Single-tuned Circuit Research Articles

Dual-Tuned Lattice Balun for Multi-Nuclear MRI and MRS.

Balun or trap circuits are critical components for suppressing common-mode currents flowing on the outer conductors of coaxial cables in RF coil systems for Magnetic Resonance Imaging (MRI) and Magnetic Resonance Spectroscopy (MRS). Common-mode currents affect coils' tuning and matching, induce losses, pick up extra noise from the surrounding environment, lead to undesired cross-talk, and cause safety concerns in animal and human imaging. First proposed for microwave antenna applications, the Lattice balun has been widely used in MRI coils. It has a small footprint and can be easily integrated with coil tuning/matching circuits. However, the Lattice balun is typically a single-tuned circuit and cannot be used for multi-nuclear MRI and MRS with two RF frequencies. This work describes a dual-tuned Lattice balun design that is suitable for multi-nuclear MRI/MRS. It was first analyzed theoretically to derive component values. RF circuit simulations were then performed to validate the theoretical analysis and provide guidance for practical construction. Based on the simulation results, a dual-tuned balun circuit was built for 7T 1H/23Na MRI and bench tested. The fabricated dual-tuned balun exhibits superior performance at the Larmor frequencies of both 1H and 23Na, with less than 0.15 dB insertion loss and better than 17 dB common-mode rejection ratio at both frequencies.

FM Demodulation Using Dynamic Control Action of a Band Pass Filter

This paper audits FM demodulation using discriminator circuits, and the FM–AM conversion using a conventional single-tuned, double-tuned and staggered-tuned circuit is discussed. The demodulation capabilities of the double- and staggered-tuned circuits are audited in the time domain. It is observed that the conventional single- and double-tuned circuit outputs are highly distorted, in particular, the single-tuned circuit output is rich in second harmonics, and a balanced slope detection technique is proposed which reduces the output THD. A novel method of dynamically controlling the center frequency of the tuned circuit is proposed, and an excellent demodulation capability with a reduction in output THD by controlling the feedback loop gain is reported. This dynamically controlling action is applied to a conventional Foster–Seeley discriminator, and it is found that for higher values of feedback gain, the output THD decreases. It has been established that by judiciously controlling the center frequency of the tuned circuit, the effective modulation index has been reduced. The maximum permissible value of input modulation by the dynamic BPF has been derived. Experimental findings coupled with analytical results are presented and are shown to be in good agreement.

A comparison of double‐tuned surface coils

The combined acquisition of proton images and localized spectra is considered essential to the practical application of NMR techniques to human and animal research. Double-tuned surface coils which have been introduced to the literature are intended to address the problem; however, a careful evaluation of available designs is lacking. The "trap" method, the loop gap resonator design, and the transformer-coupled double-tuned design are evaluated here using bench tests of signal intensity and Q as well as signal-to-noise measurements on a 2-T imager/spectrometer. Comparisons are made relative to optimized single-tuned circuits of the same size for both protons at 85 MHz and phosphorus at 34 MHz. The results suggest that the "trap" design and the transformer coupled design are very efficient (98%) in the low-frequency mode (34 MHz) while the loop gap resonator is relatively inefficient (82%). In the high-frequency mode (85 MHz) the loop gap resonator is 75% efficient while the "trap" design and the transformer coupled coil are closer to 50% efficient.

Exact Formulation of Window Functions for Analog Network Spectral Analyzers

An equation for the spectral window function for analog network analyzers is derived without assumptions on length of data interval available. The equation, given in terms of filter pole-zero locations for both the filter-bank and heterodyned-input type analyzers, can be programmed on a digital computer without difficulty. As an illustration, the growth of a spectral window with increasing length of available data is shown for a special case: a single-tuned circuit followed by a squaring circuit and perfect integrator. The error in using the usual approximation also is indicated. Use of the derived equation for quantitative comparisons of analog and digital analyzers is noted.

A theoretical appraisal of the quenched multiple domain mode in GaAs microwave diodes

Quenched multiple domain (q.m.d.) mode oscillations in bulk GaAs have been analysed to obtain the relationships between efficiency, fundamental-frequency power output, fundamental-frequency negative resistance, and d.c. bias voltage. It is found that this highly efficient mode does not have the limitations of transit-time devices and consequently has a frequency-independent power × impedance product. The results demonstrate that q.m.d. oscillators designed with multiple-tuned circuits can operate at twice the efficiency of those operated in single-tuned circuits.

Transistor Television Picture if Double Tuned Amplifiers

The recent development of suitable VHF transistors has made possible the design of transistors amplifiers at the picture intermediate frequencies. Picture i-f strips using single-tuned circuits have been successfully built. <R xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1,2<R> This paper describes the design of a picture i-f strip using double-tuned circuits.</R></R>

Transient Response of Cascaded-Tuned Circuits

The transient response of two cascaded stagger-tuned amplifier stages to a pulse of arbitrary carrier frequency is derived, starting from the response of a single-tuned circuit. The results are obtained by solving the differential equation of the network, and by employing a simple stratagem that immediately yields the arbitrary constants. The result is extended to three stagger-tuned stages, and the exten- sion to an arbitrary number of stages is indicated. The transient re- sponse of two synchronously tuned stages is also derived, based on the solution of the stagger-tuned case, No approximations are made in any of the derivations.

Alignment and Adjustment of Synchronously Tuned Multiple-Resonant-Circuit Filters

A simple method of "tuning up" a multiple-resonant-circuit filter quickly and exactly is demonstrated. The method may be summarized as follows: Very loosely couple a detector to the first resonator of the filter; then, proceeding in consecutive order, tune all odd-numbered resonators for maximum detector output, and all even-numbered resonators for minimum detector output (always making sure that the resonator immediately following the one to be resonated is completely detuned). Also considered is the correct adjustment of the two other types of constants in a filter. Filter constants can always be reduced to only three fundamental types: f <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> , d <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r</sub> (1/Q <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r</sub> ), and K <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r(r+1)</sub> . This is true whether a lumped-element 100-kc filter or a distributed-element 5,000-mc unit is being considered. dr is adjusted by considering the rth resonator as a single-tuned circuit (all other resonators completely detuned) and setting the bandwidth between the 3-db-down-points to the required value. K <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r(r+1)</sub> is adjusted by considering the rth and (r+1)th adjacent resonators as a double-tuned circuit (all other resonators completely detuned) and setting the bandwidth between the resulting response peaks to the required value. Finally, all the required values for K and Q are given for an n-resonant-circuit filter that will produce the response (V <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</sub> /V) <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> =1 +(Δf/Δf <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3db</sub> ) <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2n</sup> .

A Flat-Response Single-Tuned I. F. Amplifier

An intermediate-frequency amplifier, providing double-tuned response using single-tuned circuits with negative feedback, is described. Particular attention is centered on the problems arising in the case where relatively narrow pass bands are wanted.

Oscillation Conditions in Single Tuned Amplifiers

An application of the calculus of finite differences has been made in obtaining the complete expression for the voltage gain of an n-stage amplifier having identical grid-to-plate impedances and plate loads when driven by a generator of any given internal impedance. An application of these results was made in determining the conditions of oscillation in a multi-stage amplifier using single-tuned circuits. It was found that there is a certain minimum grid-to-plate capacitance required to cause oscillation. If the actual grid-to-plate capacitances are below this value, the system will not oscillate. There also exists a region of stable gain, zero to 21/n, wherein it is impossible to make the amplifier oscillate even with grid-to-plate capacitance arbitrarily large.

A Theoretical and Experimental Investigation of Tuned-Circuit Distortion in Frequency-Modulation Systems

The problem of distortion introduced into the modulation intelligence by tuned circuits is considered both theoretically and experimentally. Complex equations result when the effect of the intelligence modulation is considered. These equations, while not readily amenable to Fourier analysis, disclose that the distortion parameters are ΔW/BW and λ/BW where, ΔW/2π = peak-frequency swing λ/2π = modulation frequency BW = bandwidth in kilocycles measured at 3 decibels down. Double-tuned circuits critically coupled. If the effect of the modulation frequency is neglected, the equations resulting from a theoretical analysis are somewhat simplified and the distortion due to single- and double-tuned circuits can be formulated. Close agreement between calculated and measured distortion was obtained up to approximately a 5000-cycle-per-second modulation frequency. At this frequency the departure of the observed from calculated values was quite noticeable. Theoretical maximum-distortion limits for the single- and double-tuned circuits are derived. For the single-tuned circuit the theoretical maximum distortion is D <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</inf> max (single-tuned circuit) = 2λ/ΔW·100. For the double-tuned circuit it is D <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</inf> max (double-tuned circuit) = 4λ/ΔW·100 A conservative design figure relating bandwidth to frequency swing in order to insure distortion-free transmission to 15,000 cycles per second was experimentally found to be, ΔW/BW = 1/4.