Time Domain Analyzer

Time Domain Analyzer is useful for measuring impedance values along a transmission
line and for evaluating a device problem in time or distance. Time
domain display provides a more intuitive and direct look at the device under test characteristics. In addition, it gives more meaningful information concerning
the broadband response of a transmission system than other measuring techniques
by showing the effect of each discontinuity as a function of time or distance. This document
will focus on time domain analysis generated from vector
network analyzers. The intent is to provide engineers with frequency
domain background, an in-depth view of how a time domain display is created
from frequency domain data and how to apply the time domain
display to common problems in RF systems.
Agilent offers other documents that cover in detail the use of time domain displays. See
the bibliography for more details.

The measurement technique of time domain reflectometry was introduced in the
early 1960’s and works on the same principle as radar. A pulse of energy is transmitted
down a cable. When that pulse
reaches the end of the cable, or a fault along the cable, part or all of the pulse energy is
reflected back to the instrument. TDR measurements are made by launching an impulse
or a step into the test device and observing the response in time. Using a step generator
and a broadband oscilloscope, a fast edge is launched into the transmission line. The
incident and reflected voltage waves are monitored by the broadband oscilloscope at a
particular point on the line. By measuring the ratio of the input voltage to the reflected
voltage, the impedance of simple discontinuities can be calculated. The position of the
discontinuity can also be calculated as a function of time by applying the velocity of
propagation along the transmission line. The type of discontinuity can be identified by its response.

While the traditional TDR oscilloscope was useful as a qualitative tool, there were
limitations that affected its accuracy and usefulness; a) TDR output step rise time
– the spatial resolution of the measurement depends upon the step rise time; b) poor
signal-to-noise ratio due to the wideband receiver architecture.
Then, in the 70’s, it was shown that the relationship between the frequency domain and
the time domain could be described using the Fourier Transform. The Fourier Transform
of the network reflection coefficient as a function of frequency is the reflection coefficient
as a function of time; i.e., the distance along a transmission line. It was possible
to measure the response of a DUT in the frequency domain and then mathematically
calculate the inverse Fourier Transform of the data to give the time domain response.
A high performance VNA combined with fast computation power created unique measurement
capabilities. Using error-corrected data measured in the frequency domain, the
response of a network to step and impulse time stimuli can be calculated and displayed
as a function of time. This gives traditional time domain reflectometry capability in reflection
and transmission and adds measurement capability of band-limited networks. By
locating network elements in time and removing their effects from measured data, the
vector network analyzer makes more precise frequency domain measurements possible.
Figure 1 shows how both time domain and frequency domain displays
can be generated by either a time domain reflectometer oscilloscope or a vector
network analyzer. Data captured using either a TDR or VNA can be transformed
into both displays.

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NMR Hardware

This educational session lecture introduces the elements of the generic MR system hardware required to obtain images or spectra. The design criteria and function of the magnets, gradients, radiofrequency spectrometer and RF coils are examined. Examples of each, how they are designed and optimized is given (with examples) in the lecture. As far as possible examples related to the topics covered by ICMRM 11 will be given.

Magnets It is most usual for high field, homogeneity and stability magnets to be based on superconductive technology with axially symmetric coil windings. These magnets deliver the highest performance but require cryogenic cooling and are generally not portable (a 7T whole body system is 35 tons). In microscopy and materials applications the desirable parameters may be compromised in order to give portability, light weight or to fit with other constraints. These magnetic fields are then generated by a combination of electromagnet, permanent magnets and other magnetic materials. Magnetic fields may be optimized to give the best homo-geneity or gradient at a particular sweet-spot (which could be outside the magnet itself).

Gradients In order to spatially resolve the benchtop NMR signal then electromagnets are employed to give a (usually) linear profile in Bz with all three (or fewer) spatial axes. Gradient design techniques based on target field and boundary element methods are discussed. Examples of conventional cylindrical gradient design are shown. These design methods can be further exploited to give gradient designs on non-cylindrical geometries or arbitrary former shapes. Gradient design methods can be used to design both shim and pure electromagnet based field profiles.

RF Systems: Spectrometer The radiofrequency (RF) spectrometer is the central control component for the NMR analyzer system and provides system master clock and timings of gradient and RF pulses. The phase and timing stability in a high resolution system is critical and should exceed the magnet in its performance. This level of performance can be achieved if certain design specifications and criteria are followed. The modern spectrometer system is predominantly digital, with analogue components only making up the final parts nearest to the RF coils (i.e. power amplifiers, low-noise pre-amplifiers and transmit-receive switching et el). For example, in the most recent Ingenia body systems from Philips the entire acquisition system is placed on the receive coil itself within the magnet.

RF Systems: Coils After the main field strength, it is the quality and ability of the coil to faithfully pick up the NMR signal from the sample which defines the overall quality of our information. Signals and noise in an NMR experiment is discussed and the importance of optimum noise matching is introduced. Examples of coils which satisfy a range of demands in various geometries are discussed. The role of finite element RF simulation in coil design is demonstrated. This educational session lecture introduces the elements of the generic MR system hardware required to obtain images or spectra. The design criteria and function of the magnets, gradients, radiofrequency spectrometer and RF coils are examined. Examples of each, how they are designed and optimized is given (with examples) in the lecture. As far as possible examples related to the topics covered by ICMRM 11 will be given.

Magnets It is most usual for high field, homogeneity and stability magnets to be based on superconductive technology with axially symmetric coil windings. These magnets deliver the highest performance but require cryogenic cooling and are generally not portable (a 7T whole body system is 35 tons). In microscopy and materials applications the desirable parameters may be compromised in order to give portability, light weight or to fit with other constraints. These magnetic fields are then generated by a combination of electromagnet, permanent magnets and other magnetic materials. Magnetic fields may be optimized to give the best homo-geneity or gradient at a particular sweet-spot (which could be outside the magnet itself).

Gradients In order to spatially resolve the NMR signal then electromagnets are employed to give a (usually) linear profile in Bz with all three (or fewer) spatial axes. Gradient design techniques based on target field and boundary element methods are discussed. Examples of conventional cylindrical gradient design are shown. These design methods can be further exploited to give gradient designs on non-cylindrical geometries or arbitrary former shapes. Gradient design methods can be used to design both shim and pure electromagnet based field profiles.

RF Systems: Spectrometer The radiofrequency (RF) spectrometer is the central control component for the NMR system and provides system master clock and timings of gradient and RF pulses. The phase and timing stability in a high resolution system is critical and should exceed the magnet in its performance. This level of performance can be achieved if certain design specifications and criteria are followed. The modern spectrometer system is predominantly digital, with analogue components only making up the final parts nearest to the RF coils (i.e. power amplifiers, low-noise pre-amplifiers and transmit-receive switching et el). For example, in the most recent Ingenia body systems from Philips the entire acquisition system is placed on the receive coil itself within the magnet.

RF Systems: Coils After the main field strength, it is the quality and ability of the coil to faithfully pick up the NMR signal from the sample which defines the overall quality of our information. Signals and noise in an NMR experiment is discussed and the importance of optimum noise matching is introduced. Examples of coils which satisfy a range of demands in various geometries are discussed. The role of finite element RF simulation in coil design is demonstrated.