Monthly Archives: April 2014

Hold-Mode Specifications

Ideally, the holding capacitor should be completely isolated from any interference during the hold mode and the output signal should remain constant. In a real-life implementation there is always a small current flowing across the holding ca-

pacitor during the hold mode. This nonideal effect produces droop in the output signal as shown in Fig. 5. As an example, in an analog-to-digital data converter the droop should not exceed one-half of the least-significant bit value during the conversion cycle. Generally, the droop current could be a bipo­lar base current or simply junction leakage. Another specifi­cation during the hold mode is the feedthrough from the input signal. This occurs through parasitic capacitance between the input and the output nodes of a sample-and-hold circuit, al­though it can occur between other nodes in the system and the output. Figure 5 also presents this effect. Again, in refer­ence to the data-converter example, the feedthrough peak-to – peak amplitude should not exceed one least significant bit of the converter.

There are a few other factors that influence the perfor­mance during the hold mode. Nonidealities in the holding ca­pacitor can cause dielectric absorption. Consequently, the ca­pacitor exhibits a memorylike behavior, corrupting the newly stored sample in the direction of the previous sample. Electri­cal noise is also a factor, and the value of the capacitor plays an important role since the kT/C term (k is the Boltzmann constant, T the absolute temperature in kelvin, and C the holding capacitor value) is usually the main contributor.

Hold – to Sample-Mode Specifications

When switching from the hold to sample mode, there is a de­lay between the sampling edge of the clock and the moment the output settles to the steady state when it tracks the input. This time is known as the acquisition time and is also deter­mined by an error band. Since the input can change signifi­cantly while the circuit is in hold mode, the acquisition time is usually specified for a full-scale change in the input unless mentioned otherwise.




Figure 2. Coordinate system for radiation field.

An antenna can be used for both reception and transmission. This article discusses the properties of an antenna when it is used for the reception of an electromagnetic (EM) plane wave (1,2). Figure 1(a) shows an example of a receiving antenna, in which a half-wavelength dipole is used. A receiver, expressed as antenna load ZL, is connected to the center terminals of the dipole. The arrows in this figure show the flow of the power density (Poynting power) of an incident EM plane wave, which propagates toward the dipole antenna from the right side. It is observed that the power of the incident EM plane wave moves toward the center terminals and is absorbed in the antenna load ZL.




Figure 1. Reception of an electromagnetic plane wave. (a) Half­wavelength dipole antenna. (b) Array antenna on a circular cavity.





h= {(S.©)© + (S.^}


The point of interest of a receiving antenna is the power WL delivered to a receiver or antenna load ZL, as shown in an example of Fig. 1(a). To calculate WL, the induced current 10 at the antenna terminals must be obtained. For this, an equivalent circuit for the receiving antenna is introduced. The maximum value of WL is discussed on the basis of the vector effective height h.

The receiving antenna is recognized as an electrical net for collecting an EM plane wave. For example, the power of the EM plane wave in Fig. 1(b) is collected by many elements on a circular cavity of area Aap (aperture) and transferred to the center port to which a receiver (ZL) is connected. Generally, the collected power WL at the center port is less than the power Wap given by Aap times the power density at the receiv­ing antenna aperture. In other words, 100% of Aap is not used for the reception of the EM plane wave. In the final section, the aperture efficiency ^ap as a measure of receiving antenna performance is defined after the discussion of the receiving cross section Ar. (Note that some fundamental relationships used in the discussion of receiving antennas are summarized in the last part of this article.)


Consider an antenna isolated in free space specified by per­mittivity e0 and permeability xo, as shown in Fig. 2, where spherical coordinates (R, в, ф) are used with unit vectors (R, в, ф). The antenna is driven by a voltage source of frequency f. The current I(s’) flows along the antenna conductor of length L = s2 — s1, radiating the electric field E expressed as

E = – j 30k-



where h, called the vector effective height, is defined as

s =








— h • /02hd





1(s’)s’ejkr(s ) R ds’

The notations in Eqs. (1) to (3) are as follows: k(= wV^0f0 = 2w/A with ш = 2wf, where A is wavelength) is the phase con­stant, I0 is the input-terminal current [i. e., I0 = I(0)], s’ is the distance from the driving point to a source point along the antenna conductor, s’ is the unit vector tangential to the an­tenna conductor at the source point, and r(s’) is the position vector directed toward the source point from the coordinate origin.

Example. Let us consider an infinitesimal dipole antenna (kr « 0) on the z axis, assuming that the current has constant amplitude and phase over the antenna length l. Equation (3) is calculated to be S = I0ls’. From Eq. (2), h = l(s’ • в)в = —l sin вв. In the direction normal to the dipole axis (в = 90°), h = —le = lz = hd.


The very high level of neutron and gamma radiation at the vacuum vessel of a fusion reactor must be screened to limit the nuclear heat load and the radiation damage at the wind­ing components. The size of the shield (up to 1 m thick in the ITER project) may have a substantial impact on the size and cost of the superconducting magnets. After screening, the ra­diation damage on the metallic components of a supercon­ducting coil (steel, copper, NbTi and Nb3Sn), is not critical and partly recovers (e. g., for copper) upon warming up at

LCT-WH (1981)

Polo (1987)



DPC-EX (1988)

US-DPC (1988)

DPC-TJ (1988) ШУ//////////А

■11 ill! I

Toshiba (1983)

W7-X (1996)

20 mm

LHD-OV (1994)

Figure 10. Selection of cable-in-conduit super­conductors, drawn to the same scale. The strands of Polo, LHD-OV and W7-X are NbTi, all the other are Nb3Sn strands. The jacket material is steel except for ITER (Incoloy) and W7-X (alumi­num alloy).

Figure 11. Winding tool with 13 numerically controlled axes for the helical coils of the LHD (courtesy of K, Takahata, NIFS).

4 + ИЮО

room temperature. The actual weak link for radiation damage is the organic fraction of the electrical insulation. In potted windings, the glass-epoxy is broadly used, either as laminates or prepreg wraps or vacuum-impregnated fabrics, to bond to­gether the winding turns and to provide the required dielec­tric strength. The neutron and gamma act on the long molecu­lar chain of the resin, irreversibly breaking the atomic links. The mechanical strength of the composite, mostly the shear strength, is affected and macroscopic cracking may occur un­der operating loads, eventually leading to a short circuit be­tween winding sections. To limit this risk, the magnets must be designed to have low stress in the insulation, that is, limit the risk of crack propagation. Another design approach is to separate the mechanical and electrical functions, for example, including a redundant electrical insulation layer, either inter­leaved or overlapped to the glass-epoxy, to stop the crack propagation in the resin. The free radicals originated from the broken organic polymers are chemically active and evolve into gaseous molecules. The most severe consequence of radiation induced chemical reactions at 4 K is the accumulation of fro­zen gas bubbles (mostly hydrogen). Upon warming-up of large windings, the internal pressure of the evolved gas increases dramatically due to the little permeation and may lead even­tually to swelling in the insulation (20). A possible cure against postirradiation hazards of organic insulation is to re­duce the resin volume fraction and select the resin composi­tion to minimize the gas evolution rate. On the other hand, there is a broad reluctance to start an expensive and time­consuming task for the industrial development of innovative insulation systems, which will be actually needed only when a fusion reactor will work at full power on a time scale of several years. The full replacement of organic insulation sys­tems by ceramic materials with adequate mechanical proper­ties may be the ultimate, long-term goal to solve the issue of the electrical insulation in the heavily irradiated fusion magnets.

Quench Protection

In case of quench, the huge amount of energy stored in a fu­sion magnet must be actively dumped in an outer resistor. If a quench fails to be detected, the ohmic power locally dissi­pated in the slowly expanding normal zone is sufficient within one minute or less to melt the conductor and start a chain of serious failures (vacuum break, electric arc, mechanical col­lapse). A number of quench detectors have been developed and are currently applied in superconducting magnets, from the easy ones (voltage balance of different winding sections, monitoring of outlet mass flow rate) to the most sophisticated, including the laser interference on optical fibers used as dis­tributed thermometer, transmission, and reflection of super high-frequency waves in the coolant channel, acoustic emis­sion, magnetization change at the normal zone (21). However, a redundant and intrusive instrumentation is not welcome in a fusion reactor, as it may increase the risk of leaks and insu­lation failure, due to the large number of feedthrough re­quired. Whatever the quench detector is, the ultimate ques­tion always arises: What happens if the active quench protection fails? The design approach for an actual fusion magnet (i. e., not for an experimental device) will need to offer both a reliable and robust quench-protection system and a conductor/magnet layout that intrinsically limits the damage in case of failure of the protection system, for example, en­hancing the quench propagation and the enthalpy at interme­diate temperature.

Cost Optimization

Figure 12. The OV poloidal field coil of the LHD (courtesy of K. Takahata, NIFS).

In several applications of the superconducting magnets (e. g., accelerators, detectors, high-field magnets, prototypes), the achievement of the technical goal is the main care of the de­
signer, while the cost of the device does not play a major role. However, after completion of the demonstration phase for the fusion magnets, the cost optimization will be a key issue for the commercial success of fusion. On one side, the behavior of the superconductor needs to be mastered by the designer (e. g., ac loss, stability, mechanical properties), in order to set the design margins at a safe but realistic level and make effective use of the expensive superconductors. On the other hand, the choice of the manufacturing methods and tooling may have a very strong impact on the cost of the coil and should be in­cluded as a driving factor in the design. Two examples are given to show how a design choice may affect the cost.

A high electrical conductivity material (stabilizer) needs to be added to the superconductor cross-section, to allow effec­tive current-sharing and fast recovery for small thermal dis­turbances. The required stabilizer cross-section may be much larger than the superconductor. In cable-in-conduit conduc­tors, the straight choice is to equally distribute the stabilizer cross-section in each superconducting strand, specifying a high Cu : non-Cu ratio. However, the cost of the Nb3Sn strand is independent of the copper ratio. If the designer masters the mechanism of the current-sharing among strands and knows the operating values of the interstrand resistance, he or she may select a much smaller Cu : non-Cu ratio in the Nb3Sn strand and add extra copper wires in the strand bundle. Keeping the same superconductor cross-section, that is, with­out affecting the operating margins, the amount of Nb3Sn strand can be significantly reduced with a large cost saving.

A Nb3Sn conductor needs a heat treatment at 650°C to 700°C to form the brittle intermetallic composite by solid – state diffusion. If the designer does not master heat resistant electrical insulation systems, he or she will conservatively choose to first heat-treat the conductor and then insulate it and wind in the final shape (e. g., react and wind or wind and react and transfer methods). As the Nb3Sn after heat treat­ment is degraded for permanent deformation as large as 0.2% to 0.3%, the handling for post-heat treatment insulation and final assembly requires sophisticated tooling and continuous adjustment (e. g., shimming of each turn) to achieve the re­quired tolerance with minimum strain on the conductor. If a reliable insulation system is selected, compatible with the heat treatment procedure, the coil can be wound in the final form and to the final tolerance before the heat treatment (wind and react method), saving the cost of a large number of tools and manufacturing steps and avoiding the risk associ­ated to the post-heat-treatment handling.

Risk and Quality Assurance

Large superconducting magnets are usually unique items for which a thorough quality assurance program cannot be conve­niently established in advance, as is the case for series pro­duction, due to the lack of iterative improvements in the man­ufacturing procedures. The global acceptance tests of the magnets tend to replace the quality assessment of the individ­ual procedures, achievable only on the basis of a broad statis­tical database. However, an individual acceptance test of a fusion magnets cannot reproduce all the actual operating con­ditions, for example, mechanical load and peak field from other coils, nuclear radiation, mechanical and thermal cy­cling. Moreover, a global acceptance test should not be pushed to the failure limit, that is, the operating margin cannot be assessed. The lack of confidence may push the designer in a circle of overconservative choices, for example, assuming min­imum performance for material properties, welds, assembly tolerances, which adversely affect the cost and the effective­ness of the design. To avoid this trend, the designer should identify the critical area for quality assurance and select a low-risk design and procedure. For example, the resistance of a joint between conductor sections cannot be checked during the manufacture. In this case, the designer should aim for a joint layout where the resistance performance is only margin­ally affected by incorrect assembly procedure.


As discussed earlier, shadowing is caused by terrain and other environmental factors, such as foliage. The effect of shadowing causes the variations in the mean of the received signal. Let Lp(d) denote the path loss (including the effect of shadowing) at a specified distance from the transmitter. Based on extensive measurements, it has been verified that Lp(d) can be characterized as a random variable with a log­normal distribution about the mean value. When expressed in dB, the RV perturbing the local mean value of the path loss is a normal RV, as given by

L p (d) = [Lp (d) + 0](dB)

where Lp(d) is given by one of the path loss models in the preceding section and П is a normal RV with standard devia­tion a. The RV П is obtained from the log-normal RV П’, whose pdf is given earlier. Equation (49) describes the path loss for a specified value of d but with different values of shadowing/obstructions between the transmitter and re­ceiver. In practice, the path loss exponent n and the standard deviation a, are used to characterize any environment. In most cases, n and a can be calculated from measurements.

A Practical Design Model

The goal of this section is to provide a framework for combin­ing the various results in this article relating to small-scale signal variations and large-scale signal variations into a set of relevant parameters that may be used by communication systems designers for link budget calculations. The compo­nents of the different effects and their impact on the link bud­get are shown pictorially in Fig. 16.

Predicting the expected mean received signal power is an important step in designing a communication link and in esti­mating the coverage area for a specific transmitter. In Fig. 16, Pt is the transmitted signal power and Pmin is the mini­mum signal strength that must be received for the receiver to operate satisfactorily, that is, the signal strength to produce the minimum carrier-to-noise ratio (C/N) needed for accept­able communications. This is called receiver sensitivity and is expressed in dBm. There are three margins, one for each of the following practical effects:


fV (v) —




fX Y (**’’ У) V


e 2 a2

The path loss Lp is deterministic (based on the distance be­tween the transmitter and receiver), whereas the fading and shadowing are probabilistic. The amount of margin must be judiciously chosen so that the net margin is minimized but still meets the minimum signal strength requirements. If the amount of losses exceeds the margin of a communication sys­tem, then an outage occurs, which implies that the communi­cation link cannot be used until the channel conditions im­prove. This summarizes the tradeoffs that must be handled by the designers of communication systems.


A comprehensive overview of the RF signal variations related to propagation in multipath fading channels has been pre­sented. The diverse phenomena that cause signal variations are described via mathematical models. The different types of fading and their salient features are discussed in detail. This article provides a mathematical and an engineering-oriented treatment of multipath fading, thereby providing the reader with the necessary tools and the information to understand the different RF propagative issues and the way they affect wireless communication.


Derivation of Rayleigh pdf

Let X and Y be two independent identically distributed (iid) zero-mean Gaussian RVs with variance a2. Because X and Y are independent, their joint pdf is the product of their mar­ginal pdf’s:

• propagative path loss

• small-scale effects—fading margin

• large-scale effects—shadowing margin

In the previous section, the methods of determining the path loss Lp for different environments were presented. The large-scale effect due to shadowing is modeled as a log-normal random variable. Hence, a shadowing margin Ls must be in­cluded in the link budget (Fig. 16). The small-scale effects, characterized by Rayleigh/Ricean fading cause significant amplitude variations. Hence a fading margin Lf is also in­cluded in the link budget. From Fig. 16, the total transmitted power is given by

1 *2+.y2


Pt — Pmin + Lf + Ls + Lp

Using a change of variables, V 4 VX2 + Y2 and ф 4 tan 1 (Y/X), the joint pdf /V,0(v, d) is given by

r, m IX, Y

fv, e(v’e) = 7ГП

| det J (x, y) 2ло2

where J(x, y) is the Jacobian matrix for the transformation of variables. From Eq. (52), we obtain the marginal pdf of V and 0 as

Hence, 0 is uniformly distributed, and V is Rayleigh dis­tributed.

V _ V

— Є 2ff2 V > 0 а 2

0 v < 0


= J0 9)dv = 2ж

Sample – to Hold-Mode Specifications

The switching from sample to hold mode is accompanied by transients that appear in the output. The time it takes for these transients to settle within a given error bound is called the settling time, similar to the corresponding sample-mode

Sample - to Hold-Mode Specifications

End point = P2



Gain error = 1 – tan в

Start point = P1


specification discussed in the preceding subsection. This non­ideal behavior is shown in Fig. 3. Another nonideal effect is also presented in Fig. 3 and is called the pedestal error. This error appears as an offset in the output signal and is due to charge injected from the sampling switch, which could be dependent on the input signal, implying nonlinearity.

Aperture time is another important specification and is de­fined as the amount of time it takes for the sampling switch to open. This is attributed to the finite slope of the clock and a gradual transition of the sampling switch from a low-imped – ance (closed) to a high-impedance (opened) state. The signal stored at the output is a function of the aperture delay ta, the analog delay tda of the signal through the sample-and-hold cir­cuit, and the digital delay tdd of the clock signal that turns off the switch. It can be ultimately characterized as shown in Fig. 4 by an effective aperture time teff. The analog delay is caused by the frequency response of the sample-and-hold cir­cuit, and the digital delay is produced by any logic in the path of the external clock to the switch. The aperture jitter is the variation in the hold signal delay. In some applications, such as analog-to-digital data conversion, a constant delay in the sampling time is not important. However, aperture jitter could be extremely damaging, adding significant noise to the output signal and effectively lowering the resolution of the system.