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If only one unit is involved, it is the temperature measured at a point approximately 0-1 m away from the capacitor container and at two-thirds of the height from its base. crossover area With stabilized power supplies, the range of values of the output quantities within which a change of mode of operation occurs, e.g.... | Wikipedia - Glossary of power electronics - C | 233 | 1,142 | null |
Section: D. DC capacitor A capacitor essentially designed for operation with direct voltage.DC converter A converter for DC conversion. DC conversion factor for DC conversion, the ratio of the DC power value on the load side to that on the source side. (electronic) DC (power) conversion Electronic conversion from DC to... | Wikipedia - Glossary of power electronics - D | 340 | 1,610 | null |
Section: E. electronic AC (power) switch An electronic power switch capable of switching alternating current. electronic AC power controller A unit which is able to operate as a controllable direct AC voltage converter as well as an electronic AC switch. electronic DC (power) switch An electronic power switch capable o... | Wikipedia - Glossary of power electronics - E | 323 | 1,728 | null |
Section: F. false firing The firing of a latching valve device or an arm consisting of such devices at an incorrect instant. flyback converter A DC converter where the energy is transferred from the source side to the load side during the idle interval(s) of the controllable principal arm(s) after being stored in an in... | Wikipedia - Glossary of power electronics - F | 343 | 1,744 | null |
Section: I. indirect AC converter An AC converter with a DC link. indirect AC/DC converter An electronic AC/DC converter with a DC or AC link. indirect commutation A series of commutations from one principal arm to another or back to the original one by successive commutations via one or more auxiliary arms. indirect (... | Wikipedia - Glossary of power electronics - I | 335 | 1,640 | null |
internal (element) fuse A device incorporated in the capacitor which disconnects an element or a group of elements in the event of breakdown. insulation voltage (Ui) The RMS rated value of the insulation voltage of capacitive elements and terminals to case or earth. If not specified, the RMS value of the insulating vol... | Wikipedia - Glossary of power electronics - I | 254 | 1,257 | null |
Section: M. machine commutation External commutation where the commutating voltage is supplied by a rotating machine.maximum current (Imax) (capacitor) The maximum RMS current for continuous operation.maximum loss power (Pmax) (capacitor) The maximum loss power with which the capacitor may be loaded at the maximum case... | Wikipedia - Glossary of power electronics - M | 326 | 1,536 | null |
Section: N. natural characteristic (of a line commutated converter) A characteristic determined only by the basic parts of the equipment, e.g. transformer and valve device assembly. non-conducting direction (of an electronic valve device or of a valve arm) The reverse of the conducting direction. non-controllable conne... | Wikipedia - Glossary of power electronics - N | 216 | 1,052 | null |
Section: P. pair of antiparallel arms Two valve arms in parallel with opposite conducting directions. pair of arms Two series connected valve arms with the same conducting direction. parallel operation A mode of operation of stabilized power supplies in which all similar output terminals are connected together and arra... | Wikipedia - Glossary of power electronics - P | 331 | 1,777 | null |
Section: R. reactive power converter A converter for reactive power compensation that generates or consumes reactive power without the flow of active power except for the power losses in the converter. rated AC voltage (Un) (capacitor) The maximum operating peak recurrent voltage of either polarity of a reversing type ... | Wikipedia - Glossary of power electronics - R | 336 | 1,552 | null |
Section: S. slave operation A mode of operation of stabilized power supplies achieving coordinated control of interconnected stabilized supplies by setting the master supply alone. self-commutation A commutation where the commutating voltage is supplied by components within the converter or the electronic switch. self-... | Wikipedia - Glossary of power electronics - S | 344 | 1,836 | null |
stabilization In the field of power electronics the reduction of the effect of changes of influence quantities on the output quantity. stabilized power supply In the field of power electronics an equipment which takes electrical energy from a source and supplies it stabilized by means inside the equipment to one or mor... | Wikipedia - Glossary of power electronics - S | 166 | 910 | null |
Section: T. tangent of the loss angle (tanδ) of a capacitor The ratio between the equivalent series resistance and the capacitive reactance of a capacitor at specified sinusoidal alternating voltage and frequency. threshold voltage (of an electronic valve device) The value of the voltage obtained at the intersection of... | Wikipedia - Glossary of power electronics - T | 348 | 1,826 | null |
Section: V. valve device assembly An electrically and mechanically combined assembly of electronic valve devices or stacks, complete with all its connections and auxiliaries in its own mechanical structure. valve device blocking An operation to prevent further turn-on of a controllable valve device or an arm consisting... | Wikipedia - Glossary of power electronics - V | 214 | 1,054 | null |
Article: Group delay and phase delay. In signal processing, group delay and phase delay are functions that describe in different ways the delay times experienced by a signal’s various sinusoidal frequency components as they pass through a linear time-invariant (LTI) system (such as a microphone, coaxial cable, amplifie... | Wikipedia - Group delay and phase delay - Summary | 156 | 795 | null |
Section: Introduction. The group delay and phase delay properties of a linear time-invariant (LTI) system are functions of frequency, giving the time from when a frequency component of a time varying physical quantity—for example a voltage signal—appears at the LTI system input, to the time when a copy of that same fre... | Wikipedia - Group delay and phase delay - Introduction | 230 | 1,135 | null |
Section: Introduction > Phase delay. A linear time-invariant system or device has a phase response property and a phase delay property, where one can be calculated exactly from the other. Phase delay directly measures the device or system time delay of individual sinusoidal frequency components. If the phase delay func... | Wikipedia - Group delay and phase delay - Introduction > Phase delay | 214 | 1,124 | null |
Section: Introduction > Group delay > Basic modulation system. A device's group delay can be exactly calculated from the device's phase response, but not the other way around. The simplest use case for group delay is illustrated in Figure 1 which shows a conceptual modulation system, which is itself an LTI system with ... | Wikipedia - Group delay and phase delay - Introduction > Group delay > Basic modulation system | 164 | 783 | null |
Section: Introduction > Group delay > Amplitude Modulation. Amplitude modulation creates the passband signal by shifting the baseband frequency components to a much higher frequency range. Although the frequencies are different, the passband signal carries the same information as the baseband signal. The demodulator do... | Wikipedia - Group delay and phase delay - Introduction > Group delay > Amplitude Modulation | 330 | 1,640 | null |
Section: Introduction > Group delay > Angle Modulation. In an angle-modulation system—such as with frequency modulation (FM) or phase modulation (PM)—the (FM or PM) passband signal applied to an LTI system input can be analyzed as two separate passband signals, an in-phase (I) amplitude modulation AM passband signal an... | Wikipedia - Group delay and phase delay - Introduction > Group delay > Angle Modulation | 272 | 1,237 | null |
Linear time-invariant system § Fourier and Laplace transforms expresses this relationship as: y ( t ) = ( h ∗ x ) ( t ) = def ∫ − ∞ ∞ h ( t − τ ) x ( τ ) d τ = def L − 1 { H ( s ) X ( s ) } , {\displaystyle y(t)=(h*x)(t)\mathrel {\stackrel {\text{def}}{=}} \int _{-\infty }^{\infty }h(t-\tau )\,x(\tau )\,\mathrm {d} \ta... | Wikipedia - Group delay and phase delay - Theory | 318 | 818 | null |
Linear time-invariant system § Fourier and Laplace transforms expresses this relationship as: y ( t ) = ( h ∗ x ) ( t ) = def ∫ − ∞ ∞ h ( t − τ ) x ( τ ) d τ = def L − 1 { H ( s ) X ( s ) } , {\displaystyle y(t)=(h*x)(t)\mathrel {\stackrel {\text{def}}{=}} \int _{-\infty }^{\infty }h(t-\tau )\,x(\tau )\,\mathrm {d} \ta... | Wikipedia - Group delay and phase delay - Theory | 380 | 1,053 | null |
Section: Theory > LTI system response to wave packet. Suppose that such a system is driven by a wave packet formed by a sinusoid multiplied by an amplitude envelope A env ( t ) > 0 {\displaystyle \displaystyle A_{\text{env}}(t)>0} , so the input x ( t ) {\displaystyle \displaystyle x(t)} can be expressed in the followi... | Wikipedia - Group delay and phase delay - Theory > LTI system response to wave packet | 346 | 1,004 | null |
{\displaystyle \left|{\frac {d}{dt}}\log {\big (}A_{\text{env}}(t){\big )}\right|\ll \omega \ .} Applying the earlier convolution equation would reveal that the output of such an LTI system is very well approximated as: y ( t ) = | H ( i ω ) | A env ( t − τ g ) cos ( ω ( t − τ ϕ ) + θ ) . {\displaystyle y(t)={\big |}... | Wikipedia - Group delay and phase delay - Theory > LTI system response to wave packet | 349 | 1,010 | null |
Section: Theory > Mathematical definition of group delay and phase delay. The group delay, τ g {\displaystyle \displaystyle \tau _{g}} , and phase delay, τ ϕ {\displaystyle \displaystyle \tau _{\phi }} , are (potentially) frequency-dependent and can be computed from the unwrapped phase shift ϕ ( ω ) {\displaystyle \dis... | Wikipedia - Group delay and phase delay - Theory > Mathematical definition of group delay and phase delay | 215 | 758 | null |
the derivative with respect to frequency) of the phase at that frequency: τ g ( ω ) = − d ϕ ( ω ) d ω . {\displaystyle \tau _{g}(\omega )=-{\frac {d\phi (\omega )}{d\omega }}\,.} In a linear phase system (with non-inverting gain), both τ g {\displaystyle \displaystyle \tau _{g}} and τ ϕ {\displaystyle \displaystyle \ta... | Wikipedia - Group delay and phase delay - Theory > Mathematical definition of group delay and phase delay | 213 | 701 | null |
Section: Theory > LTI system response to complex sinusoid. More generally, it can be shown that for an LTI system with transfer function H ( s ) {\displaystyle \displaystyle H(s)} driven by a complex sinusoid of unit amplitude, x ( t ) = e i ω t {\displaystyle x(t)=e^{i\omega t}\ } the output is y ( t ) = H ( i ω ) e i... | Wikipedia - Group delay and phase delay - Theory > LTI system response to complex sinusoid | 307 | 744 | null |
More generally, it can be shown that for an LTI system with transfer function H ( s ) {\displaystyle \displaystyle H(s)} driven by a complex sinusoid of unit amplitude, x ( t ) = e i ω t {\displaystyle x(t)=e^{i\omega t}\ } the output is y ( t ) = H ( i ω ) e i ω t = ( | H ( i ω ) | e i ϕ ( ω ) ) e i ω t = | H ( i ω ) ... | Wikipedia - Group delay and phase delay - Theory > LTI system response to complex sinusoid | 342 | 785 | null |
Section: Theory > 1st order low- or high-pass RC filter example. The phase of a 1st-order low-pass filter formed by a RC circuit with cutoff frequency ω o = 1 R C {\displaystyle \omega _{o}{=}{\frac {1}{RC}}} is: ϕ ( ω ) = − arctan ( ω ω o ) . {\displaystyle \phi (\omega )=-\arctan({\frac {\omega }{\omega _{o}}})\,.}... | Wikipedia - Group delay and phase delay - Theory > 1st order low- or high-pass RC filter example | 251 | 690 | null |
{\displaystyle \phi (\omega )={\frac {\pi }{2}}-\arctan({\frac {\omega }{\omega _{o}}})\,.} Taking the negative derivative with respect to ω {\displaystyle \omega } for either this low-pass or high-pass filter yields the same group delay of: τ g ( ω ) = ω o ω 2 + ω o 2 . {\displaystyle {\begin{aligned}\tau _{g}(\omega ... | Wikipedia - Group delay and phase delay - Theory > 1st order low- or high-pass RC filter example | 312 | 841 | null |
{\displaystyle {\begin{aligned}\tau _{g}(\omega \ll \omega _{o})&\approx {\frac {1}{\omega _{o}}}=RC\,.\\\end{aligned}}} Similarly, right at the cutoff frequency, τ g ( ω = ω o ) = 1 2 ω o = R C 2 . {\displaystyle \tau _{g}(\omega {=}\omega _{o})={\frac {1}{2\omega _{o}}}={\frac {RC}{2}}\,.} As frequencies get even lar... | Wikipedia - Group delay and phase delay - Theory > 1st order low- or high-pass RC filter example | 170 | 445 | null |
Section: Theory > Negative group delay. Figure 2: Negative group delay filter circuit Filters will have negative group delay over frequency ranges where its phase response is positively-sloped. If a signal is band-limited within some maximum frequency B, then it is predictable to a small degree (within time periods sma... | Wikipedia - Group delay and phase delay - Theory > Negative group delay | 217 | 1,057 | null |
Section: Group delay in audio. Group delay has some importance in the audio field and especially in the sound reproduction field. Many components of an audio reproduction chain, notably loudspeakers and multiway loudspeaker crossover networks, introduce group delay in the audio signal. It is therefore important to know... | Wikipedia - Group delay and phase delay - Group delay in audio | 347 | 1,653 | null |
Section: Group delay in optics. Group delay is important in physics, and in particular in optics. In an optical fiber, group delay is the transit time required for optical power, traveling at a given mode's group velocity, to travel a given distance. For optical fiber dispersion measurement purposes, the quantity of in... | Wikipedia - Group delay and phase delay - Group delay in optics | 340 | 1,423 | null |
Consider two eigenmodes that are the 0° and 90° linear polarization states. If the state of polarization of the input signal is the linear state at 45° between the two eigenmodes, the input signal is divided equally into the two eigenmodes. The power of the transmitted signal ET,total is the combination of the transmit... | Wikipedia - Group delay and phase delay - Group delay in optics | 193 | 601 | null |
Section: True time delay. A transmitting apparatus is said to have true time delay (TTD) if the time delay is independent of the frequency of the electrical signal. TTD allows for a wide instantaneous signal bandwidth with virtually no signal distortion such as pulse broadening during pulsed operation. TTD is an import... | Wikipedia - Group delay and phase delay - True time delay | 157 | 711 | null |
Section: Group delay from transfer function polynomials. If a transfer function or Sij of a scattering parameter, is in a polynomial Laplace transform form, then the mathematical definition for group delay above may be solved analytically in closed form. A polynomial transfer function P ( S ) {\displaystyle P(S)} may b... | Wikipedia - Group delay and phase delay - Group delay from transfer function polynomials | 289 | 913 | null |
to determine ϕ ( ω ) {\displaystyle \phi (\omega )} from P ( j ω ) {\displaystyle P(j\omega )} , use the definition of ϕ ( ω ) = t a n − 1 ( P ( j ω ) i m a g / P ( j ω ) r e a l ) {\displaystyle \phi (\omega )=tan^{-1}(P(j\omega )_{imag}/P(j\omega )_{real})} . Given that j 2 N {\displaystyle j^{2N}} is always real, an... | Wikipedia - Group delay and phase delay - Group delay from transfer function polynomials | 349 | 929 | null |
d t a n − 1 ( f ( x ) ) d x = d f ( x ) / d x 1 + f ( x ) 2 f ( x ) = − j P ( j ω ) o d d P ( j ω ) e v e n d f ( x ) d x = P ( j ω ) e v e n d ( P ( j ω ) o d d ) d x − − j P ( j ω ) o d d d ( − j P ( j ω ) e v e n ) d x P ( j ω ) e v e n 2 {\displaystyle {\begin{aligned}&{\frac {dtan^{-1}(f(x))}{dx}}={\frac {df(x)/dx... | Wikipedia - Group delay and phase delay - Group delay from transfer function polynomials | 350 | 616 | null |
calculate: S e = P ( j ω ) e v e n = ∑ k = 0 N / 2 P 2 k ( j ω ) 2 k = ∑ k = 0 N / 2 P 2 k ( − 1 ) k ( ω ) 2 k S o = P ( j ω ) o d d = − j ∑ k = 1 ( N + 1 ) / 2 P 2 k − 1 ( j ω ) 2 k − 1 = ∑ k = 1 ( N + 1 ) / 2 P 2 k − 1 ( − 1 ) k − 1 ( ω ) 2 k − 1 D e = d ( P ( j ω ) e v e n ) d x = − j ∑ k = 1 N / 2 2 k P 2 k ( j ω )... | Wikipedia - Group delay and phase delay - Group delay from transfer function polynomials | 345 | 680 | null |
)^{2k}&=&\sum _{k=0}^{N/2}P_{2k}(-1)^{k}(\omega )^{2k}\\So=P(j\omega )_{odd}&=&-j\sum _{k=1}^{(N+1)/2}P_{2k-1}(j\omega )^{2k-1}&=&\sum _{k=1}^{(N+1)/2}P_{2k-1}(-1)^{k-1}(\omega )^{2k-1}\\De={\frac {d(P(j\omega )_{even})}{dx}}&=&-j\sum _{k=1}^{N/2}2kP_{2k}(j\omega )^{2k-1}&=&\sum _{k=1}^{N/2}2kP_{2k}(-1)^{k-1}(\omega )^... | Wikipedia - Group delay and phase delay - Group delay from transfer function polynomials | 348 | 429 | null |
_{k=1}^{(N+1)/2}{(2k-1)}P_{2k-1}(-1)^{k-1}(\omega )^{2k-2}\\\\{\frac {df(x)}{dx}}&=&{\frac {SeDo-SoDe}{Se^{2}}}\end{array}}} The equations above may be used to determine the group delay of polynomial P ( S ) {\displaystyle P(S)} in closed form, shown below after the equations have been reduced to a simplified form. Gro... | Wikipedia - Group delay and phase delay - Group delay from transfer function polynomials | 276 | 563 | null |
Section: Group delay from transfer function polynomials > Polynomial ratio. A polynomial ratio of the form P 2 ( S ) = P n u m ( S ) / P d e n ( S ) {\displaystyle P2(S)=P_{num}(S)/P_{den}(S)} , such as that typically found in the definition of filter designs, may have the group delay determined by taking advantage of ... | Wikipedia - Group delay and phase delay - Group delay from transfer function polynomials > Polynomial ratio | 220 | 575 | null |
Section: Group delay from transfer function polynomials > Simple filter example. A four pole Legendre filter transfer function used in the Legendre filter example is shown below. T 4 ( j ω ) = 1 2.4494897 ( j ω ) 4 + 3.8282201 ( j ω ) 3 + 4.6244874 ( j ω ) 2 + 3.0412127 ( j ω ) + 1 {\displaystyle T_{4}(j\omega )={\frac... | Wikipedia - Group delay and phase delay - Group delay from transfer function polynomials > Simple filter example | 202 | 526 | null |
P e d e n = 2.4494897 ω 4 − 4.6244874 ω 2 + 1 P o d e n = − 3.8282201 ω 3 + 3.0412127 ω D e d e n = 4 ( 2.4494897 ) ω 3 − 2 ( 4.6244874 ) ω D o d e n = 3 ( − 3.8282201 ) ω 2 + 3.0412127 {\displaystyle {\begin{aligned}&Pe_{den}=2.4494897\omega ^{4}-4.6244874\omega ^{2}+1\\&Po_{den}=-3.8282201\omega ^{3}+3.0412127\omega ... | Wikipedia - Group delay and phase delay - Group delay from transfer function polynomials > Simple filter example | 334 | 599 | null |
{\begin{aligned}&Pe_{den}=-1.1749977\\&Po_{den}=-0.7870074\\&De_{den}=-0.548984\\&Do_{den}=-8.4434476\end{aligned}}} Group Delay = g d ( T 4 ( j ω ) ) = − d ϕ ( ω ) d ω = [ 0 − − ( ( − 0.7870074 ∗ − 0.548984 ) + ( − 1.1749977 ∗ − 8.4434476 ) ) ( ( − 1.1749977 ) 2 + ( − 0.7870074 ) 2 ) ] = 5.1765430 sec at ω = 1 rad/sec... | Wikipedia - Group delay and phase delay - Group delay from transfer function polynomials > Simple filter example | 348 | 570 | null |
sec}}\\&{\text{at }}\omega =1{\text{ rad/sec}}\end{aligned}}} The group delay calculation procedure and results may be confirmed to be correct by comparing them to the results derived from the digital derivative of the phase angle, ϕ ( ω ) {\displaystyle \phi (\omega )} , using a small delta Δ ω {\displaystyle \Delta \... | Wikipedia - Group delay and phase delay - Group delay from transfer function polynomials > Simple filter example | 349 | 968 | null |
Section: Deviation from Linear Phase. Deviation from Linear Phase, ϕ D L P ( ω ) {\displaystyle \phi _{DLP}(\omega )} , sometimes referred to as just, "phase deviation", is the difference between the phase response, ϕ ( ω ) {\displaystyle \phi (\omega )} , and the linear portion of the phase response ϕ L ( ω ) {\displa... | Wikipedia - Group delay and phase delay - Deviation from Linear Phase | 317 | 1,128 | null |
Section: Deviation from Linear Phase > Advantage over group delay. An advantage of measuring or calculating ϕ D L P ( ω ) {\displaystyle \phi _{DLP}(\omega )} over measuring or calculating group delay, g d ( ω ) {\displaystyle gd(\omega )} , is ϕ D L P ( ω ) {\displaystyle \phi _{DLP}(\omega )} always converges to 0 as... | Wikipedia - Group delay and phase delay - Deviation from Linear Phase > Advantage over group delay | 236 | 784 | null |
Article: Harmonic balance. Harmonic balance is a method used to calculate the steady-state response of nonlinear differential equations, and is mostly applied to nonlinear electrical circuits. It is a frequency domain method for calculating the steady state, as opposed to the various time-domain steady-state methods. T... | Wikipedia - Harmonic balance - Summary | 326 | 1,742 | null |
Section: Example. Consider the differential equation x ¨ + x 3 = 0 {\displaystyle {\ddot {x}}+x^{3}=0} . We use the ansatz solution x = A cos ( ω t ) {\displaystyle x=A\cos(\omega t)} , and plugging in, we obtain − A ω 2 cos ( ω t ) + A 3 1 4 ( cos ( 3 ω t ) + 3 cos ( ω t ) ) = 0. {\displaystyle -A\omega ^{2}\c... | Wikipedia - Harmonic balance - Example | 285 | 655 | null |
{\displaystyle -A\omega ^{2}\cos(\omega t)+A^{3}{\frac {1}{4}}(\cos(3\omega t)+3\cos(\omega t))=0.} Then by matching the cos ( ω t ) {\displaystyle \cos(\omega t)} terms, we have ω = 3 4 A {\displaystyle \omega ={\sqrt {\frac {3}{4}}}A} , which yields approximate period T = 2 π ω ≈ 7.2552 A {\displaystyle T={\frac {2... | Wikipedia - Harmonic balance - Example | 334 | 771 | null |
Plugging these in and matching the cos ( ω t ) {\displaystyle \cos(\omega t)} , cos ( 3 ω t ) {\displaystyle \cos(3\omega t)} terms, we obtain after routine algebra: ω = 3 4 A 1 1 + y + 2 y 2 , y = A 3 / A 1 , 51 y 3 + 27 y 2 + 21 y − 1 = 0. {\displaystyle \omega ={\sqrt {\frac {3}{4}}}A_{1}{\sqrt {1+y+2y^{2}}},\qu... | Wikipedia - Harmonic balance - Example | 214 | 479 | null |
{\displaystyle \omega ={\sqrt {\frac {3}{4}}}A_{1}{\sqrt {1+y+2y^{2}}},\quad y=A_{3}/A_{1},\quad 51y^{3}+27y^{2}+21y-1=0.} The cubic equation for y {\displaystyle y} has only one real root y ≈ 0.0448 {\displaystyle y\approx 0.0448} . With that, we obtain an approximate period T = 2 π ( 1 + y ) 3 4 A 1 + y + 2 y 2 ≈ 7.4... | Wikipedia - Harmonic balance - Example | 260 | 523 | null |
Section: Algorithm. The harmonic balance algorithm is a special version of Galerkin's method. It is used for the calculation of periodic solutions of autonomous and non-autonomous differential-algebraic systems of equations. The treatment of non-autonomous systems is slightly simpler than the treatment of autonomous on... | Wikipedia - Harmonic balance - Algorithm | 307 | 1,004 | null |
The system is non-autonomous if the function t ∈ R ↦ F ( t , x , x ˙ ) {\displaystyle t\in \mathbb {R} \mapsto F(t,x,{\dot {x}})} is not constant for (some) fixed x {\displaystyle x} and x ˙ {\displaystyle {\dot {x}}} . Nevertheless, we require that there is a known excitation period T > 0 {\displaystyle T>0} such that... | Wikipedia - Harmonic balance - Algorithm | 293 | 807 | null |
A natural candidate set for the T {\displaystyle T} -periodic solutions of the system equations is the Sobolev space H p e r 1 ( ( 0 , T ) , C n ) {\displaystyle H_{\rm {per}}^{1}((0,T),\mathbb {C} ^{n})} of weakly differentiable functions on the interval [ 0 , T ] {\displaystyle [0,T]} with periodic boundary condition... | Wikipedia - Harmonic balance - Algorithm | 252 | 649 | null |
We assume that the smoothness and the structure of F {\displaystyle F} ensures that F ( t , x ( t ) , x ˙ ( t ) ) {\displaystyle F(t,x(t),{\dot {x}}(t))} is square-integrable for all x ∈ H p e r 1 ( ( 0 , T ) , C n ) {\displaystyle x\in H_{\rm {per}}^{1}((0,T),\mathbb {C} ^{n})} . The system B := { ψ k ∣ k ∈ Z } {\disp... | Wikipedia - Harmonic balance - Algorithm | 341 | 760 | null |
Therefore, each solution candidate x ∈ H p e r 1 ( ( 0 , T ) , C n ) {\displaystyle x\in H_{\rm {per}}^{1}((0,T),\mathbb {C} ^{n})} can be represented by a Fourier-series x ( t ) = ∑ k = − ∞ ∞ x ^ k exp ( i k 2 π t T ) {\displaystyle x(t)=\sum _{k=-\infty }^{\infty }{\hat {x}}_{k}\exp \left(ik{\frac {2\pi t}{T}}\righ... | Wikipedia - Harmonic balance - Algorithm | 345 | 757 | null |
_{H}:={\frac {1}{T}}\int _{0}^{T}\psi ^{*}(t)\cdot F(t,x,{\dot {x}})dt} is fulfilled. This variational equation represents an infinite sequence of scalar equations since it has to be tested for the infinite number of base functions ψ {\displaystyle \psi } in B {\displaystyle B} . The Galerkin approach to the harmonic b... | Wikipedia - Harmonic balance - Algorithm | 208 | 608 | null |
The Galerkin approach to the harmonic balance is to project the candidate set as well as the test space for the variational equation to the finitely dimensional sub-space spanned by the finite base B N := { ψ k ∣ k ∈ Z with − N ≤ k ≤ N } {\displaystyle B_{N}:=\{\psi _{k}\mid k\in \mathbb {Z} {\text{ with }}-N\leq k\leq... | Wikipedia - Harmonic balance - Algorithm | 337 | 799 | null |
This gives the finite-dimensional solution x ( t ) = ∑ k = − N N x ^ k ψ k ( t ) = ∑ k = − N N x ^ k exp ( i k 2 π t T ) {\displaystyle x(t)=\sum _{k=-N}^{N}{\hat {x}}_{k}\psi _{k}(t)=\sum _{k=-N}^{N}{\hat {x}}_{k}\exp \left(ik{\frac {2\pi t}{T}}\right)} and the finite set of equations 0 = ⟨ ψ k , F ( t , x , x ˙ ) ⟩... | Wikipedia - Harmonic balance - Algorithm | 294 | 819 | null |
To increase the efficiency of the procedure, the circuit may be partitioned into its linear and nonlinear parts, since the linear part is readily described and calculated using nodal analysis directly in the frequency domain. First, an initial guess is made for the solution, then an iterative process continues: Voltage... | Wikipedia - Harmonic balance - Algorithm | 338 | 1,442 | null |
Section: Imaging. In this context, the term high dynamic range means there is a large amount of variation in light levels within a scene or an image. The dynamic range refers to the range of luminosity between the brightest area and the darkest area of that scene or image. High dynamic range imaging (HDRI) refers to th... | Wikipedia - High dynamic range - Imaging | 226 | 1,196 | null |
Section: Imaging > Capture. In photography and videography, a technique, commonly named high dynamic range (HDR) allows the dynamic range of photos and videos to be captured beyond the native capability of the camera. It consists of capturing multiple frames of the same scene but with different exposures and then combi... | Wikipedia - High dynamic range - Imaging > Capture | 265 | 1,386 | null |
Section: Imaging > Storage. High-dynamic-range formats for image and video files are able to store more dynamic range than traditional 8-bit gamma formats. These formats include: HDR formats that can be used for both storage and transmission to HDR displays, such as: For video: HDR10 HDR10+ Dolby Vision HLG (backwards ... | Wikipedia - High dynamic range - Imaging > Storage | 310 | 1,347 | null |
Apple refers to EDR as the combination of hardware and software that allows displaying SDR and HDR content on the same screen. HEIC (HEVC codec in HEIF file format) AVIF (AV1 codec in HEIF file format) JPEG XR JPEG XL HSP, CTA 2072 HDR Still Photo Interface (a format used by Panasonic cameras for photo capture in HDR w... | Wikipedia - High dynamic range - Imaging > Storage | 222 | 988 | null |
Section: Imaging > Transmission to displays. High dynamic range (HDR) is also the common name of a technology allowing to transmit high dynamic range videos and images to compatible displays. That technology also improves other aspects of transmitted images, such as color gamut. In this context, HDR displays refers to ... | Wikipedia - High dynamic range - Imaging > Transmission to displays | 314 | 1,321 | null |
Section: Imaging > Display. The dynamic range of a display refers to range of luminosity the display can reproduce, from the black level to its peak brightness. The contrast of a display refers to the ratio between the luminance of the brightest white and the darkest black that a monitor can produce. Multiple technolog... | Wikipedia - High dynamic range - Imaging > Display | 170 | 906 | null |
Section: Non-imaging > Audio. In Audio, the term high dynamic range means there is a lot of variation in the levels of the sound. Here, the dynamic range refers to the range between the highest volume and lowest volume of the sound. XDR (audio) is used to provide higher-quality audio when using microphone sound systems... | Wikipedia - High dynamic range - Non-imaging > Audio | 152 | 781 | null |
The HOSIDFs bear an intuitive resemblance to the classical frequency response function and define the periodic output of a stable, causal, time invariant nonlinear system to a sinusoidal input signal: u ( t ) = γ sin ( ω 0 t + φ 0 ) {\displaystyle u(t)=\gamma \sin(\omega _{0}t+\varphi _{0})} This output is denoted by... | Wikipedia - Higher-order sinusoidal input describing function - Summary | 350 | 934 | null |
Section: Advantages and applications. The application and analysis of the HOSIDFs is advantageous both when a nonlinear model is already identified and when no model is known yet. In the latter case the HOSIDFs require little model assumptions and can easily be identified while requiring no advanced mathematical tools.... | Wikipedia - Higher-order sinusoidal input describing function - Advantages and applications | 221 | 1,179 | null |
Article: Instantaneous phase and frequency. Instantaneous phase and frequency are important concepts in signal processing that occur in the context of the representation and analysis of time-varying functions. The instantaneous phase (also known as local phase or simply phase) of a complex-valued function s(t), is the ... | Wikipedia - Instantaneous phase and frequency - Summary | 332 | 1,045 | null |
Section: Examples > Example 1. s ( t ) = A cos ( ω t + θ ) , {\displaystyle s(t)=A\cos(\omega t+\theta ),} where ω > 0. s a ( t ) = A e j ( ω t + θ ) , φ ( t ) = ω t + θ . {\displaystyle {\begin{aligned}s_{\mathrm {a} }(t)&=Ae^{j(\omega t+\theta )},\\\varphi (t)&=\omega t+\theta .\end{aligned}}} In this simple sinuso... | Wikipedia - Instantaneous phase and frequency - Examples > Example 1 | 220 | 612 | null |
Section: Examples > Example 2. s ( t ) = A sin ( ω t ) = A cos ( ω t − π 2 ) , {\displaystyle s(t)=A\sin(\omega t)=A\cos \left(\omega t-{\frac {\pi }{2}}\right),} where ω > 0. s a ( t ) = A e j ( ω t − π 2 ) , φ ( t ) = ω t − π 2 . {\displaystyle {\begin{aligned}s_{\mathrm {a} }(t)&=Ae^{j\left(\omega t-{\frac {\pi ... | Wikipedia - Instantaneous phase and frequency - Examples > Example 2 | 234 | 538 | null |
Section: Formulations. Instantaneous angular frequency is defined as: ω ( t ) = d φ ( t ) d t , {\displaystyle \omega (t)={\frac {d\varphi (t)}{dt}},} and instantaneous (ordinary) frequency is defined as: f ( t ) = 1 2 π ω ( t ) = 1 2 π d φ ( t ) d t {\displaystyle f(t)={\frac {1}{2\pi }}\omega (t)={\frac {1}{2\pi }}{\... | Wikipedia - Instantaneous phase and frequency - Formulations | 274 | 670 | null |
The inverse operation, which always unwraps phase, is: φ ( t ) = ∫ − ∞ t ω ( τ ) d τ = 2 π ∫ − ∞ t f ( τ ) d τ = ∫ − ∞ 0 ω ( τ ) d τ + ∫ 0 t ω ( τ ) d τ = φ ( 0 ) + ∫ 0 t ω ( τ ) d τ . {\displaystyle {\begin{aligned}\varphi (t)&=\int _{-\infty }^{t}\omega (\tau )\,d\tau =2\pi \int _{-\infty }^{t}f(\tau )\,d\tau \\[5pt]... | Wikipedia - Instantaneous phase and frequency - Formulations | 290 | 640 | null |
{\displaystyle {\begin{aligned}\varphi (t)&=\int _{-\infty }^{t}\omega (\tau )\,d\tau =2\pi \int _{-\infty }^{t}f(\tau )\,d\tau \\[5pt]&=\int _{-\infty }^{0}\omega (\tau )\,d\tau +\int _{0}^{t}\omega (\tau )\,d\tau \\[5pt]&=\varphi (0)+\int _{0}^{t}\omega (\tau )\,d\tau .\end{aligned}}} This instantaneous frequency, ω(... | Wikipedia - Instantaneous phase and frequency - Formulations | 505 | 1,016 | null |
At values of time, t, where there is no change to integer m2, the derivative of φ(t) is ω ( t ) = d φ ( t ) d t = d d t arctan ( I m [ s a ( t ) ] R e [ s a ( t ) ] ) = 1 1 + ( I m [ s a ( t ) ] R e [ s a ( t ) ] ) 2 d d t ( I m [ s a ( t ) ] R e [ s a ( t ) ] ) = R e [ s a ( t ) ] d I m [ s a ( t ) ] d t − I m [ s a... | Wikipedia - Instantaneous phase and frequency - Formulations | 340 | 719 | null |
{Im}}[s_{\mathrm {a} }(t)]}{{\mathcal {Re}}[s_{\mathrm {a} }(t)]}}\right)\\[3pt]&={\frac {1}{1+\left({\frac {{\mathcal {Im}}[s_{\mathrm {a} }(t)]}{{\mathcal {Re}}[s_{\mathrm {a} }(t)]}}\right)^{2}}}{\frac {d}{dt}}\left({\frac {{\mathcal {Im}}[s_{\mathrm {a} }(t)]}{{\mathcal {Re}}[s_{\mathrm {a} }(t)]}}\right)\\[3pt]&={... | Wikipedia - Instantaneous phase and frequency - Formulations | 341 | 514 | null |
{Re}}[s_{\mathrm {a} }(t)])^{2}+({\mathcal {Im}}[s_{\mathrm {a} }(t)])^{2}}}\\[3pt]&={\frac {1}{|s_{\mathrm {a} }(t)|^{2}}}\left({\mathcal {Re}}[s_{\mathrm {a} }(t)]{\frac {d{\mathcal {Im}}[s_{\mathrm {a} }(t)]}{dt}}-{\mathcal {Im}}[s_{\mathrm {a} }(t)]{\frac {d{\mathcal {Re}}[s_{\mathrm {a} }(t)]}{dt}}\right)\\[3pt]&=... | Wikipedia - Instantaneous phase and frequency - Formulations | 350 | 548 | null |
− 1 ] + ω [ n ] = φ [ n − 1 ] + arg { s a [ n ] } − arg { s a [ n − 1 ] } ⏟ Δ φ [ n ] = φ [ n − 1 ] + arg { s a [ n ] s a [ n − 1 ] } {\displaystyle {\begin{aligned}\varphi [n]&=\varphi [n-1]+\omega [n]\\&=\varphi [n-1]+\underbrace {\arg\{s_{\mathrm {a} }[n]\}-\arg\{s_{\mathrm {a} }[n-1]\}} _{\Delta \varphi [n]}\... | Wikipedia - Instantaneous phase and frequency - Formulations | 300 | 627 | null |
That allows φ[n] to accumulate without limit and produces an unwrapped instantaneous phase. An equivalent formulation that replaces the modulo 2π operation with a complex multiplication is: φ [ n ] = φ [ n − 1 ] + arg { s a [ n ] s a ∗ [ n − 1 ] } , {\displaystyle \varphi [n]=\varphi [n-1]+\arg\{s_{\mathrm {a} }[n]\,... | Wikipedia - Instantaneous phase and frequency - Formulations | 244 | 652 | null |
Section: Complex representation. In some applications, such as averaging the values of phase at several moments of time, it may be useful to convert each value to a complex number, or vector representation: e i φ ( t ) = s a ( t ) | s a ( t ) | = cos ( φ ( t ) ) + i sin ( φ ( t ) ) . {\displaystyle e^{i\varphi (t)}... | Wikipedia - Instantaneous phase and frequency - Complex representation | 222 | 742 | null |
Article: Inverter-based resource. An inverter-based resource (IBR) is a source of electricity that is asynchronously connected to the electrical grid via an electronic power converter ("inverter"). The devices in this category, also known as converter interfaced generation (CIG) and power electronic interface source, i... | Wikipedia - Inverter-based resource - Summary | 207 | 958 | null |
Section: Grid-forming. A grid-forming (GFM) device partially mimics the behavior of a synchronous generator: its voltage is controlled by a free-running oscillator that slows down when more energy is withdrawn from the device. Unlike a conventional generator, the GFM device has no overcurrent capacity and thus will rea... | Wikipedia - Inverter-based resource - Grid-forming | 318 | 1,523 | null |
Class 2 is further subdivided in to 2A, 2B, 2C, with 2A being the most basic of the three: Class 1 devices primarily deal with their own survival (full frequency and voltage operating ranges) and have minimal contributions to the grid, including basic reactive power management to maintain the unity power factor and lim... | Wikipedia - Inverter-based resource - Grid-forming | 255 | 1,158 | null |
Section: Features. Compliance with IEEE 1547 standard makes the IBR to support safety features: if the sensed line voltage significantly deviates from the nominal (usually outside the limits of 0.9 to 1.1 pu), the IBR shall disconnect from the after a delay (so called ridethrough time), the delay is shorter if the volt... | Wikipedia - Inverter-based resource - Features | 313 | 1,428 | null |
Section: Features > Protection functions. The IBR devices come with many protection functions built into the inverters. Experience of the late 2010s and early 2020s had shown that some of these protections are unnecessary, as they were designed with an expectation of a strong grid with little IBR penetration. NERC 2018... | Wikipedia - Inverter-based resource - Features > Protection functions | 313 | 1,441 | null |
A speedy response is also essential, so very little filtering is applied to the current sensor data; DC overvoltage indicates a problem on the DC bus of the inverter (and a fault internal to the inverter electronics); DC unbalance for multi-level inverter designs (like a 3-level neutral point clamped, NPC) have multipl... | Wikipedia - Inverter-based resource - Features > Protection functions | 295 | 1,356 | null |
Section: Vulnerabilities > Blue Cut fire. The Blue Cut fire in the Cajon Pass on August 16, 2016, has affected multiple high-voltage (500 kV and 287 kV) power transmission lines passing through the canyon. Throughout the day thirteen 500 kV line faults and two 287 kV faults were recorded. The faults themselves were tra... | Wikipedia - Inverter-based resource - Vulnerabilities > Blue Cut fire | 344 | 1,639 | null |
Section: Education and career. Professor Dan M. Ionel received the M.Eng. and Ph.D. degrees in electrical engineering from the Politehnica University of Bucharest, Romania. His doctoral program included a Leverhulme Visiting Fellowship at the University of Bath, England. He was a Postdoctoral Researcher with the SPEED ... | Wikipedia - Dan Mircea Ionel - Education and career | 296 | 1,560 | null |
Section: Selected publications. Also see The SPARK Laboratory Y. Duan and D. M. Ionel, "A Review of Recent Developments in Electrical Machine Design Optimization Methods With a Permanent-Magnet Synchronous Motor Benchmark Study," in IEEE Transactions on Industry Applications, vol. 49, no. 3, pp. 1268–1275, May–June 201... | Wikipedia - Dan Mircea Ionel - Selected publications | 347 | 1,191 | null |
2675–2685, July 2010. A. Boglietti, A. Cavagnino, D. M. Ionel, M. Popescu, D. A. Staton and S. Vaschetto, "A General Model to Predict the Iron Losses in PWM Inverter-Fed Induction Motors," in IEEE Transactions on Industry Applications, vol. 46, no. 5, pp. 1882–1890, Sept.-Oct. 2010. G. Y. Sizov, D. M. Ionel and N. A. O... | Wikipedia - Dan Mircea Ionel - Selected publications | 348 | 1,130 | null |
Ionel, A. Boglietti, A. Cavagnino, C. Cossar and M. I. McGilp, "A General Model for Estimating the Laminated Steel Losses Under PWM Voltage Supply," in IEEE Transactions on Industry Applications, vol. 46, no. 4, pp. 1389–1396, July-Aug. 2010. D. M. Ionel, M. Popescu, M. I. McGilp, T. J. E. Miller and S. J. Dellinger, "... | Wikipedia - Dan Mircea Ionel - Selected publications | 316 | 1,064 | null |
2013. S. Choi et al., "Fault Diagnosis Techniques for Permanent Magnet AC Machine and Drives—A Review of Current State of the Art," in IEEE Transactions on Transportation Electrification, vol. 4, no. 2, pp. 444–463, June 2018. M. Popescu and D. M. Ionel, "A Best-Fit Model of Power Losses in Cold Rolled-Motor Lamination... | Wikipedia - Dan Mircea Ionel - Selected publications | 331 | 1,166 | null |
Section: Selected patents. Ionel, D.M., AO Smith Corp, 2011. Interior permanent magnet motor including rotor with flux barriers. U.S. Patent 7,932,658. Ionel, D.M., Dellinger, S.J., Lesak, A.E. and Mattingly, J., AO Smith Corp, 2011. Interior permanent magnet motor and rotor. U.S. Patent 7,923,881. Ionel, D.M., Delling... | Wikipedia - Dan Mircea Ionel - Selected patents | 350 | 1,063 | null |
U.S. Patent 7,687,965. Ionel, D.M., Dellinger, S.J. and Lesak, A.E., AO Smith Corp, 2007. Electric motor having a stator. U.S. Patent US20050017590A1 Ionel, D.M., and Dellinger, S.J., O Smith Corp, 2005. Brushless permanent magnet machine with axial modules of rotor magnetization skew and method of producing the same. ... | Wikipedia - Dan Mircea Ionel - Selected patents | 182 | 522 | null |
Article: Johnson–Nyquist noise. Johnson–Nyquist noise (thermal noise, Johnson noise, or Nyquist noise) is the voltage or current noise generated by the thermal agitation of the charge carriers (usually the electrons) inside an electrical conductor at equilibrium, which happens regardless of any applied voltage. Thermal... | Wikipedia - Johnson–Nyquist noise - Summary | 299 | 1,582 | null |
Section: History of thermal noise. In 1905, in one of Albert Einstein's Annus mirabilis papers the theory of Brownian motion was first solved in terms of thermal fluctuations. The following year, in a second paper about Brownian motion, Einstein suggested that the same phenomena could be applied to derive thermally-agi... | Wikipedia - Johnson–Nyquist noise - History of thermal noise | 334 | 1,607 | null |
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