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Copper Roughness and Attenuation As circuit operating frequencies increase, more of the signal travels in the outermost part of the conductor.The skin depth that is, the region where much of the signal travels is shown in Fig. 9.2 as a function of frequency. As shown in this graph, the skin depth approaches the average roughness of 0.5 oz. copper foil above 1 GHz. Signal attenuation due to conductor losses related to the roughness of the foil becomes an important factor at these frequencies, and should be considered by the design engineer.

Skin depth ( m)

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Drawing UPC-A Barcodes with C# - CodeProject
6 Apr 2005 ... Demonstrates a method to draw UPC-A barcodes using C#. ... NET 2003 - 7.87 Kb. Image 1 for Drawing UPC-A Barcodes with C# ...

0.5 oz Commercial foil average roughness, Ra ( m) 5

0 0.01

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UPC-A C# class that will generate UPC-A codes. ... Background. I originally built this application in VB. NET . While I was learning C#. NET , I decided to re-write it ...

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In physics we seek invariance, i.e., we seek laws of physics written in an invariant form that is true for all observers. Tensors are a key ingredient in this recipe, because if a tensor equation is true in one coordinate system then it is true in all coordinate systems. This can greatly simplify analysis because we can often transform to a coordinate system where the mathematics will be easier. There we can nd the form of a result we need and then express it in another coordinate system if desired. A simple example of this is provided by the vacuum eld equations. We will see that these can be expressed in the form of a (0, 2) tensor called the Ricci tensor, where Rab = 0 It is immediately obvious that this equation is true in any coordinate system. Let s transform to a different coordinate system using the [Lambda] matrix discussed Rab =

1 Frequency (GHz)

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A study of several different copper foil types correlated roughness and attenuation values.6 Figures 9.3 and 9.4 show pictures of the foils to highlight their relative roughness differences. Figure 9.5 shows the roughness distributions of these foils. Finally, in Fig. 9.6, the loss values associated with each of these foil types are graphed versus frequency. Up to about 1 GHz, there is very little difference in the observed loss across the several foil types. However, at higher frequencies, the difference becomes much greater, correlating to the roughness of the individual foil types; the greater the roughness, the greater the measured attenuation.

50 m

The roughness that results from the oxide/oxide alternative surface preparation process during printed circuit manufacturing is also important. Figures 9.7 and 9.8 compare the roughness obtained from two of these processes. The base copper foil and FR-4 resin system used were held constant. The test vehicles from which these cross sections were taken were also measured for attenuation. This measurement technique was used to calculate an effective dissipation factor, Df, for these material sets. The measured Df for the sample in Fig. 9.7, with the relatively smooth profile, was 0.021 at 1 GHz. The measured Df for the sample in Fig. 9.8, with the rougher profile, was 0.026. Obviously, the rougher profile created by the oxide alternative process in Fig. 9.8 resulted in a significantly higher loss value.

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10 Frequency (GHz)

To satisfy requirements for impedance, layer count, and overall PCB thickness, a broad range of laminate dielectric thicknesses are needed. Table 9.2 shows many common laminate dielectric thicknesses, along with typical constructions and resin contents. Individual laminate suppliers may have preferred constructions, so not every construction shown in this section will be available from every laminate supplier. In addition, some of the high-performance resin systems will have slightly different constructions or resin contents in order to target certain performance characteristics, such as dielectric constant.

Single-Ply versus Multiple-Ply Constructions With dielectrics below 0.0040 in., there is often no choice but to use a single ply of fiberglass cloth to achieve the desired thickness. With dielectrics in the 0.0040 in. to 0.0080 in. range,

IPC-FC-231C: Flexible bare dielectrics for use in flexible printed wiring IPC-FC-232C: Specification for adhesive coated dielectric films for use as cover sheets for flexible printed wiring IPC-FC-234: Pressure sensitive adhesives assembly guidelines for single-sided and double-sided printed circuits IPC-FC-241C: Flexible metal-clad dielectrics for use in fabrication of flexible printed wiring IPC-RF-245: Performance specification for rigid-flex printed boards IPC-D-249: Design standard for flexible single and double-sided printed boards IPC-FC-250A: Specification for single and double-sided flexible printed wiring IPC-FA-251: Guidelines for assembly of single and double-sided flex circuits IPC-6013A: Qualification and performance specification for flexible printed boards

JIS-C 5016: Test methods for flexible printed wiring boards JIS-C 5017: Flexible printed wiring boards, single-sided and double-sided JIS-C 6471: Test methods for copper-clad laminates of flexible printed wiring boards JIS-C 6472: Copper-clad laminates for flexible printed wiring boards (polyester film, polyimide film)

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