Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

IEEE Transactions on Magnetics

Quantum noise in the quantum theory of mixing

M. J. Feldman

Published Mar 1, 1987• 27 citations
Publisher

Abstract

The minimum noise temperature obtainable in the quantum theory of mixing, allowing arbitrary terminations at all considered frequencies, is shown to be hω/2k, the same result as for other high-gain linear amplifiers. The conditions for attaining this absolute minimum noise appear to be fulfilled in only two cases, approximated by the super-Schottky mixer with large LO, and by the SIS mixer with small LO. For the ideal SIS mixer, the minimum noise requires one particular value of source impedance, regardless of the image termination. The origin of the quantum noise is discussed.

DOI
10.1109/tmag.1987.1065089

Related papers

Noise parameters of SIS mixers

Larry R. D’Addario

It has been shown that low-noise receivers can be constructed at millimeter wavelengths by using mixers containing superconducting tunnel junctions as the nonlinear elements. This is possible because of both the low intrinsic noise of these devices and their potential for high conversion gain. Here, the quantum theory of mixing is used to derive the full-noise parameters and small-signal parameters of sinusoidally pumped SIS (superconductor-insulator-superconductor) junctions. These are then put into a form that allows the theory of two-port linear networks to be brought to bear, allowing calculation of such useful parameters as minimum noise temperature, optimum source impedance, available (or exchangeable) gain at minimum noise, and stability factor. These quantities are properties of the pumped junction that do not depend on the source or load impedance, but do depend on the terminations at the image and harmonic sideband frequencies. The harmonic sidebands are taken to be shorted, and the image termination dependence is studied. Numerical results are presented for both ideal (BSC theory) and practical (measured current-voltage characteristic) junctions. The noise parameters of the cascade connection of an SIS mixer and a (noisy) IF amplifier are considered, leading to a specification of the optimum coupling network between the two. It is noted that the SIS mixer is usually not unconditionally stable, but that oscillation can be avoided by careful design of the IF coupling network.< >

IEEE Transactions on Microwave Theory and Techniques•Jul 1, 1988•19 citations

An analytic investigation of the superconductor quasiparticle mixer in the low power limit

M. J. Feldman

The properties of an SIS (Superconductor-insulator-superconductor) mixer using a slightly nonideal junction, with finite local oscillator (LO) power, are determined by analytic expansion of the equations of the quantum theory of mixing. The result is that the conversion gain using any reasonably good quality SIS junction is essentially equal to that using a perfect junction. Quite to the contrary, the minimum noise temperature is controlled by the leakage current of the junction: the increase in the minimum added-noise temperature over the quantum limit T/sub Q/=h omega /2k is given by delta T/sub Q/=(h omega /k) square root I/sub 0/I/sub 2//I/sub 1/; this minimum requires that the LO voltage across the junction is V/sub LO/=(64I/sub 0//I/sub 2/) /sup 1/4/h omega /e. (I/sub n/ is the current measured on the unpumped I-V curve of the junction at voltage V/sub 0/+nh omega /e). Therefore, although an SIS mixer using an ideal junction can reach the quantum noise limit only in the limit of zero LO power, even the most nearly ideal junctions require a considerable LO for best sensitivity.

IEEE Transactions on Magnetics•Mar 1, 1991•11 citations

Quantum noise in SIS mixers

Alexander B Zorin

A quantum-statistical analysis of the signal and noise performance of the quasiparticle (SIS) heterodyne mixers is presented. In contrast with the earlier theories, the quantum properties of the signal source have been taken into consistent consideration. In the quantum range of sensitivity the noise properties of the mixer can be characterized by the noise parameter ΘNintroduced earlier for the parametric amplifiers. Using the conventional 3-port model of the mixer circuit and the microscopic theory of the superconducting tunnel junctions we have obtained a general expression for ΘNand evaluated it numerically for various quasiparticle current step widths, dc bias voltages, local oscillator powers, signal frequencies ωs, signal source admittances Ysand operation temperatures T. In a reasonable range of these parameters,\Theta_{N}^{DSB}has turned out to be less than the so-called quantum limith\omega_{s}/2. On the contrary, in the single sideband mode of the mixer performance, ΘNis always larger thanh\omega_{s}/2. The difference between the two modes of operation is discussed from the point of view of the quantum theory of measurements.

IEEE Transactions on Magnetics•Mar 1, 1985•19 citations

Quantum Noise Studies with Superconducting Tunnel Junction Mixers

Mark F. Bocko

We have completed our theoretical and experimental investigations of the noise properties of superconducting tunnel junction (SIS) mixers operated as both a phase insensitive linear amplifier and as a phase sensitive linear amplifier. We proposed a technique by which a SIS mixer could be operated as a phase sensitive linear amplifier, i.e., the gain and noise temperature of the amplifier are a function of the phase of the incoming signal. In this technique two phase coherent local oscillators at different frequencies are combined in the mixer simultaneously so both a phase preserving and phase conjugating mixing process occur resulting in a phase sensitive mixer.

•Mar 14, 1993•0 citations

Noise Wave Modeling of an SIS Mixer and Its IF Circuit Using Tucker's Quantum Theory of Mixing

Edward Tong, Paul Grimes, Lingzhen Zeng

Tucker's Quantum Theory of Mixing (QTM) is widely used to model the conversion gain and noise temperature of SIS mixers. In particular, the theory describes the phenomenon of non-classical conversion gain and that of infinite or even negative output impedances in inductively tuned SIS mixers. Common microwave noise theory is inadequate to describe the operation of the IF circuit connected to such mixers. In this paper, we report the use of the noise wave formalism to model the noise properties of a Double-Side-Band SIS mixer together with an IF isolator and low noise amplifier cascade. Starting from QTM, we derive the 4 noise parameters of the SIS mixer, together with an approximate 2-port chain matrix with an upper-side-band RF input port and an IF output port. These matrices are cascaded with the noise correlation matrix of the IF circuit to form a complete noise model of the SIS receiver. Optimum source impedance for the receiver can be derived from this noise model, which can be used in efficient CAD modeling of a complete SIS receiver.

IEEE Transactions on Applied Superconductivity•Mar 18, 2019•2 citations

Quantum noise in heterodyne detection

Michael J. Wengler, D. P. Woody

A fully quantum mechanical theory of diode mixers which includes quantization of the external circuit is presented. We find that Tucker's theory for SIS mixer conversion efficiencies is correct, but that his expression for the measurement noise must be augmented by an amount corresponding to half a photon at every frequency to which the mixer responds. Noise in high quality SIS mixers is shown to be accurately described by the conceptually simpler photodiode mixer noise theory. The radiation coupling efficiency term, η, which appears in photodiode theory turns out to be the coupling efficiency between the signal source admittance and the admittance which the SIS presents to the LO. Our theory reduces to Caves' quantum linear amplifier formalism, and therefore predicts measurement noises bounded by the quantum lower limit ofhv/k_{B}. Predictions of performance versus frequency for SIS's are made. We predict that NbN SIS's will behave as nearly ideal photodiodes for frequencies as high as 3000 GHz.

IEEE Journal of Quantum Electronics•May 1, 1987•61 citations
The minimum noise temperature obtainable in the quantum theory of mixing, allowing arbitrary terminations at all considered frequencies, is shown to be hω/2k, the same result as for other high-gain linear amplifiers. The conditions for attaining this absolute minimum noise appear to be fulfilled in only two cases, approximated by the super-Schottky mixer with large LO, and by the SIS mixer with small LO. For the ideal SIS mixer, the minimum noise requires one particular value of source impedance, regardless of the image termination. The origin of the quantum noise is discussed.
It has been shown that low-noise receivers can be constructed at millimeter wavelengths by using mixers containing superconducting tunnel junctions as the nonlinear elements. This is possible because of both the low intrinsic noise of these devices and their potential for high conversion gain. Here, the quantum theory of mixing is used to derive the full-noise parameters and small-signal parameters of sinusoidally pumped SIS (superconductor-insulator-superconductor) junctions. These are then put into a form that allows the theory of two-port linear networks to be brought to bear, allowing calculation of such useful parameters as minimum noise temperature, optimum source impedance, available (or exchangeable) gain at minimum noise, and stability factor. These quantities are properties of the pumped junction that do not depend on the source or load impedance, but do depend on the terminations at the image and harmonic sideband frequencies. The harmonic sidebands are taken to be shorted, and the image termination dependence is studied. Numerical results are presented for both ideal (BSC theory) and practical (measured current-voltage characteristic) junctions. The noise parameters of the cascade connection of an SIS mixer and a (noisy) IF amplifier are considered, leading to a specification of the optimum coupling network between the two. It is noted that the SIS mixer is usually not unconditionally stable, but that oscillation can be avoided by careful design of the IF coupling network.< >
The properties of an SIS (Superconductor-insulator-superconductor) mixer using a slightly nonideal junction, with finite local oscillator (LO) power, are determined by analytic expansion of the equations of the quantum theory of mixing. The result is that the conversion gain using any reasonably good quality SIS junction is essentially equal to that using a perfect junction. Quite to the contrary, the minimum noise temperature is controlled by the leakage current of the junction: the increase in the minimum added-noise temperature over the quantum limit T/sub Q/=h omega /2k is given by delta T/sub Q/=(h omega /k) square root I/sub 0/I/sub 2//I/sub 1/; this minimum requires that the LO voltage across the junction is V/sub LO/=(64I/sub 0//I/sub 2/) /sup 1/4/h omega /e. (I/sub n/ is the current measured on the unpumped I-V curve of the junction at voltage V/sub 0/+nh omega /e). Therefore, although an SIS mixer using an ideal junction can reach the quantum noise limit only in the limit of zero LO power, even the most nearly ideal junctions require a considerable LO for best sensitivity.
A quantum-statistical analysis of the signal and noise performance of the quasiparticle (SIS) heterodyne mixers is presented. In contrast with the earlier theories, the quantum properties of the signal source have been taken into consistent consideration. In the quantum range of sensitivity the noise properties of the mixer can be characterized by the noise parameter ΘNintroduced earlier for the parametric amplifiers. Using the conventional 3-port model of the mixer circuit and the microscopic theory of the superconducting tunnel junctions we have obtained a general expression for ΘNand evaluated it numerically for various quasiparticle current step widths, dc bias voltages, local oscillator powers, signal frequencies ωs, signal source admittances Ysand operation temperatures T. In a reasonable range of these parameters,\Theta_{N}^{DSB}has turned out to be less than the so-called quantum limith\omega_{s}/2. On the contrary, in the single sideband mode of the mixer performance, ΘNis always larger thanh\omega_{s}/2. The difference between the two modes of operation is discussed from the point of view of the quantum theory of measurements.
We have completed our theoretical and experimental investigations of the noise properties of superconducting tunnel junction (SIS) mixers operated as both a phase insensitive linear amplifier and as a phase sensitive linear amplifier. We proposed a technique by which a SIS mixer could be operated as a phase sensitive linear amplifier, i.e., the gain and noise temperature of the amplifier are a function of the phase of the incoming signal. In this technique two phase coherent local oscillators at different frequencies are combined in the mixer simultaneously so both a phase preserving and phase conjugating mixing process occur resulting in a phase sensitive mixer.
Tucker's Quantum Theory of Mixing (QTM) is widely used to model the conversion gain and noise temperature of SIS mixers. In particular, the theory describes the phenomenon of non-classical conversion gain and that of infinite or even negative output impedances in inductively tuned SIS mixers. Common microwave noise theory is inadequate to describe the operation of the IF circuit connected to such mixers. In this paper, we report the use of the noise wave formalism to model the noise properties of a Double-Side-Band SIS mixer together with an IF isolator and low noise amplifier cascade. Starting from QTM, we derive the 4 noise parameters of the SIS mixer, together with an approximate 2-port chain matrix with an upper-side-band RF input port and an IF output port. These matrices are cascaded with the noise correlation matrix of the IF circuit to form a complete noise model of the SIS receiver. Optimum source impedance for the receiver can be derived from this noise model, which can be used in efficient CAD modeling of a complete SIS receiver.
A fully quantum mechanical theory of diode mixers which includes quantization of the external circuit is presented. We find that Tucker's theory for SIS mixer conversion efficiencies is correct, but that his expression for the measurement noise must be augmented by an amount corresponding to half a photon at every frequency to which the mixer responds. Noise in high quality SIS mixers is shown to be accurately described by the conceptually simpler photodiode mixer noise theory. The radiation coupling efficiency term, η, which appears in photodiode theory turns out to be the coupling efficiency between the signal source admittance and the admittance which the SIS presents to the LO. Our theory reduces to Caves' quantum linear amplifier formalism, and therefore predicts measurement noises bounded by the quantum lower limit ofhv/k_{B}. Predictions of performance versus frequency for SIS's are made. We predict that NbN SIS's will behave as nearly ideal photodiodes for frequencies as high as 3000 GHz.