July 04, 2010

Wall Switches

Posted by: repair : Category: Builder

When a switch fails, it’s usually because the contact points are worn or have oxidized. When this happens, the switch must be replaced. You can re-place it with an exact duplicate or with a dimmer or silent switch. Directions be-low and on the facing page tell how to replace most types of switches and dimmers. Silent switches are simply quiet versions of these types.

Types of switches. Most switches in a home are single-pole or three-way.

Single-pole switches control a light or receptacle from one location only and have two screws of the same color. Three-way switches operate in pairs to control a light or receptacle from two locations. They have two screws of the same color, either brass or silver, and one called the common terminal screw of another color, either copper or black. (The brass or silver screws of a pair of switches connect the switches to each other.) Both types of switches are wired into hot wires only.

Both types may also have a set of back-wired terminals (shown at right) as well as terminal screws. Attaching a switch with back-wired terminals is easy; simply strip the wires (the wire-stripping gauge on the back shows you how much to strip) and push the ends into the holes (see facing page).

Dimmer switches let you adjust the brightness of a light. Wired like single-pole switches, they have either terminal screws or lead wires (see facing page).

Types of Switches

Replacing a switch. When you’re buying a replacement, carefully read the information stamped on the back of the new switch; the new one should have the same amp and voltage ratings as the old.

If your home’s wiring is aluminum, use only replacement switches marked CO/ALR. Replace unmarked switches and switches marked CU/AL with switches marked CO/ALR. Don’t back-wire switches to aluminum wiring; attach aluminum wires to terminal screws only.

CAUTION: Always shut off the power to the circuit before you begin work. Use a, circuit tester to make sure the circuit you’re working on is dead before you touch any wires.

Replacing a single-Pole Switch

Replacing a single-Pole Switch

Replacing a Backwired Single-Pole Switch

Replacing a Backwired Single-Pole Switch

Replacing a Three-Way Switch

Replacing a Three-Way Switch

Installing Two Types of Dimmers

Installing Two Types of Dimmers

By : E-book Home repair

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March 31, 2010

The FIFO

Posted by: repair : Category: Memory

The memory devices discussed thus far are essentially linear arrays of bitssurrounded by a minimal quantity of interface logic to move bits between theport(s) and the array. First-in-?rst-out (FIFO) memories are special-purposedevices that implement a basic queue structure that has broad application incomputer and communications architecture. Unlike other memory devices,a typical FIFO has two unidirectional ports without address inputs: one forwriting and another for reading. As the name implies, the ?rst data written isthe ?rst read, and the last data written is the last read. A FIFO is not a randomaccess memory but a sequential access memory. Therefore, unlike a conventionalmemory, once a data element has been read once, it cannot be read again,because the next read will return the next data element written to the FIFO.By their nature, FIFOs are subject to over?ow and under?ow conditions.Their ?nite size, often referred to as depth, means that they can ?ll up if readsdo not occur to empty data that has already been written. An over?ow occurswhen an attempt is made to write new data to a full FIFO. Similarly, an emptyFIFO has no data to provide on a read request, which results in an under?ow.
A FIFO is created by surrounding a dual-port memory array generally SRAM,but DRAM could be made to work as well for certain applications with a writepointer, a read pointer, and control logic as shown in Fig. 4.18.

FIGURE 4.18 Basic FIFO architecture.

A FIFO is not addressed in a linear fashion; rather, it is made to form a continuousring of mem- ory that is addressed by the two internal pointers. The fullness of theFIFO is determined not by the absolute values of the pointers but by their relativevalues. An empty FIFO begins with its read and write pointers set to the samevalue. As entries are written, the write pointer increments. As entries are read,the read pointer increments as well. If the read pointer ever catches up to thewrite pointer such that the two match, the FIFO is empty again. If the read pointerfails to advance, the write pointer will eventually wrap around the end of thememory array and become equal to the read pointer. At this point, the FIFO isfull and cannot accept any more data until reading resumes. Full and empty ?agsare generated by the FIFO to provide status to the writing and reading logic.Some FIFOs contain more detailed fullness status, such as signals that representprogrammable fullness thresholds.
The interfaces of a FIFO can be asynchronous (no clock) or synchronous(with a clock). If syn- chronous, the two ports can be designed to operate witha common clock or different clocks. Al- though older asynchronous FIFOs arestill manufactured, synchronous FIFOs are now more common. SynchronousFIFOs have the advantage of improved interface timing, because ?ops placedat a devices inputs and outputs reduce timing requirements to the familiar setup,hold, and clock-to-out speci?cations. Without such a registered interface,timing speci?cations become a function of the devices internal logic paths.
One common role that a FIFO ?lls is in clock domain crossing. In such anapplication, there is a need to communicate a series of data values from ablock of logic operating on one clock to another block operating on a differentclock. Exchanging data between clock domains requires special attention,because there is normally no way to perform a conventional timing analysisacross two differ- ent clocks to guarantee adequate setup and hold times atthe destination ?ops. Either an asynchronous FIFO or a dual-clock synchronousFIFO can be used to solve this problem, as shown in Fig. 4.19.
The dual-port memory at the heart of the FIFO is an asynchronous elementthat can be accessed by the logic operating in either clock domain. A dual-clocksynchronous FIFO is designed to handle arbitrary differences in the clocksbetween the two halves of the device. When one or more bytes are writtenon clock A, the write-pointer information is carried safely across to the clockB domain within the FIFO via inter-clock domain synchronization logic. Thisenables the read-control inter- face to determine that there is data waiting tobe read. Logic on clock B can read this data long after it has been safelywritten into the memory array and allowed to settle to a stable state.
Another common application for a FIFO is rate matching where a particulardata source is bursty and the data consumer accepts data at a more regular rate.One example is a situation where a se- quence of data is stored in DRAM andneeds to be read out and sent over a communications interface one byte at a time.The DRAM is shared with a CPU that competes with the communicationsinterface for memory bandwidth. It is known that DRAMs are most ef?cientwhen operated in a page-mode burst. Therefore, rather than perform acomplete read-transaction each time a single byte is needed for thecommunications interface, a burst of data can be read and stored in a FIFO.Each time the interface is ready for a new byte, it reads it from the FIFO.In this case, only a single-clock FIFO is required, because these devicesoperate on a common clock domain. To keep this process running smoothly,control logic is needed to watch the state of the FIFO and perform a new burstread from DRAM when the FIFO begins to run low on data. This scheme isillustrated in Fig. 4.20.

FIGURE 4.19 Clock domain crossing with synchronous FIFO.

For data-rate matching to work properly, the average bandwidth over time ofthe input and output ports of the FIFO must be equal, because FIFO capacity is?nite. If data is continuously written faster than it can be read, the FIFO willeventually over?ow and lose data. Conversely, if data is continuously read fasterthan it can be written, the FIFO will under?ow and cause invalid bytes to beinserted into the outgoing data stream. The depth of a FIFO indicates how largea read/write rate disparity can be tolerated without data loss. This disparity isexpressed as the product of rate mismatch and time. A small mismatch can betolerated for a longer time, and a greater rate disparity can be tolerated fora shorter time.
In the rate-matching example, a large rate disparity of brief duration is balancedby a small rate disparity of longer duration. When the DRAM is read, a burstof data is suddenly written into the FIFO, creating a temporarily large ratedisparity. Over time, the communications interface reads one byte at a time whileno writes are taking place, thereby compensating with a small disparity over time.
DRAM reads to re?ll the FIFO must be carefully timed to simultaneously preventover?ow and under?ow conditions. A threshold of FIFO fullness needs to beestablished below which a DRAM read is triggered. This threshold must guaranteethat there is suf?cient space available in the FIFO to accept a full DRAM burst,avoiding an over?ow. It must also guarantee that under the worst-case responsetime of the DRAM, enough data exists in the FIFO to satisfy the communicationsinterface, avoiding an under?ow. In most systems, the time between issuing aDRAM read request and actu- ally getting the data is variable. This variabilityis due to contention with other requesters (e.g., the CPU) and waiting foroverhead operations (e.g., refresh) to complete.

FIGURE 4.20 Synchronous FIFO application: data rate matching.

By : E-book Complete_Digital_Design

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December 10, 2009

Statically Indeterminate Members

Posted by: repair : Category: Mechanical Engineering

Members that have more supports or constraints than the minimum
required for static equilibrium are called statically indeterminate.
They can be analyzed if a suf?cient number of additional relationships
are available. These are fundamentally similar to one another in terms
of compatibility for displacements, and are described separately
for special cases.

Statically Indeterminate Axially Loaded Members

Several subsets of these are common; three are shown schematically
in Figure 1.5.27.

1. From a free-body diagram of part (a), assuming upward forces
F_A and F_B at ends A and B, respectively, the force equilibrium
equation is

F_A + F_B ? P = 0

FIGURE 1.5.27 Statically indeterminate axially loaded members.

The displacement compatibility condition is that both ends are ?xed, so

? _A/B = 0

Then

Alternatively, ?rst assume that F_B = 0, and calculate the total downward
displacement (tensile) of the free end B. Then calculate the required force
F_B to compressively deform the rod upward so that after the superposition
there is no net displacement of end B. The results are the same as above
for elastically deforming members.

2. Constrained thermal expansion or contraction of part (b) is handled as
above, using the expression for thermally induced deformation,

?_r =? ? TL

where ? = linear coef?cient of thermal expansion
?T = change in temperature
3. The force equilibrium equation of part (c) is

P?F_A ? F_B = 0

Here the two different component materials are deforming
together by the same amount, so

providing two equations with two unknowns, FA and FB.
Note that rigid supports are not necessarily realistic to assume
in all cases.

Statically Indeterminate Beams

As for axially loaded members, the redundant reactions of beams
are determined from the given conditions of geometry
(the displacement compatibility conditions). There are various
approaches for solving problems of statically indeterminate beams,
using the methods of integration, moment-areas, or superposition.
Handbook formulas for the slopes and de?ections of beams are
especially useful, noting that the boundary conditions must be well
de?ned in any case. The method of superposition is illustrated
in Figure 1.5.28.

FIGURE 1.5.28 A statically indeterminate beam.

Choosing the reaction at C as the redundant support reaction
(otherwise, the moment at A could be taken as redundant),
and ?rst removing the unknown reaction C_y, the statically
determinate and stable primary beam is obtained in Figure 1.5.28b.
Here the slope and de?ection at A are both zero. The slopes
at B and C are the same because segment BC is straight. Next the
external load P is removed, and a cantilever beam ?xed at A and with
load C_y is considered in Figure 1.5.28c. From the original boundary
conditions at C, y₁ + y₂= 0, and the problem can be solved easily
using any appropriate method.

Statically Indeterminate Torsion Members

Torsion members with redundant supports are analyzed essentially
the same way as other kinds of statically indeterminate members.
The unknown torques, for example, are determined by setting up a
solution to satisfy the requirements of equilibrium (?T = 0),
angular displacement compatibility, and torque-displacement
(angle = TL/JG) relationships. Again, the boundary conditions must
be reasonably well de?ned.

Buckling

The elastic buckling of relatively long and slender members under
axial compressive loading could result in sudden and catastrophic large
displacements. The critical buckling load is the smallest for a given
ideal column when it is pin-supported at both ends; the critical load is
larger than this for other kinds of supports. An ideal column is made
of homogeneous material, is perfectly straight prior to loading,
and is loaded only axially through the centroid of its cross-sectional
area.

Critical Load. Eulers Equation

The buckling equation (Eulers equation) for a pin-supported
column gives the critical or maximum axial load P_cr as

where E = modulus of elasticity
I = smallest moment of inertia of the cross-sectional area
L = unsupported length of the pinned column
A useful form of this equation gives the critical average stress prior
to any yielding, for arbitrary end conditions,

where r = ?I/A= radius of gyration of cross-sectional area A
L/r = slenderness ratio
k = effective-length factor; constant, dependent on the end constraints
kL/r = effective-slenderness ratio
The slenderness ratio indicates, for a given material, the tendency for
elastic buckling or failure by yielding (where the Euler formula is not applicable).
For example, buckling is expected in mild steel if L/r is approximately 90
or larger, and in an aluminum alloy if L/r > 60. Yielding would occur ?rst at
smaller values of L/r. Ratios of 200 or higher indicate very slender
members that cannot support large compressive loads.
Several common end conditions of slender columns are shown
schematically in Figure 1.5.29.

FIGURE 1.5.29 Common end conditions of slender columns.

Secant Formula

Real columns are not perfectly straight and homogeneous and are likely
to be loaded eccentrically. Such columns ?rst bend and de?ect laterally,
rather than buckle suddenly. The maximum elastic compressive
stress in this case is caused by the axial and bending loads and is
calculated for small de?ections from the secant formula,

where e is the eccentricity of the load P (distance from the neutral
axis of area A) and c is measured from the neutral axis to the outer
layer of the column where ?_max occurs. The load and stress are
nonlinearly related; if there are several loads on a column, the loads
should be properly combined ?rst before using the secant formula,
rather than linearly superposing several individually determined stresses.
Similarly, factors of safety should be applied to the resultant load.

Inelastic Buckling

For columns that may yield before buckling elastically, the generalized
Euler equation, also called the Engesser equation, is appropriate.
This involves substituting the tangent modulus E_T (tangent to the
stress-strain curve) for the elastic modulus E in the Euler equation,

Note that E_T must be valid for the stress ?cr, but E_T is dependent on
stress when the deformations are not entirely elastic. Thermal or
plastic-strain events may even alter the stress-strain curve of the
material, thereby further changing E_T. Thus, Equation 1.5.49 should
be used with caution in a trial-and-error procedure.

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