I don't have a large stock of carbon composition resistors anymore. I originally decided to select values in a geometric series of 10, 33, 100, 330, etc. Then I looked at the Boonton 250A RX meter and noticed that the resistance dial only goes down to 15 ohms. Then I realized that something in the neighborhood of 50 ohms would give useful information to those trying to construct low power terminations for impedance matched systems.After attempting to make a measurement on the 15 ohm resistor I found it to be so inductive that it was beyond the range of the RX meter even at the lowest frequency. So my first two resistors are 22 ohm and 47 ohm. The sequence held for the rest of them up to 100 k ohm. At that resistance the dial on the RX meter has a mark at 100 k and the next higher mark is at infinity. There are no intermediate marks and interpolation between them is impossible. I tested a few values going up to 10 Meg ohms and found their reactive component to be about 0.6 pf of capacitance. The resistance change which afflicts most other values could not be detected on the instrument's dial.
In going through my old stock I found a couple of rather unique resistors. They are 4 watt. I put one, a 33 k ohm resistor into the test lot along with a 33k ohm 1 watt. They are shown in the photo below.
Note that the DC values of all carbon composition resistors, with the exception of the 100 k ohm, are above the marked value. These resistors range in age from 20 to 70 years. This information reinforces a common procedure used by those who restore old electronics. They always test or sometimes just replace carbon comp resistors.
Note how the effective resistance of resistors changes at high frequencies. This effect exists for all types of resistors tested but is largest for the carbon composition type. Note that the smaller resistors increase in value while the larger ones decrease in value.
I have imagined a group of development engineers in the 1940s trying to design a wide band amplifier for use in radar or nuclear radiation measurement. Skin effect was well known by then so they would have expected resistors to increase in value at high frequencies. The resistive element in a carbon comp resistor is a cylinder of the carbon and clay mixture that one would think would display the same skin effect as a copper wire of the same dimensions. They must have been quite puzzled when the amplifier persisted in rolling off at the high end even after all capacitances in the circuit had been accounted for. The RX meter may have been invented to answer the questions raised by such an amplifier development project.
Quite honestly I have no idea what mechanism would make a 100 k ohm resistor have a resistance of 10 k ohms at 200 MHz.
Column Headings and Interpretation of Data.
Frequency (MHz). The first column is Frequency in MHz. See the main resistors page for an explanation of why the numbers are what they are instead of being nice round numbers.RX Meter Rp (ohms). This column is the transcription of the Rp (parallel resistance in ohms) dial reading on the RX Meter. When it comes to interpreting how a resistor will behave in a circuit this is one of the two most important parameters. If the RX meter reads 300 ohms at a given frequency then you can count on it being a 300 ohm resistor in parallel with what ever reactance is indicated by the Cp dial.
RX Meter Cp (pf). This column is the transcription of the Cp (effective parallel capacitance in picofarads) dial reading on the RX meter. Negative values indicate inductance. The indicated capacitance is that which will resonate with the effective inductance at the test frequency.
Calculations.
All columns to the right are values that are calculated with formulas in the cells.Lp (H). The formula in this cell calculates the effective inductance in Henrys of the resistor.
Lp = Xp/(2 Pi f)
Where Xp is the effective parallel reactance calculated in the next cell to the right, and f is the test frequency. XL evaluates formulae in the order referenced rather than simply working from left to right. Good thing. A negative capacitance reading on the RX Meter indicates that the reactive element is really inductive. The effective inductance is that which will resonate with the indicated capacitance at the frequency used in the test. The cells are formatted in scientific notation. The first cell in this column in the first table has the entry 1.44E-03 which is read as 1.44 times 10 to the -3 or 1.44 millihenrys. If the Cp cell contains a positive value of capacitance this cell in this column is blank.
When using one of these low value resistors you might be tempted to tune out the inductance with a paralleled capacitor. This might be done if the resistor is being used in the signal path of a narrow band amplifier. However if it is used in a wide band amplifier, tuning out the inductance at one frequency will make for increased capacitance at higher frequencies. Although the inductance of the 22 ohm resistor at 0.5 MHz seems like a lot, take a sneak peak ahead at the "Xp", "Q", and "Angle Theta" columns. These have not been explained yet but I won't tell if you won't. Xp is 4.52 k ohms. This is 188 times the DC value of the resistor. The Q is 5.9 times 10 to the -3. Resonance effectively disappears when Q is less than 0.707. The phase angle is only 0.29 degrees. This is so small as to have no measurable effect on the performance of an amplifier.
Xp. This value is calculated from the formula,
Xp = -1/(2 pi f Cp)
Where f is frequency and Cp is the capacitance from the Cp column. The minus sign arises from the fact that I leads E in a capacitor. When the lagging E phasor is divided by the leading I phasor the resulting impedance phasor is pointing downward which makes it negative. The impedance phasor for an inductor points upward which is positive. As these signs are opposite to the Cp dial a minus sign is inserted in the equation to make the answer come out right.
This is the other important datum for interpreting the results of a measurement. If Xp is 100 times the value of Rp the phase shift is only 0.57 degrees and you are very safe in assuming negligible effect on performance. For a ratio of 10 to 1 the phase shift is still only 5.7 degrees but if you have more than one such effect in a string of cascaded networks the effect can accumulate fast and seriously degrade performance.
Q. The value of Q, the quality factor, is calculated by the formula,
Q = Rp/ABS(Xp).
Where Rp is the dial reading of the parallel resistive component and Xp is the calculated parallel reactive component of the capacitive or inductive dial reading. The ABS function removes the negative sign where it occurs so the Q will not change signs as the reactance does.
Q is not as important for interpretation as some other values but is a necessary intermediate value for calculating the series components of impedance.
Rs. Rs is the calculated effective series resistance when the network is transformed from a parallel circuit to a series circuit. It is calculated from the formula,
Rs = Rp/(1+Q^2).
Where Rp is the Rp dial reading and Q was calculated earlier.
This value is useful in combination with jXs when calculations must be made using the results of measurements made with the RX meter. This is the standard R + jX way of representing impedances in electric circuit calculations.
jXs. jXs is the calculated effective series reactance when the network is transformed from a parallel circuit to a series circuit. It is calculated from the formula,
Xs = Xp Q^2/(1+Q^2).
Where Xp and Q were calculated earlier. See Rs above for interpretation.
Impedance Z, and Angle Theta. For calculations impedance can also be expressed as Z at an angle of Theta. These values are given to aid the user should this form be needed. They are calculated by,
Z = SQRT(Rs^2 + Xs^2), and
Theta = ARC TAN(Xs/Rs).
Back to Resistor's Behavior Introductory Page.
Resistor Behavior at MF, HF, and VHF
Carbon Composition
22 ohm, 2 watt, 10%. DC Value = 24.1 ohms
Frequency (MHz)
RX Meter Rp (ohms)
RX Meter Cp (pf)
Lp (H)
Xp
Q
Rs
jXs
Magnitude Z
Angle Theta (degrees)
0.50
23.0
-70.4
1.44E-03
4.52E+03
5.09E-03
23.00
1.17E-01
23.00
0.29
0.97
23.3
-67.0
3.99E-04
2.44E+03
9.54E-03
23.30
2.22E-01
23.30
0.55
1.89
23.3
-70.0
1.01E-04
1.20E+03
1.94E-02
23.29
4.52E-01
23.30
1.11
3.68
23.3
-69.6
2.68E-05
6.21E+02
3.75E-02
23.27
8.73E-01
23.28
2.15
7.17
23.3
-67.8
7.27E-06
3.27E+02
7.12E-02
23.18
1.65E+00
23.24
4.07
13.95
23.8
-64.4
2.02E-06
1.77E+02
1.34E-01
23.38
3.14E+00
23.59
7.65
27.14
25.2
-65.8
5.22E-07
8.91E+01
2.83E-01
23.33
6.60E+00
24.25
15.79
52.82
31.0
-53.5
1.70E-07
5.63E+01
5.50E-01
23.79
1.31E+01
27.16
28.83
102.78
53.0
-31.0
7.73E-08
5.00E+01
1.06E+00
24.93
2.65E+01
36.35
46.70
200.00
123.0
-12.1
5.23E-08
6.58E+01
1.87E+00
27.35
5.11E+01
58.00
61.87
47 ohm, 1 watt, 5%. DC Value = 56.1 ohms
Frequency (MHz)
RX Meter Rp
RX Meter Cp (pf)
Lp (H)
Xp
Q
Rs
jXs
Magnitude Z
Angle Theta
0.50
56.1
-12.4
8.17E-03
2.57E+04
2.19E-03
56.10
1.23E-01
56.10
0.13
0.97
56.1
-12.6
-2.12E-03
1.30E+04
4.32E-03
56.10
2.42E-01
56.10
0.25
1.89
56.1
-12.9
-5.48E-04
6.52E+03
8.61E-03
56.10
4.83E-01
56.10
0.49
3.68
56.2
-12.8
-1.46E-04
3.38E+03
1.67E-02
56.18
9.36E-01
56.19
0.95
7.17
56.3
-13.0
-3.79E-05
1.71E+03
3.30E-02
56.24
1.85E+00
56.27
1.89
13.95
56.5
-11.9
-1.09E-05
9.59E+02
5.89E-02
56.30
3.32E+00
56.40
3.37
27.14
57.0
-12.0
-2.86E-06
4.89E+02
1.17E-01
56.23
6.56E+00
56.62
6.65
52.82
59.0
-11.8
-7.69E-07
2.55E+02
2.31E-01
56.01
1.29E+01
57.49
13.01
102.78
66.6
-10.0
-2.40E-07
1.55E+02
4.30E-01
56.20
2.42E+01
61.18
23.27
200.00
99.5
-7.7
-8.22E-08
1.03E+02
9.63E-01
51.64
4.97E+01
71.68
43.91
100 ohm, 2 watt, 10%. DC Value = 102.9 ohms
Frequency (MHz)
RX Meter Rp
RX Meter Cp (pf)
Lp (H)
Xp
Q
Rs
jXs
Magnitude Z
Angle Theta
0.50
103.8
-0.4
2.53E-01
7.96E+05
1.30E-04
103.80
1.35E-02
103.80
0.01
0.97
103.9
-0.5
5.35E-02
3.27E+05
3.18E-04
103.90
3.30E-02
103.90
0.02
1.89
104.0
-0.8
8.83E-03
1.05E+05
9.90E-04
104.00
1.03E-01
104.00
0.06
3.68
103.9
-1.1
1.70E-03
3.93E+04
2.65E-03
103.90
2.75E-01
103.90
0.15
7.17
103.8
-1.0
4.93E-04
2.22E+04
4.68E-03
103.80
4.85E-01
103.80
0.27
13.95
103.5
-1.3
1.00E-04
8.78E+03
1.18E-02
103.49
1.22E+00
103.49
0.68
27.14
103.0
-1.3
2.64E-05
4.51E+03
2.28E-02
102.95
2.35E+00
102.97
1.31
52.82
102.2
-1.4
6.49E-06
2.15E+03
4.75E-02
101.97
4.84E+00
102.08
2.72
102.78
100.5
-1.6
1.50E-06
9.68E+02
1.04E-01
99.43
1.03E+01
99.96
5.93
200.00
99.5
-2.1
3.02E-07
3.79E+02
2.63E-01
93.08
2.44E+01
96.24
14.71
330 ohm, 1 watt, 10%. DC Value = 336 ohms
Frequency (MHz)
RX Meter Rp
RX Meter Cp (pf)
Xp
Q
Rs
jXs
Magnitude Z
Angle Theta
0.50
342
1.9
-1.68E+05
2.04E-03
342.00
-6.98E-01
342.00
-0.12
0.97
342
1.6
-1.02E+05
3.35E-03
342.00
-1.14E+00
342.00
-0.19
1.89
342
1.3
-6.47E+04
5.29E-03
341.99
-1.81E+00
342.00
-0.30
3.68
340
1.0
-4.32E+04
7.87E-03
339.98
-2.68E+00
339.99
-0.45
7.17
340
0.8
-2.78E+04
1.23E-02
339.95
-4.16E+00
339.97
-0.70
13.95
340
0.6
-1.90E+04
1.79E-02
339.89
-6.08E+00
339.95
-1.02
27.14
338
0.6
-9.77E+03
3.46E-02
337.60
-1.17E+01
337.80
-1.98
52.82
333
0.6
-5.02E+03
6.63E-02
331.54
-2.20E+01
332.27
-3.79
102.78
322
0.5
-3.10E+03
1.04E-01
318.56
-3.31E+01
320.27
-5.94
200.00
292
0.4
-1.99E+03
1.47E-01
285.84
-4.20E+01
288.90
-8.35
1 k ohm, 1 watt, 10%. DC Value = 1051 ohms
Frequency (MHz)
RX Meter Rp
RX Meter Cp (pf)
Xp
Q
Rs
jXs
Magnitude Z
Angle Theta
0.50
1,070
1.2
-2.65E+05
4.03E-03
1.07E+03
-4.32E+00
1,070
-0.23
0.97
1,070
1.2
-1.36E+05
7.85E-03
1.07E+03
-8.40E+00
1,070
-0.45
1.89
1,070
1.2
-7.01E+04
1.53E-02
1.07E+03
-1.63E+01
1,070
-0.88
3.68
1,060
1.2
-3.60E+04
2.94E-02
1.06E+03
-3.12E+01
1,060
-1.69
7.17
1,060
1.1
-2.02E+04
5.25E-02
1.06E+03
-5.55E+01
1,059
-3.01
13.95
1,060
1.0
-1.14E+04
9.29E-02
1.05E+03
-9.76E+01
1,055
-5.31
27.14
1,040
1.0
-5.86E+03
1.77E-01
1.01E+03
-1.79E+02
1,024
-10.06
52.82
1,010
0.9
-3.35E+03
3.02E-01
9.26E+02
-2.79E+02
967
-16.79
102.78
930
0.8
-1.94E+03
4.80E-01
7.56E+02
-3.63E+02
838
-25.66
200.00
795
0.8
-9.95E+02
7.99E-01
4.85E+02
-3.88E+02
621
-38.63
3.3 k ohm, 2 watt, 10%. DC Value = 3.98 k ohms
Frequency (MHz)
RX Meter Rp
RX Meter Cp (pf)
Xp
Q
Rs
jXs
Magnitude Z
Angle Theta
0.50
4,100
1.3
-2.45E+05
1.67E-02
4.10E+03
-6.86E+01
4,099
-0.96
0.97
4,100
1.1
-1.49E+05
2.76E-02
4.10E+03
-1.13E+02
4,098
-1.58
1.89
4,100
1.1
-7.64E+04
5.36E-02
4.09E+03
-2.19E+02
4,094
-3.07
3.68
4,080
1.2
-3.60E+04
1.13E-01
4.03E+03
-4.57E+02
4,054
-6.47
7.17
4,020
1.1
-2.02E+04
1.99E-01
3.87E+03
-7.70E+02
3,943
-11.26
13.95
3,950
0.8
-1.43E+04
2.77E-01
3.67E+03
-1.02E+03
3,807
-15.48
27.14
3,790
0.9
-6.51E+03
5.82E-01
2.83E+03
-1.65E+03
3,276
-30.19
52.82
3,500
0.8
-3.77E+03
9.29E-01
1.88E+03
-1.75E+03
2,564
-42.90
102.78
3,040
0.8
-1.94E+03
1.57E+00
8.77E+02
-1.38E+03
1,633
-57.51
200.00
2,320
0.7
-1.14E+03
2.04E+00
4.49E+02
-9.17E+02
1,021
-63.89
10 k ohm, 1 watt, 10%. DC Value = 10.55 k ohms
Frequency (MHz)
RX Meter Rp
RX Meter Cp (pf)
Xp
Q
Rs
jXs
Magnitude Z
Angle Theta
0.50
11,200
1.5
-2.12E+05
5.28E-02
1.12E+04
-5.89E+02
11,184
-3.02
0.97
11,100
1.4
-1.17E+05
9.50E-02
1.10E+04
-1.05E+03
11,050
-5.43
1.89
11,000
1.2
-7.01E+04
1.57E-01
1.07E+04
-1.69E+03
10,867
-8.92
3.68
10,800
1.2
-3.60E+04
3.00E-01
9.91E+03
-2.97E+03
10,345
-16.70
7.17
10,400
1.1
-2.02E+04
5.15E-01
8.22E+03
-4.23E+03
9,245
-27.26
13.95
9,600
0.9
-1.27E+04
7.57E-01
6.10E+03
-4.62E+03
7,653
-37.14
27.14
8,600
0.9
-6.51E+03
1.32E+00
3.14E+03
-4.14E+03
5,193
-52.85
52.82
7,200
0.8
-3.77E+03
1.91E+00
1.55E+03
-2.96E+03
3,337
-62.38
102.78
5,580
0.8
-1.94E+03
2.88E+00
5.99E+02
-1.73E+03
1,829
-70.87
200.00
3,680
0.7
-1.14E+03
3.24E+00
3.21E+02
-1.04E+03
1,086
-72.83
33 k ohm, 1 watt, 10%. DC Value = 36.0 k ohms
Frequency (MHz)
RX Meter Rp
RX Meter Cp (pf)
Xp
Q
Rs
jXs
Magnitude Z
Angle Theta
0.50
37,000
1.6
-1.99E+05
1.86E-01
3.58E+04
-6.65E+03
36,376
-10.54
0.97
35,000
1.4
-1.17E+05
3.00E-01
3.21E+04
-9.62E+03
33,528
-16.68
1.89
34,000
1.3
-6.47E+04
5.26E-01
2.66E+04
-1.40E+04
30,094
-27.73
3.68
32,000
1.2
-3.60E+04
8.89E-01
1.79E+04
-1.59E+04
23,917
-41.63
7.17
20,700
1.0
-2.22E+04
9.32E-01
1.11E+04
-1.03E+04
15,140
-43.00
13.95
23,000
0.9
-1.27E+04
1.81E+00
5.36E+03
-9.72E+03
11,102
-61.14
27.14
18,600
0.8
-7.33E+03
2.54E+00
2.50E+03
-6.34E+03
6,819
-68.49
52.82
14,000
0.8
-3.77E+03
3.72E+00
9.45E+02
-3.51E+03
3,637
-74.94
102.78
10,000
0.7
-2.21E+03
4.52E+00
4.67E+02
-2.11E+03
2,160
-77.53
200.00
5,690
0.7
-1.14E+03
5.01E+00
2.18E+02
-1.09E+03
1,115
-78.70
33 k ohm, 4 watt, 10%. DC Value = 37.6 k ohms
Frequency (MHz)
RX Meter Rp
RX Meter Cp (pf)
Xp
Q
Rs
jXs
Magnitude Z
Angle Theta
0.50
38,000
3.2
-9.95E+04
3.82E-01
3.32E+04
-1.27E+04
35,498
-20.91
0.97
35,000
2.8
-5.84E+04
5.99E-01
2.58E+04
-1.54E+04
30,024
-30.93
1.89
31,000
2.6
-3.23E+04
9.59E-01
1.62E+04
-1.55E+04
22,377
-43.79
3.68
21,500
2.2
-1.96E+04
1.09E+00
9.78E+03
-1.07E+04
14,499
-47.59
7.17
17,900
1.7
-1.31E+04
1.37E+00
6.22E+03
-8.52E+03
10,550
-53.89
13.95
14,500
1.2
-9.51E+03
1.53E+00
4.36E+03
-6.65E+03
7,951
-56.75
27.14
12,050
1.2
-4.89E+03
2.47E+00
1.70E+03
-4.20E+03
4,528
-67.93
52.82
10,700
1.1
-2.74E+03
3.91E+00
6.58E+02
-2.57E+03
2,654
-75.64
102.78
8,350
1.0
-1.55E+03
5.39E+00
2.78E+02
-1.50E+03
1,523
-79.49
200.00
5,990
1.0
-7.96E+02
7.53E+00
1.04E+02
-7.82E+02
789
-82.43
100 k ohm, 1 watt, 10%. DC Value = 110.9 k ohms
Frequency (MHz)
RX Meter Rp
RX Meter Cp (pf)
Xp
Q
Rs
jXs
Magnitude Z
Angle Theta
0.50
110,000
1.3
-2.45E+05
4.49E-01
9.15E+04
-4.11E+04
100,340
-24.19
0.97
110,000
1.1
-1.49E+05
7.40E-01
7.11E+04
-5.26E+04
88,435
-36.49
1.89
100,000
1.0
-8.41E+04
1.19E+00
4.14E+04
-4.93E+04
64,348
-49.95
3.68
80,000
1.0
-4.32E+04
1.85E+00
1.81E+04
-3.34E+04
38,013
-61.63
7.17
60,000
0.9
-2.47E+04
2.43E+00
8.68E+03
-2.11E+04
22,815
-67.65
13.95
40,700
0.6
-1.90E+04
2.14E+00
7.29E+03
-1.56E+04
17,228
-64.96
27.14
35,000
0.7
-8.38E+03
4.18E+00
1.90E+03
-7.92E+03
8,146
-76.54
52.82
28,000
0.7
-4.30E+03
6.50E+00
6.46E+02
-4.21E+03
4,255
-81.26
102.78
16,900
0.6
-2.58E+03
6.55E+00
3.85E+02
-2.52E+03
2,551
-81.32
200.00
10,000
0.6
-1.33E+03
7.54E+00
1.73E+02
-1.30E+03
1,315
-82.45