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Softwaretechnik-Trends

Signal and Image Port Output Power in the Quantum Theory of Mixing

Qing Ke, M. J. Feldman

Published May 1, 1994• 0 citations
OpenAlex

Abstract

The quantum theory of mixing is essential for the interpretation of experimental superconducting quasiparticle (SIS) mixers. When the bias and tuning parameters are known, the theory is quite successful at predicting the mixer performance, gain and noise temperature. However, the theory usually predicts much higher conversion gain for some other set of bias and tuning parameters, and this is not seen in experiment. Thus the theory is less useful for engineering design of SIS mixers. We believe we have resolved this longstanding discrepancy. We find there are two distinct optimum operation modes for ideal SIS mixers. The high gain mode predicted by the theory will not be accessible in real experiments. To understand this we present the equations of a DSB SIS mixer in a novel form, in terms of the complex plane phase angle between the amplitude modulation input admittance vector and the local oscillator input admittance vector.

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The output noise temperature, rather than the standard input noise temperature, is shown to be the fundamental measure of the shot noise of the superconducting (SIS) quasiparticle mixer. This conclusion is based on extensive numerical computations of the properties of optimized SIS (superconductor-insulator-superconductor) receivers and also on analytic calculations with separate consideration of correlated and uncorrelated noise sources. The quantum theory of mixing is used to derive a simple analytic expression for the mixer output noise which is independent of frequency, and qualitatively explains the dependence of the output temperature on each of the receiver's operating parameters. The derivation leads to a novel understanding of the SIS mixer which, distinguishes between its correlated and uncorrelated noise sources. The authors predict T(receiver)=2*T(mixer) for many SIS receivers. Numerous experiments substantiate the analysis.>

IEEE Transactions on Applied Superconductivity•Mar 1, 1993•13 citations
The quantum theory of mixing is essential for the interpretation of experimental superconducting quasiparticle (SIS) mixers. When the bias and tuning parameters are known, the theory is quite successful at predicting the mixer performance, gain and noise temperature. However, the theory usually predicts much higher conversion gain for some other set of bias and tuning parameters, and this is not seen in experiment. Thus the theory is less useful for engineering design of SIS mixers. We believe we have resolved this longstanding discrepancy. We find there are two distinct optimum operation modes for ideal SIS mixers. The high gain mode predicted by the theory will not be accessible in real experiments. To understand this we present the equations of a DSB SIS mixer in a novel form, in terms of the complex plane phase angle between the amplitude modulation input admittance vector and the local oscillator input admittance vector.
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.
A detailed analysis of the effects of the quantum susceptance on the performance of superconductor-insulator-superconductor (SIS) mixers is performed. It is found that the principal effects of the quantum susceptance are to change the DC bias at which optimum coupling of the signal to the mixer occurs, and to change the output admittance at the IF frequency, thus changing the available gain. It is shown that at the signal port the principal effect is to change the bias voltage at which optimum coupling to the mixer occurs. A more dramatic effect occurs at the IF port, where the quantum susceptance leads to negative values of the output conductance, which causes the available gain to be infinite.
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.
This paper is an elaboration upon Tucker’s quantum theory of mixing, which has proven very valuable in interpreting recent experiments in superconducting quasiparticle mixing. Tucker’s formula for the conversion gain of a three-frequency quantum mixer in the low intermediate frequency (IF) limit is generalized to include arbitrary source reactance; one choice of source reactance is found to resonate out the quantum reactance in the conversion expression. The signal reflection gain is evaluated; it becomes infinite simultaneously with the IF conversion gain. Infinite gain occurs only within the region of negative dc differential resistance. A number of relationships among the complex elements of the small-signal admittance matrix is presented; the nonlinear reactive elements are shown to be small under certain conditions when the conversion gain is maximized. The local oscillator (LO) power required for quantum mixing is calculated and found to be related to the gain denominator. This implies that certain quantum mixers at high gain will exhibit a constant gain-powerwidth product and a gain-proportional noise temperature component. A particularly simple expression for the conversion gain of an optimized quantum mixer is developed, which agrees with previous experiments. The origin of nonclassical behavior, including conversion gain and the nonlinear quantum reactance, is discussed. We conclude that the nonlinear quantum reactance, though it certainly must exist, is not itself responsible for conversion gain and has a minor, perhaps insignificant, effect upon the properties of a quantum mixer.
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 output noise temperature, rather than the standard input noise temperature, is shown to be the fundamental measure of the shot noise of the superconducting (SIS) quasiparticle mixer. This conclusion is based on extensive numerical computations of the properties of optimized SIS (superconductor-insulator-superconductor) receivers and also on analytic calculations with separate consideration of correlated and uncorrelated noise sources. The quantum theory of mixing is used to derive a simple analytic expression for the mixer output noise which is independent of frequency, and qualitatively explains the dependence of the output temperature on each of the receiver's operating parameters. The derivation leads to a novel understanding of the SIS mixer which, distinguishes between its correlated and uncorrelated noise sources. The authors predict T(receiver)=2*T(mixer) for many SIS receivers. Numerous experiments substantiate the analysis.>