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Section: Tetrahedron of state. The tetrahedron of state is a tetrahedron that graphically shows the conversion between effort and flow. The adjacent image shows the tetrahedron in its generalized form. The tetrahedron can be modified depending on the energy domain. Using the tetrahedron of state, one can find a mathema... | Wikipedia - Bond graph - Tetrahedron of state | 333 | 1,303 | null |
p ( t ) = β« e ( t ) d t {\displaystyle p(t)=\int e(t)\,dt} Relationship between generalized flow and generalized effort, involving the constant C. e ( t ) = 1 C β« f ( t ) d t {\displaystyle e(t)={\frac {1}{C}}\int f(t)\,dt} All of the mathematical relationships remain the same when switching energy domains, only the sy... | Wikipedia - Bond graph - Tetrahedron of state | 246 | 824 | null |
Section: Components. If an engine is connected to a wheel through a shaft, the power is being transmitted in the rotational mechanical domain, meaning the effort and the flow are torque (Ο) and angular velocity (Ο) respectively. A word bond graph is a first step towards a bond graph, in which words define the component... | Wikipedia - Bond graph - Components | 346 | 1,187 | null |
As the engine is applying a torque to the wheel, it will be represented as a source of effort for the system. The wheel can be presented by an impedance on the system. Further, the torque and angular velocity symbols are dropped and replaced with the generalized symbols for effort and flow. While not necessary in the e... | Wikipedia - Bond graph - Components | 332 | 1,088 | null |
Section: Components > Association of elements > Series association. Suppose that an element has the following behavior: e ( t ) = Ξ± g ( q ( t ) ) {\displaystyle e(t)=\alpha g(q(t))} where g ( x ) {\displaystyle g(x)} is a generic function (it can even differentiate/integrate its input) and Ξ± {\displaystyle \alpha } is ... | Wikipedia - Bond graph - Components > Association of elements > Series association | 250 | 703 | null |
Then it is valid: g β 1 ( e ( t ) ) = Ξ± i q i ( t ) βΉ 1 Ξ± i g β 1 ( e ( t ) ) = q i ( t ) βΉ ( β i 1 Ξ± i ) g β 1 ( e ( t ) ) = q ( t ) βΉ g ( g β 1 ( e ( t ) ) ) = g ( 1 β i 1 Ξ± i q ( t ) ) βΉ Ξ± eq = β₯ i = 1 N Ξ± i {\displaystyle g^{-1}\left(e(t)\right)=\alpha _{i}q_{i}(t)\implies {\frac {1}{\alpha _{i}}}g^{-1}(e(t))=q_{i}... | Wikipedia - Bond graph - Components > Association of elements > Parallel association | 342 | 592 | null |
Section: Components > Two-port elements > Transformer. A transformer applies a relationship between flow in flow out, and effort in effort out. Examples include an ideal electrical transformer or a lever. Denoted β β β β 1 T R β β β β 2 r : 1 {\displaystyle {\begin{matrix}{\overset {\textstyle _{1}}{\underset {\textsty... | Wikipedia - Bond graph - Components > Two-port elements > Transformer | 268 | 654 | null |
Section: Components > Two-port elements > Gyrator. A gyrator applies a relationship between flow in effort out, and effort in flow out. An example of a gyrator is a DC motor, which converts voltage (electrical effort) into angular velocity (angular mechanical flow). β β β β 1 G Y β β β β 2 g : 1 {\displaystyle {\begin{... | Wikipedia - Bond graph - Components > Two-port elements > Gyrator | 277 | 661 | null |
Section: Components > Multi-port elements > 0-junctions. 0-junctions behave such that all effort values (and its time integral/derivative) are equal across the bonds, but the sum of the flow values in equals the sum of the flow values out, or equivalently, all flows sum to zero. In an electrical circuit, the 0-junction... | Wikipedia - Bond graph - Components > Multi-port elements > 0-junctions | 184 | 698 | null |
all e 's are equal {\displaystyle {\text{all }}e{\text{'s are equal}}} β f in = β f out {\displaystyle \sum f_{\text{in}}=\sum f_{\text{out}}} An example is shown below. β β β β 1 0 βΎ 2 β β β β 3 {\displaystyle {\overset {\textstyle _{1}}{\underset {\textstyle }{-\!\!\!-\!\!\!-\!\!\!\rightharpoondown }}}{\stackrel {\te... | Wikipedia - Bond graph - Components > Multi-port elements > 0-junctions | 292 | 596 | null |
Section: Components > Multi-port elements > 1-junctions. 1-junctions behave opposite of 0-junctions. 1-junctions behave such that all flow values (and its time integral/derivative) are equal across the bonds, but the sum of the effort values in equals the sum the effort values out, or equivalently, all efforts sum to z... | Wikipedia - Bond graph - Components > Multi-port elements > 1-junctions | 177 | 688 | null |
all f 's are equal {\displaystyle {\text{all }}f{\text{'s are equal}}} β e in = β e out {\displaystyle \sum e_{\text{in}}=\sum e_{\text{out}}} An example is shown below. β β β β 1 1 βΎ 2 β β β β 3 {\displaystyle {\overset {\textstyle _{1}}{\underset {\textstyle }{-\!\!\!-\!\!\!-\!\!\!\rightharpoondown }}}{\stackrel {\te... | Wikipedia - Bond graph - Components > Multi-port elements > 1-junctions | 292 | 596 | null |
Section: Causality. Bond graphs have a notion of causality, indicating which side of a bond determines the instantaneous effort and which determines the instantaneous flow. In formulating the dynamic equations that describe the system, causality defines, for each modeling element, which variable is dependent and which ... | Wikipedia - Bond graph - Causality | 334 | 1,705 | null |
Consequently, the side opposite from the casual stroke controls the effort. Sources of flow ( S f {\displaystyle S_{f}} ) define flow, so they host the causal stroke: S f | β β β β {\displaystyle S_{f}\;|\!\!\!-\!\!\!-\!\!\!-\!\!\!\rightharpoonup \!\!\!} Sources of effort ( S e {\displaystyle S_{e}} ) define effort, so... | Wikipedia - Bond graph - Causality | 214 | 546 | null |
a source of effort ( S e {\displaystyle S_{e}} ). That would be drawn as follows: motor S e β β β β | Ο Ο wheel {\displaystyle {\begin{array}{r}{\text{motor}}\\S_{e}\end{array}}\;{\overset {\textstyle \tau }{\underset {\textstyle \omega }{-\!\!\!-\!\!\!-\!\!\!\rightharpoonup \!\!\!|}}}\;{\text{wheel}}} Symmetrically, t... | Wikipedia - Bond graph - Causality | 266 | 836 | null |
In addition, the two passive components with time-dependent behavior, I {\displaystyle I} and C {\displaystyle C} , can only have one sort of causation: an I {\displaystyle I} component determines flow; a C {\displaystyle C} component defines effort. So from a junction, J {\displaystyle J} , the preferred causal orient... | Wikipedia - Bond graph - Causality | 275 | 786 | null |
So from a junction, J {\displaystyle J} , the preferred causal orientation is as follows: J β β β β | I and J | β β β β C {\displaystyle J\;{\overset {\textstyle }{\underset {\textstyle }{-\!\!\!-\!\!\!-\!\!\!\rightharpoonup \!\!\!|}}}\;I\qquad {\text{and}}\qquad J\;{\overset {\textstyle }{\underset {\textstyle }{|\!\!... | Wikipedia - Bond graph - Causality | 350 | 917 | null |
The equations can be seen below. e ( t ) = I f Λ ( t ) and f ( t ) = C e Λ ( t ) {\displaystyle e(t)=I{\dot {f}}(t)\qquad {\text{and}}\qquad f(t)=C{\dot {e}}(t)} It is possible for a bond graph to have a causal bar on one of these elements in the non-preferred manner. In such a case a "causal conflict" is said to have ... | Wikipedia - Bond graph - Causality | 154 | 492 | null |
A resistor has no time-dependent behavior: apply a voltage and get a flow instantly, or apply a flow and get a voltage instantly, thus a resistor can be at either end of a causal bond: J β β β β | R and J | β β β β R {\displaystyle J\;{\overset {\textstyle }{\underset {\textstyle }{-\!\!\!-\!\!\!-\!\!\!\rightharpoonup ... | Wikipedia - Bond graph - Causality | 334 | 772 | null |
}{-\!\!\!-\!\!\!-\!\!\!-\!\!\!-\!|}}}\;\qquad {\text{or}}\qquad \;{\overset {\textstyle }{\underset {\textstyle }{|\!\!\!-\!\!\!-\!\!\!-\!\!\!-\!\!\!-}}}\;TF\;{\overset {\textstyle }{\underset {\textstyle }{|\!\!\!-\!\!\!-\!\!\!-\!\!\!-\!\!\!-}}}\;} A gyrator transforms flow to effort and effort to flow, so if flow is ... | Wikipedia - Bond graph - Causality | 330 | 605 | null |
}{-\!\!\!-\!\!\!-\!\!\!-\!\!\!-\!|}}}\;\qquad {\text{or}}\qquad \;{\overset {\textstyle }{\underset {\textstyle }{-\!\!\!-\!\!\!-\!\!\!-\!\!\!-\!|}}}\;GY\;{\overset {\textstyle }{\underset {\textstyle }{|\!\!\!-\!\!\!-\!\!\!-\!\!\!-\!\!\!-}}}\;} | Wikipedia - Bond graph - Causality | 177 | 245 | null |
Section: Causality > Junctions. In a 0-junction, efforts are equal; in a 1-junction, flows are equal. Thus, with causal bonds, only one bond can cause the effort in a 0-junction and only one can cause the flow in a 1-junction. Thus, if the causality of one bond of a junction is known, the causality of the others is als... | Wikipedia - Bond graph - Causality > Junctions | 260 | 798 | null |
S f β β β β 0 β β β β T R β β β β 0 β β β β C 5 β r : 1 β C 2 R 6 {\displaystyle {\begin{matrix}S_{f}&{\overset {\textstyle }{\underset {\textstyle }{\!\!\!-\!\!\!-\!\!\!-\!\!\!\rightharpoonup }}}&0&{\overset {\textstyle }{\underset {\textstyle }{\!\!\!-\!\!\!-\!\!\!-\!\!\!\rightharpoonup }}}&TR&{\overset {\textstyle }... | Wikipedia - Bond graph - Causality > Determining causality | 349 | 622 | null |
S f | β β β β 0 β β β β T R β β β β 0 β β β β C 5 β r : 1 β C 2 R 6 {\displaystyle {\begin{matrix}S_{f}&{\overset {\textstyle }{\underset {\textstyle }{|\!\!\!-\!\!\!-\!\!\!-\!\!\!\rightharpoonup }}}&0&{\overset {\textstyle }{\underset {\textstyle }{\!\!\!-\!\!\!-\!\!\!-\!\!\!\rightharpoonup }}}&TR&{\overset {\textstyl... | Wikipedia - Bond graph - Causality > Determining causality | 349 | 620 | null |
S f | β β β β 0 β β β β T R β β β β 0 | β β β β C 5 β Β― r : 1 β C 2 R 6 {\displaystyle {\begin{matrix}S_{f}&{\overset {\textstyle }{\underset {\textstyle }{|\!\!\!-\!\!\!-\!\!\!-\!\!\!\rightharpoonup }}}&0&{\overset {\textstyle }{\underset {\textstyle }{\!\!\!-\!\!\!-\!\!\!-\!\!\!\rightharpoonup }}}&TR&{\overset {\text... | Wikipedia - Bond graph - Causality > Determining causality | 350 | 595 | null |
S f | β β β β 0 | β β β β T R | β β β β 0 | β β β β C 5 β Β― r : 1 β _ C 2 R 6 {\displaystyle {\begin{matrix}S_{f}&{\overset {\textstyle }{\underset {\textstyle }{|\!\!\!-\!\!\!-\!\!\!-\!\!\!\rightharpoonup }}}&0&{\overset {\textstyle }{\underset {\textstyle }{|\!\!\!-\!\!\!-\!\!\!-\!\!\!\rightharpoonup }}}&TR&{\overset... | Wikipedia - Bond graph - Causality > Determining causality | 331 | 579 | null |
S f | β β β β 0 | β β β β T R | β β β β 0 | β β β β C 5 β _ β r : 1 β _ C 2 R 6 {\displaystyle {\begin{matrix}S_{f}&{\overset {\textstyle }{\underset {\textstyle }{|\!\!\!-\!\!\!-\!\!\!-\!\!\!\rightharpoonup }}}&0&{\overset {\textstyle }{\underset {\textstyle }{|\!\!\!-\!\!\!-\!\!\!-\!\!\!\rightharpoonup }}}&TR&{\overs... | Wikipedia - Bond graph - Causality > Determining causality | 335 | 593 | null |
f 1 = f 2 = f 3 e 2 = e 4 = e 7 e 1 = e 2 + e 3 f 2 = f 4 + f 7 e 3 = e 5 = e 6 f 7 = f 6 = f 8 f 3 = f 5 + f 6 e 7 + e 6 = e 8 {\displaystyle {\begin{matrix}f_{1}=f_{2}=f_{3}&&e_{2}=e_{4}=e_{7}\\e_{1}=e_{2}+e_{3}&&f_{2}=f_{4}+f_{7}\\&&\\e_{3}=e_{5}=e_{6}&&f_{7}=f_{6}=f_{8}\\f_{3}=f_{5}+f_{6}&&e_{7}+e_{6}=e_{8}\end{mat... | Wikipedia - Bond graph - Converting from other systems > Parallel power | 263 | 473 | null |
f 1 = f 2 = f 3 e 2 = e 4 = e 7 e 1 = e 2 + e 3 f 2 = f 4 + f 7 e 3 = e 5 = e 6 f 7 = f 6 = f 8 f 3 = f 5 + f 6 e 7 + e 6 = e 8 {\displaystyle {\begin{matrix}f_{1}=f_{2}=f_{3}&&e_{2}=e_{4}=e_{7}\\e_{1}=e_{2}+e_{3}&&f_{2}=f_{4}+f_{7}\\&&\\e_{3}=e_{5}=e_{6}&&f_{7}=f_{6}=f_{8}\\f_{3}=f_{5}+f_{6}&&e_{7}+e_{6}=e_{8}\end{mat... | Wikipedia - Bond graph - Converting from other systems > Parallel power | 439 | 837 | null |
For example, because e 3 = e 6 {\textstyle e_{3}=e_{6}} and e 2 = e 7 {\textstyle e_{2}=e_{7}} you can replace the variables in the equation e 1 = e 2 + e 3 {\textstyle e_{1}=e_{2}+e_{3}} resulting in e 1 = e 6 + e 7 {\textstyle e_{1}=e_{6}+e_{7}} and since e 6 + e 7 = e 8 {\textstyle e_{6}+e_{7}=e_{8}} , we now know t... | Wikipedia - Bond graph - Converting from other systems > Parallel power | 264 | 754 | null |
Section: Converting from other systems > Examples > Simple electrical system. A simple electrical circuit consisting of a voltage source, resistor, and capacitor in series. The first step is to draw 0-junctions at all of the nodes: 0 0 0 0 {\displaystyle {\begin{matrix}&0&&0&\\&&&&\\&&&&\\&0&&0&\end{matrix}}} The next ... | Wikipedia - Bond graph - Converting from other systems > Examples > Simple electrical system | 339 | 960 | null |
The arrows on junctions should point towards ground (following a similar path to current). For resistance, inertance, and compliance elements, the arrows always point towards the elements. The result of drawing the arrows can be seen below, with the 0-junction marked with a star as the ground. Now that we have the Bond... | Wikipedia - Bond graph - Converting from other systems > Examples > Simple electrical system | 187 | 887 | null |
Section: Converting from other systems > Examples > Simple linear mechanical. A simple linear mechanical system, consisting of a mass on a spring that is attached to a wall. The mass has some force being applied to it. An image of the system is shown below. For a mechanical system, the first step is to place a 1-juncti... | Wikipedia - Bond graph - Converting from other systems > Examples > Simple linear mechanical | 350 | 1,150 | null |
1 mass | 0 β C : 1 k | 1 wall {\displaystyle {\begin{matrix}&&\\&&\\1_{\text{mass}}&&\\|&&\\0&-&C:{\frac {1}{k}}\\|&&\\1_{\text{wall}}&&\end{matrix}}} Next you want to add the sources and I bonds on the 1-junction where they act. There is one source, the source of effort (force) and one I bond, the mass of the mass bot... | Wikipedia - Bond graph - Converting from other systems > Examples > Simple linear mechanical | 337 | 903 | null |
Section: Converting from other systems > Examples > Advanced linear mechanical. A more advanced linear mechanical system can be seen below. Just like the above example, the first step is to make 1-junctions at each of the distant velocities. In this example there are three distant velocity, Mass 1, Mass 2, and the wall... | Wikipedia - Bond graph - Converting from other systems > Examples > Advanced linear mechanical | 168 | 785 | null |
Section: State equations. Once a bond graph is complete, it can be utilized to generate the state-space representation equations of the system. State-space representation is especially powerful as it allows complex multi-order differential system to be solved as a system of first-order equations instead. The general fo... | Wikipedia - Bond graph - State equations | 315 | 1,034 | null |
For example, if you have the following bond graph you would have the following x Λ ( t ) {\textstyle {\dot {\mathbf {x} }}(t)} , x ( t ) {\textstyle \mathbf {x} (t)} , and u ( t ) {\textstyle \mathbf {u} (t)} matrices: x Λ ( t ) = [ p Λ 3 ( t ) q Λ 6 ( t ) ] and x ( t ) = [ p 3 ( t ) q 6 ( t ) ] and u ( t ) = [ e 1 ( t... | Wikipedia - Bond graph - State equations | 350 | 775 | null |
e 1 = input {\textstyle e_{1}={\text{input}}} e 3 = e 1 β e 2 β e 4 {\textstyle e_{3}=e_{1}-e_{2}-e_{4}} f 1 = f 2 = f 4 = f 3 {\textstyle f_{1}=f_{2}=f_{4}=f_{3}} e 2 = R 2 f 2 {\textstyle e_{2}=R_{2}f_{2}} f 3 = 1 I 3 β« e 3 d t = 1 I 3 p 3 {\textstyle f_{3}={\frac {1}{I_{3}}}\int e_{3}\,dt={\frac {1}{I_{3}}}p_{3}} f ... | Wikipedia - Bond graph - State equations | 347 | 562 | null |
{1}{C_{6}}}\int f_{6}\,dt={\frac {1}{C_{6}}}q_{6}} f 7 = 1 R 7 e 7 {\textstyle f_{7}={\frac {1}{R_{7}}}e_{7}} These equations can be manipulated to yield the state equations. For this example, you are trying to find equations that relate p Λ 3 ( t ) {\textstyle {\dot {p}}_{3}(t)} and q Λ 6 ( t ) {\textstyle {\dot {q}}_... | Wikipedia - Bond graph - State equations | 323 | 690 | null |
To start you should recall from the tetrahedron of state that p Λ 3 ( t ) = e 3 ( t ) {\textstyle {\dot {p}}_{3}(t)=e_{3}(t)} starting with equation 2, you can rearrange it so that e 3 = e 1 β e 2 β e 4 {\displaystyle e_{3}=e_{1}-e_{2}-e_{4}} . e 2 {\displaystyle e_{2}} can be substituted for equation 4, while in equat... | Wikipedia - Bond graph - State equations | 244 | 736 | null |
Following these substituted yields the first state equation which is shown below. p Λ 3 ( t ) = e 3 ( t ) = e 1 ( t ) β R 2 I 3 p 3 ( t ) β r C 6 q 6 ( t ) {\displaystyle {\dot {p}}_{3}(t)=e_{3}(t)=e_{1}(t)-{\frac {R_{2}}{I_{3}}}p_{3}(t)-{\frac {r}{C_{6}}}q_{6}(t)} The second state equation can likewise be solved, by r... | Wikipedia - Bond graph - State equations | 336 | 704 | null |
The result of which is below. [ p Λ 3 ( t ) q Λ 6 ( t ) ] = [ β R 2 I 3 β r C 6 r I 3 β 1 R 7 β
C 6 ] [ p 3 ( t ) q 6 ( t ) ] + [ 1 0 ] [ e 1 ( t ) ] {\displaystyle {\begin{bmatrix}{\dot {p}}_{3}(t)\\{\dot {q}}_{6}(t)\end{bmatrix}}={\begin{bmatrix}-{\frac {R_{2}}{I_{3}}}&-{\frac {r}{C_{6}}}\\{\frac {r}{I_{3}}}&-{\frac ... | Wikipedia - Bond graph - State equations | 310 | 570 | null |
Section: International conferences on bond graph modeling (ECMS and ICBGM). A bibliography on bond graph modeling may be extracted from the following conferences : ECMS-2013 27th European Conference on Modelling and Simulation, May 27β30, 2013, Γ
lesund, Norway ECMS-2008 22nd European Conference on Modelling and Simulat... | Wikipedia - Bond graph - International conferences on bond graph modeling (ECMS and ICBGM) | 272 | 1,189 | null |
β Papers ICBGM-2003 International Conference on Bond Graph Modeling and Simulation (ICBGM'2003) January 19β23, 2003, Orlando, Florida, USA β Papers 14TH European Simulation symposium October 23β26, 2002 Dresden, Germany ESS'2001 13th European Simulation symposium, Marseilles, France October 18β20, 2001 ICBGM-2001 Inter... | Wikipedia - Bond graph - International conferences on bond graph modeling (ECMS and ICBGM) | 291 | 1,263 | null |
Section: Education. Bond came to Purdue University in 1957 to study electrical engineering on National Merit Scholarship and Purdue's Special Merit Scholarship. He describes always having been interested in electrical engineering, and ending up at Purdue by luck, recounting that "My high school principal's son was inte... | Wikipedia - Arthur J. Bond - Education | 206 | 948 | null |
Section: Student organizing. Bond was a student leader at Purdue during the time when the civil rights movement was in full swing. He would become a founding member of Purdue's Black Cultural Center and a founder of the National Society of Black Engineers. At Purdue, Bond led students to demand that Purdue open up its ... | Wikipedia - Arthur J. Bond - Student organizing | 297 | 1,533 | null |
Section: Career. Upon receiving his doctorate, Bond became an assistant professor of electrical engineering at Purdue for five years, and then an associate professor at Purdue Calumet. He then went to work in industry for RCA, AlliedSignal, and Bendix. In 1989, Bond joined Tuskegee University as head of its department ... | Wikipedia - Arthur J. Bond - Career | 286 | 1,415 | null |
Section: Honors. 1968: Bachelor of Science in Electrical Engineering, Purdue University. 1969: Masters of Science in Electrical Engineering, Purdue University. 1971: Co-Founder of The Society of Black Engineers (now NSBE). 1974: Assistant Professor, Purdue University. 1979: Associate Professor, Purdue University, Calum... | Wikipedia - Arthur J. Bond - Honors | 214 | 1,133 | null |
Article: Breaking capacity. Breaking capacity or interrupting rating is the current that a fuse, circuit breaker, or other electrical apparatus is able to interrupt without being destroyed or causing an electric arc with unacceptable duration. The prospective short-circuit current that can occur under short circuit con... | Wikipedia - Breaking capacity - Summary | 183 | 1,074 | null |
Section: Choosing breaking capacity. Calculation of the required breaking capacity involves determining the supply impedance and voltage. Supply impedance is calculated from the impedance of the elements making up the supply system. Customers of an electrical supply utility can request the maximum value of prospective ... | Wikipedia - Breaking capacity - Choosing breaking capacity | 189 | 1,065 | null |
Section: Breaking capacities. Miniature circuit breakers and fuses may be rated to interrupt as little as 85 amperes and are intended for supplementary protection of equipment, not the primary protection of a building wiring system. In North American practice, approved general-purpose low-voltage fuses must interrupt a... | Wikipedia - Breaking capacity - Breaking capacities | 179 | 920 | null |
Article: Cavity perturbation theory. In mathematics and electronics, cavity perturbation theory describes methods for derivation of perturbation formulae for performance changes of a cavity resonator. These performance changes are assumed to be caused by either introduction of a small foreign object into the cavity, or... | Wikipedia - Cavity perturbation theory - Summary | 163 | 885 | null |
Section: Introduction. When a resonant cavity is perturbed, e.g. by introducing a foreign object with distinct material properties into the cavity or when the shape of the cavity is changed slightly, electromagnetic fields inside the cavity change accordingly. This means that all the resonant modes (i.e. the quasinorma... | Wikipedia - Cavity perturbation theory - Introduction | 211 | 1,039 | null |
Section: General theory. It is convenient to denote cavity frequencies with a complex number Ο ~ = Ο β i Ξ³ / 2 {\displaystyle {\tilde {\omega }}=\omega -i\gamma /2} , where Ο = R e ( Ο ~ ) {\displaystyle \omega =Re({\tilde {\omega }})} is the angular resonant frequency and Ξ³ = 2 I m ( Ο ~ ) {\displaystyle \gamma =2Im({... | Wikipedia - Cavity perturbation theory - General theory | 336 | 1,269 | null |
However energy consideration in electromagnetism is only valid for Hermitian systems for which energy is conserved. For cavities, energy is conserved only in the limit of very small leakage (infinite Q's), so that Expression (1) is only valid in this limit. For instance, it is apparent that Expression (1) predicts a ch... | Wikipedia - Cavity perturbation theory - General theory | 333 | 1,359 | null |
In this framework, the frequency shift and the Q change are predicted by The accuracy of the seminal equation 2 has been verified in a variety of complicated geometries. For low-Q cavities, such as plasmonic nanoresonators that are used for sensing, equation 2 has been shown to predict both the shift and the broadening... | Wikipedia - Cavity perturbation theory - General theory | 188 | 830 | null |
Section: Material perturbation. When a material within a cavity is changed (permittivity and/or permeability), a corresponding change in resonant frequency can be approximated as: where Ο {\displaystyle \omega } is the angular resonant frequency of the perturbed cavity, Ο 0 {\displaystyle \omega _{0}} is the resonant f... | Wikipedia - Cavity perturbation theory - Material perturbation | 264 | 1,006 | null |
Section: Shape perturbation. When a general shape of a resonant cavity is changed, a corresponding change in resonant frequency can be approximated as: Expression (5) for change in resonant frequency can additionally be written in terms of time-average stored energies as: where Ξ W m {\displaystyle \Delta W_{m}} and Ξ ... | Wikipedia - Cavity perturbation theory - Shape perturbation | 176 | 826 | null |
Section: Applications. Microwave measurement techniques based on cavity perturbation theory are generally used to determine the dielectric and magnetic parameters of materials and various circuit components such as dielectric resonators. Since ex-ante knowledge of the resonant frequency, resonant frequency shift and el... | Wikipedia - Cavity perturbation theory - Applications | 153 | 838 | null |
Section: Examples > TE10n rectangular waveguide cavity. For rectangular waveguide cavity, field distribution of dominant T E 10 n {\displaystyle TE_{10n}} mode is well known. Ideally, the material to be measured is introduced into the cavity at the position of maximum electric or magnetic field. When the material is in... | Wikipedia - Cavity perturbation theory - Examples > TE10n rectangular waveguide cavity | 279 | 1,101 | null |
In this case, we can use perturbation theory to derive expressions for real and imaginary components of complex material permittivity Ο΅ r = Ο΅ r β² + j Ο΅ r β³ {\displaystyle \epsilon _{r}=\epsilon _{r}'+j\epsilon _{r}''} as: where f c {\displaystyle f_{c}} and f s {\displaystyle f_{s}} represent resonant frequencies of or... | Wikipedia - Cavity perturbation theory - Examples > TE10n rectangular waveguide cavity | 301 | 1,144 | null |
Similarly, if the material is introduced into the cavity at the position of maximum magnetic field, then the contribution of electric field to perturbed frequency shift is very small and can be ignored. In this case, we can use perturbation theory to derive expressions for complex material permeability ΞΌ r = ΞΌ r β² + j ... | Wikipedia - Cavity perturbation theory - Examples > TE10n rectangular waveguide cavity | 158 | 531 | null |
Article: Center frequency. In electrical engineering and telecommunications, the center frequency of a filter or channel is a measure of a central frequency between the upper and lower cutoff frequencies. It is usually defined as either the arithmetic mean or the geometric mean of the lower cutoff frequency and the upp... | Wikipedia - Center frequency - Summary | 198 | 1,086 | null |
Article: Circuit reliability. Circuit reliability (also time availability) (CiR) is the percentage of time an electronic circuit was available for use in a specified period of scheduled availability. Circuit reliability is given by T s = T a + T o {\displaystyle T_{s}=T_{a}+T_{o}} where T o {\displaystyle T_{o}} is the... | Wikipedia - Circuit reliability - Summary | 150 | 598 | null |
Article: Circuit Scribe. Circuit Scribe is a ball-point pen containing silver conductive ink one can use to draw circuits instantly on flexible substrates like paper. Circuit Scribe made its way onto Kickstarter (an online site where people can fund projects) on November 19, 2013, with its goal of raising $85,000 for t... | Wikipedia - Circuit Scribe - Summary | 161 | 767 | null |
Section: Development > Ink. The ink is created by placing an aqueous solution of silver nitrate into a flask of water combined with polyacrylic acid (PAA) and diethanolamine (DEA), the capping agent and reducing agent, respectively. After about twenty hours, the silver nitrate is dissolved, forming particles with a dia... | Wikipedia - Circuit Scribe - Development > Ink | 350 | 1,521 | null |
Section: Development > Kickstarter Campaign. Circuit Scribe launched its campaign on Kickstarter to receive funding and included a list of pledges which people could donate a certain amount and get a corresponding gift: Pledge $5+: STEM Education Workbook Pledge $20+: Circuit Scribe Pledge $25+: Early Bird Basic Kit Pl... | Wikipedia - Circuit Scribe - Development > Kickstarter Campaign | 213 | 889 | null |
Section: Uses > Arduino. Circuit Scribe allows users to create a paper Arduino (or a βpaperduinoβ), which is demonstrated by the research team. The team first found the schematics on the Arduino website and modified them so that they would work on a pen plotter. With a few modifications, they arranged the components an... | Wikipedia - Circuit Scribe - Uses > Arduino | 347 | 1,581 | null |
Article: Circuit topology (electrical). The circuit topology of an electronic circuit is the form taken by the network of interconnections of the circuit components. Different specific values or ratings of the components are regarded as being the same topology. Topology is not concerned with the physical layout of comp... | Wikipedia - Circuit topology (electrical) - Summary | 325 | 1,728 | null |
Section: Series and parallel topologies. A network with two components or branches has only two possible topologies: series and parallel. Even for these simplest of topologies, the circuit can be presented in varying ways. A network with three branches has four possible topologies. Note that the parallel-series topolog... | Wikipedia - Circuit topology (electrical) - Series and parallel topologies | 171 | 736 | null |
Section: Y and Ξ topologies. Y and Ξ are important topologies in linear network analysis due to these being the simplest possible three-terminal networks. A Y-Ξ transform is available for linear circuits. This transform is important because some networks cannot be analysed in terms of series and parallel combinations. ... | Wikipedia - Circuit topology (electrical) - Y and Ξ topologies | 218 | 1,076 | null |
Section: Bridge topology. Bridge topology is an important topology with many uses in both linear and non-linear applications, including, amongst many others, the bridge rectifier, the Wheatstone bridge and the lattice phase equaliser. Bridge topology is rendered in circuit diagrams in several ways. The first rendering ... | Wikipedia - Circuit topology (electrical) - Bridge topology | 251 | 1,261 | null |
Section: Bridged T and twin-T topologies. Bridged T topology is derived from bridge topology in a way explained in the Zobel network article. Many derivative topologies are also discussed in the same article. There is also a twin-T topology, which has practical applications where it is desirable to have the input and o... | Wikipedia - Circuit topology (electrical) - Bridged T and twin-T topologies | 179 | 836 | null |
Section: Infinite topologies. Ladder topology can be extended without limit and is much used in filter designs. There are many variations on ladder topology, some of which are discussed in the Electronic filter topology and Composite image filter articles. The balanced form of ladder topology can be viewed as being the... | Wikipedia - Circuit topology (electrical) - Infinite topologies | 193 | 1,004 | null |
Section: Graph theory > History. Graph theory has been used in the network analysis of linear, passive networks almost from the moment that Kirchhoff's laws were formulated. Gustav Kirchhoff himself, in 1847, used graphs as an abstract representation of a network in his loop analysis of resistive circuits. This approac... | Wikipedia - Circuit topology (electrical) - Graph theory > History | 335 | 1,686 | null |
Section: Graph theory > Graphs and circuit diagrams. Networks are commonly classified by the kind of electrical elements making them up. In a circuit diagram these element-kinds are specifically drawn, each with its own unique symbol. Resistive networks are one-element-kind networks, consisting only of R elements. Like... | Wikipedia - Circuit topology (electrical) - Graph theory > Graphs and circuit diagrams | 347 | 1,735 | null |
Section: Graph theory > Equivalence. Graphs are equivalent if one can be transformed into the other by deformation. Deformation can include the operations of translation, rotation and reflection; bending and stretching the branches; and crossing or knotting the branches. Two graphs which are equivalent through deformat... | Wikipedia - Circuit topology (electrical) - Graph theory > Equivalence | 212 | 1,135 | null |
Section: Graph theory > Trees and links. A tree is a graph in which all the nodes are connected, either directly or indirectly, by branches, but without forming any closed loops. Since there are no closed loops, there are no currents in a tree. In network analysis, we are interested in spanning trees, that is, trees th... | Wikipedia - Circuit topology (electrical) - Graph theory > Trees and links | 219 | 950 | null |
Section: Graph theory > Tie sets and cut sets. The goal of circuit analysis is to determine all the branch currents and voltages in the network. These network variables are not all independent. The branch voltages are related to the branch currents by the transfer function of the elements of which they are composed. A ... | Wikipedia - Circuit topology (electrical) - Graph theory > Tie sets and cut sets | 341 | 1,716 | null |
This set of loops consists of those loops formed by replacing a single link of a given tree of the graph of the circuit to be analysed. Since replacing a single link in a tree forms exactly one unique loop, the number of loop currents so defined is equal to l. The term loop in this context is not the same as the usual ... | Wikipedia - Circuit topology (electrical) - Graph theory > Tie sets and cut sets | 348 | 1,706 | null |
There is an approach to choosing network variables with voltages which is analogous and dual to the loop current method. Here the voltage associated with pairs of nodes are the primary variables and the branch voltages are found in terms of them. In this method also, a particular tree of the graph must be chosen in ord... | Wikipedia - Circuit topology (electrical) - Graph theory > Tie sets and cut sets | 233 | 1,072 | null |
Section: Graph theory > Nullity and rank. The nullity, N, of a graph with s separate parts and b branches is defined by: N = b β n + s {\displaystyle N=b-n+s\ } The nullity of a graph represents the number of degrees of freedom of its set of network equations. For a planar graph, the nullity is equal to the number of m... | Wikipedia - Circuit topology (electrical) - Graph theory > Nullity and rank | 176 | 643 | null |
Section: Graph theory > Solving the network variables. Once a set of geometrically independent variables have been chosen the state of the network is expressed in terms of these. The result is a set of independent linear equations which need to be solved simultaneously in order to find the values of the network variabl... | Wikipedia - Circuit topology (electrical) - Graph theory > Solving the network variables | 218 | 1,144 | null |
Section: Graph theory > Duality. Two graphs are dual when the relationship between branches and node pairs in one is the same as the relationship between branches and loops in the other. The dual of a graph can be found entirely by a graphical method. The dual of a graph is another graph. For a given tree in a graph, t... | Wikipedia - Circuit topology (electrical) - Graph theory > Duality | 341 | 1,565 | null |
Section: Graph theory > Node and mesh elimination. Operations on a set of network equations have a topological meaning which can aid visualisation of what is happening. Elimination of a node voltage from a set of network equations corresponds topologically to the elimination of that node from the graph. For a node conn... | Wikipedia - Circuit topology (electrical) - Graph theory > Node and mesh elimination | 224 | 1,133 | null |
Section: Graph theory > Mutual coupling. In conventional graph representation of circuits, there is no means of explicitly representing mutual inductive couplings, such as occurs in a transformer, and such components may result in a disconnected graph with more than one separate part. For convenience of analysis, a gra... | Wikipedia - Circuit topology (electrical) - Graph theory > Mutual coupling | 213 | 1,113 | null |
Section: Graph theory > Active components. There are two basic approaches available for dealing with mutual couplings and active components. In the first of these, Samuel Jefferson Mason in 1953 introduced signal-flow graphs. Signal-flow graphs are weighted, directed graphs. He used these to analyse circuits containing... | Wikipedia - Circuit topology (electrical) - Graph theory > Active components | 229 | 1,251 | null |
Section: Graph theory > Active components > Hypergraphs. Another way of extending classical graph theory for active components is through the use of hypergraphs. Some electronic components are not represented naturally using graphs. The transistor has three connection points, but a normal graph branch may only connect ... | Wikipedia - Circuit topology (electrical) - Graph theory > Active components > Hypergraphs | 335 | 1,749 | null |
Section: Graph theory > Non-homogeneous variables. Classical network analysis develops a set of network equations whose network variables are homogeneous in either current (loop analysis) or voltage (node analysis). The set of network variables so found is not necessarily the minimum necessary to form a set of independ... | Wikipedia - Circuit topology (electrical) - Graph theory > Non-homogeneous variables | 155 | 832 | null |
Section: Graph theory > Network synthesis. Graph theory can be applied to network synthesis. Classical network synthesis realises the required network in one of a number of canonical forms. Examples of canonical forms are the realisation of a driving-point impedance by Cauer's canonical ladder network or Foster's canon... | Wikipedia - Circuit topology (electrical) - Graph theory > Network synthesis | 237 | 1,154 | null |
Section: Graph theory > Infinite networks. Perhaps the earliest network with an infinite graph to be studied was the ladder network used to represent transmission lines developed, in its final form, by Oliver Heaviside in 1881. Certainly all early studies of infinite networks were limited to periodic structures such as... | Wikipedia - Circuit topology (electrical) - Graph theory > Infinite networks | 348 | 1,822 | null |
Section: Non-CTL for replacement only. Circuitboards and panelboards built prior to 1965 did not have circuit total limiting devices or features built-in. To support these old panels, non-CTL circuit breakers that bypass the rejection feature are still sold "for replacement use only." As a result, numerous unsafe situa... | Wikipedia - Circuit total limitation - Non-CTL for replacement only | 221 | 1,074 | null |
Section: Calculations. Copper losses result from Joule heating and so are also referred to as "I squared R losses", in reference to Joule's First Law. This states that the energy lost each second, or power, increases as the square of the current through the windings and in proportion to the electrical resistance of the... | Wikipedia - Copper loss - Calculations | 230 | 904 | null |
Section: Background. Investigations on power properties of circuits with nonsinusoidal voltages and currents were initiated by Ch.P. Steinmetz in 1892 and were continued for more than a century. The main contributions to these studies were made by C.I. Budeanu (1927), S. Fryze (1931), W. Shepherd and P. Zakikhani (1972... | Wikipedia - CPC theory - Background | 186 | 751 | null |
Section: Development. The development of CPC-based power theory by Leszek S. Czarnecki was initiated in 1983 when he challenged the correctness of existing power theories as applied to single-phase linear, time-invariant (LTI) loads with nonsinusoidal voltage, and next, he revealed the existence of a scattered current,... | Wikipedia - CPC theory - Development | 265 | 1,305 | null |
Section: Key concepts. Decomposition of the load current into mutually orthogonal components associated with distinctive, energy transfer-related phenomena, is the key concept behind the Currentsβ Physical Components (CPC) - based power theory. There are five such current components: Active current. It is associated wi... | Wikipedia - CPC theory - Key concepts | 156 | 852 | null |
Section: Operation. A current limiting reactor is used when the prospective short-circuit current in a distribution or transmission system is calculated to exceed the interrupting rating of the associated switchgear. The inductive reactance is chosen to be low enough for an acceptable voltage drop during normal operati... | Wikipedia - Current limiting reactor - Operation | 157 | 858 | null |
Article: Curtailment (electricity). In the electric power industry, curtailment is an involuntary reduction of the electric generator output ("dispatch down") made to maintain the grid stability (for example, for the grid balancing). While curtailment is a standard technique that had been applied throughout the history... | Wikipedia - Curtailment (electricity) - Summary | 189 | 988 | null |
Section: Examples. After ERCOT built a new transmission line from the Competitive Renewable Energy Zone in West Texas to the central cities in the Texas Interconnection in 2013, curtailment was reduced from 8-16% to near zero. Curtailment of wind power in western China was around 20% in 2018. In 2018, curtailment in th... | Wikipedia - Curtailment (electricity) - Examples | 209 | 814 | null |
Section: Types > Computer hardware. Some hardware can be attached to a computing system in a daisy chain configuration by connecting each component to another similar component, rather than directly to the computing system that uses the component. Only the last component in the chain directly connects to the computing ... | Wikipedia - Daisy chain (electrical engineering) - Types > Computer hardware | 344 | 1,737 | null |
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