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Journal of Applied Physics

Theory of the singly quasidegenerate Josephson junction parametric amplifier

O. H. Soerensen, Bjørn Dueholm, J. Mygind, N. F. Pedersen

Published Oct 1, 1980• 12 citations
Publisher

Abstract

A comprehensive account of the theory of the singly quasidegenerate Josephson junction parametric amplifier is given. In this mode the signal and idler frequencies are both approximately equal to half the pump frequency, and hence the signal and idler channels have a common termination. It is shown that the performance of the amplifier characterized by properties such as gain-bandwidth product, noise temperature, and saturation depends strongly on the embedding microwave circuit. In particular any uncompensated series reactance may deteriorate the overall performance. Internal shot and Johnson noise as well as incident thermal radiation is included in the discussion. It is shown that the noise temperature is virtually independent of noise injected from external sources and that minimum noise temperature is automatically achieved if the amplifier is tuned to maximize the gain-bandwidth product. The analytical results are illustrated by self-consistent numerical solutions of the circuit equations.

DOI
10.1063/1.327507

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The signal and noise properties of two basic types of externally pumped parametric amplifiers, using Josephson junctions with low capacitance, are calculated. The first type is a single- frequency nondegenerate amplifier and second one is a two-frequency degenerate amplifier, referred to sometimes as SUPARAMP. Calculations are based on the conventional RSJ model of the Josephson junction. In contrast to the works published earlier, the most realistic open circuit approximation is used for idler combinational frequencies, as well as for the pumping frequency harmonics. A single-frequency amplifier is shown to have relatively low noise temperatures (T_{N} \approx 25T) at signal frequencies of the order of the Josephson junction characteristic frequency ωc. On the other hand, SUPARAMP can have much lower noise but at lower frequencies, and it behaves approximately as a usual parametric amplifier with a critical frequency\omega_{cr} \approx 0.2 \omega_{c}.

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S. Wahlsten, S. Rudner, T. Claeson

Arrays of 10 or 40 series-connected small densely packed Josephson tunnel junctions were successfully operated as parametric amplifiers at 10 GHz. Between 50 and 90% of the junctions in an array were observed to work coherently in the amplification process. Signal gain exceeding 24 dB was achieved with a pump power as low as −50 to −70 dBm. A power width (i.e., the range of the pump power for a gain within 3 dB of the peak gain) of 0.25 dB and a bandwidth of 15 MHz were measured for 20-dB gain. The power width was in accordance with theory but the bandwidth was reduced, probably due to noise saturation effects. The latter effects can be reduced by lowering the input noise temperature or by including an external band limitation. The noise temperature was also increased by saturation; however, with an external bandwidth of 60 MHz, a noise temperature of 30±20 K was measured. The application of a magnetic field has proved extremely useful as a means of tuning the amplifiers to stable high-gain operating points. This tuning was also utilized in evaluating the amplifier parameters, and the theory by Feldman, Parrish, and Chiao has been verified. The upper frequency limit for a lead tunnel junction amplifier ought to be well above 300 GHz.

Journal of Applied Physics•Jul 1, 1978•60 citations
A comprehensive account of the theory of the singly quasidegenerate Josephson junction parametric amplifier is given. In this mode the signal and idler frequencies are both approximately equal to half the pump frequency, and hence the signal and idler channels have a common termination. It is shown that the performance of the amplifier characterized by properties such as gain-bandwidth product, noise temperature, and saturation depends strongly on the embedding microwave circuit. In particular any uncompensated series reactance may deteriorate the overall performance. Internal shot and Johnson noise as well as incident thermal radiation is included in the discussion. It is shown that the noise temperature is virtually independent of noise injected from external sources and that minimum noise temperature is automatically achieved if the amplifier is tuned to maximize the gain-bandwidth product. The analytical results are illustrated by self-consistent numerical solutions of the circuit equations.
Gain and noise properties of a non-degenerate one-frequency parametric amplifier using a self-pumped Josephson junction are investigated both theoretically and experimentally. The amplifier uses the phenomenon of microwave negative resistance of the junction. Theoretical analysis made in usual resistively shunted junction (RSJ) model shows that the minimum noise temperature is equal to approximately 42T. It takes place at a signal frequency f close to the junction characteristic frequency f0. Maximum effectivity (the product of the square root of power gain and relative bandwidth) can reach 0.4 at f≃f0. Gain up to 20 dB was obtained at X-band using amplifier with Nb-Ta point-contact junction. Minimum noise temperature at T = 4.2K was about 200K.
The signal and noise properties of two basic types of externally pumped parametric amplifiers, using Josephson junctions with low capacitance, are calculated. The first type is a single- frequency nondegenerate amplifier and second one is a two-frequency degenerate amplifier, referred to sometimes as SUPARAMP. Calculations are based on the conventional RSJ model of the Josephson junction. In contrast to the works published earlier, the most realistic open circuit approximation is used for idler combinational frequencies, as well as for the pumping frequency harmonics. A single-frequency amplifier is shown to have relatively low noise temperatures (T_{N} \approx 25T) at signal frequencies of the order of the Josephson junction characteristic frequency ωc. On the other hand, SUPARAMP can have much lower noise but at lower frequencies, and it behaves approximately as a usual parametric amplifier with a critical frequency\omega_{cr} \approx 0.2 \omega_{c}.
Crossover between thermal and quantum noise in the externally-pumped Josephson-junction parametric amplifiers is theoretically followed. Two different approaches are used for the analysis : i. Josephson junction is replaced with its RSJ model with the equilibrium source of fluctuations; ii. microscopic theory of the tunnel junctions is used, which takes into account not only thermal and quantum but also shot noise. Because of inconvenience of the noise temperature TNfor the amplifier sensitivity characterization in the quantum limit, we express our results in terms of the figure ΘNwhich is essentially the amplifier output noise energy, reduced to its input (in the classical limit,\Theta_{N}=k_{B}T_{N}). For the nondegenerate amplifier, the minimum value of ΘN. equals hω/2 and is due to quantum noise (zero-point oscillations) in the idle-frequency resonator of the amplifier. For the degenerate amplifier, sensitive to only one quadrature component of the input signal, ΘNcan be made much less than the above "quantum limit" even at operation temperatures much higher thanh\omega/k_{B}, if the Josephson junction characteristic frequency ωcis high enough,h\omega_{c}\gsimk_{B}T. Our analysis of the experimental situatlon shows that the values\Theta_{N}<h\omega/2can be achieved using two-dimensional arrays of a large number (N\simeq100) single-tunnel-junction interferometers with low inductances, inductively coupled to a microwave cavity.
The high-frequency amplification properties of transformer coupled, resistively shunted Josephson tunnel junctions have been investigated. The importance of the shunt loop inductance is stressed. It allows a high cutoff frequency, of significance for good high-frequency performance. The self-pumped parametric amplifier showed none of the excessive noise rise, which has hitherto plagued the development of externally pumped Josephson junction amplifiers. Around 10 GHz, we estimated a noise temperature less than 30 K for an amplifier pumped by a Josephson oscillation with a frequency well above twice the signal frequency. The corresponding gain of 5 dB may be increased in a better impedance matched circuit. The gain was very stable against variations in the bias conditions. A gain-bandwidth product as high as 0.3 was registered. The experimental results agreed well with the established theory for self-pumped parametric Josephson amplifiers. It should be possible to extend the low noise amplification by this device to mm wave frequencies. A relaxation oscillation occurred at a subharmonic of the Josephson frequency when the shunt loop inductance became large. The amplification in this mode followed closely the predictions of a simple model, where the signal modulated the switching of the sawtooth-like (relatively low frequency) relaxation current. Gains of about 15 dB were measured around 10 GHz, but the amplification was sensitive to bias conditions and noisy in this case where the relaxation frequency fell well below the signal frequency. Much improved properties were registered when the inductance was decreased so that the relaxation frequency approached the Josephson frequency and exceeded twice the signal frequency. The behavior then resembled that of a Josephson mode parametric amplifier, but the high content of harmonics of a relaxation oscillation meant that the amplifier became noisier due to converted noise from the many idler frequencies.
A unified theory of the singly and doubly degenerate Josephson-junction parametric amplifier is presented. Experiments with single junctions on both amplifier modes at frequencies 10, 35, and 70 GHz are discussed. Low-noise temperature (∼100 K, single sideband (SSB)) and reasonable gain (∼8 dB) were obtained at 35 GHz in the singly degenerate mode. On the basis of the theory and experiments, a general procedure for optimizing junction parameters is discussed and illustrated by the specific design of a 100-GHz amplifier.
Arrays of 10 or 40 series-connected small densely packed Josephson tunnel junctions were successfully operated as parametric amplifiers at 10 GHz. Between 50 and 90% of the junctions in an array were observed to work coherently in the amplification process. Signal gain exceeding 24 dB was achieved with a pump power as low as −50 to −70 dBm. A power width (i.e., the range of the pump power for a gain within 3 dB of the peak gain) of 0.25 dB and a bandwidth of 15 MHz were measured for 20-dB gain. The power width was in accordance with theory but the bandwidth was reduced, probably due to noise saturation effects. The latter effects can be reduced by lowering the input noise temperature or by including an external band limitation. The noise temperature was also increased by saturation; however, with an external bandwidth of 60 MHz, a noise temperature of 30±20 K was measured. The application of a magnetic field has proved extremely useful as a means of tuning the amplifiers to stable high-gain operating points. This tuning was also utilized in evaluating the amplifier parameters, and the theory by Feldman, Parrish, and Chiao has been verified. The upper frequency limit for a lead tunnel junction amplifier ought to be well above 300 GHz.