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IEEE Transactions on Applied Superconductivity

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

Edward Tong, Paul Grimes, Lingzhen Zeng

Published Mar 18, 2019• 2 citations
Publisher

Abstract

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.

DOI
10.1109/tasc.2019.2899844

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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.
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 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.
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 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.>
The development of ultra-low-noise receivers at frequencies of >200 GHz is primarily driven by astronomical applications. The most sensitive millimeter-wave receivers that have presently been constructed make use of the strong mixing afforded by superconductor-insulator-superconductor (SIS) tunnel junctions. In a collaborative project between UKC and RAL, a 230 GHz laboratory receiver has been built using a lead alloy SIS junction as the mixing element, mounted in 4:1 reduced-height waveguide, terminated at one end with a circular cross-section, adjustable backshort. Best results indicate a double-sideband receiver noise temperature of T/sub R/(DSB) approximately=120 K, which represents state-of-the-art performance at this frequency. Initial difficulties in achieving good mixing performance prompted an investigation into the importance of the 'quality' of mixer block backshort tuning elements. An analysis of the mixer equivalent circuit is presented which allows for loss in a non-ideal mixer block, and 3-port mixer model calculations are discussed which incorporate this analysis into the Tucker quantum theory of mixing.
High-Tcsuperconducting (HTS) harmonic mixers are attractive frontends for terahertz wireless communication and sensing applications. However, the investigation of HTS harmonic mixers has long been hindered by the lack of effective theoretical method in device modeling. This article presents a modeling approach for analyzing the noise and conversion properties of HTS harmonic mixers. By quantitively analyzing the contribution of the parasitic components to frequency conversion, a parasitics-selection based equivalent circuit model is built with the architecture complexity reduced to a six-port network. Besides, a fast hybrid-solution method that combines the single-tone current excitation and perturbation-derivation processing techniques, is developed for efficiently calculating the conversion impedance matrix for harmonic mixing. Detailed derivations are then carried out to acquire the semianalytic expressions of noise temperature and conversion gain after solving the noise correlation matrix for harmonic mixing. The presented modeling method has been verified by the fourth harmonic mixing experiments for a dual-band antenna-coupled HTS Josephson-junction mixer module. The measured and simulated results are in good agreement in terms of the noise temperature and conversion gain as well as their dependance on dc biasing, local oscillator pumping, and operating temperatures. The results have validated the effectiveness of the presented modeling method for analyzing the properties of HTS Josephson junction mixers.