I have a moderately large stock of 1/2 watt 5% resistors. 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 0.4 pf of capacitance. The resistance change which afflicts most other values could not be detected on the instrument's dial.
Note that the DC values of all 1/2 watt carbon film resistors are below the marked value. I wonder if this is by design. Carbon Films are not known for drifting up with age. The resistors were randomly chosen so it seems unlikely that 9 resistors would have all been below value. The subsequent 1 watt table will reinforce this trend.
Note how the effective resistance of resistors changes at high frequencies. This effect exists for all types of resistors tested but is less for the carbon film than for the carbon composition type. Note that the smaller resistors increase in value while the larger ones decrease in value.
Quite honestly I have no idea what mechanism would make a 100 k ohm resistor have a resistance of 23.2 k ohms at 200 MHz.
Unlike carbon composition resistors, carbon film resistors do not consist of a bulk resistive element but as the name says a film element. A cylinder of plastic that has a high insulation resistance is coated with a film of carbon and the cylinder is mounted in a lathe where a laser cuts a helix in the film. The resistance is being continuously measured and when it gets close enough The laser and lathe are turned off. The cylinder is removed from the lathe and leads are connected and the coating applied. I doubt if any of this is done by hand.
For higher precision the lathe has to turn more slowly so the process takes longer. That is one of the reasons why they cost more. The other is that the market will bear the higher price.
Column Headings and Interpretation of Data.
This information is repeated to make each page stand alone. You won't have to keep flipping back and forth between pages to understand the column headings.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 1.46E-03 which is read as 1.46 times 10 to the -3 or 1.46 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 4.59 k ohms. This is 210 times the DC value of the resistor. The Q is 4.58 times 10 to the -3. Resonance effectively disappears when Q is less than 0.707. The phase angle is only 0.26 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
1/2 Watt, 5%, Carbon Film
22 ohm. DC Value = 21.8 ohms
Frequency (MHz)
RX Meter Rp (ohms)
RX Meter Cp (pf)
Lp (H)
Xp
Q
Rs
jXs
Magnitude Z
Angle Theta (degrees)
0.50
21.0
-69.4
1.46E-03
4.59E+03
4.58E-03
21.00
9.61E-02
21.00
0.26
0.97
21.0
-68.4
3.91E-04
2.39E+03
8.78E-03
21.00
1.84E-01
21.00
0.50
1.89
21.0
-68.0
1.04E-04
1.24E+03
1.70E-02
20.99
3.57E-01
21.00
0.97
3.68
21.0
-65.8
2.84E-05
6.57E+02
3.20E-02
20.98
6.71E-01
20.99
1.83
7.17
21.1
-64.2
7.68E-06
3.46E+02
6.10E-02
21.02
1.28E+00
21.06
3.49
13.95
21.3
-64.1
2.03E-06
1.78E+02
1.20E-01
21.00
2.51E+00
21.15
6.82
27.14
22.1
-59.3
5.80E-07
9.89E+01
2.24E-01
21.05
4.70E+00
21.57
12.60
52.82
26.0
-52.7
1.72E-07
5.72E+01
4.55E-01
21.54
9.80E+00
23.67
24.45
102.78
38.5
-34.3
6.99E-08
4.51E+01
8.53E-01
22.29
1.90E+01
29.29
40.46
200.00
90.0
-14.7
4.31E-08
5.41E+01
1.66E+00
23.91
3.98E+01
46.39
58.97
47 ohm. DC Value = 46.2 ohms
Frequency (MHz)
RX Meter Rp
RX Meter Cp (pf)
Lp (H)
Xp
Q
Rs
jXs
Magnitude Z
Angle Theta
0.50
46.1
-14.9
6.80E-03
2.14E+04
2.16E-03
46.10
9.95E-02
46.10
0.12
0.97
46.1
-15.0
1.78E-03
1.09E+04
4.23E-03
46.10
1.95E-01
46.10
0.24
1.89
46.1
-14.6
4.84E-04
5.76E+03
8.01E-03
46.10
3.69E-01
46.10
0.46
3.68
46.1
-15.0
1.24E-04
2.88E+03
1.60E-02
46.09
7.38E-01
46.09
0.92
7.17
46.2
-14.7
3.35E-05
1.51E+03
3.06E-02
46.16
1.41E+00
46.18
1.75
13.95
46.3
-14.7
8.86E-06
7.76E+02
5.97E-02
46.14
2.75E+00
46.22
3.41
27.14
46.8
-14.6
2.35E-06
4.02E+02
1.17E-01
46.17
5.38E+00
46.49
6.65
52.82
48.1
-13.9
6.53E-07
2.17E+02
2.22E-01
45.84
1.02E+01
46.96
12.51
102.78
54.0
-12.0
2.00E-07
1.29E+02
4.18E-01
45.95
1.92E+01
49.81
22.71
200.00
74.3
-8.3
7.63E-08
9.59E+01
7.75E-01
46.42
3.60E+01
58.73
37.77
100 ohm. DC Value = 99.3 ohms
Frequency (MHz)
RX Meter Rp
RX Meter Cp (pf)
Lp (H)
Xp
Q
Rs
jXs
Magnitude Z
Angle Theta
0.50
101.0
-2.9
3.49E-02
1.10E+05
9.20E-04
101.00
9.29E-02
101.00
0.05
0.97
100.0
-3.1
8.63E-03
5.28E+04
1.90E-03
100.00
1.90E-01
100.00
0.11
1.89
100.0
-3.2
2.21E-03
2.63E+04
3.81E-03
100.00
3.81E-01
100.00
0.22
3.68
100.0
-3.2
5.83E-04
1.35E+04
7.41E-03
99.99
7.41E-01
100.00
0.42
7.17
100.0
-3.1
1.59E-04
7.16E+03
1.40E-02
99.98
1.40E+00
99.99
0.80
13.95
100.0
-3.1
4.20E-05
3.68E+03
2.72E-02
99.93
2.72E+00
99.96
1.56
27.14
100.1
-3.1
1.11E-05
1.89E+03
5.29E-02
99.82
5.28E+00
99.96
3.03
52.82
101.0
-3.0
3.03E-06
1.00E+03
1.01E-01
99.99
1.01E+01
100.49
5.74
102.78
102.5
-3.0
7.99E-07
5.16E+02
1.99E-01
98.61
1.96E+01
100.54
11.23
200.00
110.2
-2.8
2.26E-07
2.84E+02
3.88E-01
95.80
3.71E+01
102.75
21.19
330 ohm. DC Value = 327 ohms
Frequency (MHz)
RX Meter Rp
RX Meter Cp (pf)
Xp
Q
Rs
jXs
Magnitude Z
Angle Theta
0.50
333
0.2
-1.59E+06
2.09E-04
333.00
-6.97E-02
333.0
-0.01
0.97
333
0.1
-1.64E+06
2.04E-04
333.00
-6.78E-02
333.0
-0.01
1.89
333
0.01
-8.41E+06
3.96E-05
333.00
-1.32E-02
333.0
0.00
3.68
333
0.05
-8.64E+05
3.85E-04
333.00
-1.28E-01
333.0
-0.02
7.17
332
0.02
-1.11E+06
2.99E-04
332.00
-9.93E-02
332.0
-0.02
13.95
332
0.1
-1.14E+05
2.91E-03
332.00
-9.66E-01
332.0
-0.17
27.14
331
0.05
-1.17E+05
2.82E-03
331.00
-9.34E-01
331.0
-0.16
52.82
330
0.05
-6.03E+04
5.48E-03
329.99
-1.81E+00
330.0
-0.31
102.78
325
0.03
-5.16E+04
6.30E-03
324.99
-2.05E+00
325.0
-0.36
200.00
310
0.01
-7.96E+04
3.90E-03
310.00
-1.21E+00
310.0
-0.22
1 k ohm. DC Value = 991 ohms
Frequency (MHz)
RX Meter Rp
RX Meter Cp (pf)
Xp
Q
Rs
jXs
Magnitude Z
Angle Theta
0.50
1,010
0.5
-6.37E+05
1.59E-03
1.01E+03
-1.60E+00
1,010
-0.09
0.97
1,010
0.4
-4.09E+05
2.47E-03
1.01E+03
-2.49E+00
1,010
-0.14
1.89
1,010
0.4
-2.10E+05
4.81E-03
1.01E+03
-4.85E+00
1,010
-0.28
3.68
1,010
0.4
-1.08E+05
9.35E-03
1.01E+03
-9.44E+00
1,010
-0.54
7.17
1,010
0.4
-5.55E+04
1.82E-02
1.01E+03
-1.84E+01
1,010
-1.04
13.95
1,010
0.4
-2.85E+04
3.54E-02
1.01E+03
-3.57E+01
1,009
-2.03
27.14
1,005
0.4
-1.47E+04
6.86E-02
1.00E+03
-6.86E+01
1,003
-3.92
52.82
1,020
0.4
-7.53E+03
1.35E-01
1.00E+03
-1.36E+02
1,011
-7.71
102.78
970
0.4
-3.87E+03
2.51E-01
9.13E+02
-2.29E+02
941
-14.07
200.00
900
0.4
-1.99E+03
4.52E-01
7.47E+02
-3.38E+02
820
-24.34
3.3 k ohm. DC Value = 3.25 k ohms
Frequency (MHz)
RX Meter Rp
RX Meter Cp (pf)
Xp
Q
Rs
jXs
Magnitude Z
Angle Theta
0.50
3,330
0.5
-6.37E+05
5.23E-03
3.33E+03
-1.74E+01
3,330
-0.30
0.97
3,330
0.4
-4.09E+05
8.14E-03
3.33E+03
-2.71E+01
3,330
-0.47
1.89
3,350
0.4
-2.10E+05
1.59E-02
3.35E+03
-5.34E+01
3,350
-0.91
3.68
3,350
0.4
-1.08E+05
3.10E-02
3.35E+03
-1.04E+02
3,348
-1.78
7.17
3,340
0.4
-5.55E+04
6.02E-02
3.33E+03
-2.00E+02
3,334
-3.44
13.95
3,350
0.4
-2.85E+04
1.17E-01
3.30E+03
-3.88E+02
3,327
-6.70
27.14
3,340
0.4
-1.47E+04
2.28E-01
3.18E+03
-7.23E+02
3,257
-12.84
52.82
3,280
0.4
-7.53E+03
4.35E-01
2.76E+03
-1.20E+03
3,007
-23.53
102.78
3,090
0.4
-3.87E+03
7.98E-01
1.89E+03
-1.51E+03
2,415
-38.60
200.00
2,730
0.4
-1.99E+03
1.37E+00
9.47E+02
-1.30E+03
1,608
-53.92
10 k ohm. DC Value = 9.90 k ohms
Frequency (MHz)
RX Meter Rp
RX Meter Cp (pf)
Xp
Q
Rs
jXs
Magnitude Z
Angle Theta
0.50
10,500
0.5
-6.37E+05
1.65E-02
1.05E+04
-1.73E+02
10,499
-0.94
0.97
10,300
0.4
-4.09E+05
2.52E-02
1.03E+04
-2.59E+02
10,297
-1.44
1.89
10,300
0.3
-2.80E+05
3.68E-02
1.03E+04
-3.78E+02
10,293
-2.11
3.68
10,300
0.4
-1.08E+05
9.54E-02
1.02E+04
-9.73E+02
10,253
-5.45
7.17
10,300
0.4
-5.55E+04
1.86E-01
9.96E+03
-1.85E+03
10,127
-10.51
13.95
10,300
0.4
-2.85E+04
3.61E-01
9.11E+03
-3.29E+03
9,688
-19.86
27.14
10,200
0.4
-1.47E+04
6.96E-01
6.87E+03
-4.78E+03
8,372
-34.83
52.82
10,300
0.4
-7.53E+03
1.37E+00
3.59E+03
-4.91E+03
6,080
-53.82
102.78
8,800
0.3
-5.16E+03
1.70E+00
2.25E+03
-3.84E+03
4,452
-59.61
200.00
7,700
0.3
-2.65E+03
2.90E+00
8.17E+02
-2.37E+03
2,508
-70.99
33 k ohm. DC Value = 32.7 k ohms
Frequency (MHz)
RX Meter Rp
RX Meter Cp (pf)
Xp
Q
Rs
jXs
Magnitude Z
Angle Theta
0.50
34,500
0.5
-6.37E+05
5.42E-02
3.44E+04
-1.86E+03
34,449
-3.10
0.97
34,500
0.4
-4.09E+05
8.44E-02
3.43E+04
-2.89E+03
34,378
-4.82
1.89
35,000
0.4
-2.10E+05
1.67E-01
3.41E+04
-5.67E+03
34,525
-9.46
3.68
35,000
0.4
-1.08E+05
3.24E-01
3.17E+04
-1.03E+04
33,295
-17.96
7.17
35,000
0.4
-5.55E+04
6.31E-01
2.50E+04
-1.58E+04
29,605
-32.24
13.95
36,000
0.4
-2.85E+04
1.26E+00
1.39E+04
-1.75E+04
22,357
-51.61
27.14
33,000
0.4
-1.47E+04
2.25E+00
5.44E+03
-1.22E+04
13,396
-66.05
52.82
30,000
0.4
-7.53E+03
3.98E+00
1.78E+03
-7.09E+03
7,306
-75.90
102.78
22,300
0.4
-3.87E+03
5.76E+00
6.52E+02
-3.76E+03
3,814
-80.15
200.00
25,000
0.4
-1.99E+03
1.26E+01
1.57E+02
-1.98E+03
1,983
-85.45
100 k ohm. DC Value = 98.5 k ohms
Frequency (MHz)
RX Meter Rp
RX Meter Cp (pf)
Xp
Q
Rs
jXs
Magnitude Z
Angle Theta
0.50
100,000
0.4
-7.96E+05
1.26E-01
9.84E+04
-1.24E+04
99,220
-7.16
0.97
100,000
0.4
-4.09E+05
2.45E-01
9.44E+04
-2.31E+04
97,138
-13.74
1.89
105,000
0.4
-2.10E+05
5.00E-01
8.40E+04
-4.20E+04
93,929
-26.55
3.68
101,000
0.4
-1.08E+05
9.35E-01
5.39E+04
-5.04E+04
73,769
-43.08
7.17
102,000
0.4
-5.55E+04
1.84E+00
2.33E+04
-4.28E+04
48,753
-61.45
13.95
101,000
0.4
-2.85E+04
3.54E+00
7.46E+03
-2.64E+04
27,450
-74.23
27.14
95,000
0.4
-1.47E+04
6.48E+00
2.21E+03
-1.43E+04
14,487
-81.23
52.82
80,000
0.4
-7.53E+03
1.06E+01
7.03E+02
-7.47E+03
7,500
-84.62
102.78
36,000
0.4
-3.87E+03
9.30E+00
4.12E+02
-3.83E+03
3,849
-83.86
200.00
23,200
0.3
-2.65E+03
8.75E+00
2.99E+02
-2.62E+03
2,635
-83.48