## Monthly Archives: March 2014

## MANUFACTURING ERRORS

The theoretical design of a high-homogeneity magnet can be simple because only axial terms in the z field need to be considered. However, the manufacturing process introduces errors in conductor placement which generate both even – and odd-order axial and, most significantly, radial field gradients. Further, the materials of the coil forms, the nonisotropic contraction of the forms and windings during cool-down to helium temperature and the effects of the large forces between the windings may also introduce inhomogeneity. Typically, the homogeneity of an as-wound set of NMR solenoids is not better than 10~5 over a 5 mm diameter spherical volume (dsv) at the center. For high-resolution NMR, an effective homogeneity of 10~9 over at least 5 mm dsv is required. The improvement of the raw homogeneity to this level is achieved by three steps, superconducting shim coils, room temperature shim coils and, in NMR magnets only, sample spinning. (Additionally, in cases of poor raw homogeneity, ferromagnetic shims may be used occasionally in NMR magnets and routinely in MRI magnets to compensate for large errors or significant high-order harmonics.) The presence of radial field gradients necessitates a more comprehensive field analysis than is convenient with Cartesian coordinates.

Figure 2. Principle of harmonic compensation. Coaxial solenoids generating field harmonics of opposite sign. |

Figure 3. The system of spherical coordinates specifying field points and current sources. |

## LINEAR ANTENNAS

Historically, using a piece of radiating straight wire as an The radiation resistance (Rr) is defined as the positive resis – aerial, or antenna, was a natural choice for wireless commu – tance across which the real power radiated (Prad) can be

(13a) (13b) |

P |

(6) |

rad |

G = |

(14) |

The input resistance of an antenna is a sum of radiation resistance plus the positive resistance due to ohmic losses. Radiation Intensity, Directivity, and Gain The antenna radiates real power in the far zone in space over a solid angle of 4w radians. The radiation intensity U(e, ф), the real power radiated per unit solid angle, is a product of the radiation intensity Prad, the real power per unit solid area on the surface, multiplied by the square (r2) of the distance and is given by |

thought of as being dissipated. The relationship among Pr, Rr, the input resistance, and the current I is |

7? ‘ p |

Antenna Gain and Radiation Efficiency An antenna is a passive device, but it can be designed to radiate more energy in a desired direction. The gain (G) of an antenna is defined as |

The radiation intensity in the maximum direction of radiation (U0) The radiation intensity of a lossless isotropic source with the same input |

The mathematical expressions for D\ and D± are 4nU„ A, = |

P rad У + rad± 4nU± |

Prad« + Pr |

D = |

(7) |

(8) |

(15) |

U(0, ф) = Г2Р^Є, Ф)

The total power can be estimated by integrating the radiation over a large sphere enclosing the antenna over 4w radians:

Г рп r2n

Prad = I U dn = I I U sin 0 d0 dф

Js Je=0JS=

=0 J ф =0

An isotropic source, such as an ideal point source, radiates uniformly in all directions and is independent of в and ф, and the radiation intensity U0 is related to the real power radiated by the simple formula:

All practical antennas have losses, and therefore efficiencies of practical antennas are less than 100%. The antenna efficiency (^) is defined as the ratio of the real power radiated in space by the antenna to the real power input at its feed terminals:

Radiation efficiency (n) =

Real power radiated by the test antenna (Prad) Total real input at the antenna feed terminals (Pin)

The antenna efficiency ^ is related to the directivity D and the gain G through the relationship

P t t rad |

G = nD |

(16) |

(9) |

The Vector and Scalar Potentials and Field Calculations Using Potentials. Most of the time a direct solution of Maxwell’s equations subject to the boundary conditions for a practical problem becomes difficult. Therefore, it is customary to use intermediatory (or auxiliary) functions, called potential functions, to obtain solutions of electromagnetic problems. There are four such functions; two of them are scalar (one electric and one magnetic) and two of them are vector (one electric and one magnetic) potentials. The magnetic vector potential A is related to the magnetic flux density through the relation B = VX A and the electric scalar potential V is related to E and A through the relation E = – VV – A. The steps to determine the fields at any point due to the linear antenna are as follows: (a) Define the current distribution on the dipole, (b) find expressions for the four potentials, and (c) transfer the cartesian components of the magnetic vector potentials to those in spherical polar coordinates; (d) once the magnetic vector potential is determined, the magnetic field at any point is obtained, and (e) what remains to be done is to use Maxwell’s equation to determine the electric fields at any point from the magnetic field obtained. Before we proceed to determine radiated fields, let us discuss the four potentials for this example. The magnetic current Im is equal to zero since the wire carries a filamentary electric current and hence the electric vector potential F is |

The directivity is a measure of how efficiently the antenna is directing the radiation in space, according to the 1983 IEEE standard (14). The directivity D, a dimensionlesss quantity, of an antenna is given by |

_ U _ AnU |

(10) |

U0 |

P. |

The directivity is dependent on the direction. If the direction is not specified, the default is the direction of maximum radiation intensity. The dimensionless maximum directivity Dmax, denoted by D0, is expressed as |

y. Umax v° = ~u~ |

4nUm |

(11) |

P |

rad |

Many practical antennas work with dual polarizations in mutually perpendicular directions, and then the directivity is defined in that particular direction; the total maximum directivity is a sum of directivities in mutually perpendicular directions and is expressed as |

For the infinitesimal dipole (Fig. 1), the current on the infinitesimal dipole is given by

z |

(18) |

Je (X, У, z) = zJo

where

x’ = y’ = 0, since the length of the dipole is infinitesimal and of length dl

R = V[(x – x’)2 + (y – y’)2 + (z – z’)2] = V(x2 + y2 + z2) =

r(let)

With these, the magnetic vector potential A is given by

z Figure 1. (a) The infinitesimal dipole and (b) its coordinate system. This figure geometrically shows how the field at any observation point from an infinitesimal dipole, which is a building block, can be estimated. |

A(x, y, z) = z — exp(—jkr) dz’ = z ^ exp(—jkr) 4r 4n r for r = 0 (excluding the source) (19) The components of A are given by (20a) |

Mo/o exp(_cos Q |

4n r |

^ exp(— jkr ) sin в 4n r |

(20b) (20c) |

Ae = —Az sin 9 = – Аф = 0 |

Due to symmetry of the radiating dipole, we have д/дф = 0; thus we obtain |

‘ d A dAr’ — (гАф) – — d r d9 |

Н = Ф^г |

(21) |

The expressions for magnetic fields are given by |

zero since it is a function of magnetic current only. In this situation, the magnetic vector potential A is given by |

Hr = H9 = 0 k0I0 dl |

(22) |

sin9 exp(—jkr) |

1 + Jkr. |

+dl/2 T, , , /,ехр(-ДД) J(x, у, z )———- ^—— dz |

/ |

A — 4тг |

(17) |

R |

—dl/2 |

The electric field can be found from a curl relationship, where (x’, y’, z’) are source coordinates, (x, y, z) are the field namely, coordinates, R is the distance between the observation point

and any point on the source (Fig. 1). Jz is the z-directed elec – 1

trie current element, and the linear path С is along the length E = -—V x H (23)

of the source.

This gives the three longitudinal and transverse electric field components as

1 1 + Jkr |

cos9 exp(— jkr) |

(24a) (24b) (24c) |

1 |

1 |

exp(— jkr) |

1 + ^- – |

jkr (kr)2 |

## METHODOLOGY The Recording Technology

The modern ECG system still relies on attaching a set of wires to the skin to couple the potentials on the body surface directly to electronic amplification systems. The electrodes that contact the skin are usually made of a silver/silver chloride (Ag/AgCl) electrode. A conductive electrode jelly or paste acts as the interface between the skin and the metal. This electrode-tissue interface relies on establishing a stable chemical reaction

between the ionic charge carriers in the

body and the electron charge carrier in the metal electrode (7). The Ag/AgCl electrode is preferred because it is a nonpolarizing electrode through which current freely passes. Generally, this chemical reaction stabilizes in a minute or so and does not interfere or alter the nature of the electrical signal from the heart. There are times, however, when the chemical reaction does not readily equilibrate, for example, when the subject is ambulatory, resulting in a recording susceptible to artifact.

Then the electrode wires are directed to the inputs of a special differential amplifier used to record bioelectric events. These bioelectric amplifiers must meet a number of technical requirements to record the millivolt level ECG signals and to ensure safety when connected to a human being. In general, the bioelectric amplifier has differential inputs with a high input impedance (>100 МП) and a bandwidth between 0.05 Hz and 150 Hz. There are two sets of standards which most manufacturers rely on for the ECG. They are published by the American Heart Association (8) and the Association for the Advancement of Medical Instrumentation (9).

Digitizing the ECG signal is relatively straightforward with a standard analog-to-digital converter (ADC). The dynamic range of the ADC is the voltage range over which the analog input voltage is converted to a binary number. Hence the ADC may have an input range of ±1.0 V. Another figure of merit for the ADC is the number of bits in the converted binary digit. Most commercial ECG systems use a 16-bit converter which has a dynamic range of 216 or about 96 dB. This is a very high dynamic range for the typical ECG signal, but it does allow the ECG system to accommodate a widely varying baseline drift which can occur when the tissue-electrode interface is not well established. This artifact, known as baseline wander, can be problematic when interpreting the ECG. There are several digital methods which correct for the baseline wander, and the large dynamic range of the ADC allows these algorithms to operate without the amplified ECG signal reaching the limits of the ±1.0 V ADC range.

## Modeling and measurement of power consumption in WSNs

In order to ensure the expected lifetime in a WSN it is important to properly define the workflow of the nodes, evaluating and measuring their power consumption. Such evaluation may provide feedback during application design phase, consenting to improve the overall energy efficiency. The power consumption profiling of a node is also an important stage in the deployment of a WSN, since it consents to properly configure the duty-cycle and the number of transmissions as a function of the available energy. There are several methods to estimate the power consumption of a WSN node, including theoretical estimation, direct measurements, and usage simulations tools.

Theoretical estimation relies on an abstraction of the network, including the surrounding environment. However, due to the difficulty of describing the environment, realistic models are not easily realized and evaluated and even simplified models can be very complex, resulting impractical, or not accurate [27].

Direct measurements, relying on physical sensor node, offer the best accuracy on energy consumption estimation and evaluation, and are often used. Due to the complexity of the network sometime measuring the energy consumption of a whole sensor network results a very complex task. Not only measurements should be collected in different places, but WSN state and distributed power consumption measurements may require a common time reference shared by the involved nodes, so that local measurements are properly synchronized.

A hybrid framework, envisions single node measurements, to be carried out with an oscilloscope or specific instrumentation under fixed conditions. Then measurement taken on a single node may be projected to the entire WSN only under some specific conditions (e. g. when the WSN nodes are homogeneous ad performs similar task). A wide measurement campaign can be carried out on limited size WSNs using specific systems [28].

Due to the variety of available platforms and environmental constraints, the design, implementation and deployment of a sensor network application are complex tasks. Thus it is often useful to simulate, at various stage of development, one or more components of the networks. Thus, accurate simulators may be a useful tool for the assessment of the WSN performance, especially given knowledge of available energy source, and the achievable duty cycle and operational life. Typical requirements are then accurate simulation of network behavior in response to specific events, accurate simulation of individual node behavior, and time awareness. Moreover, a WSN node typically includes mixed signal processing devices. As anticipated, a well known mixed signal contributor to power consumption is the radio interface, responsible for a large portion of energy consumption. Other significant contributors may be active sensors and A/D converters, whose conversion time, on a microcontroller platform, may be lower than a microsecond. In this case, not only a low level finite state machine should be modeled, but, for calibration purposes, an accurate measurement system is needed, capable of tracking state transitions lasting a few microseconds.

Specific solutions have been proposed in recent years for various wireless systems. For instance, some simulators have been developed for PAN network devices, such as Bluetooth. In [29], a Bluetooth device has been described as a finite state machine, each state being associated to link manager level activities, such as a scan/inquiry operation. Then, average power consumption was measured for each of the identified state transitions, each lasting a few milliseconds, using Digital Multi Meters (DMM). As a result, the average power consumption of a Bluetooth device executing a given application could be predicted with good accuracy [29]. While effective, such approach features a large time granularity that may be suboptimal for WSN applications. In fact, WSN nodes are often arranged in a peer to peer or mesh configuration, where several asynchronous and short events may occur, and featuring various low-power/sleep modes. Moreover, a deep optimization of power consumption may require a simulation tool to profile the energy cost of the internal work of each node. This requires to model events with time constants that may be lower than a microsecond [30].

Thus, other WSN simulators have been recently developed, focused on the simulation of the protocol and MAC level, on processor profiling, on attempting to combine both features [31]. In network focused simulation frameworks, sensor nodes are generally represented using a layered architecture, where each layer is responsible to model specific hardware or software aspect of the node. Moreover, in order to study the energy consumption profile of the node, accurate timing information is needed. Thus, such simulators alone, being oriented to model the network activity and the information flow, lead to a coarse representation of the node states, and are not suitable for accurate energy consumption estimation. Another class of simulators emulates the platform executing the same code of the node. Using this technique it is possible to obtain a fine-grained timing, permitting the simulation of interrupts and low-level peripheral interaction. Such simulators are usually called instruction-level simulators. Due to the strict hardware dependence each simulator is usually capable to emulate only a few platforms, relying on configuration files that describe the peculiar characteristics of a given platform. It should be noted that, in order to obtain an accurate simulation of power consumption, also platform components embedded in the WSN node with the CPU may be significant contributors to power consumption, and should be properly kept into account. An example is provided in section 5, where a case study is discussed.

Finally, simulation tools should be coupled to proper measurement techniques, keeping into account potential and limitation of the available instrumentation. For instance, in [29] accurate measurements have been carried out using DMMs, and measurement uncertainty has been modeled by describing the effect of measuring phenomena of comparable duration with the DMM integration time. More generally, the requirements of a measurement system should include accuracy, and the capability of capturing and measuring phenomena with short duration and a potentially low repetition frequency.

In the next subsections different methods to evaluate by experiment or by simulation the energy consumption of a WSN node are presented.

## ATTITUDE CONTROL

Attitude control is the field of engineering science that deals with the control of the rotational motion of a rigid body about a reference point (typically the center of mass). Attitude control systems are commonly used in controlling the orientation of spacecraft or aircraft. As a spacecraft orbits the Earth, it may have to move in space in such a way that its antenna always points to a ground station for communication or its on-board telescope keeps pointing to a distant star. A fighter aircraft may be required to turn very fast and maneuver aggressively to shoot down enemy airplanes or to avoid an incoming missile. A civilian airplane may need to keep a con-

ATTITUDE CONTROL OF SPACECRAFT

A rigid satellite or spacecraft in orbit offers the most obvious example of a rotating rigid body. Attitude control for spacecraft arises in the process of orienting the spacecraft along a specified, predetermined direction. According to Wertz (1), it consists of two problems—attitude stabilization, or maintaining a specific orientation, and attitude maneuver control, or, controlling the spacecraft from one attitude orientation to another. Attitude orientation is specified either with respect to an inertial reference frame or with respect to another moving object. For instance, attitude stabilization of a spacecraft with one axis toward the Earth implies a continuously changing orientation with respect to an inertial frame. There are two main methods for spacecraft stabilization: (1) passive methods, and (2) active methods.