hard magnetic material a ferromagnetic material that retains its magnetization when the magnetizing field is removed; a magnetic material with significant coercivity. hard real-time See hard real-time system. hard real-time system a real-time system in which missing even one deadline results in system failure. Compare with soft real-time, firm real-time. hard X-ray having sufficient photon energy to penetrate “hard” material; usually more than about 15 keV. hard-decision decoding decoding of encoded information given symbol decisions of the individually coded message symbols. Compare with soft-decision decoding. hardware computer constructs that have a physical manifestation. hardware accelerator a piece of hardware dedicated to performing a particular function (such as image convolution or matrix-vector products) which would otherwise be performed in software. Although much less flexible, dedicated hardware implementations can give significant speed improvements over software, and are especially useful for real-time applications. hardware interrupt an interrupt generated by a hardware device, for example, keyboard, the DMA, PIC, the serial adapter, the printer adapter, etc. Other hardware interrupts can be generated by the control unit or by the ALU, for example, for the presence of a division per zero, for attempting to execute an unknown instruction. This last class of hardware interrupts is called internal exception. hardware noise radio frequency emissions due to arcing of utility lines at defective connectors. harmonic (1) the name associated with a number used to denote the frequency components that exist in a certain fourier series representation for a certain function of time f (t). The Fourier series representation is given f (t) = ∞ Fn ∗[cos (nωo t) + j sin (nωo t)] n=−∞ where n = 0, 1, 2, 3, . . ., ωo = 2π/T , j = √ −1, T is the period of the function f (t), Fn is the coefficient of the Fourier series for a certain value of n: 1st harmonic has Fn = F1 and [cos (1ω0 t) + j sin (1ω0 t)] 2nd harmonic has Fn = F2 and [cos (2ω0 t) + j sin (2ω0 t)] 3rd harmonic has Fn = F3 and [cos (3ω0 t) + j sin (3ω0 t)] etc. (2) sinusoidal component of a periodic waveform that has a frequency equal to an integer multiple of the basic frequency (or fundamental frequency). Thus the third harmonic of a power system voltage in the U.S. has a frequency of 3×60, or 180 Hz. For electric systems powered by sinusoidal sources, harmonics are introduced by nonlinear devices such as saturated iron cores and power electronic devices. harmonic amplifier a type of amplifier that utilizes various forms of harmonic and mixing actions. These amplifiers may pump up the fundamental by increasing the switching efficiency of the active device. Others may actually be used as frequency multipliers or frequency converters (mixers). All class F, G, and H amplifiers fit into this general 2000 by CRC Press LLC c www.FreeEngineeringbooksPdf.com group. Parameters such as device characteristics, quiescent bias point, RF load line, significant harmonic and/or mixing frequencies, and amplitude and waveform of the applied signal(s) should be included with the class definition, thus defining the major contributors to the physical actions taking place in one of these amplifiers. harmonic analysis the branch of mathematics dealing with the decomposition of signal functions as a linear combination of basis functions which represent “waves” of various frequencies. When the basis functions are sines and cosines each with a frequency that is an integer multiple of the signal’s frequency, we have trigonometric harmonic analysis, in other words classical Fourier analysis, which provides the amplitudes and phases of the constituent sinusoids. ( See Fourier transform. ) With other basis functions, for example wavelets, we have non-trigonometric harmonic analysis ( See wavelet, wavelet transform). Abstract harmonic analysis studies the generalization of Fourier analysis to abstract spaces. harmonic balance technique one of several techniques for analyzing nonlinear circuits. The nonlinear circuit is divided into two portions of linear and nonlinear elements, and a portion of linear elements is calculated in a frequency domain and a portion of nonlinear elements is calculated in a time domain, respectively. The calculated voltages or currents at connecting nodes of these portions are balanced by using Fourier transforming or inverse Fourier transforming. harmonic component a Fourier component of order greater than one of a periodic waveform. harmonic content the internally generated, harmonically related spectral output from a device or circuit. Harmonic energy is that energy that is at exact multiples of the fundamental frequency, generated by the nonlinearities within the device or circuit acting on the fundamental frequency. harmonic converter found in a microwave receiver, this component uses the technique of harmonic mixing to convert the RF signal to a lower IF frequency for further processing. Harmonic converters can be used as part of a vector network analyzer. harmonic distortion caused by the nonlinear transfer characteristics of a device or circuit. When a sinusoidal signal of a single frequency (the fundamental frequency) is applied at the input of a nonlinear circuit, the output contains frequency components that are integer multiples of the fundamental frequency (harmonics). The resulting distortion is called harmonic distortion. harmonic frequency integral multiples of fundamental frequency. For example, for a 60-Hz supply, the harmonic frequencies are 120, 180, 240, 300, . . .. harmonic generation in nonlinear optics, the process in which a laser beam interacts with a material system to produce new frequency components at integer multiples of the frequency of the incident beam. Under carefully controlled circumstances, the lower-order harmonics (e.g., second and third) can be generated with high (> 50%) efficiency. Under different circumstances, harmonics as high as the 30th can be generated. harmonic load-pull measurement a measurement method where transfer characteristics of a device at the fundamental frequency can be measured by electrically changing the load impedance at harmonic frequencies. harmonic orthogonal set the set of functions ej ωt . It is called harmonic because each basis function is a harmonic of a certain frequency and because the inner product between any two functions is zero: +∞ j ω t j ω t 1 e 2 dt = 0, ω = ω 1 2 −∞ e 2000 by CRC Press LLC c www.FreeEngineeringbooksPdf.com +∞ −∞ ej ωt1 ej ωt2 dω = 0, t1 = t2 . harmonic tuning the process of tuning an amplifier circuit to a frequency that is an integral multiple of the fundamental frequency at which the circuit would normally operate. harmonically pumped mixer mixer where the intermediate frequency (IF) signal is at a frequency which is the sum or difference of the RF and an integer multiple (usually two) of the LO (local oscillator) frequency. Hartley oscillator a particular case of LCoscillators when X1 + X2 + 2Xm is realized as a single tapped coil, and X3 is a capacitor. Well suited for variable-frequency operation by varying a single capacitor. Hartley oscillators are usually not used at VHFs of higher frequencies. Similarly, the circuit is avoided at very low audio frequencies. It is important to distinguish the Hartley oscillator from the Armstrong topology. In the Armstrong oscillator, no ohmic connection exists between the two inductors. Instead, coupling is entirely magnetic. Harvard architecture a computer design feature where there are two separate memory units: one for instructions and the other for data only. The name originates from an early computer development project at Harvard University in the late 1940s. Compare with Princeton architecture. hash table a table storing a mapping function whose domain is sparsely used and that is accessed by indices that are computed from the search field (“key”) using a many–one mapping (called a hash function). Hash tables are used for many memory and name mapping functions, such as symbol tables in assemblers and compilers. hashed page table a page table where the translation of each virtual page number is stored in a position determined by a hash function applied to the virtual page number. 2000 by CRC Press LLC c This technique is used to reduce the size of page tables. hashing the act of translating a search key into a table index using a many–one mapping. See also hash table. Hausdorff distance an important distance measure, used in fractal geometry, among other places. Given a distance function d defined on a Euclidean space E, one derives from it the Hausdorff distance Hd on the family of all compact (i.e., bounded and topologically closed) subsets of E; for any two compact subsets K, L of E, Hd (K, L) is the least r ≥ 0 such that each one of K, L is contained in the other’s dilation by a closed ball of radius r, that is: Br (p) and L ⊆ Br (p), K⊆ p∈L p∈K where Br (p) = {q ∈ E | d(p, q) ≤ r}. Hayes-compatible modem refers to a modem when it is capable of responding at the commands of modems made by Hayes Microcomputer Products. The Hayes set of commands represents a sort of standard for modems. haystack response bandpass frequency response characterized by flat midband response with sloping sides. hazard a momentary output error that occurs in a logic circuit because of input signal propagation along different delay paths in the circuit. hazardous location a classification system used to define locations that are susceptible to fire and explosion hazards associated with normal electrical arcing. A class I hazardous location contains a flammable concentration of flammable vapors. A class II hazardous location contains a combustible