experimental phenomena related to their operations, namely the effect of impedance mismatch, the presence of upper idler modes, the presence of quantum and thermal noise, the generation of squeezed states, and the preservation of pre-squeezed states during amplification. Our analysis uses momentum operators to describe the spatial evolution of quantised modes along a TWPA. We calculate the restriction placed on pump amplitude as well as amplifier gain as a result of impedance mismatch between a TWPA and its external system. We apply our analysis to upper idler modes and demonstrate that they will result in suppressed gain. We show that an ideal TWPA is indeed quantum-limited -i.e. it introduces a half-quantum of zero-point fluctuation which is the minimum possible noise contribution for a phase-preserving linear amplifier. We analyse the thermal noise associated with a TWPA by considering the effect of distributed sources along an amplifier transmission line. Our analysis predicts a doubling of thermal noise in the high gain limit as a result of wave-mixing between signal and idler modes. We study the operation of a TWPA in the presence of a DC bias current, and have shown that highly squeezed states can in principle be generated. However, amplifying a pre-squeezed state using a non-degenerate TWPA generally reduces the squeezing advantage.

show abstract

Theory of a Negative-Resistance Transmission Line Amplifier with Distributed Noise Generators

Cited by 10 publications

References 4 publications

The Long Outer-Hair-Cell RC Time Constant: A Feature, Not a Bug, of the Mammalian Cochlea

The Long Outer-Hair-Cell RC Time Constant: A Feature, Not a Bug, of the Mammalian Cochlea

Quantum analysis of second-order effects in superconducting travelling-wave parametric amplifiers

Quantum analysis of second-order effects in superconducting travelling-wave parametric amplifiers

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