• 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.

  • 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

  • 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 by
    E*I*cos Ø
    p . f . = —————- = cos Ø
    E*I
    Where:
    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 = --- ,


    R

    E

     R = --- ,


    I

    E = I*R P = I*E
    where:
    I = current in Amperes,
    R = resistance in ohms,
    E = potential across R in volts,
    P = power in watts.


  • 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
    CURRENT
    SHUNT
    RESISTANCE
    0-10   ma
    0-50   ma
    0-100 ma
    0-500 ma
    3.0       ohms
    0.551   ohms
    0.272   ohms
    0.0541 ohms
    Measuring 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
    VOLTAGE
    MULTIPLIER
    RESISTANCE
    0-10      volts
    0-50      volts
    0-100    volts
    0-250    volts
    0-500    volts
    0-1,000 volts
          10,000 ohms
    50,000 ohms
    100,000 ohms
    250,000 ohms
    500,000 ohms
    1,000,000 ohms

  • 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 of
    which 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 Grounded
    With Negative
    Battery Terminal Grounded
    Using NPN Transistors
    With Positive
    Battery Terminal Grounded
    With Negative
    Battery Terminal Grounded

  • 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 almost
    as 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.

  • 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

  • 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 transistor
    Triode 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, where
    A direct realtionship exists between
    the alpha and beta of a transistor.
      (with Vc constant)            

  • 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