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Multi-Level Interaction in Parametric Design

Multi-Level Interaction in Parametric Design
Multi-Level Interaction in Parametric Design

Multi-Level Interaction in Parametric Design

Robert Aish1and Robert Woodbury2

1Bentley Systems,Incorporated

robert.aish@https://www.doczj.com/doc/b6454961.html,

2Simon Fraser University,School of Interactive Arts and Technology,14th Floor, Central City Tower,13450102Avenue,Surrey,BC,CANADA,V3T5X3

rw@sfu.ca,

WWW home page:http://www.siat.sfu.ca

Abstract.Parametric design systems model a design as a constrained

collection of schemata.Designers work in such systems at two levels:def-

inition of schemata and constraints;and search within a schema collec-

tion for meaningful instances.Propagation-based systems yield e?cient

algorithms that are complete within their domain,require explicit speci-

?cation of a directed acyclic constraint graph and allow relatively simple

debugging strategies based on antecedents and consequents.The require-

ment to order constraints appears to be useful in expressing speci?c de-

signer intentions and in disambiguating interaction.A key feature of such

systems in practice appears to be a need for multiple views onto the con-

straint model and simultaneous interaction across views.We describe

one multiple-view structure,its development and re?nement through a

large group of architecture practitioners and its realization in the system

Generative Components.

1Architectural practice and parametric design Conventional CAD systems focus design attention on the representation of the artifact being designed.Currently industry attention is on systems in which a designed artifact is represented parametrically,that is,the representation admits rapid change of design dimensions and structure.Parameterization increases complexity of both designer task and interface as designers must model not only the artifact being designed,but a conceptual structure that guides variation. Parameterization has both positive and negative task,outcome and perceptual consequences for designers.Positively,parameterization can enhance search for designs better adapted to context,can facilitate discovery of new forms and kinds of form-making,can reduce the time and e?ort required for change and reuse, and can yield better understandings of the conceptual structure of the artifact being designed.Negatively,parameterization may require additional e?ort,may increase complexity of local design decisions and increases the number of items to which attention must be paid in task completion.

Parametric modeling has become the basis for most mechanical CAD systems and now is beginning to emerge as a tool for architectural design.While there is a general appreciation of the concepts and advantages of parametric modeling,

application to projects at the scale and complexity of buildings raises impor-tant theoretical and practical issues.In a deep sense,parametric modelling is not new:building components have been adapted to context for centuries.What is new is the parallel development of fabrication technology that enables mass customization.Building components can be adapted to their context and para-metric modelling can represent both context and adapted designs.In a design market partly driven by novelty,the resulting ability to envision and construct new architectural forms rewards?rms having such expertise.There are rela-tively few such?rms,most of which have had long experience and have built substantial reputations on distinctive form and construction.But many?rms and students(future practitioners)are interested.The con?uence of technology and interest appears as exploration in a new design space:architecture and its supporting technologies of parametric design and fabrication are experiencing both co-development and rapid change.

Emblematic of this change is the SmartGeometry group.It comprises senior practitioners,a CAD system developer and academics.Its website leads with the declaration:

Architecture is fundamentally about relationships.Many of those re-lationships are geometric in nature or?nd a geometric expression.The SmartGeometry group has been created in the belief that Computer Aided Design lends itself to capturing the geometric relationships that form the foundation of architecture....The group is dedicated to educat-ing the construction professions in the new skills which will be required to use these new systems e?ectively....The group conducts a series of schools and seminars where this new technology is explored in the con-text of highly experienced professionals.(Minor verb tense changes made to the quotation.)(https://www.doczj.com/doc/b6454961.html,)

To date,several such workshops have been conducted and workshop partici-pants have continued to develop both designs and ideas for needed system sup-port.The outcomes of the workshops and work that follows from them comprise designs,some intended for actual construction,some as explorations of design possibility.Figures1and2show work done by two workshop participants.

SmartGeometry works,as it must,through using(and developing)systems that support design relationships.Much of its work parallels and is in?uenc-ing the development over the last eight years of a speci?c parametric design system Generative Components(GC)by Bentley Systems,Inc.The primary de-signer and developer of GC is Robert Aish.At the time of writing,GC was not on the commercial market and its development path lay outside of the Bent-ley product process.Its design and development have been extensively a?ected by members of the SmartGeometry group,the professional members of which have acted largely in addition to their professional roles inside their respective ?rms.Academics and graduate students have been involved in design,review and trial workshops to an extent unusual for a corporate project.The existence of a motivated independent user community and a relatively open and relatively

https://www.doczj.com/doc/b6454961.html,rs Hesselgren is a Senior Associate Partner and Director of R&D at KPF Architects.The images represent form explorations for a project currently (as of Spring 2005)under development at KPF.(by permission of the

author)

(a)

(b)

(c)

Fig.2.Neri Oxman is a recent graduate of the Architectural Association in London and currently (as of Spring 2005)is at KPF Research in London.(a)Design prototype for a helical high-rise structure ?rst modeled in a conventional 3D software package and post-rationalized in GC as a set of helical strands and tiling elements set in a cylindrical coordinate 3D space.The work represented was awarded a FEIDAD 2004Design Merit Award.(b)&(c)Explorations in GC towards new graph nodes and an idiom of use employing a topologically-de?ned ’hosting environment’that dictates the position and geometrical articulation of any 4point de?ned component to populate the mat.(c)A four-point based component developed to populate its hosting environment.(by permission of the author)

well-resourced system development process provides opportunities for early and frequent veri?cation of design choices against actual need and for research con-necting task to system at a scale largely not possible in research labs using systems built from scratch.

GC is a propagation-based system–implyting that part of a user’s task is de-termining how particular relationships are processed in addition to specifying the relationships themselves.There are practical reasons for this.First propagation-based systems are e?cient and sound.They are predictable,in that choices of what controls and what is controlling are required and are often important to designers.They are easily extensible at the local(node)level and provide mul-tiple points of entry for more sophisticated extension.Although algorithmically simple,they are complex in use–the task of simultaneous model creation and design demands sophisticated language-level and user interfaces.The interface appears to be the principal technical obstacle to further practical use.

2Propagation-based constraint systems

At the representation level,a propagation-based constraint system comprises an acyclic directed graph and two algorithms,one for ordering the graph and one for propagating values through the graph.

The nodes of the graph are schemata,that is,they are objects containing vari-ables and constraints amongst the variables.Variables within a node are either independent or dependent and both variables and nodes are typed.Every type of node provides an e?cient update algorithm for updating speci?c values for the dependent variables subject to the constraints and given values for the indepen-dent variables,as well as display algorithms for displaying the node symbolically and in3D.The arcs of the directed graph denote uses of nodes or variables from within nodes as the independent variables in a node’s constraints.An arc from node A to node B exists if a variable in A is identi?ed with an independent vari-able in B.An incoming arc to a node binds one or more independent variables in the node.Graphs are constrained to be acyclic:any operation that introduces a cycle has unde?ned e?ect.Graphs may have arbitrarily many nodes with un-bound independent variables;these are the independent nodes of the graph and their unbound independent variables are the independent variables of the graph. All other nodes and variables are dependent.The antecedent nodes of a node are those that bind its independent variables.The consequent nodes of a node are those that are bound by any of its variables.

A graph models a usually in?nite collection of instances,each of which is determined by assigning values to the independent variables of the graph.Graphs are typically presented to the user through one or more of their instances.

To compute an instance,graphs are?rst ordered and then values are propa-gated through the graph.Both algorithms are theoretically simple and both are e?cient.The ordering algorithm is topological ordering,which has worst case time complexity of O(n+e)where n is the number of nodes and e is the number

of edges in the graph.The propagation algorithm is also linear,with complexity O(n+e),presuming that the internal node algorithms are O(1).

The representation is well-known as the basis for such common tools as spreadsheets,project management tools and data?ow programming languages. In design applications,the graphs tend to be large and the nodes represent schemata of arbitrary complexity.These issues are typically addressed through constraint languages,which provide tools for expressing node algorithms and for building complex graphs from nodes and less complex graphs.

Propagation-based systems are the most simple type of constraint system. The?rst CAD system was a constraint system.Sutherland’s Sketchpad[Sut63] provided both a propagation-based mechanism and a simultaneous solver based on relaxation.It was the?rst report of a feature that became central to many constraint languages–the merge operator that combines two similar structures to a single structure governed by the union of the constraints on its arguments. Constraint management systems,for example,Borning’s Delta Blue[SMFBB93] provide primitives and constraints that are not pre-bundled together and with which the user can overconstrain the system,but is required to give some value (or utility)for the resolution of di?erent constraints.A constraint manager does not need access to the structure of the primitives or the constraints.Rather its algorithm aims to?nd a particular directed acyclic graph that resolves the most highly valued constraints.Constraint solvers represent primitives and con-straints over them with algorithms speci?c to the class of constraints being solved,for instance,di?erential equations.Constraint logic programming sys-tems integrate constraint satisfaction within a logic programming framework and use constraints to limit the search process of the logic program.Di?erent constraint domains de?ne di?erent classes of constraint logic programming.For instance,in CLP(R),the constrained variables are real numbers and the solver is typically limited to linear relations with a delayed binding mechanism that ad-mits solution for some non-linear problems.Algebraic constraint systems such as Magritte[Gos83]apply symbolic algebra either directly or to rewrite sub-graphs so that a graph suitable for propagation exists.Constraint languages such as ASCEND[PMW93]address the problem of building(and solving)large sets of equations in which the equation structure has signi?cant regularity.

3Parametric modeling as a task

A parametric model ampli?es the e?ort of building a representation by providing an interpretation of a model as a typically in?nite set of instances,each deter-mined by a particular selection of values for the model’s independent variables.

The parametric modeling task proceeds in concert with the task of creating a design.At the end of the process there exists both a graph structure and a speci?c instance that represents a concrete design.The main e?ect of separating graph and instance is to defer decisions.The graph embodies decisions about chosen relationships and defers computation of precise values(and in some cases structure)that depend on the relationships.For example,a graph representing

a roof structure may have the roof’s support lines as its inputs and may produce di?erent roofs designs depending on the location of the support lines.In contrast, non-parametric modeling systems tend to invert such a decision structure.The precise location of an object is required to model it at all and objects that depend on other objects must be explicitly modeled in precise context.

The cost of decision deferral is a higher level of abstraction in https://www.doczj.com/doc/b6454961.html,ers of parametric systems must explicitly develop relationships between objects and, at some level,code those into a node or graph.When a system does not support a particular relationship,it must be developed.Figure3shows an example of computing the shortest line between two skew lines.If such a relationship is not already part of a system it must be coded.If the needed sub-relationships are not supported,they too must be coded.Such work is necessary in practice.It turns out that the relationships that designers need to model their work comprise a set far too large and idiosyncratic to anticipate and provide as node types in a modelling environment.Designers using parametric systems must develop,and must be able to develop,relationships speci?c to the task at hand.

Another cost of parametric model is complexity of both representation and interface.At the representation level a designer must understand new concepts such as the graph itself,node compilation,intensionality and a set of mathemat-ical ideas related to descriptive geometry and linear algebra.The present state of interfaces for parametric modeling systems dictates multiple,related interaction devices for di?erent aspects of the https://www.doczj.com/doc/b6454961.html,ing GC as an example,we demonstrate several novel aspects of task complexity and supporting interface. 4Representational features

4.1Object compilation

Nodes are typically de?ned by specifying independent and dependent variables and an update algorithm for the node.In GC the speci?cation is a C#method where the method signature contains the independent variables,the method returns the dependent variables and the method itself speci?es the update algo-rithm.The system uses code re?ection to compile user-provided node speci?ca-tions into update and display methods.

Conceptually,a node can be arbitrarily complex.To the ordering and prop-agation algorithms of a parametric design system a node provides independent and dependent variables and an update algorithm.A subgraph can be consid-ered as a single node whose independent and dependent variables are those of the subgraph and whose algorithm is that of the global propagation algorithm applied to the subgraph.GC provides a second level of node compilation called feature compilation that,through code re?ection,collapses a subgraph into a new object with its own update method.Figures5(a)and5(b)show the e?ect of compiling a graph representing a Bezier curve into a single node.Such com-piled nodes can be reused in other contexts where,to a user,they represent a single modelling concept.

(a)(b)

Fig.3.Two views of a shortest line segment between skew lines.The graph (not shown)comprises a cross product,three vector projections,a converse vector projection and three construction lines.

(a)(b)(c)(d)

Fig.4.Single points,each expressed as a parametric point on a line.(a)A symbolic model representing a line between parametric points each on their own line.The same symbolic model represents (b),(c)and (d).A line between the two parametric points with single index values (1&2)for the parameters of its de?ning points.(c)Each of the de?ning points of the line has multiple parameter values.The number of lines is equal to the length of the shortest collection.(d)A line collection under the Cartesian product interpretation of a collection.

4.2Objects as collections

In GC a node’s independent variables may be either singletons or collections .A collection has the interpretation that each object in the collection speci?es a node in and of itself.When multiple independent variables are collection-valued,collections propagate to dependent variables in two distinct ways as shown in Figure 4.The ?rst produces a collection of objects,of size equal to the shortest of the input collections,by using the i th value of each of the input collections as independent inputs.The second produces a collection by using the Cartesian product of the input collection as arguments.In both cases,the collection ?nds interpretation as a single node in the graph,while its elements are accessed through an array-indexing convention.The identi?cation of singletons and collections supports a form of programming-by-example whereby the work done to create a single instance can be propagated to multiple instances simply by providing additional input arguments.

4.3Intensionality

Intensionality means that two symbol structures can be identical in all aspects yet remain distinct.From a representational perspective a symbol is a declara-tion that there exists an object with the properties given in the symbol.There may exist many such objects and multiple symbols may refer to the same object. Changing the properties of a symbol does not a?ect the existence of the sym-bol–representationally it modi?es the represented object,while maintaining object identity.Intensionality appears to be a necessary property in parametric modelling.In GC,it appears as merge operator and variable update methods. The merge operator is analogous to Sutherland’s[Sut63]and essentially iden-tical to Borning’s[Bor81].The design of update methods is modelled on Delta Blue[SMFBB93].Update methods are uniquely distinguished by their signa-tures and a group of suitably designed update methods forms a clique through which a node with a method belonging to the clique may circulate,that is,users may change a node’s update method from within its clique.

5Representational views

In this section we sketch several interface views in GC.Such features have either been developed independently several times or are otherwise recurrent features of parametric design systems.It appears that multiple views and the attendant complexity in use is,at least at present,a necessary feature of parametric design systems.We include three views:3D,symbolic graph and object(the latter being itself a composite of other views).Due to space,we omit a fourth view,namely the programmatic view through which elements may be directly programmed using the system’s API.

5.13D interaction

Most demonstrations of parametric modelling systems are made in a3D in-teractive view.Such views comprise a3D scene in which graphical objects are displayed.Graph nodes are represented by displaying the instance of the node associated with the current settings of the graph independent variables.The node display algorithm is determined by the node type:nodes of type Point display as a geometric point,nodes of type Line as a line.Some node types,for example global variables,do not have a direct representation in a3D interactive view.Further,not all nodes need be displayed at once–it is common for nodes to have display properties such as hidden and construction that simplify a view while retaining the underlying model structure.Key node display algorithms are crafted with intent to support user intuitions about how a node is computed.For example,a point constrained to be on a curve may be displayed as a point plus a handle for dragging the point along the curve.Nodes in a3D interactive view may be constrained by other nodes by identifying their independent variable with either nodes their contained variables.

Users engage with a3D interactive view to de?ne graphs,and to manipulate independent variables to?nd useful graph instances that may be concretely realized.Expressing even relatively simple ideas as a graph turns out to be labour intensive and saving labour has motivated a number of interaction devices.

5.2Object view:names,expression entry,functions and scripting Individual variables within a node can be bound by identifying nodes or vari-ables directly,through expressions over other nodes and variables,through user-provided functions or through statements in a high-level scripting language.Ex-pressions,functions and scripts introduce the requirement that each node and each variable has a https://www.doczj.com/doc/b6454961.html,s can be automatically generated but it turns out that naming and name re-factoring are critical aspects of model building.Vari-ables may have nodes as their values and this introduces the need for pathnames from a node recursively through nodes held in its variables.A pathname from a node may trace upstream through antecedent nodes or downstream through consequent nodes in any combination.A node or variable thus may have mul-tiple names either as a global name(nodes only)or a path beginning at some node.The hierarchy of direct identi?cation,expressions,functions and scripting was not an a priori design decision.It emerged through sustained conversation with the SmartGeometry group(and others)which established the need for a learning sca?old from the GUI to a full procedural language.Designers move up this sca?old progressively,using new features as both need and skill develop. Each step in the hierarchy necessarily has its own interface.

Expressions and their attendant pathnames introduce a need to understand and interact with the structure of a graph.This is typically supported with name completion(not described here)and a symbolic graph view.

5.3Symbolic graph view

A symbolic graph view presents a2D or3D visualization of the graph.Its chief uses are to select nodes for editing and as arguments to bind other nodes and variables,to explain the structure and expected behaviour of a graph,and as an aid to debugging.It is also important in selecting subgraphs for compilation into a node(see Section4.1above).Nodes may be represented in the symbolic graph view and not in a corresponding3D interactive view,which makes the symbolic graph view the sole locus for interactive selection of such objects.

The layout of a symbolic graph greatly a?ects its utility.In a strictly para-metric modeller the fact of data propagation establishes the useful convention that a graph may be laid out so that the visual?ow never reverses.This is not enough:Figure5shows that a well laid out graph can add information critical to understanding a model.Such is important in reuse,which has subtasks of examining and editing graph structure.Good layout is task-and model-speci?c and a matter for authorial intent.Symbolic graph views have speci?c and limited utility yet occupy a considerable portion of available screen space.

(a)

(b)

(c)

Fig.5.(a)Symbolic graph (left)3D interaction (right)views in GC.The small window in the centre is the general interface to GC.An order 4Bezier curve implemented with the deCasteljau algorithm.The symbolic model has four conceptual parts:the base coordinate system at the top,the slider control on the left,the systolic array in the middle and a single node Bezier curve on the right.Each has a corresponding 3D display.As the point on the slider is moved from left to right,the point de?ning the Bezier curve traces out the curve.The nodes in the symbolic graph view have been manually laid out to correspond with both the deCasteljau algorithm and the layout of the control points in the 3D view.(b)A symbolic graph view of the Bezier curve graph after it has been compiled to a single node.The inputs are preserved in the form of four points and a single global variable for the curve parameter.(c)A symbolic graph view in which relatively minor changes to the layout have been made,resulting in a signi?cant degradation of clarity.

6Emergent features

The fact of independent variables that can be directly manipulated in an interface a?ords the emergent feature that a parametric design system can,to some extent,be its own interface.It turns out that users often spend a considerable portion of their e?ort building graphs that control other graphs.Such patterns of use have been the impetus to develop generic node types that are,in e?ect,elements of the GC user interface.

6.1Law curves

Figure 6demonstrate the so-called law curves in GC that support the mapping from an independent control variable to a dependent control variable .The law

(a)(b)

Fig.6.(a)A law curve frame .The ordinate values of the curve become inputs for the parametric model shown in (b).

curve frame is nothing more than a node in the graph.It provides a curve con-trolled by independent variables and a collection of independent control variables that specify abscissa values at which the curve is to be sampled.Its output is an equal-sized collection of dependent control variables that specify the respective ordinate values of the control curve.

6.2Fabrication planning

As mentioned in Section 1,a principal enabler for parametric design in practice has been the development of fabrication technology by which models,prototypes and entire components can be created by computer-controlled machinery (CNC).Fabrication planning can be brought into a parametric design system by nodes and graphs that transform a design to objects suitable for input to a CNC machine.The shape of objects to be fabricated need not be separate from the design process,but can become an aspect of the interaction with a model.Figure 7shows windows to a GC model where a specialized node computes the layout for fabrication and an illustration of the resulting laser-cut model.

7Summary

The advantage of using Generative Components is that it helps me

think about what I am doing.The disadvantage is that it forces me to so think.–Lars Hesselgren

The structure of design work using parametric systems remains poorly un-derstood.Designers must simultaneously attend to both the speci?c,concrete design instance and the graph structure that captures its conceptual and mathe-matical structure.At the same time they must attend to the mulitfaceted design task at hand.We should neither under-estimate nor under-value the change to the structure of work and design process required.It is crucial to recognize that nothing can be created in a parametric system for which the designer has not

(a)(b)

Fig.7.Wilson Chang is a graduate of the Master’s program in Interactive Arts and Technology at Simon Fraser University and is currently (Spring 2005)in private prac-tice.(a)A model comprising a layout for a structural system and the collection of structural members laid out on a plane.The structural members are parameterized by the layout.(b)A physical model whose components have been laser-cut using the structural member descriptions.(by permission of the author)

explicitly externalized the relevant conceptual and constructive structure.This runs counter to the often-deliberate cultivation of ambiguity that appears to be part of healthly design processes.Abstract concepts such as intensionality and compilation appear to be essential to e?ective use.Multiple views appear to be necessary.Such concepts,their attendant tasks and the complexity of working across views provide bene?ts and impose cognitive costs.Some of these costs may be overcome by clever graphical interventions such as guided layout of a symbolic model.However,any such move must be tested against a robust user community –it far too easy to work on a sophisticated solution to an unim-portant problem.In contrast,problems such as the need for a hierarchy from the GUI to the algorithm demand both long conversation with sophisticated designer/users and apt solutions to the appropriate problems that emerge.References

[Bor81] A.Borning.The programming language aspects of thinglab,a constraint-

oriented simulation laboratory.ACM Transactions on Programming Lan-

guages and Systems ,3(4):353–387,Oct.1981.

[Gos83]J.Gosling.The Algebraic Manipulation of Constraints .PhD thesis,Com-

puter Science Department,Carnegie-Mellon University,May 1983.

[PMW93]P.Piela,R.McKelvey,and A.Westerberg.An introduction to the ascend

modeling system:It’s language and interactive environment.Journal of

Magagement information system ,9(3):91–121,1993.

[SMFBB93]M.Sannella,J.Maloney,B.N.Freeman-Benson,and A.Borning.Multi-

way versus one-way constraints in user interfaces:Experience with the

deltablue algorithm.Softw.,Pract.Exper.,23(5):529–566,1993.

[Sut63]I.E.Sutherland.Sketchpad:A man-machine graphical communication sys-

tem.Technical Report 296,MIT Lincoln Lab.,1963.

常用二极管参数

常用整流二极管 型号VRM/Io IFSM/ VF /Ir 封装用途说明1A5 600V/1.0A 25A/1.1V/5uA[T25] D2.6X3.2d0.65 1A6 800V/1.0A 25A/1.1V/5uA[T25] D2.6X3.2d0.65 6A8 800V/6.0A 400A/1.1V/10uA[T60] D9.1X9.1d1.3 1N4002 100V/1.0A 30A/1.1V/5uA[T75] D2.7X5.2d0.9 1N4004 400V/1.0A 30A/1.1V/5uA[T75] D2.7X5.2d0.9 1N4006 800V/1.0A 30A/1.1V/5uA[T75] D2.7X5.2d0.9 1N4007 1000V/1.0A 30A/1.1V/5uA[T75] D2.7X5.2d0.9 1N5398 800V/1.5A 50A/1.4V/5uA[T70] D3.6X7.6d0.9 1N5399 1000V/1.5A 50A/1.4V/5uA[T70] D3.6X7.6d0.9 1N5402 200V/3.0A 200A/1.1V/5uA[T105] D5.6X9.5d1.3 1N5406 600V/3.0A 200A/1.1V/5uA[T105] D5.6X9.5d1.3 1N5407 800V/3.0A 200A/1.1V/5uA[T105] D5.6X9.5d1.3 1N5408 1000V/3.0A 200A/1.1V/5uA[T105] D5.6X9.5d1.3 RL153 200V/1.5A 60A/1.1V/5uA[T75] D3.6X7.6d0.9 RL155 600V/1.5A 60A/1.1V/5uA[T75] D3.6X7.6d0.9 RL156 800V/1.5A 60A/1.1V/5uA[T75] D3.6X7.6d0.9 RL203 200V/2.0A 70A/1.1V/5uA[T75] D3.6X7.6d0.9 RL205 600V/2.0A 70A/1.1V/5uA[T75] D3.6X7.6d0.9 RL206 800V/2.0A 70A/1.1V/5uA[T75] D3.6X7.6d0.9 RL207 1000V/2.0A 70A/1.1V/5uA[T75] D3.6X7.6d0.9 RM11C 1000V/1.2A 100A/0.92V/10uA D4.0X7.2d0.78 MR750 50V/6.0A 400A/1.25V/25uA D8.7x6.3d1.35 MR751 100V/6.0A 400A/1.25V/25uA D8.7x6.3d1.35 MR752 200V/6.0A 400A/1.25V/25uA D8.7x6.3d1.35 MR754 400V/6.0A 400A/1.25V/25uA D8.7x6.3d1.35 MR756 600V/6.0A 400A/1.25V/25uA D8.7x6.3d1.35 MR760 1000V/6.0A 400A/1.25V/25uA D8.7x6.3d1.35 常用整流二极管(全桥) 型号VRM/Io IFSM/ VF /Ir 封装用途说明RBV-406 600V/*4A 80A/1.10V/10uA 25X15X3.6 RBV-606 600V/*6A 150A/1.05V/10uA 30X20X3.6 RBV-1306 600V/*13A 80A/1.20V/10uA 30X20X3.6 RBV-1506 600V/*15A 200A/1.05V/50uA 30X20X3.6 RBV-2506 600V/*25A 350A/1.05V/50uA 30X20X3.6 常用肖特基整流二极管SBD 型号VRM/Io IFSM/ VF Trr1/Trr2 封装用途说明EK06 60V/0.7A 10A/0.62V 100nS D2.7X5.0d0.6 SK/高速 EK14 40V/1.5A 40A/0.55V 200nS D4.0X7.2d0.78 SK/低速 D3S6M 60V/3.0A 80A/0.58V 130p SB340 40V/3.0A 80A/0.74V 180p SB360 60V/3.0A 80A/0.74V 180p SR260 60V/2.0A 50A/0.70V 170p MBR1645 45V/16A 150A/0.65V <10nS TO220 超高速

常用二极管参数

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joinin剑桥小学英语

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1N4733 5V1 1N4734 5V6 1N4735 6V2 1N4736 6V8 1N4737 7V5 1N4738 8V2 1N4739 9V1 1N4740 10V 1N4741 11V 1N4742 12V 1N4743 13V 1N4744 15V 1N4745 16V 1N4746 18V 1N4747 20V 1N4748 22V 1N4749 24V 1N4750 27V 1N4751 30V 1N4752 33V 1N4753 36V 1N4754 39V 1N4755 43V 1N4756 47V 1N4757 51V DZ是稳压管的电器编号,是和1N4148和相近的,其实1N4148就是一个0.6V的稳压管,下面是稳压管上的编号对应的稳压值,有些小的稳压管也会在管体 上直接标稳压电压,如5V6就是5.6V的稳压管。 1N4728A 3.3 1N4729A 3.6 1N4730A 3.9 1N4731A 4.3 1N4732A 4.7 1N4733A 5.1 1N4734A 5.6 1N4735A 6.2 1N4736A 6.8 1N4737A 7.5 1N4738A 8.2 1N4739A 9.1 1N4740A 10 1N4741A 11 1N4742A 12 1N4743A 13

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1N 系列常用整流二极管的主要参数
反向工作 峰值电压 URM/V 额定正向 整流电流 整流电流 IF/A 正向不重 复浪涌峰 值电流 IFSM/A 正向 压降 UF/V 反向 电流 IR/uA 工作 频率 f/KHZ 外形 封装
型 号
1N4000 1N4001 1N4002 1N4003 1N4004 1N4005 1N4006 1N4007 1N5100 1N5101 1N5102 1N5103 1N5104 1N5105 1N5106 1N5107 1N5108 1N5200 1N5201 1N5202 1N5203 1N5204 1N5205 1N5206 1N5207 1N5208 1N5400 1N5401 1N5402 1N5403 1N5404 1N5405 1N5406 1N5407 1N5408
25 50 100 200 400 600 800 1000 50 100 200 300 400 500 600 800 1000 50 100 200 300 400 500 600 800 1000 50 100 200 300 400 500 600 800 1000
1
30
≤1
<5
3
DO-41
1.5
75
≤1
<5
3
DO-15
2
100
≤1
<10
3
3
150
≤0.8
<10
3
DO-27
常用二极管参数: 05Z6.2Y 硅稳压二极管 Vz=6~6.35V,Pzm=500mW,

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□变更 变更项目原登记内容申请变更登记内容 □备案 分公司 □增设□注销名称 注册号/统一 社会信用代码登记机关登记日期 清算组 成员 负责人联系电话 其他□董事□监事□经理□章程□章程修正案□财务负责人□联络员 □申请人声明 本公司依照《公司法》、《公司登记管理条例》相关规定申请登记、备案,提交材料真实有效。通过联络员登录企业信用信息公示系统向登记机关报送、向社会公示的企业信息为本企业提供、发布的信息,信息真实、有效。 法定代表人签字:公司盖章(清算组负责人)签字:年月日

附表1 法定代表人信息 姓名固定电话 移动电话电子邮箱 身份证件类型身份证件号码 (身份证件复印件粘贴处) 法定代表人签字:年月日

附表2 董事、监事、经理信息 姓名职务身份证件类型身份证件号码_______________ (身份证件复印件粘贴处) 姓名职务身份证件类型身份证件号码_______________ (身份证件复印件粘贴处) 姓名职务身份证件类型身份证件号码_______________ (身份证件复印件粘贴处)

剑桥小学英语Join_In

《剑桥小学英语Join In ——Book 3 下学期》教材教法分析2012-03-12 18:50:43| 分类:JOIN IN 教案| 标签:|字号大中小订阅. 一、学情分析: 作为毕业班的学生,六年级的孩子在英语学习上具有非常显著的特点: 1、因为教材的编排体系和课时不足,某些知识学生已遗忘,知识回生的现象很突出。 2、有的学生因受学习习惯及学习能力的制约,有些知识掌握较差,学生学习个体的差异性,学习情况参差不齐、两级分化的情况明显,对英语感兴趣的孩子很喜欢英语,不喜欢英语的孩子很难学进去了。 3、六年级的孩子已经进入青春前期,他们跟三、四、五年级的孩子相比已经有了很大的不同。他们自尊心强,好胜心强,集体荣誉感也强,有自己的评判标准和思想,对知识的学习趋于理性化,更有自主学习的欲望和探索的要求。 六年级学生在英语学习上的两极分化已经给教师的教学带来很大的挑战,在教学中教师要注意引导学生调整学习方式: 1、注重培养学生自主学习的态度 如何抓住学习课堂上的学习注意力,吸引他们的视线,保持他们高涨的学习激情,注重过程的趣味化和学习内容的简易化。 2、给予学生独立思考的空间。 3、鼓励学生坚持课前预习、课后复习的好习惯。 六年级教材中的单词、句子量比较多,难点也比较多,学生课前回家预习,不懂的地方查英汉词典或者其它资料,上课可以达到事半功倍的效果,课后复习也可以很好的消化课堂上的内容。 4、注意培养学生合作学习的习惯。 5、重在培养学生探究的能力:学习内容以问题的方式呈现、留给学生更多的发展空间。 二、教材分析: (一).教材特点: 1.以学生为主体,全面提高学生的素质。

常见二极管参数大全

1N系列稳压管

快恢复整流二极管

常用整流二极管型号和参数 05Z6.2Y 硅稳压二极管 Vz=6~6.35V,Pzm=500mW, 05Z7.5Y 硅稳压二极管 Vz=7.34~7.70V,Pzm=500mW, 05Z13X硅稳压二极管 Vz=12.4~13.1V,Pzm=500mW, 05Z15Y硅稳压二极管 Vz=14.4~15.15V,Pzm=500mW, 05Z18Y硅稳压二极管 Vz=17.55~18.45V,Pzm=500mW, 1N4001硅整流二极管 50V, 1A,(Ir=5uA,Vf=1V,Ifs=50A) 1N4002硅整流二极管 100V, 1A, 1N4003硅整流二极管 200V, 1A, 1N4004硅整流二极管 400V, 1A, 1N4005硅整流二极管 600V, 1A, 1N4006硅整流二极管 800V, 1A, 1N4007硅整流二极管 1000V, 1A, 1N4148二极管 75V, 4PF,Ir=25nA,Vf=1V, 1N5391硅整流二极管 50V, 1.5A,(Ir=10uA,Vf=1.4V,Ifs=50A) 1N5392硅整流二极管 100V,1.5A, 1N5393硅整流二极管 200V,1.5A, 1N5394硅整流二极管 300V,1.5A, 1N5395硅整流二极管 400V,1.5A, 1N5396硅整流二极管 500V,1.5A, 1N5397硅整流二极管 600V,1.5A, 1N5398硅整流二极管 800V,1.5A, 1N5399硅整流二极管 1000V,1.5A, 1N5400硅整流二极管 50V, 3A,(Ir=5uA,Vf=1V,Ifs=150A) 1N5401硅整流二极管 100V,3A, 1N5402硅整流二极管 200V,3A, 1N5403硅整流二极管 300V,3A, 1N5404硅整流二极管 400V,3A,

有限合伙企业登记注册操作指南

有限合伙企业登记注册操作指南 风险控制部 20xx年x月xx日

目录 一、合伙企业的概念 (4) 二、有限合伙企业应具备的条件 (4) 三、有限合伙企业设立具备的条件 (4) 四、注册有限合伙企业程序 (5) 五、申请合伙企业登记注册应提交文件、证件 (6) (一)合伙企业设立登记应提交的文件、证件: (6) (二)合伙企业变更登记应提交的文件、证件: (7) (三)合伙企业注销登记应提交的文件、证件: (8) (四)合伙企业申请备案应提交的文件、证件: (9) (五)其他登记应提交的文件、证件: (9) 六、申请合伙企业分支机构登记注册应提交的文件、证件 (9) (一)合伙企业分支机构设立登记应提交的文件、证件 (10) (二)合伙企业分支机构变更登记应提交的文件、证件: (10) (三)合伙企业分支机构注销登记应提交的文件、证件: (11) (四)其他登记应提交的文件、证件: (12) 七、收费标准 (12) 八、办事流程图 (12) (一)有限合伙企业创办总体流程图(不含专业性前置审批) (12) (二)、工商局注册程序 (15)

(三)、工商局具体办理程序(引入网上预审核、电话预约方式) (16) 九、有限合伙企业与有限责任公司的区别 (16) (一)、设立依据 (16) (二)、出资人数 (16) (三)、出资方式 (17) (四)、注册资本 (17) (五)、组织机构 (18) (六)、出资流转 (18) (七)、对外投资 (19) (八)、税收缴纳 (20) (九)、利润分配 (20) (十)、债务承担 (21) 十、常见问题解答与指导 (21)

常用稳压二极管技术参数及老型号代换.

常用稳压二极管技术参数及老型号代换 型号最大功耗 (mW) 稳定电压(V) 电流(mA) 代换型号国产稳压管日立稳压管 HZ4B2 500 3.8 4.0 5 2CW102 2CW21 4B2 HZ4C1 500 4.0 4.2 5 2CW102 2CW21 4C1 HZ6 500 5.5 5.8 5 2CW103 2CW21A 6B1 HZ6A 500 5.2 5.7 5 2CW103 2CW21A HZ6C3 500 6 6.4 5 2CW104 2CW21B 6C3 HZ7 500 6.9 7.2 5 2CW105 2CW21C HZ7A 500 6.3 6.9 5 2CW105 2CW21C HZ7B 500 6.7 7.3 5 2CW105 2CW21C HZ9A 500 7.7 8.5 5 2CW106 2CW21D HZ9CTA 500 8.9 9.7 5 2CW107 2CW21E HZ11 500 9.5 11.9 5 2CW109 2CW21G HZ12 500 11.6 14.3 5 2CW111 2CW21H HZ12B 500 12.4 13.4 5 2CW111 2CW21H HZ12B2 500 12.6 13.1 5 2CW111 2CW21H 12B2 HZ18Y 500 16.5 18.5 5 2CW113 2CW21J HZ20-1 500 18.86 19.44 2 2CW114 2CW21K HZ27 500 27.2 28.6 2 2CW117 2CW21L 27-3 HZT33-02 400 31 33.5 5 2CW119 2CW21M RD2.0E(B) 500 1.88 2.12 20 2CW100 2CW21P 2B1 RD2.7E 400 2.5 2.93 20 2CW101 2CW21S RD3.9EL1 500 3.7 4 20 2CW102 2CW21 4B2 RD5.6EN1 500 5.2 5.5 20 2CW103 2CW21A 6A1 RD5.6EN3 500 5.6 5.9 20 2CW104 2CW21B 6B2 RD5.6EL2 500 5.5 5.7 20 2CW103 2CW21A 6B1 RD6.2E(B) 500 5.88 6.6 20 2CW104 2CW21B RD7.5E(B) 500 7.0 7.9 20 2CW105 2CW21C RD10EN3 500 9.7 10.0 20 2CW108 2CW21F 11A2 RD11E(B) 500 10.1 11.8 15 2CW109 2CW21G RD12E 500 11.74 12.35 10 2CW110 2CW21H 12A1 RD12F 1000 11.19 11.77 20 2CW109 2CW21G RD13EN1 500 12 12.7 10 2CW110 2CW21H 12A3 RD15EL2 500 13.8 14.6 15 2CW112 2CW21J 12C3 RD24E 400 22 25 10 2CW116 2CW21H 24-1

剑桥小学英语join in五年级测试卷

五 年 级 英 语 测 试 卷 学校 班级 姓名 听力部分(共20分) 一、Listen and colour . 听数字,涂颜色。(5分) 二、 Listen and tick . 听录音,在相应的格子里打“√”。 (6分) 三、Listen and number.听录音,标序号。(9分) pig fox lion cow snake duck

sheep 笔试部分(共80分) 一、Write the questions.将完整的句子写在下面的横线上。(10分) got it Has eyes on a farm it live sheep a it other animals eat it it Is 二、Look and choose.看看它们是谁,将字母填入括号内。(8分) A. B. C. D.

E. F. G. H. ( ) pig ( ) fox ( ) sheep ( ) cat ( ) snake ( ) lion ( ) mouse ( ) elephant 三、Look at the pictures and write the questions.看图片,根据答语写出相应的问题。(10分) No,it doesn’t. Yes,it is.

Yes,it does. Yes,it has. Yes,it does. 四、Choose the right answer.选择正确的答案。(18分) 1、it live on a farm? 2. it fly?

3. it a cow? 4. it eat chicken? 5. you swim? 6. you all right? 五、Fill in the numbers.对话排序。(6分) Goodbye. Two apples , please. 45P , please. Thank you.

公司注册登记流程(四证)

→客户提供:场所证明租赁协议身份证委托书三张一寸相片 →需准备材料:办理税务登记证时需要会计师资格证与财务人员劳动合同 →提交名称预审通知书→公司法定代表人签署的《公司设立登记申请书》→全体股东签署的《指定代表或者公共委托代理人的证明》(申请人填写股东姓名)→全体股东签署的公司章程(需得到工商局办事人员的认可)→股东身份证复印件→验资报告(需到计师事务所办理:需要材料有名称预审通知书复印件公司章程股东身份证复印件银行开具验资账户进账单原件银行开具询证函租赁合同及场所证明法人身份证原件公司开设临时存款账户的复印件)→任职文件(法人任职文件及股东董事会决议)→住所证明(房屋租赁合同)→工商局(办证大厅)提交所有材料→公司营业执照办理结束 →需带材料→公司营业执照正副本原件及复印件→法人身份证原件→代理人身份证→公章→办理人开具银行收据交款元工本费→填写申请书→组织机构代码证办

理结束 →需带材料→工商营业执照正副本复印件原件→组织机构正副本原件及复印件→公章→公司法定代表人签署的《公司设立登记申请书》→公司章程→股东注册资金情况表→验资报告书复印件→场所证明(租赁合同)→法人身份证复印件原件→会计师资格证(劳动合同)→税务登记证办理结束 →需带材料→工商营业执照正副本复印件原件→组织机构正副本原件及复印件→税务登记证原件及复印件→公章→法人身份证原件及复印件→代理人身份证原件及复印件→法人私章→公司验资账户→注以上复印件需四份→办理时间个工作日→办理结束 →需带材料→工商营业执照正副本复印件原件→组织机构正副本原件及复印件→公章→公司法定代表人签署的《公司设立登记申请书》→公司章程→股东注册资金情况表→验资报告书复印件→场所证明(租赁合同)→法人身份证复印件原件→会计师资格证(劳动合同)→会计制度→银行办理的开户许可证复印件→税务登记证备案办理结束

常用稳压管型号参数对照

常用稳压管型号参数对照 3V到51V 1W稳压管型号对照表1N4727 3V0 1N4728 3V3 1N4729 3V6 1N4730 3V9 1N4731 4V3 1N4732 4V7 1N4733 5V1 1N4734 5V6 1N4735 6V2 1N4736 6V8 1N4737 7V5

1N4739 9V1 1N4740 10V 1N4741 11V 1N4742 12V 1N4743 13V 1N4744 15V 1N4745 16V 1N4746 18V 1N4747 20V 1N4748 22V 1N4749 24V 1N4750 27V 1N4751 30V

1N4753 36V 1N4754 39V 1N4755 43V 1N4756 47V 1N4757 51V 摩托罗拉IN47系列1W稳压管IN4728 3.3v IN4729 3.6v IN4730 3.9v IN4731 4.3 IN4732 4.7 IN4733 5.1

IN4735 6.2 IN4736 6.8 IN4737 7.5 IN4738 8.2 IN4739 9.1 IN4740 10 IN4741 11 IN4742 12 IN4743 13 IN4744 15 IN4745 16 IN4746 18 IN4747 20

IN4749 24 IN4750 27 IN4751 30 IN4752 33 IN4753 34 IN4754 35 IN4755 36 IN4756 47 IN4757 51 摩托罗拉IN52系列 0.5w精密稳压管IN5226 3.3v IN5227 3.6v

(完整版)剑桥小学英语Joinin六年级复习题(二)2-3单元.doc

2011-2012 学年度上学期六年级复习题(Unit2-Unit3 ) 一、听力部分 1、听录音排序 ( ) () ()() () 2、听录音,找出与你所听到的单词属同一类的单词 () 1. A. spaceman B. pond C . tiger () 2. A.mascots B. potato C . jeans () 3. A. door B. behind C . golden () 4. A. sometimes B. shop C . prince () 5. A. chair B. who C . sell 3、听录音,将下面人物与他的梦连线 Sarah Tim Juliet Jenny Peter 4、听短文,请在属于Mr. Brown的物品下面打√ ( ) ( ) ( ) ( ) ( ) ( ) ( ) 5、听问句选答句 () 1. A. Yes, I am B. Yes, I have C . Yes, you do () 2. A.Pink B. A friendship band C . Yes. () 3. A. OK B. Bye-bye. C . Thanks, too. () 4. A. Monday. B. Some juice. C . Kitty. () 5. A. I ’ve got a shookbag. B. I ’m a student. C . It has got a round face. 6、听短文,选择正确答案 () 1. Where is Xiaoqing from? She is from . A.Hebei B. Hubei C . Hunan () 2. She goes to school at . A.7:00 B.7:30 C . 7:15 () 3. How many classes in the afternoon? classes. A. four B. three C . two () 4. Where is Xiaoqing at twelve o ’clock? She is . A. at home B. at school C .in the park () 5. What does she do from seven to half past eight? She . A.watches TV B. reads the book C. does homework

很全的二极管参数

G ENERAL PURPOSE RECTIFIERS – P LASTIC P ASSIVATED J UNCTION 1.0 M1 M2 M3 M4 M5 M6 M7 SMA/DO-214AC G ENERAL PURPOSE RECTIFIERS – G LASS P ASSIVATED J UNCTION S M 1.0 GS1A GS1B GS1D GS1G GS1J GS1K GS1M SMA/DO-214AC 1.0 S1A S1B S1D S1G S1J S1K S1M SMB/DO-214AA 2.0 S2A S2B S2D S2G S2J S2K S2M SMB/DO-214AA 3.0 S3A S3B S3D S3G S3J S3K S3M SMC/DO-214AB F AST RECOVERY RECTIFIERS – P LASTIC P ASSIVATED J UNCTION MERITEK ELECTRONICS CORPORATION

U LTRA FAST RECOVERY RECTIFIERS – G LASS P ASSIVATED J UNCTION

S CHOTTKY B ARRIER R ECTIFIERS

S WITCHING D IODES Power Dissipation Max Avg Rectified Current Peak Reverse Voltage Continuous Reverse Current Forward Voltage Reverse Recovery Time Package Part Number P a (mW) I o (mA) V RRM (V) I R @ V R (V) V F @ I F (mA) t rr (ns) Bulk Reel Outline 200mW 1N4148WS 200 150 100 2500 @ 75 1.0 @ 50 4 5000 SOD-323 1N4448WS 200 150 100 2500 @ 7 5 0.72/1.0 @ 5.0/100 4 5000 SOD-323 BAV16WS 200 250 100 1000 @ 7 5 0.8 6 @ 10 6 5000 SOD-323 BAV19WS 200 250 120 100 @ 100 1.0 @ 100 50 5000 SOD-323 BAV20WS 200 250 200 100 @ 150 1.0 @ 100 50 5000 SOD-323 BAV21WS 200 250 250 100 @ 200 1.0 @ 100 50 5000 SOD-323 MMBD4148W 200 150 100 2500 @ 75 1.0 @ 50 4 3000 SOT-323-1 MMBD4448W 200 150 100 2500 @ 7 5 0.72/1.0 @ 5.0/100 4 3000 SOT-323-1 BAS16W 200 250 100 1000 @ 7 5 0.8 6 @ 10 6 3000 SOT-323-1 BAS19W 200 250 120 100 @ 100 1.0 @ 100 50 3000 SOT-323-1 BAS20W 200 250 200 100 @ 150 1.0 @ 100 50 3000 SOT-323-1 BAS21W 200 250 250 100 @ 200 1.0 @ 100 50 3000 SOT-323-1 BAW56W 200 150 100 2500 @ 75 1.0 @ 50 4 3000 SOT-323-2 BAV70W 200 150 100 2500 @ 75 1.0 @ 50 4 3000 SOT-323-3 BAV99W 200 150 100 2500 @ 75 1.0 @ 50 4 3000 SOT-323-4 BAL99W 200 150 100 2500 @ 75 1.0 @ 50 4 3000 SOT-323- 5 350mW MMBD4148 350 200 100 5000 @ 75 1.0 @ 10 4 3000 SOT-23-1 MMBD4448 350 200 100 5000 @ 75 1.0 @ 10 4 3000 SOT-23-1 BAS16 350 200 100 1000 @ 75 1.0 @ 50 6 3000 SOT-23-1 BAS19 350 200 120 100 @ 120 1.0 @ 100 50 3000 SOT-23-1 BAS20 350 200 200 100 @ 150 1.0 @ 100 50 3000 SOT-23-1 BAS21 350 200 250 100 @ 200 1.0 @ 100 50 3000 SOT-23-1 BAW56 350 200 100 2500 @ 70 1.0 @ 50 4 3000 SOT-23-2 BAV70 350 200 100 5000 @ 70 1.0 @ 50 4 3000 SOT-23-3 BAV99 350 200 100 2500 @ 70 1.0 @ 50 4 3000 SOT-23-4 BAL99 350 200 100 2500 @ 70 1.0 @ 50 4 3000 SOT-23-5 BAV16W 350 200 100 1000 @ 75 0.86 @ 10 6 3000 SOD-123 410-500mW BAV19W 410 200 120 100 @ 100 1.0 @ 100 50 3000 SOD-123 BAV20W 410 200 200 100 @ 150 1.0 @ 100 50 3000 SOD-123 BAV21W 410 200 250 100 @ 200 1.0 @ 100 50 3000 SOD-123 1N4148W 410 150 100 2500 @ 75 1.0 @ 50 4 3000 SOD-123 1N4150W 410 200 50 100 @ 50 0.72/1.0 @ 5.0/100 4 3000 SOD-123 1N4448W 500 150 100 2500 @ 7 5 1.0 @ 200 4 3000 SOD-123 1N4151W 500 150 75 50 @ 50 1.0 @ 10 2 3000 SOD-123 1N914 500 200 100 25 @ 20 1.0 @ 10 4 1000 10000 DO-35 1N4148 500 200 100 25 @ 20 1.0 @ 10 4 1000 10000 DO-35 LL4148 500 150 100 25 @ 20 1.0 @ 10 4 2500 Mini-Melf SOT23-1 SOT23-2 SOT23-3 SOT23-4 SOT23-5 SOT323-1 SOT323-2 SOT323-3 SOT323-4 SOT323-5

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