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

(top)

---

Metric Conversion AWG Chart

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

(top)

---

AWG Rules.

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:

AWG Resistance:

• AWG 15 copper is about 10 milliOhm per meter.
• Adding 3 to the AWG number doubles the resistance; Subtracting 3 halves.
• Adding 10 to the AWG number tenfolds the resistance; Subtracting 10 reduces by a factor 10.

AWG Diameter:

• AWG 18 has a solid core diameter of about 1.0 mm.
• Adding 6 to the AWG number halves the diameter; Subtracting 6 doubles.
• Adding 20 to the AWG number reduces the diameter by a factor of 10; Subtracting 20 tenfolds.

(top)

---

Capacitance

• Capacitance Calculator (Plate) (SBC)
• ESR
• Exercise Capacitor Charge and Discharge
• Calculator, Plate Capacitance
• Basic Considerations: DF, Q, and ESR
• Basic Considerations: DF, Q, and ESR (pdf)
• Capacitance and Coating Properties: A Calculator
• 
• Dissipation Factor
• Capacitor PF and DF (pdf)

(top)

Dissipation Factor

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 low-loss 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).

(top)  (Capacitance)

---

Air Flow Equations

Cubic Feet Per Minute to Linear Feet per minute

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 cross-sectional area through which the air flows:

144(CFM)/(LENGTH(INCHES)x(HEIGHT(INCHES)) = LFM (Linear Feet per Minute)
196.85 LFM = 1 Meter/sec

(top)

---

Exercise Capacitor Charge and Discharge

(top)

Charging and Discharging a Capacitor

(top)

Here is a summary of the essential points:

• When an EMF E is applied to a resistor R and a capacitor C in series, the charge q on the capacitor and the potential difference V across the capacitor increase with time in the following manner:

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.

• When a charged capacitor C with an initial charge q₀ is connected in a closed circuit with a resistor R, the charge and the potential difference across the capacitor decrease with time in the following manner:

q(t) = q₀ e^-t/RC,

V(t) = (q₀/C) e^-t/RC.

Notice again that the discharging process is also determined by a time scale set by the time constant t = RC.

(top)

Exercise:

Goal: To understand the charging and discharging of a capacitor through a resistive circuit

(top)

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 black-brown-blue 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?

(top)

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:

• First, hook up all the elements of the circuit shown above: make sure that the switch is not in either of the closed positions. Once your circuit is hooked up, check with an instructor before you proceed further!
• Next, hook up the voltage probes from the computer interface box as shown: make sure that you have the red and black probes and the polarity of the battery connected exactly as shown in the diagram.
• Make sure that your ULI interface box is turned on and that the voltage probes are connected to input 1 --your instructors should have already set this up.
• From the start menu, go to the program group "ULI" and start the program called LOGGER.
• Click on the dialog box that says "COM1": you should see a graph after a short delay.
• The program controls are all activated by clicking on the right mouse button: do this and go to the FILE menu; select "OPEN"
• Open the file called "cap.lxp". If the file is not there, you can get it from here. Save it in your floppy disk or in the C:\TEMP directory.
• This will bring up a graph with default settings chosen by your instructor. These defaults are for data acquisition rate (how many data points per second are acuired), plot axes, etc.
• Before acquiring the data, discuss in your group what you expect to observe when the switch is in position A and when it is then switched to position B.
• One of your group members should now be ready to throw the switch to position A while another group member gets ready to hit the "start" button. The program will start acquiring data a short while after the "start" button is pressed. Throw the switch once you see this happening.
• Once your data indicates that the capacitor is completely charged, throw the switch to the B position. This will discharge the capacitor.
• Play around taking data with the switch in different positions, and compare with your expectations.
• If you believe that you have a reasonably good measurement, go to the "FILE" menu and "EXPORT" the data as a TEXT FILE.
• You must have at least one file with a smooth charge and another with a clear discharge, but you can get more data if you want.
• You can now quit LOGGER and import your data into an Excel spreadsheet. The first column is TIME in seconds and the second column is the VOLTAGE across the capacitor in volts. Ignore (delete) the third column.

B. Analyzing the data

I. Charging the capacitor

• Draw a circuit diagram that represents the circuit you used to CHARGE the capacitor -- you may assume that the batteries are ideal. Measure the emf of the batteries and the resistance of your resistor with your multimeter.
• Write down a loop equation for the circuit at a time t when the charge on the capacitor is q. (Assume that you began charging the capacitor at t = 0.)
• Suppose that the potential difference across the capacitor at time t is V(t). Show that the data you acquired is consistent with the following equation for V(t) :

V(t) = E (1 - e^-t/RC),

(top)

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 log-log scale show a linear trend. What quantities are these? Make two columns in Excel with these quantities and make a log-log plot. Is it linear? (Note: what is t=0 in your data?)

What is the value of V(t) for t = 0, t = RC and t = 2RC? If the law is exponential as suggested by the formula we are using, what would you expect those values to be?

• From the experimental data, extract a value for the "time constant" RC of the circuit.
• Measure the value of the resistor R with a multimeter, and then using your measurement of the time constant, determine the value of the capacitance C.

II. Discharging the capacitor

• First, draw a circuit diagram that represents the circuit you used to DISCHARGE the capacitor.
• Write down a loop equation for the circuit, assuming that you began discharging the capacitor at t = 0 and that the charge on the capacitor at time t is q.
• Show that your experimental data are consistent with the following expression for the voltage V(t) across the capacitor as a function of time (q0 is the charge at t = 0):

V(t) = (q₀/C) e^-t/RC

• From your experimental data, determine the time constant RC and compare it with the time constant you obtained earlier.
• What is the total charge q₀ in the capacitor when it is completely charged?
• After how many time constants is the voltage across the capacitor (a) 99% of its initial value; (b) 37% of its initial value?

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 V₀, V₀/2, and V₀/5.

---

Equivalent Series Resistance (ESR)

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:
ESR = (Xc/Q = Xc (tan ð), with Q = 1/DF.

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 non-linear 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, high-performance applications, such as power supplies and high-current filter networks.

As Figure 4 shows, the significance of loss-contributing 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

More info: see: http://www.ecnmag.com/ecnmag/issues/2001/02012001/ec12ss1.asp

(top)

---

PCB Dielectric Constant

ANSI	Designator	MIL-P-13949	Material Rinforcement/Resin	Dielectric Constant
FR-4		GF	Woven Glass/Epoxy	4.2 - 4.9
FR-5		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

(top)

---

Impedance

• PCB Impedance Control: Formulas and Resources - Ultracad
• Dual (Asymmetric) Stripline Impedance and Capacitance Modeling
• PCB Trace Impedance Calculator
• Asymmetric Stripline Impedance Calculator
• Asymmetric Stripline Characteristic Impedance and Capacitance Calculator
• Download Salkow's Freeware Stripline and Microstrip PCB Calculator
• 1 % Resistor Chart
• Click on Utils - Trace Impedance Calculators
• Calculation Program, Impedance - Java Script
• Reference for above Calculation Program, Impedance - Java Script
• IPC Design Resources -Trace Impedance Calculators
• Calculators, Online Impedance
• Microstrip Analysis/Synthesis Calculator
• Minimum Loss matching Pad
• Stripline (Differential) Impedance Calculator
• PWA Edge Etch Taper and prepreg Effects White Paper

(top)

---

(top)

Capacitance - Half Wave Rectification

Capacitance - Full Wave Rectification

(top)

---

VIA - INDUCTANCE

(top)

---

General

• CALCULATORS ON-LINE CENTER ENGINEERING ELECTRICAL & COMPUTER
• 1 % Resistor Chart

---

Mechanical

---

American Wire Gauge

Same as American Wire Gauge table below except in a comma delimited File Format


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


(top)


---

Conversions


(TOP)


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	=	Foot-pounds
Btu	x	252	=	Gram-calories
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	2.9x10sup-4/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	=	Foot-pounds per minute
Horsepower	x	550	=	Foot-pounds per second
Horsepower	x	746	=	Watts
Kilowatts	x	1.341	=	Horsepower
TorqueTorque
Multiply		By		To Obtain
Gram-centimeters	x	0.0139	=	Ounce-inches
Newton-meters	x	0.7376	=	Pound-feet
Newton-meters	x	8.851	=	Pound-inches
Ounce-inches	x	72	=	Gram-centimeters
Pound-feet	x	1.3558	=	Newton-meters
Pound-inches	x	0.113	=	Newton-meters
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

(top)  (back)


---

Vacuum Torr Conversion Table


(top)  (back)


---

(TOP) Intranet Website - For information or questions regarding this web page, please contact Steve Salkow