Calculators and References 




Quality engineering and design requires an understanding of material compatibility. Galvanic corrosion (some times called dissimilar metal corrosion) is the process by which the materials in contact with each other oxidizes or corrodes. There are three conditions that must exist for galvanic corrosion to occur. First there must be two electrochemically dissimilar metals present. Second, there must be an electrically conductive path between the two metals. And third, there must be a conductive path for the metal ions to move from the more anodic metal to the more cathodic metal. If any one of these three conditions does not exist, galvanic corrosion will not occur. Often when design requires that dissimilar metals come in contact, the galvanic compatibility is managed by finishes and plating. The finishing and plating selected facilitate the dissimilar materials being in contact and protect the base materials from corrosion.
METALLURGICAL CATEGORY 
ANODIC INDEX (V) 
Gold, solid and plated, Goldplatinum alloy 
0.00 
Rhodium plated on silverplated copper 
0.05 
Silver, solid or plated; monel metal. High nickelcopper alloys 
0.15 
Nickel, solid or plated, titanium an s alloys, Monel 
0.30 
Copper, solid or plated; low brasses or bronzes; silver solder; German silvery high coppernickel alloys; nickelchromium alloys 
0.35 
Brass and bronzes 
0.40 
High brasses and bronzes 
0.45 
18% chromium type corrosionresistant steels 
0.50 
Chromium plated; tin plated; 12% chromium type corrosionresistant steels 
0.60 
Tinplate; tinlead solder 
0.65 
Lead, solid or plated; high lead alloys 
0.70 
Aluminum, wrought alloys of the 2000 Series 
0.75 
Iron, wrought, gray or malleable, plain carbon and low alloy steels 
0.85 
Aluminum, wrought alloys other than 2000 Series aluminum, cast alloys of the silicon type 
0.90 
Aluminum, cast alloys other than silicon type, cadmium, plated and chromate 
0.95 
Hotdipzinc plate; galvanized steel 
1.20 
Zinc, wrought; zincbase diecasting alloys; zinc plated 
1.25 
Magnesium & magnesiumbase alloys, cast or wrought 
1.75 
Beryllium 
1.85 
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AWG  Diameter  Diameter  Square  Resistance  Resistance 

mm  inch  mm2  ohm/km  ohm/1000 feet  
46  0,04  0,0013  13700  
44  0,05  0,0020  8750  
42  0,06  0,0028  6070  
41  0,07  0,0039  4460  
40  0,08  0,0050  3420  
39  0,09  0,0064  2700  
38  0,10  0,0040  0,0078  2190  
37  0,11  0,0045  0,0095  1810  
36  0,13  0.005  0,013  1300  445 
35  0,14  0,0056  0,015  1120  
34  0,16  0.0063  0,020  844  280 
33  0,18  0,0071  0,026  676  
AWG  Diameter  Diameter  Square  Resistance  Resistance 
mm  inch  mm2  ohm/km  ohm/1000feet  
32  0,20  0.008  0,031  547  174 
30  0,25  0.01  0,049  351  113 
28  0,33  0.013  0,08  232.0  70.8 
27  0,46  0.018  0,096  178  54.4 
26  0,41  0.016  0,13  137  43.6 
25  0,45  0,0179  0,16  108  
24  0,51  0.02  0,20  87,5  27.3 
22  0,64  0.025  0,33  51,7  16.8 
20  0,81  0.032  0,50  34,1  10.5 
18  1,02  0.04  0,78  21,9  6.6 
16  1,29  0.051  1,3  13,0  4.2 
14  1,63  0.064  2,0  8,54  2.6 
AWG  Diameter  Diameter  Square  Resistance  Resistance 
mm  inch  mm2  ohm/km  ohm/1000feet  
13  1,80  0,0720  2,6  6,76  
12  2,05  0.081  3,3  5.4  1.7 
10  2.59  0.102  5.26  3.4  1.0 
8  3.73  0.147  8.00  2.2  0.67 
6  4.67  0.184  13.6  1.5  0.47 
4  5.90  0.232  21.73  0.8  0.24 
2  7.42  0.292  34.65  0.5  0.15 
1  8.33  0.328  43.42  0.4  0.12 
0  9.35  0.368  55.10  0.31  0.096 
00  10.52  0.414  69.46  0.25  0.077 
000  11.79  0.464  83.23  0.2  0.062 
0000  13.26  0.522  107.30  0.16  0.049 
AWG  Inches  mm  AWG  Inches  mm  
40  0.0031  0.079  24  0.0201  0.511  
39  0.0035  0.089  23  0.0226  0.574  
38  0.004  0.102  22  0.0253  0.643  
37  0.0045  0.114  21  0.0285  0.724  
36  0.005  0.127  20  0.032  0.813  
35  0.0056  0.142  19  0.0359  0.912  
34  0.0063  0.16  18  0.0403  1.02  
33  0.0071  0.18  17  0.0453  1.15  
32  0.008  0.203  16  0.0508  1.29  
31  0.0089  0.226  15  0.0571  1.45  
30  0.01  0.254  14  0.0641  1.63  
29  0.0113  0.287  13  0.072  1.83  
28  0.0126  0.32  12  0.0808  2.05  
27  0.0142  0.361  11  0.0907  2.3  
26  0.0159  0.404  10  0.1019  2.6  
25  0.0179  0.455 
AWG to Metric Conversion Chart  
AWG Number  Ø [Inch]  Ø [mm]  Ø [mm²]  Resistance [Ohm/m] 
4/0 = 0000  0.460  11.7  107  0.000161 
3/0 = 000  0.410  10.4  85.0  0.000203 
2/0 = 00  0.365  9.26  67.4  0.000256 
1/0 = 0  0.325  8.25  53.5  0.000323 
1  0.289  7.35  42.4  0.000407 
2  0.258  6.54  33.6  0.000513 
3  0.229  5.83  26.7  0.000647 
4  0.204  5.19  21.1  0.000815 
5  0.182  4.62  16.8  0.00103 
6  0.162  4.11  13.3  0.00130 
7  0.144  3.66  10.5  0.00163 
8  0.128  3.26  8.36  0.00206 
9  0.114  2.91  6.63  0.00260 
AWG Number  Ø [Inch]  Ø [mm]  Ø [mm²]  Resistance [Ohm/m] 
10  0.102  2.59  5.26  0.00328 
11  0.0907  2.30  4.17  0.00413 
12  0.0808  2.05  3.31  0.00521 
13  0.0720  1.83  2.62  0.00657 
14  0.0641  1.63  2.08  0.00829 
15  0.0571  1.45  1.65  0.0104 
16  0.0508  1.29  1.31  0.0132 
17  0.0453  1.15  1.04  0.0166 
18  0.0403  1.02  0.823  0.0210 
19  0.0359  0.912  0.653  0.0264 
AWG Number  Ø [Inch]  Ø [mm]  Ø [mm²]  Resistance [Ohm/m] 
20  0.0320  0.812  0.518  0.0333 
21  0.0285  0.723  0.410  0.0420 
22  0.0253  0.644  0.326  0.0530 
23  0.0226  0.573  0.258  0.0668 
24  0.0201  0.511  0.205  0.0842 
25  0.0179  0.455  0.162  0.106 
26  0.0159  0.405  0.129  0.134 
27  0.0142  0.361  0.102  0.169 
28  0.0126  0.321  0.0810  0.213 
29  0.0113  0.286  0.0642  0.268 
AWG Number  Ø [Inch]  Ø [mm]  Ø [mm²]  Resistance [Ohm/m] 
30  0.0100  0.255  0.0509  0.339 
31  0.00893  0.227  0.0404  0.427 
32  0.00795  0.202  0.0320  0.538 
33  0.00708  0.180  0.0254  0.679 
34  0.00631  0.160  0.0201  0.856 
35  0.00562  0.143  0.0160  1.08 
36  0.00500  0.127  0.0127  1.36 
37  0.00445  0.113  0.0100  1.72 
38  0.00397  0.101  0.00797  2.16 
39  0.00353  0.0897  0.00632  2.73 
40  0.00314  0.0799  0.00501  3.44 
Some rules of thumb helping you to learn AWG resistance and diameter.P>
The AWG numbering system is logarithmic and works much like calculating with deciBels:
Dissipation Factor (DF) DF and "loss tangent" are largely equivalent terms describing capacitor dielectric losses. DF refers specifically to losses encountered at low frequencies, typically 120 Hz to 1 KHz. At high frequencies, capacitor dielectric losses are described in terms of loss tangent (tan ð). The higher the loss tangent, the greater the capacitor's equivalent series resistance (ESR) to signal power. In addition, the poorer its Quality Factor (low Q), the greater its loss (heating) and the worse its noise characteristics.
When a capacitor is used as a series element in a signal path, its forward transfer coefficient is measured as a function of the dielectric phase angle, (theta). This angle is the difference in phase between the applied sinusoidal voltage and its current component. In an ideal capacitor, (theta) equals 90°. In lowloss capacitors, it is very close to 90 o . (See Figure 3) For small and moderate capacitor values, losses within the capacitor occur primarily in the dielectric, the medium for the energy transfer and storage. The dielectric loss angle, ð, is the difference between (theta) and 90 o and is generally noted as tan o. The name "loss tangent" simply indicates that tan ð goes to zero as the losses go to zero. Note that the dielectric's DF is also the tangent of the dielectric loss angle. These terms are used interchangeably in the literature.
Figure 3: This shows capacitive vector represented in the impedance plane.
In an ideal capacitor, (theta) = 90° and tan ð = 0 (for R = 0).
Cubic Feet per Minute (CFM) A measure of the volume of air flowing in a system. The conversion of cubic feet per minute to linear feet per minute is dependent upon the crosssectional area through which the air flows:
Charging and Discharging a Capacitor 
Here is a summary of the essential points:
q(t) = CE (1  e^{t/RC}),
V(t) = E (1  e^{t/RC}).
The time scale for the charging process is determined by the time constant t = RC.
q(t) = q_{0} e^{t/RC},
V(t) = (q_{0}/C) e^{t/RC}.
Notice again that the discharging process is also determined by a time scale set by the time constant t = RC.
Exercise: 
Goal: To understand the charging and discharging of a capacitor through a resistive circuit 
In this activity, you will construct an RC circuit [see figure below], study how a capacitor gets charged and discharged, and use the data to measure the capacitance of the capacitor. In the experiment, you will measure the potential difference across a capacitor using probes that are interfaced to your computer. This voltage will be acquired as a function of time at a rate of 50 points/second and plotted on the screen. You must then save this data and analyze it using Excel.
The capacitor is a big orange ceramic capacitor, and the resistor is a blackbrownblue one, as shown in the figure. The approximate values are R=1MW and C=1mC. What "time constant" would these values give you if put in series in an RC circuit?
A. Acquiring the data
We will now a digital data acquisition system. The "hardware" is the "ULI" box, connected to the computer, and from which we have two probes, one black and one red. The software is a program called "Logger". The hardware will convert the potential difference between the probes into a digital signal, and the program will collect and graph the data on the screen. We want to get and plot the data for the potential difference across the capacitor while it is being charged and then while it is being discharged.
These are the instructions to get the data:
B. Analyzing the data
I. Charging the capacitor
V(t) = E (1  e^{t/RC}),
where E is the total EMF of the two batteries.
Hint: if the data is consistent with this formula, then you can define two quantities that when plotted in loglog scale show a linear trend. What quantities are these? Make two columns in Excel with these quantities and make a loglog plot. Is it linear? (Note: what is t=0 in your data?)
II. Discharging the capacitor
V(t) = (q_{0}/C) e^{t/RC}
Attach to your report graphs with your data showing: (a) the capacitor being charged, and (b) the capacitor being discharged. Indicate in the graph the points at time = 0, 1, 2 and 3 time constants, and the points at which the voltage is V_{0}, V_{0}/2, and V_{0}/5.
Equivalent series resistance (ESR) is responsible for the energy dissipated as heat and is directly proportional to the DF. A capacitor should be depicted as an ESR in series with an ideal capacitance (C).
ESR is determined by:From this, we can see that "lossy" capacitors and those that present large amounts of Xc will be highly resistive to the signal power.
Circuit designs employing low Q capacitors usually produce large quantities of unwanted heat because tan ð and DF (or 1/Q) typically increase in a nonlinear fashion with rising frequency and temperature. With some capacitors, this effect is enhanced by the naturally occurring decreased capacitance at high frequencies. High currents also produce increase heat, which in turn again increases the ESR and DF.
Even with substantial changes in current flow, high Q (low DF) capacitors will not exhibit the value shifts common to equivalent components exhibiting high DF, ESR, and other parasitics. Low ESR reduces the unwanted heating effects that degrade capacitors. This is an important goal in designing these components for high current, highperformance applications, such as power supplies and highcurrent filter networks.
As Figure 4 shows, the significance of losscontributing factors depends to some degree on the value of the capacitor.
Figure 3: This shows capacitive vector represented in the impedance plane. In an ideal capacitor, (theta) = 90° and tan ð = 0 (for R = 0).
The equivalent circuit of a capacitor is made up of four basic characteristics as shown in Figure 1, three of which are frequency dependant (Z, ESR and ESL) and one is DC dependent (Rp). This discussion will be limited to the frequency dependent characteristics of ESL, ESR and Z, along with one additional component called capacitive reactance (Xc)
ESL is the equivalent series inductance, and is expressed mathematically as ESL=2*PI*f*L; where f = frequency and L = inductance. ESL is simply the sum of all the inductive components within a capacitor. Equivalent series resistance, like ESL, is simply the sum of all the resistive components within a capacitor. Expressed mathematically as ESR = D.F. /(2*PI*f*C) = D.F.*Xc; where D.F. = dissipation factor, f = frequency, C= capacitance and Xc = capacitive reactance. Xc is defined as 1/(2*PI*f*C). Z is the impedance of the capacitor. It is expressed mathematically as
ANSI  Designator  MILP13949  Material Rinforcement/Resin  Dielectric Constant 
FR4  GF  Woven Glass/Epoxy  4.2  4.9  
FR5  GH  Woven Glass/Epoxy  4.2  4.9  
GP  Nonwoven Glass/Teflon  2.2  2.4  
GR  Nonwoven Glass/Teflon  2.2  2.4  
GT  Woven Glass/Teflon  2.6  2.8  
GX  Woven Glass/Teflon  2.4  2.6  
GPY  GI  Woven Glass/Polyimide  4.0  4.7  
GY  Woven Glass/Teflon  2.1  2.45  
AE  Woven Aramid/Epoxy  3.8  4.5  
AI  Woven Aramid/Polyimide  3.6  4.4  
QI  Woven Quartz/Polyimide  3.0  3.8  
GM  Woven Glass/BT  4.0  4.7  
CF  Nonwoven Polyester/Epoxy  4.2  4.9  
GC  Woven Glass/Cyanate Ester  4.0  4.7  
X1  Teflon  2.2  
X2  Polyimide  3.5 
Gauge  dia.(in)  Area (Sq.In.) 
0000  0.460000  0.1661901110 
000  0.409600  0.1317678350 
00  0.364800  0.1045199453 
0  0.324900  0.0829065680 
1  0.289300  0.0657334432 
2  0.257600  0.0521172188 
3  0.229400  0.0413310408 
4  0.204300  0.0327813057 
5  0.181900  0.0259869262 
6  0.162000  0.0206119720 
7  0.144300  0.0163539316 
8  0.128500  0.0129686799 
9  0.114400  0.0102787798 
10  0.101900  0.0081552613 
11  0.090740  0.0064667648 
12  0.080810  0.0051288468 
13  0.071960  0.0040669780 
14  0.064080  0.0032250357 
15  0.057070  0.0025580278 
16  0.050820  0.0020284244 
17  0.045260  0.0016088613 
18  0.040300  0.0012755562 
19  0.035890  0.0010116643 
20  0.031960  0.0008022377 
21  0.028460  0.0006361497 
22  0.025350  0.0005047141 
23  0.022570  0.0004000853 
24  0.020100  0.0003173084 
25  0.017900  0.0002516492 
26  0.015940  0.0001995566 
27  0.014200  0.0001583676 
28  0.012640  0.0001254826 
29  0.011260  0.0000995787 
30  0.010030  0.0000790117 
31  0.008928  0.0000626034 
32  0.007950  0.0000496391 
33  0.007080  0.0000393691 
34  0.006305  0.0000312219 
35  0.005615  0.0000247622 
36  0.005000  0.0000196349 
37  0.004453  0.0000155738 
38  0.003965  0.0000123474 
39  0.003531  0.0000097923 
40  0.003145  0.0000077684 
41  0.002800  0.0000061575 
42  0.002490  0.0000048695 
43  0.002220  0.0000038708 
44  0.001970  0.0000030480 
45  0.001760  0.0000024328 
46  0.001570  0.0000019359 
Multiply  By  To Obtain  
Acres  x  43560  =  Square Feet 
Acres  x  4840  =  Square Yards 
Circular Mils  x  7.854x10e7  =  Square Inches 
Circular Mils  x  0.7854  =  Square Mils 
Square Centimeters  x  0.155  =  Square Inches 
Sq. Feet  x  144  =  Square Inches 
Sq. Feet  x  0.0929  =  Square Meters 
Sq. Inches  x  6.452  =  Square Centimeters 
Sq. Meters  x  1.196  =  Square Yards 
Sq. Miles  x  640  =  Acres 
Sq. Mils  x  1.273  =  Circular Mils 
MSI  x  1.55  =  Square Meters 
Sq. Yards  x  0.8361  =  Square Meters 
EnergyEnergy Or Work  
Multiply  By  To Obtain  
Btu  x  778.2  =  Footpounds 
Btu  x  252  =  Gramcalories 
Horsepower  x  746  =  Watts 
Watts  x  0.001341  =  Horsepower 
Btu per hour  x  3.412969  =  Watts 
Kilowatts  x  1.341  =  Horsepower 
ForceForce and WeightWeight  
Multiply  By  To Obtain  
Grams  x  0.0353  =  Ounces 
Kilograms  x  2.205  =  Pounds 
Newtons  x  0.00248  =  Pounds(force) 
Ounces  x  28.35  =  Grams 
Pounds (U.S.avoirdupois)  x  453.59  =  Grams 
Pounds Force  x  4.448  =  Newtons 
Tonsbr (short)  x  907.2  =  Kilograms 
Tonsbr (short)  x  2000  =  Pounds 
LengthLength  
Multiply  By  To Obtain  
Centimeters  x  0.3937  =  Inches 
Fathoms  x  6  =  Feet 
Feet  x  12  =  Inches 
Feet  x  0.3048  =  Meters 
Inches  x  2.54  =  Centimeters 
Kilometers  x  0.6214  =  Miles 
Meters  x  3.281  =  Feet 
Meters  x  39.37  =  Inches 
Meters  x  1.094  =  Yards 
Miles  x  5280  =  Feet 
Miles  x  1.609  =  Kilometers 
Rods  x  5.5  =  Yards 
Yards  x  0.9144  =  Meters 
PlanePlane Angle  
Multiply  By  To Obtain  
Degrees  x  0.0175  =  Radians 
Minutes  x  0.01667  =  Degrees 
Minutes  x  2.9x10sup4/sup  =  Radians 
Quadrants  x  90  =  Degrees 
Quadrants  x  1.5708  =  Radians 
Radians  x  57.3  =  Degrees 
PowerPower  
Multiply  By  To Obtain  
Btu per hour  x  0.293  =  Watts 
Horsepower  x  33000  =  Footpounds per minute 
Horsepower  x  550  =  Footpounds per second 
Horsepower  x  746  =  Watts 
Kilowatts  x  1.341  =  Horsepower 
TorqueTorque  
Multiply  By  To Obtain  
Gramcentimeters  x  0.0139  =  Ounceinches 
Newtonmeters  x  0.7376  =  Poundfeet 
Newtonmeters  x  8.851  =  Poundinches 
Ounceinches  x  72  =  Gramcentimeters 
Poundfeet  x  1.3558  =  Newtonmeters 
Poundinches  x  0.113  =  Newtonmeters 
VolumeVolume (Gallons and quarts are U.S.)  
Multiply  By  To Obtain  
Cubic Feet  x  0.0283  =  Cubic Meters 
Cubic Feet  x  7.481  =  Gallons 
Cubic Inches  x  0.5541  =  Ounces (fluid) 
Cubic Meters  x  35.31  =  Cubic Feet 
Cubic Meters  x  1.308  =  Cubic Yards 
Cubic Yards  x  0.7646  =  Cubic Meters 
Gallons  x  0.1337  =  Cubic Feet 
Gallons  x  3.785  =  Liters 
Liters  x  0.2642  =  Gallons 
Liters  x  1.057  =  Quarts (liquid) 
Ounces (fluid)  x  1.805  =  Cubic Inches 
Quarts (liquid)  x  0.9463  =  Liters 
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