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NASA NTRS2006

Coherent Detector Arrays for Continuum and Spectral Line Applications

This viewgraph presentation reviews the requirements for improved coherent detector arrays for use in continuum and spectral line applications. With detectors approaching fundamental limits, large arrays offer the only path to sensitivity improvement. Monolithic Microwave Integrated Circuit (MMIC) technology offers a straightforward path to massive focal plane millimeter wave arrays: The technology will readily support continuum imagers, polarimeters and spectral line receivers from 30-110 GHz. Science programs, particularly large field blind surveys will benefit from simultaneous observations of hundreds or thousands of pixels 1000 element array is competitive with a cost less than $2M.

instrumentation↗

NASA NTRS2003

A 94 GHz RF Electronics Subsystem for the CloudSat Cloud Profiling Radar

The CloudSat spacecraft, scheduled for launch in 2004, will carry the 94 GHz Cloud Profiling Radar (CPR) instrument. The design, assembly and test of the flight Radio Frequency Electronics Subsystem (RFES) for this instrument has been completed and is presented here. The RFES consists of an Upconverter (which includes an Exciter and two Drive Amplifiers (DA's)), a Receiver, and a Transmitter Calibrator assembly. Some key performance parameters of the RFES are as follows: dual 100 mW pulse-modulated drive outputs at 94 GHz, overall Receiver noise figure < 5.0 dB, a highly stable W-band noise source to provide knowledge accuracy of Receiver gain of < 0.4 dB over the 2 year mission life, and a W-band peak power detector to monitor the transmitter output power to within 0.5 dB over life. Some recent monolithic microwave integrated circuit (MMIC) designs were utilized which implement the DA's in 0.1 micron GaAs high electron-mobility transistor (HEMT) technology and the Receiver low-noise amplifier (LNA) in 0.1 micron InP HEMT technology.

radio frequency electronics subsystem (RFES)↗

NASA NTRS2007

Array Phase Shifters: Theory and Technology

While there are a myriad of applications for microwave phase shifters in instrumentation and metrology, power combining, amplifier linearization, and so on, the most prevalent use is in scanning phased-array antennas. And while this market continues to be dominated by military radar and tracking platforms, many commercial applications have emerged in the past decade or so. These new and potential applications span low-Earth-orbit (LEO) communications satellite constellations and collision warning radar, an aspect of the Intelligent Vehicle Highway System or Automated Highway System. In any case, the phase shifters represent a considerable portion of the overall antenna cost, with some estimates approaching 40 percent for receive arrays. Ferrite phase shifters continue to be the workhorse in military-phased arrays, and while there have been advances in thin film ferrite devices, the review of this device technology in the previous edition of this book is still highly relevant. This chapter will focus on three types of phase shifters that have matured in the past decade: GaAs MESFET monolithic microwave integrated circuit (MMIC), micro-electromechanical systems (MEMS), and thin film ferroelectric-based devices. A brief review of some novel devices including thin film ferrite phase shifters and superconducting switches for phase shifter applications will be provided. Finally, the effects of modulo 2 phase shift limitations, phase errors, and transient response on bit error rate degradation will be considered.

Romanofsky, Robert R.↗

NASA NTRS2005

High-efficiency solid state power amplifier

A high-efficiency solid state power amplifier (SSPA) for specific use in a spacecraft is provided. The SSPA has a mass of less than 850 g and includes two different X-band power amplifier sections, i.e., a lumped power amplifier with a single 11-W output and a distributed power amplifier with eight 2.75-W outputs. These two amplifier sections provide output power that is scalable from 11 to 15 watts without major design changes. Five different hybrid microcircuits, including high-efficiency Heterostructure Field Effect Transistor (HFET) amplifiers and Monolithic Microwave Integrated Circuit (MMIC) phase shifters have been developed for use within the SSPA. A highly efficient packaging approach enables the integration of a large number of hybrid circuits into the SSPA.

Wallis, Robert E.↗

NASA NTRS2009

InP Heterojunction Bipolar Transistor Amplifiers to 255 GHz

Two single-stage InP heterojunction bipolar transistor (HBT) amplifiers operate at 184 and 255 GHz, using Northrop Grumman Corporation s InP HBT MMIC (monolithic microwave integrated circuit) technology. At the time of this reporting, these are reported to be the highest HBT amplifiers ever created. The purpose of the amplifier design is to evaluate the technology capability for high-frequency designs and verify the model for future development work.

Radisic, Vesna↗

NASA NTRS2009

Submillimeter Confocal Imaging Active Module

The term submillimeter confocal imaging active module (SCIAM) denotes a proposed airborne coherent imaging radar system that would be suitable for use in reconnaissance, surveillance, and navigation. The development of the SCIAM would include utilization and extension of recent achievements in monolithic microwave integrated circuits capable of operating at frequencies up to and beyond a nominal radio frequency of 340 GHz. Because the SCIAM would be primarily down-looking (in contradistinction to primarily side-looking), it could be useful for imaging shorter objects located between taller ones (for example, objects on streets between buildings). The SCIAM would utilize a confocal geometry to obtain high cross-track resolution, and would be amenable to synthetic-aperture processing of its output to obtain high along-track resolution. The SCIAM (see figure) would include multiple (two in the initial version) antenna apertures, separated from each other by a cross-track baseline of suitable length (e.g., 1.6 m). These apertures would both transmit the illuminating radar pulses and receive the returns. A common reference oscillator would generate a signal at a controllable frequency of (340 GHz + (Delta)f)/N, where (Delta)f is an instantaneous swept frequency difference and N is an integer. The output of this oscillator would be fed to a frequency- multiplier-and-power-amplifier module to obtain a signal, at 340 GHz + (Delta)f, that would serve as both the carrier signal for generating the transmitted pulses and a local-oscillator (LO) signal for a receiver associated with each antenna aperture. Because duplexers in the form of circulators or transmit/receive (T/R) switches would be lossy and extremely difficult to implement, the antenna apertures would be designed according to a spatial-diplexing scheme, in which signals would be coupled in and out via separate, adjacent transmitting and receiving feed horns. This scheme would cause the transmitted and received beams to be aimed in slightly different directions, and, hence, to not overlap fully on the targets on the ground. However, a preliminary analysis has shown that the loss of overlap would be small enough that the resulting loss in signal-to-noise ratio (SNR) would be much less than the SNR loss associated with the use of a 340-GHz T/R switch.

Hong, John↗

NASA NTRS2009

Ka-Band Waveguide Hybrid Combiner for MMIC Amplifiers with Unequal and Arbitrary Power Output Ratio

The design, simulation and characterization of a novel Ka-band (32.05 +/- 0.25 GHz) rectangular waveguide branchline hybrid unequal power combiner is presented. The manufactured combiner was designed to combine input signals, which are nearly in phase and with an amplitude ratio of two. The measured return loss and isolation of the branch-line hybrid are better than 22 and 27 dB, respectively. The application of the branch-line hybrid for combining two monolithic microwave integrated circuit (MMIC) power amplifiers with output power ratio of two is demonstrated. The measured combining efficiency is 92.9% at the center frequency of 32.05 GHz.

Simons, Rainee N.↗

NASA NTRS2009

Tests of Low-Noise MMIC Amplifier Module at 290 to 340 GHz

A document presents data from tests of a low-noise amplifier module operating in the frequency range from 290 to 340 GHz said to be the highest-frequency low-noise, solid-state amplifier ever developed. The module comprised a three-stage monolithic microwave integrated circuit (MMIC) amplifier integrated with radial probe MMIC/waveguide transitions and contained in a compact waveguide package, all according to the concepts described in the immediately preceding article and in the referenced prior article, "Integrated Radial Probe Transition From MMIC to Waveguide" (NPO-43957), NASA Tech Briefs Vol. 31, No. 5 (May 2007), page 38. The tests included measurements by the Y-factor method, in which noise figures are measured repeatedly with an input noise source alternating between an "on" (hot-load) condition and an "off" (cold-load) condition. (The Y factor is defined as the ratio between the "on" and "off" noise power levels.) The test results showed that, among other things, the module exhibited a minimum noise figure of about 8.7 dB at 325 GHz and that the gain at that frequency under the bias conditions that produced the minimum noise figure was between about 9 and 10 dB.

Gaier, Todd↗

NASA NTRS2009

Three MMIC Amplifiers for the 120-to-200 GHz Frequency Band

Closely following the development reported in the immediately preceding article, three new monolithic microwave integrated circuit (MMIC) amplifiers that would operate in the 120-to-200-GHz frequency band have been designed and are under construction at this writing. The active devices in these amplifiers are InP high-electron-mobility transistors (HEMTs). These amplifiers (see figure) are denoted the LSLNA150, the LSA200, and the LSA185, respectively. Like the amplifiers reported in the immediately preceding article, the LSLNA150 (1) is intended to be a prototype of low-noise amplifiers (LNAs) to be incorporated into spaceborne instruments for sensing cosmic microwave background radiation and (2) has potential for terrestrial use in electronic test equipment, passive millimeter-wave imaging systems, radar receivers, communication receivers, and systems for detecting hidden weapons. The HEMTs in this amplifier were fabricated according to 0.08- m design rules of a commercial product line of InP HEMT MMICs at HRL Laboratories, LLC, with a gate geometry of 2 fingers, each 15 m wide. On the basis of computational simulations, this amplifier is designed to afford at least 15 dB of gain, with a noise figure of no more than about 6 dB, at frequencies from 120 to 160 GHz. The measured results of the amplifier are shown next to the chip photo, with a gain of 16 dB at 150 GHz. Noise figure work is ongoing. The LSA200 and the LSA185 are intended to be prototypes of transmitting power amplifiers for use at frequencies between about 180 and about 200 GHz. These amplifiers have also been fabricated according to rules of the aforesaid commercial product line of InP HEMT MMICs, except that the HEMTs in these amplifiers are characterized by a gate geometry of 4 fingers, each 37 m wide. The measured peak performance of the LSA200 is characterized by a gain of about 1.4 dB at a frequency of 190 GHz; the measured peak performance of the LSA185 is characterized by a gain of about 2.7 dB at a frequency of 181 GHz. The measured gain results of each chip are shown next to their respective photos.

Samoska, Lorene↗

NASA NTRS2009

System for Automated Calibration of Vector Modulators

Vector modulators are used to impose baseband modulation on RF signals, but non-ideal behavior limits the overall performance. The non-ideal behavior of the vector modulator is compensated using data collected with the use of an automated test system driven by a LabVIEW program that systematically applies thousands of control-signal values to the device under test and collects RF measurement data. The technology innovation automates several steps in the process. First, an automated test system, using computer controlled digital-to-analog converters (DACs) and a computer-controlled vector network analyzer (VNA) systematically can apply different I and Q signals (which represent the complex number by which the RF signal is multiplied) to the vector modulator under test (VMUT), while measuring the RF performance specifically, gain and phase. The automated test system uses the LabVIEW software to control the test equipment, collect the data, and write it to a file. The input to the Lab - VIEW program is either user-input for systematic variation, or is provided in a file containing specific test values that should be fed to the VMUT. The output file contains both the control signals and the measured data. The second step is to post-process the file to determine the correction functions as needed. The result of the entire process is a tabular representation, which allows translation of a desired I/Q value to the required analog control signals to produce a particular RF behavior. In some applications, corrected performance is needed only for a limited range. If the vector modulator is being used as a phase shifter, there is only a need to correct I and Q values that represent points on a circle, not the entire plane. This innovation has been used to calibrate 2-GHz MMIC (monolithic microwave integrated circuit) vector modulators in the High EIRP Cluster Array project (EIRP is high effective isotropic radiated power). These calibrations were then used to create correction tables to allow the commanding of the phase shift in each of four channels used as a phased array for beam steering of a Ka-band (32-GHz) signal. The system also was the basis of a breadboard electronic beam steering system. In this breadboard, the goal was not to make systematic measurements of the properties of a vector modulator, but to drive the breadboard with a series of test patterns varying in phase and amplitude. This is essentially the same calibration process, but with the difference that the data collection process is oriented toward collecting breadboard performance, rather than the measurement of output from a network analyzer.

Lux, James↗

NASA NTRS2007

Power-Amplifier Module for 145 to 165 GHz

A power-amplifier module that operates in the frequency range of 145 to 165 GHz has been designed and constructed as a combination of (1) a previously developed monolithic microwave integrated circuit (MMIC) power amplifier and (2) a waveguide module. The amplifier chip was needed for driving a high-electron-mobility-transistor (HEMT) frequency doubler. While it was feasible to connect the amplifier and frequency-doubler chips by use of wire bonds, it was found to be much more convenient to test the amplifier and doubler chips separately. To facilitate separate testing, it was decided to package the amplifier and doubler chips in separate waveguide modules. Figure 1 shows the resulting amplifier module. The amplifier chip was described in "MMIC HEMT Power Amplifier for 140 to 170 GHz" (NPO-30127), NASA Tech Briefs, Vol. 27, No. 11, (November 2003), page 49. To recapitulate: This is a three-stage MMIC power amplifier that utilizes HEMTs as gain elements. The amplifier was originally designed to operate in the frequency range of 140 to 170 GHz. The waveguide module is based on a previously developed lower frequency module, redesigned to support operation in the frequency range of 140 to 220 GHz. Figure 2 presents results of one of several tests of the amplifier module - measurements of output power and gain as functions of input power at an output frequency of 150 GHz. Such an amplifier module has many applications to test equipment for power sources above 100 GHz.

Samoska, Lorene↗

NASA NTRS2010

Ka-Band Waveguide Two-Way Hybrid Combiner for MMIC Amplifiers

The design, simulation, and characterization of a novel Ka-band (32.05 0.25 GHz) rectangular waveguide two-way branch-line hybrid unequal power combiner (with port impedances matched to that of a standard WR-28 waveguide) has been created to combine input signals, which are in phase and with an amplitude ratio of two. The measured return loss and isolation of the branch-line hybrid are better than 22 and 27 dB, respectively. The measured combining efficiency is 92.9 percent at the center frequency of 32.05 GHz. This circuit is efficacious in combining the unequal output power from two Ka-band GaAs pseudomorphic high electron mobility transistor (pHEMT) monolithic microwave integrated circuit (MMIC) power amplifiers (PAs) with high efficiency. The component parts include the branch-line hybrid-based power combiner and the MMIC-based PAs. A two-way branch-line hybrid is a four-port device with all ports matched; power entering port 1 is divided in phase, and into the ratio 2:1 between ports 3 and 4. No power is coupled to port 2. MMICs are a type of integrated circuit fabricated on GaAs that operates at microwave frequencies, and performs the function of signal amplification. The power combiner is designed to operate over the frequency band of 31.8 to 32.3 GHz, which is NASA's deep space frequency band. The power combiner would have an output return loss better than 20 dB. Isolation between the output port and the isolated port is greater than 25 dB. Isolation between the two input ports is greater than 25 dB. The combining efficiency would be greater than 90 percent when the ratio of the two input power levels is two. The power combiner is machined from aluminum with E-plane split-block arrangement, and has excellent reliability. The flexibility of this design allows the combiner to be customized for combining the power from MMIC PAs with an arbitrary power output ratio. In addition, it allows combining a low-power GaAs MMIC with a high-power GaN MMIC. The arbitrary port impedance allows matching the output impedance of the MMIC PA directly to the waveguide impedance without transitioning first into a transmission line with characteristic impedance of 50 ohms. Thus, by eliminating the losses associated with a transition, the overall SSPA efficiency is enhanced. For reducing the cost and weight when required in very large quantities, such as in the beam-forming networks of phased-array antenna systems, the combiner can be manufactured using metal-plated plastic. Two hybrid unequal power combiners can be cascaded to realize a non-binary combiner (for e.g., a three-way) and can be synergistically optimized for low VSWR (voltage standing wave ratio), low insertion loss, high isolation, and wide bandwidth using commercial off-the-shelf electromagnetic software design tools.

Simons, Rainee N.↗

NASA NTRS2007

VCO PLL Frequency Synthesizers for Spacecraft Transponders

Two documents discuss a breadboard version of advanced transponders that, when fully developed, would be installed on future spacecraft to fly in deep space. These transponders will be required to be capable of operation on any deepspace- communications uplink frequency channel between 7,145 and 7,235 MHz, and any downlink frequency channel between 8,400 and 8,500 MHz. The document focuses on the design and operation of frequency synthesizers for the receiver and transmitter. Heretofore, frequency synthesizers in deep-space transponders have been based on dielectric resonator oscillators (DROs), which do not have the wide tuning bandwidth necessary to tune over all channels in the uplink or downlink frequency bands. To satisfy the requirement for tuning bandwidth, the present frequency synthesizers are based on voltage-controlled-oscillator (VCO) phase-locked loops (PLLs) implemented by use of monolithic microwave integrated circuits (MMICs) implemented using inGaP heterojunction bipolar transistor (HBT) technology. MMIC VCO PLL frequency synthesizers similar to the present ones have been used in commercial and military applications but, until now, have exhibited too much phase noise for use in deep-space transponders. The present frequency synthesizers contain advanced MMIC VCOs, which use HBT technology and have lower levels of flicker (1/f) phase noise. When these MMIC VCOs are used with high-speed MMIC frequency dividers, it becomes possible to obtain the required combination of frequency agility and low phase noise.

Smith, Scott↗

NASA NTRS2010

High Efficiency Ka-Band Solid State Power Amplifier Waveguide Power Combiner

A novel Ka-band high efficiency asymmetric waveguide four-port combiner for coherent combining of two Monolithic Microwave Integrated Circuit (MMIC) Solid State Power Amplifiers (SSPAs) having unequal outputs has been successfully designed, fabricated and characterized over the NASA deep space frequency band from 31.8 to 32.3 GHz. The measured combiner efficiency is greater than 90 percent, the return loss greater than 18 dB and input port isolation greater than 22 dB. The manufactured combiner was designed for an input power ratio of 2:1 but can be custom designed for any arbitrary power ratio. Applications considered are NASA s space communications systems needing 6 to 10 W of radio frequency (RF) power. This Technical Memorandum (TM) is an expanded version of the article recently published in Institute of Engineering and Technology (IET) Electronics Letters.

Wintucky, Edwin G.↗

NASA NTRS2010

Two-Stage, 90-GHz, Low-Noise Amplifier

A device has been developed for coherent detection of the polarization of the cosmic microwave background (CMB). A two-stage amplifier has been designed that covers 75-110 GHz. The device uses the emerging 35-nm InP HEMT technology recently developed at Northrop Grumman Corporation primarily for use at higher frequencies. The amplifier has more than 18 dB gain and less than 35 K noise figure across the band. These devices have noise less than 30 K at 100 GHz. The development started with design activities at JPL, as well as characterization of multichip modules using existing InP. Following processing, a test campaign was carried out using single-chip modules at 100 GHz. Successful development of the chips will lead to development of multichip modules, with simultaneous Q and U Stokes parameter detection. This MMIC (monolithic microwave integrated circuit) amplifier takes advantage of performance improvements intended for higher frequencies, but in this innovation are applied at 90 GHz. The large amount of available gain ultimately leads to lower possible noise performance at 90 GHz.

Samoska, Lorene A.↗

NASA NTRS2006

MMIC DHBT Common-Base Amplifier for 172 GHz

Figure 1 shows a single-stage monolithic microwave integrated circuit (MMIC) power amplifier in which the gain element is a double-heterojunction bipolar transistor (DHBT) connected in common-base configuration. This amplifier, which has been demonstrated to function well at a frequency of 172 GHz, is part of a continuing effort to develop compact, efficient amplifiers for scientific instrumentation, wide-band communication systems, and radar systems that will operate at frequencies up to and beyond 180 GHz. The transistor is fabricated from a layered structure formed by molecular beam epitaxy in the InP/InGaAs material system. A highly doped InGaAs base layer and a collector layer are fabricated from the layered structure in a triple mesa process. The transistor includes two separate emitter fingers, each having dimensions of 0.8 by 12 m. The common-base configuration was chosen for its high maximum stable gain in the frequency band of interest. The input-matching network is designed for high bandwidth. The output of the transistor is matched to a load line for maximum saturated output power under large-signal conditions, rather than being matched for maximum gain under small-signal conditions. In a test at a frequency of 172 GHz, the amplifier was found to generate an output power of 7.5 mW, with approximately 5 dB of large-signal gain (see Figure 2). Moreover, the amplifier exhibited a peak small-signal gain of 7 dB at a frequency of 176 GHz. This performance of this MMIC single-stage amplifier containing only a single transistor represents a significant advance in the state of the art, in that it rivals the 170-GHz performance of a prior MMIC three-stage, four-transistor amplifier. [The prior amplifier was reported in "MMIC HEMT Power Amplifier for 140 to 170 GHz" (NPO-30127), NASA Tech Briefs, Vol. 27, No. 11 (November 2003), page 49.] This amplifier is the first heterojunction- bipolar-transistor (HBT) amplifier built for medium power operation in this frequency band. The performance of the amplifier as measured in the aforementioned tests suggests that InP/InGaAs HBTs may be superior to high-electron-mobility (HEMT) transistors in that the HBTs may offer more gain per stage and more output power per transistor.

Paidi, Vamsi↗

NASA NTRS2010

Demonstration of a Submillimeter-Wave HEMT Oscillator Module at 330 GHz

In this work, radial transitions have been successfully mated with a HEMT-based MMIC (high-electron-mobility-transistor-based monolithic microwave integrated circuit) oscillator circuit. The chip has been assembled into a WR2.2 waveguide module for the basic implementation with radial E-plane probe transitions to convert the waveguide mode to the MMIC coplanar waveguide mode. The E-plane transitions have been directly integrated onto the InP substrate to couple the submillimeter-wave energy directly to the waveguides, thus avoiding wire-bonds in the RF path. The oscillator demonstrates a measured 1.7 percent DC-RF efficiency at the module level. The oscillator chip uses 35-nm-gate-length HEMT devices, which enable the high frequency of oscillation, creating the first demonstration of a packaged waveguide oscillator that operates over 300 GHz and is based on InP HEMT technology. The oscillator chip is extremely compact, with dimensions of only 1.085 x 320 sq mm for a total die size of 0.35 sq mm. This fully integrated, waveguide oscillator module, with an output power of 0.27 mW at 330 GHz, can provide low-mass, low DC-power-consumption alternatives to existing local oscillator schemes, which require high DC power consumption and large mass. This oscillator module can be easily integrated with mixers, multipliers, and amplifiers for building high-frequency transmit and receive systems at submillimeter wave frequencies. Because it requires only a DC bias to enable submillimeter wave output power, it is a simple and reliable technique for generating power at these frequencies. Future work will be directed to further improving the applicability of HEMT transistors to submillimeter wave and terahertz applications. Commercial applications include submillimeter-wave imaging systems for hidden weapons detection, airport security, homeland security, and portable low-mass, low-power imaging systems

Radisic, Vesna↗

NASA NTRS2010

Differential Resonant Ring YIG Tuned Oscillator

A differential SiGe oscillator circuit uses a resonant ring-oscillator topology in order to electronically tune the oscillator over multi-octave bandwidths. The oscillator s tuning is extremely linear, because the oscillator s frequency depends on the magnetic tuning of a YIG sphere, whose resonant frequency is equal to a fundamental constant times the DC magnetic field. This extremely simple circuit topology uses two coupling loops connecting a differential pair of SiGe bipolar transistors into a feedback configuration using a YIG tuned filter creating a closed-loop ring oscillator. SiGe device technology is used for this oscillator in order to keep the transistor s 1/f noise to an absolute minimum in order to achieve minimum RF phase noise. The single-end resonant ring oscillator currently has an advantage in fewer parts, but when the oscillation frequency is greater than 16 GHz, the package s parasitic behavior couples energy to the sphere and causes holes and poor phase noise performance. This is because the coupling to the YIG is extremely low, so that the oscillator operates at near the unloaded Q. With the differential resonant ring oscillator, the oscillation currents are just in the YIG coupling mechanisms. The phase noise is even better, and the physical size can be reduced to permit monolithic microwave integrated circuit oscillators. This invention is a YIG tuned oscillator circuit making use of a differential topology to simultaneously achieve an extremely broadband electronic tuning range and ultra-low phase noise. As a natural result of its differential circuit topology, all reactive elements, such as tuning stubs, which limit tuning bandwidth by contributing excessive open loop phase shift, have been eliminated. The differential oscillator s open-loop phase shift is associated with completely non-dispersive circuit elements such as the physical angle of the coupling loops, a differential loop crossover, and the high-frequency phase shift of the n-p-n transistors. At the input of the oscillator s feedback loop is a pair of differentially connected n-p-n SiGe transistors that provides extremely high gain, and because they are bulk-effect devices, extremely low 1/f noise (leading to ultralow RF phase noise). The 1/f corner frequency for n-p-n SiGe transistors is approximately 500 Hz. The RF energy from the transistor s collector output is connected directly to the top-coupling loop (the excitation loop) of a single-sphere YIG tuned filter. A uniform magnetic field to bias the YIG must be at a right angle to any vector associated with an RF current in a coupling loop in order for the precession to interact with the RF currents.

Parrott, Ronald A.↗