Mike Gaidis deserves much of the credit for his contributions to the FTS system and the device design and testing. A Fourier transform spectrometer (FTS) has been constructed specifically to study the frequency response of SIS receivers.
List of Tables
Chapter 1 Introduction
- Submillimeter astronomy
- Heterodyne receiver principles
- A brief review of SIS receivers
- Thesis overview
It is desirable that the mixer has linear gain, that is, the output IF power is proportional to the power of the input signal. Several groups around the world have been involved, for example the Max Planck Institute for Extraterrestrial Physics in Germany (Rothermel et al.
Chapter 2 Theories of SIS Mixers
- Superconductivity
- Semiconductor picture of SIS tunnel junctions
- Heterodyne theory for SIS mixers
- Current in an SIS junction
- Heterodyne mixing in SIS junctions
- Three-port approximations
- Comments on quantum effects
The function of the mixer is to convert this input signal power to the output frequency w0, and couple it to the input of the load YL =Yo, i.e., the input to the input of the IF amplifier. We first take the unpumped and pumped de IV curves and derive the parameter a, i.e., the pumping power LO.
Chapter 3 Quasi-optical SIS Receivers
- Introduction
- A quasi-optical twin-slot antenna SIS receiver
One of the main challenges in designing quasi-optical mixers is to achieve efficient radiation coupling. For example, a hyperhemispheric lens will reduce the beam width by a factor of n, where n is the refractive index of the lens (Kasilingam & Rutledge 1986). The injection optics, the mixer block, the twin-slot antenna and the mixer chip will now be described in more detail. a) The signal/LO injection optics.
The LO (signal) coupling efficiency is equal to the reflectivity (transmissivity) of the beam splitter, which is a function of frequency. This part of the thesis is largely based on the work reported in the paper by Gaidis et al. The beam pattern of the entire quasi-optical system, which includes the double-slot antenna, the hyperhemispherical silicon lens, and the polyethylene lens, has been measured in our laboratory (Miller 1995).
Chapter 4 Modeling of SIS Mixers with Integrated Tuning Circuits
- Review of RF tuning circuits
- General characteristics of a transmission line
- Design equations for microstrip lines
- Surface impedance
- Superconductors
- Superconducting and normal-metal transmission lines
- Optimization of the twin-slot double-junction SIS mixer
The characteristic impedance Z0 of the transmission line, determined by the ratio of the voltage to the current in the line, is. The losses contributed by the conductors are represented by R, which is related to the surface resistance of the conductors. The surface impedance Zs of the two strips contributes to the series impedance of the transmission line, so now Z = jwL+2Zs/w andY is unchanged.
The evaluation of the surface impedance also requires boundary conditions regarding electron scattering from the surface of the conductor. As we can see, at a given frequency, the surface impedance in such limits depends only on a/l, which is a constant of the material (independent of temperature). So we can look at half the circuit to study RF matching.
Chapter 5 Fourier Transform Spectroscopic Study of SIS Detectors
- Background on Fourier transform spectroscopy
- Construction of a laboratory FTS
- FTS system description
- FTS alignment
- Direct and heterodyne detection of SIS receivers with theFTS
- Direct detection
The right-hand side of (5.7) is the inverse Fourier transform of the interferogram and is called its spectrum. The finite difference in the optical path sets the frequency resolution of the FTS and causes spurious sidebands in the transformed spectra. Since water absorption is severe at submillimeter depths, the optical path of the FTS must be free of water vapor.
The optical portion of the FTS system is covered by a plastic box made of quarter inch thick acrylic. This support consists of a cross which is bolted to the back of the mirror (or mirror holder). By turning the screws in the right direction, the angle of the mirror can be adjusted.
- Design and fabrication of all-Nb SIS mixers
- Direct detection with the Fourier transform spectrometer
- Heterodyne measurements
- Theoretical analysis for 839 G Hz test results
- Mixer performance calculation with 839 GHz LO
- Comparison with experimental data
- Chapter summary
The abnormally low noise temperature of the 750 GHz device at 4.2 K and 761 GHz is the result of a more powerful LO. Using our PCIRCUIT program, we find that the RF embedding admittance at 839 GHz is about 2.24 + j2.34, normalized to the normal state conductance of the junction (10.5 n)-1• The circuit file used in the PCIRCUIT. program and the calculated RF embedding impedance as a fuuktiou of frequency are presented in Appendix."X D.2. Here 7isol is the noise contribution of the isolator connecting the junction to the IF amplifier.
It is equal to the temperature of the final load, in our case 2. r is the reflection coefficient between the junction and the IF amplifier:. The breakdown of total receiver noise into contributions from the front-end RF optics, mixer and IF amplifier is clearly shown in Table 6.6. We believe that a significant reduction in receiver noise temperature can be achieved if we can reduce the loss of the front end optics and the tuning circuit.
Chapter 7 Wiring
SIS Mixers with Normal-metal AI
Design and FTS measurement of SIS mixers with AI wiring
Any unprotected Nb must be removed, exposing the AI ground plane to the microstrip lines. To compare with the normal skin effect model, we also plot the simulation calculated with a normal skin effect for an Al resistance ratio of 5. The response, compared to the anomalous skin effect case, shifts by about 3% towards higher frequencies. The remaining circuit parameters used in the simulations are all nominal design values.
85 fF I J.Lm2 appears to be a good estimate for the specific junction capacitance if the lithographically undercut junction area is negligible. All simulations are calculated using a specific capacitance of 85 fF / J.Lm2 and nominal design values for other parameters. For example, we cannot determine the resistivity ratio of the Al film from the FTS data.
Heterodyne measurement results
The frequency responses of these Al wiring devices are extremely wide, with bandwidths spanning GHz, as a result of the low Q resonant circuitry. For example, the noise temperature of the receiver at 982 GHz drops from rv 1450 K to rv 950 K after correction for the beam splitter. The figure shows the best uncorrected noise temperatures from the DSB receiver, with data obtained at LHe 4.2 K and also at pumped LHe temperature.
An uncorrected DSB receiver noise temperature of 840 K at 1042 GHz was obtained at a bath temperature of 2.5 K. From the sloping IV curve, we can deduce the resistivity ratio of the Al film. If an appropriate series resistance is used in the voltage correction procedure through (7.1), the two dips in the IF power curve at the photon stages must be separated by twice the intermediate voltage.
Device 1028
The uncorrected receiver noise temperatures and the noise after beamsplitter correction are given at a bath temperature of 4.2 K and,.._, 2.5 K. 7.7, together with the measured FTS data and the simulated RF coupling efficiency for a better assessment of the large bandwidth available.
As we mentioned earlier, we were not able to obtain optimal pumping of the node due to the lack of LO power at 982 GHz when using a beam splitter with a thickness of 25 J.Lm. However, the receiver noise temperature increased (as expected) because the thicker beamsplitter introduced more signal loss. To calculate the receiver performance, the transmission and noise of the front-end optics are estimated and listed in Table 7.6.
The calculated IF output powers for the hot and cold load for the case of a 25 J.Lm beam splitter are shown in Fig. Note that when a 51 J.Lm beam splitter is used, the mixer has a better performance (lower mixer noise and smaller mixer conversion loss), because the junction is better pumped. If there is sufficient LO power and a 10 J.Lm beam splitter can be used, the uncorrected receiver noise is expected to be rv 850K.
Device 716
The uncorrected DSB receiver noise temperatures are given in Table 7.8 and also shown in the figure. To compare the direct detection response with the heterodyne detection result, the inverse receiver noise temperature is also plotted in the figure. The inverse value is scaled vertically to show a clear correlation between the measured FTS response and the receiver noise.
The figure shows that the receiver heterodyne frequency range can be predicted with FTS direct detection measurements. Consequently, the frequency dependence of the receiver noise is mainly inversely determined by the RF coupling efficiency GRF·. We attempted to calculate the receiver performance of device 716 operating at LO frequencies of 660 GHz and 780 GHz as we did for device 1028.
Device 428
In contrast to the calculations for unit 1028, the deviations between the calculated and measured IF effects are large here. Again, the calculated and measured Y-factors differ by large amounts, with the calculated being lower than the measured by approximately 12%. They are unlikely to be caused by excess mixer noise, as that would produce a lower measured Y factor than the calculated one.
Using (7.4) the calculated receiver noise temperature is found to be 271 K. 7.16b shows the calculated and measured IF output power for the hot load. Like the 716 device, the calculated IF output power is less than the measured one by a large amount a) Comparison between measured and calculated pumped IV. The calculated and measured values are compared in Table 7.11, together with the breakdown of noise contributions from different sections.
7 .6 Chapter summary
Chapter 8 Summary
In Chapter 1 and Chapter 2 we covered some experimental and theoretical background for the SIS mixers. Good agreement was found between this approximate result and the rigorous solution of the Mattis-Bardeen equations. The mixer noise is usually a few times the quantum-limited noise level, regardless of whether the mixer has Nb-wire or Al-wiring.
At 1050 GHz, the RF coupling of the Al wiring device was predicted to be 50% higher than that of the Nb wiring device. 35% reduction in mixer conversion loss, accounting for 25-35% of the measured 40% drop in receiver noise temperature. The underestimation could not be explained by possible errors in the evaluation of the transmission and noise of the front optics and RF tuning circuits.
Appendix A Numerical Solution for the Anomalous Skin Effect
Once Ex(z) is known, the integral over the current density required for the surface impedance is calculated. 1 We use SUBROUTINE fred2 and FUNCTION fredin in Chapter 18, Numerical Recipes in FORTRAN, 2nd Edition, Cambridge Univ.
Appendix B Matrix Representation of Two-port Networks
A very important description of networks, especially in the microwave frequency range, is the scattering matrix S. The power gain of the transducer is determined by the scattering matrix of the two ports and the source and load impedances. The load ZL is connected to the source via a two-port network characterized by its scattering matrix S.
The basic connections between two-port networks are series, parallel and cascade connections, as shown in Figure. When two networks are cascaded, a2 and b2 of N1 become b1 and a1 of N2, so the cascade connection has a chain scattering. Matrix. A number of interconnected two-port networks can be reduced to a single two-port network with a scattering matrix S.
Appendix C PCIRCUIT D ocumentation
This specifies a two-port whose scattering parameters and noise parameters are specified numerically in the circuit file (see circuit file section for format). This specifies a two-port whose scattering parameters and noise parameters are specified numerically in a data file. This specifies a two-port consisting of an impedance placed in parallel across the two ports and specified numerically in the circuit file.
This specifies a two-port consisting of an impedance placed in parallel across the two ports, and which is specified numerically in a data file. Cascades AA and BB with two ports, with the resulting two ports now included in AA. Places AA and BB with two ports in series, with the resulting two ports now included in AA.
