Perfect Quadrature Research Articles

A prominence eruption from the Sun to the Parker Solar Probe with multi-spacecraft observations

In the early hours of 2021 April 25, the Solar Probe Cup on board Parker Solar Probe registered the passage of a solar wind structure characterized by a clear and constant He2+/H+ density ratio above 6% during three hours. The He2+ contribution remained present but fainting and intermittent within a twelve-hour window. Solar Orbiter and Parker Solar Probe were in nearly perfect quadrature, allowing for optimal observing configuration in which the material impacting the Parker Solar Probe was in the Solar Orbiter plane of the sky and visible off the limb. In this work, we report the journey of the helium-enriched plasma structure from the Sun to the Parker Solar Probe by combining multi-spacecraft remote-sensing and in situ measurements. We identify an erupting prominence as the likely source, behind the Sun relative to the Earth, but visible to multiple instruments on both the Solar-Terrestrial Relations Observatory-A and Solar Orbiter. The associated CME was also observed by coronagraphs and heliospheric imagers from both spacecrafts before reaching the Parker Solar Probe at 46 R⊙, 8 h after the spacecraft registered a crossing of the heliospheric current sheet. Except for extraordinary helium enhancement, the CME showed ordinary plasma signatures and a complex magnetic field with an overall strength enhancement. The images from the Wide-field Imager for Solar Probe (WISPR) aboard Parker Solar Probe show a structure entering the field of view a few hours before the in situ crossing, followed by repetitive transient structures that may be the result of flying through the CME body. We believe this to be the first example of a CME being imaged by WISPR directly before and during being detected in situ. This study highlights the potential of combining the Parker Solar Probe in situ measurements in the inner heliosphere with simultaneous remote-sensing observations in (near) quadrature from other spacecrafts.

Second order compensation scheme for Haven’s technique to annul amplitude and phase mismatch for quadrature circuits

This paper, elucidates a second order Haven’s technique for generation of a pair of sinusoids in perfect quadrature phase. The effects of input amplitude mismatch on output phase mismatch and vice versa have been expounded. The proposed second order Haven’s Technique essentially estimates and corrects the amplitude and phase mismatches. This method aids in correcting amplitude and phase mismatch of any arbitrary magnitude. The developed technique is valid for mismatches occurring in both narrow band as well as wideband. Separate closed form expressions for compensation of both input amplitude and input phase mismatches have been derived. This study facilitates to determine the magnitude of phase angle error for a given amplitude mismatch and vice versa. Error plots for Haven’s technique have been generated and analysed. It is depicted that for every 1% of amplitude mismatch the phase mismatch increases by 0.6 degrees. The developed technique is modelled and simulated using available EDA tool for narrow band as well as wideband signals. The simulation results of the proposed technique confirm that for both narrow band and wideband signals, the input amplitude as well as phase mismatches are annulled completely. The developed Haven’s technique can find potential utility in implementation of Image Reject Mixer Architectures and Quadrature Oscillators for generation of quadrature waveforms.

On the tuning of high-resolution NMR probes.

Three optimum conditions for the tuning of NMR probes are compared: the conventional tuning optimum, which is based on radio-frequency pulse efficiency, the spin noise tuning optimum based on the line shape of the spin noise signal, and the newly introduced frequency shift tuning optimum, which minimizes the frequency pushing effect on strong signals. The latter results if the radiation damping feedback field is not in perfect quadrature to the precessing magnetization. According to the conventional RLC (resistor–inductor–capacitor) resonant circuit model, the optima should be identical, but significant deviations are found experimentally at low temperatures, in particular on cryogenically cooled probes. The existence of different optima with respect to frequency pushing and spin noise line shape has important consequences on the nonlinearity of spin dynamics at high polarization levels and the implementation of experiments on cold probes.

Conversion from linear to circular polarization in FPGA

Context: Radio astronomical receivers are now expanding their frequency range to cover large (octave) fractional bandwidths for sensitivity and spectral flexibility, which makes the design of good analogue circular polarizers challenging. Better polarization purity requires a flatter phase response over increasingly wide bandwidth, which is most easily achieved with digital techniques. They offer the ability to form circular polarization with perfect polarization purity over arbitrarily wide fractional bandwidths, due to the ease of introducing a perfect quadrature phase shift. Further, the rapid improvements in field programmable gate arrays provide the high processing power, low cost, portability and reconfigurability needed to make practical the implementation of the formation of circular polarization digitally. Aims: Here we explore the performance of a circular polarizer implemented with digital techniques. Methods: We designed a digital circular polarizer in which the intermediate frequency signals from a receiver with native linear polarizations were sampled and converted to circular polarization. The frequency-dependent instrumental phase difference and gain scaling factors were determined using an injected noise signal and applied to the two linear polarizations to equalize the transfer characteristics of the two polarization channels. This equalization was performed in 512 frequency channels over a 512 MHz bandwidth. Circular polarization was formed by quadrature phase shifting and summing the equalized linear polarization signals. Results: We obtained polarization purity of -25 dB corresponding to a D-term of 0.06 over the whole bandwidth. Conclusions: This technique enables construction of broad-band radio astronomy receivers with native linear polarization to form circular polarization for VLBI.

An alternative tuning approach to enhance NMR signals

By using spin-noise type measurement we show that the resonance frequency of the reception circuit of classical NMR spectrometers does not match the Larmor frequency even if, in emission, the electronic circuit is perfectly tuned at the Larmor frequency and matches the amplifier impedance. We also show that this spin-noise method can be used to ensure a match between the Larmor frequency and the reception circuit resonance frequency. In these conditions, (i) the radiation damping field is in perfect quadrature to the magnetization and (ii) the NMR signal level and potentially the signal-to-noise ratio, are enhanced. This choice induces a change of the probe resonance frequency by several hundreds of kHz for 500 or 700 MHz spectrometer. We show that the resulting mismatch condition for emission can be removed by adding other tuning and matching degrees of freedom located on the excitation line (or by symmetry on the reception line) decoupled to the probe resonance circuit by the crossed diodes.

Design of two‐channel perfect reconstruction QMF

AbstractThis paper proposes a design method for the FIR two‐channel perfect quadrature mirror filter (QMF) with the linear phase. The two‐channel perfect QMF can be designed by Vetterli's method, where a system of equations representing the condition for the perfect reconstruction of the signal is solved. The filter designed by this method, however, does not, in general, have good frequency characteristics.This paper presents the design for the two‐channel QMF with a perfect reconstruction and a good amplitude characteristic. The method is based on Vetterli's method, and a constraint to approximate the amplitude characteristic in the frequency domain is added to the condition of perfect reconstruction in time domain. Then Remez' algorithm is applied to the derived system of equations.The construction of the two‐channel perfect QMF, when the coefficient is quantized, also is discussed. Furthermore, a method is shown in which the two‐dimensional (2‐D) perfect QMF is designed by applying the McClellan transformation to the obtained 1‐D QMF. The condition for the McClellan transformation for the perfect reconstruction is derived.

Sensitivity considerations in cascaded lattice-type quadrature-modulation networks

Generalised quadrature-modulation (QM) circuits, introduced by Saraga, can be used to process independently the two sidebands of a double-sideband signal. Such circuits can be realised as a cascade of ‘lattice-type’ sections in which the arms of the lattice are linear, time-invariant, 2-port networks. This paper investigates the sensitivity of the transmission zeros (which exist at the frequencies of perfect quadrature) of the overall QM circuit to variations in the transfer functions of the lattice-arm networks. It is shown that variations occurring in the final section of a cascaded QM circuit can destroy the perfect quadrature, and hence the ‘potential’ transmission zeros, produced by earlier perfect sections. An example is given to illustrate the effect.