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IEEE Transactions on Magnetics

Numerical computation of two-LO SIS mixer gain and noise

Z.N. Zhang, Mark F. Bocko, Michael J. Wengler

Published Mar 1, 1989• 1 citation
Publisher

Abstract

The authors present numerical calculations of the gain and noise of a two-LO (local oscillator) mixer based on an ideal SIS (superconductor-insulator-superconductor) IV curve. They demonstrate the phase-sensitive response of the mixer with two-LO pumping and present calculations of the noise for various DC bias conditions and embedding impedances. Preliminary results indicate that for certain DC bias conditions and signal terminations, the noise added to a signal by the two-LO mixer operated in the single-sideband mode can be a factor of 25 less than that added by a conventional single-sideband single-LO mixer.>

DOI
10.1109/20.92467

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It is noted that it is possible to operate a mixer as a phase-sensitive linear amplifier by pumping with two local oscillators (LOs) separated in frequency by twice the IF (intermediate frequency) and symmetrically located about the signal frequency. In principle a phase-sensitive amplifier can detect a signal without adding any noise. The authors present a formalism developed to describe two-LO mixers, and extend the quantum mixer theory to calculate expressions for the gain and noise of a two-LO mixer. The full quantum mechanical formulation used here enables an analysis of the mixer noise for general input states, for example, a squeezed state. It is demonstrated that a two-LO mixer is phase-sensitive. The results are pertinent to the design of phase-sensitive heterodyne receivers with SIS (superconductor-insulator-superconductor) quasiparticle mixers.>

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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
The authors present numerical calculations of the gain and noise of a two-LO (local oscillator) mixer based on an ideal SIS (superconductor-insulator-superconductor) IV curve. They demonstrate the phase-sensitive response of the mixer with two-LO pumping and present calculations of the noise for various DC bias conditions and embedding impedances. Preliminary results indicate that for certain DC bias conditions and signal terminations, the noise added to a signal by the two-LO mixer operated in the single-sideband mode can be a factor of 25 less than that added by a conventional single-sideband single-LO mixer.>
A conventional superconductor-insulator-superconductor (SIS) mixer, that is pumped by a single-frequency local oscillator (LO) functions as a phase-insensitive linear amplifier and may achieve a noise level near the quantum limit of one-half photon added noise per unit bandwidth. A phase-sensitive linear amplifier may have less noise than this quantum limit. To overcome the quantum noise limit with an SIS mixer, a two-LO technique which makes the mixer's gain dependent upon the phase of the incoming signal was used. The phase sensitive gain of this two-LO mixer is experimentally demonstrated. The gain variation from maximum to minimum is more than 20 dB. Theoretical predictions of the noise of the two-LO mixer are presented.
It is noted that it is possible to operate a mixer as a phase-sensitive linear amplifier by pumping with two local oscillators (LOs) separated in frequency by twice the IF (intermediate frequency) and symmetrically located about the signal frequency. In principle a phase-sensitive amplifier can detect a signal without adding any noise. The authors present a formalism developed to describe two-LO mixers, and extend the quantum mixer theory to calculate expressions for the gain and noise of a two-LO mixer. The full quantum mechanical formulation used here enables an analysis of the mixer noise for general input states, for example, a squeezed state. It is demonstrated that a two-LO mixer is phase-sensitive. The results are pertinent to the design of phase-sensitive heterodyne receivers with SIS (superconductor-insulator-superconductor) quasiparticle mixers.>
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.< >
Calculations based on the quantum theory of mixing in single-particle tunnel junctions show that there is a fairly simple strategy for optimizing the performance of double-sideband superconductor-insulator-superconductor (SIS) quasiparticle mixers. The best mixer noise temperature is obtained when the signal source is matched to the local oscillator (LO) admittance of the junction. This applies over a very wide range of LO and DC bias conditions. These calculations support the contention that it is the energy dissipation in the device which is important in determining the noise performance, not the small signal admittance or the power gain. This appears to be another demonstration of the Callen and Welton fluctuation-dissipation theorem. which states that it is the dissipation of energy which is responsible for the noise generation in a wide range of devices, and it is this energy dissipation mechanism to which the signal should be coupled to minimize the noise.
The authors have made a detailed study of the gain and noise of a SIS (superconductor-insulator-superconductor) heterodyne receiver at 345 GHz. An array of two Nb-Al/sub 2/O/sub 3/-Nb SIS junctions in series are used as the mixing element. The array is operated in a waveguide mount with a backshort and an E-plane tuner. The best receiver noise temperature achieved is 140 K DSB (double sideband). The embedding impedances were determined by fitting theory to the measured pumped curves. High-quality fits were obtained, providing the first detailed test of the Tucker-theory at frequencies above 300 GHz. The impedances found by this method are in very good agreement with impedances measured in a scale model at 3.3 GHz. From these embedding impedances, the gain and noise of the mixer were calculated over a full bias range using the Tucker theory in the three-port low-IF approximation. The measured dependence of mixer gain and noise on bias voltage, pump power and embedding impedance is in good agreement with theory. However the absolute values show discrepancies that appear to be independent of the bias parameters of the mixer.>
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.