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Table of Standard Annealed Bare Copper Wire Using American Wire Gauge (B&S)
GAUGE DIAMETER INCHES AREA WEIGHT LENGTH RESISTANCE AT 68° F CURRENT CAPACITY (AWG) or (B&S) Min. Nom. Max. Circular Mils Pounds per M’ Feet per Lb. Ohms per M’ Feet per Ohm Ohms per Lb. (Amps) Rubber Insulated 0000 .4554 .4600 .4646 211600. 640.5 1.561 .04901 20400. .00007652 225 000 .4055 .4096 .4137 167800. 507.9 1.968 .06180 16180. .0001217 175 00 .3612 .3648 .3684 133100. 402.8 2.482 .07793 12830. .0001935 150 0 .3217 .3249 .3281 105500. 319.5 3.130 .09827 10180. .0003076 125 1 .2864 .2893 .2922 83690. 253.3 3.947 .1239 8070. .0004891 100 2 .2550 .2576 .2602 66370. 200.9 4.977 .1563 6400. .0007778 90 3 .2271 .2294 .2317 52640. 159.3 6.276 .1970 5075. .001237 80 4 .2023 .2043 .2063 41740. 126.4 7.914 .2485 4025. .001966 70 5 .1801 .1819 .1837 33100. 100.2 9.980 .3133 3192 .003127 55 6 .1604 .1620 .1636 26250. 79.46 12.58 .3951 2531. .004972 50 7 .1429 .1443 .1457 20820. 63.02 15.87 .4982 2007. .007905 – 8 .1272 .1285 .1298 16510. 49.98 20.01 .6282 1592. .01257 35 9 .1133 .1144 .1155 13090. 39.63 25.23 .7921 1262. .01999 – 10 .1009 .1019 .1029 10380. 31.43 31.82 .9989 1001. .03178 25 11 .08983 .09074 .09165 8234. 24.92 40.12 1.260 794. .05063 – 12 .08000 .08081 .08162 6530. 19.77 50.59 1.588 629.6 .08035 20 13 .07124 .07196 .07268 5178. 15.68 63.80 2.003 499.3 .1278 – 14 .06344 .06408 .06472 4107. 12.43 80.44 2.525 396.0 .2032 15 15 .05650 .05707 .05764 3257. 9.858 101.4 3.184 314.0 .3230 – 16 .05031 .05082 .05133 2583. 7.818 127.9 4.016 249.0 .5136 6 17 .04481 .04526 .04571 2048. 6.200 161.3 5.064 197.5 .8167 – 18 .03990 .04030 .04070 1624. 4.917 203.4 6.385 156.5 1.299 3 19 .03553 .03589 .03625 1288. 3.899 256.5 8.051 124.2 2.065 – 20 .03164 .03196 .03228 1022. 3.092 323.4 10.15 98.5 3.283 – 21 .02818 .02846 .02874 810.1 2.452 407.8 12.80 78.11 5.221 – 22 .02510 .02535 .02560 642.4 1.945 514.2 16.14 61.96 8.301 – 23 .02234 .02257 .02280 509.5 1.542 648.4 20.36 49.13 13.20 – 24 .01990 .02010 .02030 404.0 1.223 817.7 25.67 38.96 20.99 – 25 .01770 .01790 .01810 320.4 .9699 1031. 32.37 30.90 33.37 – 26 .01578 .01594 .01610 254.1 .7692 1300. 40.81 24.50 53.06 – 27 .01406 .01420 .01434 201.5 .6100 1639. 51.47 19.43 84.37 – 28 .01251 .01264 .01277 159.8 .4837 2067. 64.90 15.41 134.2 – 29 .01115 .01126 .01137 126.7 .3836 2607. 81.83 12.22 213.3 – 30 .00993 .01003 .01013 100.5 .3042 3287. 103.2 9.691 339.2 – 31 .008828 .008928 .009028 79.7 .2413 4145. 130.1 7.685 539.3 – 32 .007850 .007950 .008050 63.21 .1913 5227. 164.1 6.095 857.6 – 33 .006980 .007080 .007180 50.13 .1517 6591. 206.9 4.833 1364. – 34 .006205 .006305 .006405 39.75 .1203 8310. 260.9 3.833 2168. – 35 .005515 .005615 .005715 31.52 .09542 10480. 329.0 3.040 3448. – 36 .004900 .005000 .005100 25.00 .07568 13210. 414.8 2.411 5482. – 37 .004353 .004453 .004553 19.83 .06001 16660. 523.1 1.912 8717. – 38 .003865 .003965 .004065 15.72 .04759 21010. 659.6 1.516 13860. – 39 .003431 .003531 .003631 12.47 .03774 26500. 831.8 1.202 22040. – 40 .003045 .003145 .003245 9.888 .02993 33410. 1049. 0.9534 35040. – 41 .00270 .00280 .00290 7.8400 .02373 42140. 1323. .7559 55750. – 42 .00239 .00249 .00259 6.2001 .01877 53270. 1673. .5977 89120. – 43 .00212 .00222 .00232 4.9284 .01492 67020. 2104. .4753 141000. – 44 .00187 .00197 .00207 3.8809 .01175 85100. 2672. .3743 227380. – 45 .00166 .00176 .00186 3.0976 .00938 106600. 3348. .2987 356890. – 46 .00147 .00157 .00167 2.4649 .00746 134040. 4207. .2377 563900. – *Note: Values from National Electrical Code.
Note: per M’ means Per 1000 ft.
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Coil Winding Data
Turns Per Inch Coil Winding Formulas Gauge (AWG) or (B&S) Number Of Turns per Linear Inch The following approximations for winding r-f coils are accurate to within approx. 1% for nearly all small air-core coils, where Enamel S.S.C. D.S.C. and S.C.C. D.C.C. 1 – – 3.3 3.3 L = self inductance in microhenrys
N = total number of turns
r = mean radius in inches
l= length of coil in inches
b = depth of coil in inches.2 – – 3.8 3.6 3 – – 4.2 4.0 4 – – 4.7 4.5 5 – – 5.2 5.0 single-Layer Wound Coils 6 – – 5.9 5.6 7 – – 6.5 6.2 8 7.6 – 7.4 7.1 9 8.6 – 8.2 7.8 10 9.6 – 9.3 8.9 11 10.7 – 10.3 9.8 12 12.0 – 11.5 10.9 13 13.5 – 12.8 12.0 14 15.0 – 14.2 13.8 15 16.8 – 15.8 14.7 16 18.9 18.9 17.9 16.4 17 21.2 21.2 19.9 18.1 Multi-Layer Wound Coils 18 23.6 23.6 22.0 19.8 19 26.4 26.4 24.4 21.8 20 29.4 29.4 27.0 23.8 21 33.1 32.7 29.8 26.0 22 37.0 36.5 34.1 30.0 23 41.3 40.6 37.6 31.6 24 46.3 45.3 41.5 35.6 25 51.7 50.4 45.6 38.6 26 58.0 55.6 50.2 41.8 27 64.9 61.5 55.0 45.0 28 72.7 68.6 60.2 48.5 29 81.6 74.8 65.4 51.8 Spiral Wound Coils 30 90.5 83.3 71.5 55.5 31 101. 92.0 77.5 59.2 32 113. 101. 83.6 62.6 33 127. 110. 90.3 66.3 34 143. 120. 97.0 70.0 35 158. 132. 104. 73.5 36 175. 143. 111. 77.0
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Ohm’s Law for A-C Circuits
The fundamental Ohm’s law formulas for
a-c circuits are given by:I = E / Z Z = E / I E = I*Z P = E*I*cos Ø Where: I = current in amperes, Z = impedance in Ohms, E = volts across, P = power in watts, Ø = phase angle in degrees. Phase Angle The phase angle is defined as the difference in degrees by which current leads voltage in a capacitive circuit, or lags voltage in an inductive circuit, and in series circuits is equal to the angle whose tangent is given by the ratio X/R and is expressed by: arc tan (X/R) Where: X = the inductive or capacitive reactance in ohms, R = the non-reactive resistance in ohms, of the combined resistive and reactive components of the circuit under consideration. Therefore: in a purely resistive circuit, Ø = 0° in a purely reactive circuit, Ø = 90° and in a resonant. circuit, Ø = 0° also when: Ø = 0°, cos Ø = l and P = E*I, Ø = 90°, cos Ø = 0 and P = 0. ————– Degrees x 0.0175 = radians.
1 radian = 57.3°Power Factor The power-factor of any a-c circuit is equal to
the true power in watts divided by the apparent
power in volt-amperes which is equal to the
cosine of the phase angle, and is expressed byE*I*cos Ø
p . f . = —————- = cos Ø
E*IWhere: p.f. = the circuit load power factor, E*I*cos Ø = the true power in watts, E*I* = the apparent power in voltamperes, E = the applied potential in volts I = load current in amperes. Therefore: in a purely resistive circuit. Ø = 0° and p.f. = 1 and in a reactive circuit, Ø = 90° and p.f. = 0 and in a resonant circuit, Ø = 0° and p.f. = 1 Ohm’s Law for D-C Circuits The fundamental Ohm’s law formulas for d-c circuits are given by, E
I = --- ,
RE
R = --- ,
IE = I*R P = I*E where: I = current in Amperes, R = resistance in ohms, E = potential across R in volts, P = power in watts.
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D-C Meter Formulas
Meter Resistance The d-c resistance of a milliameter or voltmeter movement may be determined as
follows:1. Connect the meter in series with a
suitable battery and variable resist-
ance R1 as shown in the diagram above.2. Vary R1 until a full scale reading is
obtained.3. Connect another variable resistor R1
across the meter and vary its value
until a half scale reading is obtained.4. Disconnect R2 from the circuit and
measure its d-c resistance.The meter resistance RM is equal to the measured resistance of R2. Caution: Be sure that R1 has sufficient resistance to prevent an off scale reading
of the meter. The correct value depends
upon the sensitivity of meter, and voltage
of the battery. The following formula can
be used if the full scale current of the meter
is known:R1 = voltage of the battery used
full scale current of meter in amperes For safe results, use twice the value com-
puted. Also, never attempt to measure the
resistance of a meter with an ohmeter. To
do so would in all proability result in a
burned-out or severly damaged meter,
since the current required for the operation
of some ohmeters and bridges is far in
excess of the full scale current required by
the movement of the average meter you
may be checking.Ohms per Volt Rating of a Voltmeter Where: = ohms per volt, Ifs = full scale current in amperes. R = shunt value in ohms, N = the new full scale reading divided by the original full scale reading,
both being stated in the same units,RM = meter resistance in ohms Multi-Range Shunts R1 = intermediate or tapped shunt value in ohms, R1+2 = total resistance required for the low- est scale reading wanted, RM = meter resistance in ohms, N = the new full scale reading divided by the original full scale reading,
both being stated in the same units,Voltage Multipliers R = multiplier resistance in ohms, Efs = full scale reading required in volts, Ifs = full scale current of meter in am- peres, RM = meter resistance in ohms Measuring Resistance with Milliammeter and battery* RX = unknown resistance in ohms, RM = meter resistance in ohms, or effec- tive meter resistance if a shunted
range is used,I1 = current reading with switch open, I2 = current reading with switch closed, RL = current limiting resistor of suffi- cient value to keep meter reading
on scale when switch is open*Approximately true only when current limiting
resistor is large as compared to meter resistance.
FULL SCALE
CURRENTSHUNT
RESISTANCE0-10 ma
0-50 ma
0-100 ma
0-500 ma3.0 ohms
0.551 ohms
0.272 ohms
0.0541 ohmsMeasuring Resistance–(Continued) with Milliammeter, Battery and Known Resistor RX = unkown resistance in ohms, RY = kown resistance in ohms, RM = meter resistance in ohms, I1 = current reading with switch closed, I2 = current reading with switch open, with voltmeter and Battery RX = unkown resistance in ohms, RM = meter resistance in ohms, including multiplier resistance if a multiplied
range is used,E1 = voltmeter reading with switch closed, E2 = voltmeter reading with switch open,
FULL SCALE
VOLTAGEMULTIPLIER
RESISTANCE0-10 volts
0-50 volts
0-100 volts
0-250 volts
0-500 volts
0-1,000 volts10,000 ohms
50,000 ohms
100,000 ohms
250,000 ohms
500,000 ohms
1,000,000 ohms
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Common-Emitter Amplifier Circuits
Using Transistors Only
In comparing the PNP and NPN circuits this interchange in the transistor, circuits shown here, note that the current flow in
the components of one is completely re-
versed in the other. With the vacuum tube,
this complete interchange of current and
voltage polarities does not exist. Because ofwhich have no parallel in vacuum-tube
circuitry can be produced. Nevertheless,
the circuits of transistorized equipment are
still auite similar in many respects to those
of equipment employing vacuum tubes.Using PNP Transistors With Positive
Battery Terminal GroundedWith Negative
Battery Terminal GroundedUsing NPN Transistors With Positive
Battery Terminal GroundedWith Negative
Battery Terminal Grounded
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Transistor Amplifier Circuit Configurations
With Vacuum & Tube Counterparts
The transistors of primary interest to the exclusively for most amplification purposes radio engineer and service technician are
the PNP and NPN Junction types, whose
transistor actions are identically alike, ex-
cept that symbolically, the emitter arrow
points towards the base in the PNP and
away from the base in the NPN. The
common-emitter circuits are used almostas are the common or grounded-cathode
vacuum tube circuits. The common-base
and common-grid as well as common-
collector common-plate circuits are used
more for special applications such as
impedance matching to and from audio
transmission lines, etc.PNP CONTIGURATIONS NPN CONTIGURATIONS VACUUM-TUBE CONTIGURATIONS Common emitter–Common cathode. Common base–Common grid. Common collector–Common plate.
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Transistor Alpha-Beta Relationships
Beta
ALPHA
1 0.5000 2 0.6666 3 0.7500 4 0.8000 5 0.8333
6 0.8571 7 0.8750 8 0.8889 9 0.9000 10 0.9091
11 0.9167 12 0.9231 13 0.9286 14 0.9333 15 0.9375
16 0.9412 17 0.9444 18 0.9474 19 0.9500 20 0.9524
21 0.9545 22 0.9565 23 0.9583 24 0.9600 25 0.9615
26 0.9630 27 0.9643 28 0.9655 29 0.9667 30 0.9677
31 0.9688 32 0.9697 33 0.9706 34 0.9714 35 0.9722
36 0.9730 37 0.9737 38 0.9744 39 0.9750 40 0.9756 Beta
ALPHA
41 0.9762 42 0.9767 43 0.9773 44 0.9778 45 0.9783
46 0.9787 47 0.9792 48 0.9796 49 0.9800 50 0.9804
51 0.9808 52 0.9811 53 0.9815 54 0.9818 55 0.9821
56 0.9825 57 0.9828 58 0.9831 59 0.9833 60 0.9836
61 0.9839 62 0.9841 63 0.9844 64 0.9846 65 0.9848
66 0.9851 67 0.9853 68 0.9855 69 0.9857 70 0.9859
71 0.9861 72 0.9863 73 0.9865 74 0.9867 75 0.9868
76 0.9870 77 0.9872 78 0.9873 79 0.9875 80 0.9877 Beta
ALPHA
81 0.9878 82 0.9880 83 0.9881 84 0.9882 85 0.9884
86 0.9885 87 0.9886 88 0.9888 89 0.9889 90 0.9890
91 0.9891 92 0.9892 93 0.9894 94 0.9895 95 0.9896
96 0.9897 97 0.9898 98 0.9899 99 0.9900 100 0.9901
110 0.9910 120 0.9917 125 0.9921 130 0.9924 140 0.9929
150 0.9934 160 0.9938 170 0.9942 180 0.9945 190 0.9948
200 0.9950 210 0.9953 220 0.9955 230 0.9957 240 0.9959
250 0.9960 260 0.9962 270 0.9963 280 0.9964 290 0.9966
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Transistor Formulas and Symbols
Common Emitter Configuration
Transistors can be made to amplify, detect, or to oscillate in much the same
manner as vacuum-tubes. Shown in the drawings below, is a comparison
between a triode vacuum-tube and a PNP transistor; where the transistorTriode Vacuum Tube PNP Transistor base is comparable to the tube grid, the transistor emitter is comparable to
the tube cathode, and the transistor collector is comparable to the tube plate.Transistor Formulas Transistor Symbols Input resistance, = Current gain common base Ae (Av) = Voltage gain Current Gain, Ai = Current gain (with Vc constant) Ap = Power gain Voltage Gain, B = Current gain common emitter (with Ic constant) Ib = Base current Ic = Collector current Output Resistance, Ie = Emitter current Ii = Input current Pi = Input power Power Gain, Po = Output power Ri = Input resistance Ro = Output resistance The current gain of the common base Vb = Base voltage configuration is alpha, where (with Vc constant) Vc = Collector voltage Vi = Input voltage The current gain of the common
emitter is beta, whereA direct realtionship exists between
the alpha and beta of a transistor.(with Vc constant)
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Peak, R.M.S. and Average A-C Values of E & I
Numerical Comparison Table
Peak
R.M.S.
Average
1 0.707 0.637 2 1.414 1.274 3 2.121 1.911 4 2.828 2.548 5 3.535 3.185 6 4.242 3.822 7 4.949 4.459 8 5.656 5.096 9 6.363 5.733 10 7.070 6.369 11 7.777 7.006 12 8.484 7.643 13 9.191 8.280 14 9.898 8.917 15 10.605 9.554 16 11.312 10.191 17 12.019 10.828 18 12.727 11.465 19 13.433 12.102 20 14.140 12.738 21 14.847 13.375 22 15.554 14.012 23 16.261 14.643 24 16.968 15.286 25 17.675 15.923 26 18.382 16.560 27 19.089 17.197 28 19.796 17.834 29 20.503 18.471 30 21.210 19.107 31 21.917 19.744 32 22.625 20.381 33 23.332 21.018 34 24.039 21.655 35 24.746 22.292 36 25.453 22.929 37 26.160 23.566 38 26.867 24.203 39 27.574 24.840 40 28.281 25.476 41 28.988 26.113 42 29.695 26.750 43 30.402 27.387 44 31.109 28.024 45 31.816 28.661 46 32.523 29.298 47 33.230 29.935 48 33.937 30.572 49 34.644 31.209 50 35.351 31.845 Peak
R.M.S.
Average
51 36.058 32.482 52 36.765 33.119 53 37.472 33.756 54 38.179 34.393 55 38.886 35.030 56 39.593 35.667 57 40.300 36.304 58 41.007 36.941 59 41.714 37.578 60 42.421 38.214 61 <43.128 38.851 62 43.835 39.488 63 44.542 40.125 64 45.249 40.762 65 45.956 41.399 66 46.663 42.036 67 47.370 42.673 68 48.077 43.310 69 48.784 43.947 70 49.491 44.583 71 50.198 45.220 72 50.905 45.857 73 51.612 46.494 74 52.319 47.131 75 53.026 47.768 76 53.733 48.405 77 54.440 49.042 78 55.147 49.679 79 55.854 50.316 80 56.561 50.952 81 57.268 51.589 82 57.975 52.226 83 58.682 52.863 84 59.389 53.500 85 60.096 54.137 86 60.803 54.774 87 61.510 55.411 88 62.217 56.048 89 62.924 56.685 90 63.631 57.321 91 64.338 57.958 92 65.045 58.595 93 65.752 59.232 94 66.459 59.869 95 67.166 60.506 96 67.873 61.143 97 68.580 61.780 98 69.287 62.417 99 69.994 63.054 100 70.701 63.693