The coil's self-capacitance measurement by multifrequency method — online calculator

Firstly, we would like to draw your attention to the fact that the concept of “self-capacitance of an inductance coil” is not well-defined and is often confused with the concept of “parasitic capacitance”, which includes all sorts of assembly and external parasitic capacitance of the radio engineering design. In any case, the value of the self-capacitance depends on many factors, including the winding form (multilayer, single-layer), the influence of the coil-former, core, shield, frequency, etc. You can read more about the investigation of the self-capacitance of an unloaded single-layer air-core coil here.

To find the coil's self-capacitance, you need at least a grid dip oscillator or standard-frequency generator. Radio amateurs usually calculate the self-capacitance using the dual-frequency method. From the beginning, the first external capacitor C₁ is connected to the coil and the resonant frequency of the resulting oscillating circuit is measured: f₁. Then the same is done with the second circuit capacitor C₂. Based on the results of these measurements, both the self-inductance and the self-capacitance of the coil are calculated. However, measuring only two points can lead to completely unacceptable errors, which is described in more detail below in the text. In this calculator, the self-capacitance is calculated based on the results of three to ten similar measurements, which allows us to hope for a more reliable result.

Important! Accuracy and reliability of the result when processing statistical data are different things. After the ± sign, the confidence interval is displayed, in which the exact value of the result is admittedly to be. At the same time, if some measurement data are fault (unreliable), the result may also be unreliable despite the small value of the confidence interval.

Although calculating the coil's self-capacitance using several measurement points is more reliable, it cannot be fully reliable. The reasons for this are listed below, as well as recommendations for more accurate measurements:

• It is significant to understand that we are not actually looking for the self-capacitance of the unloaded coil, but the parasitic capacitance of the all measuring circuit. In this case, the mounting capacitance of the measuring board and the input capacitance of the measuring device are usually summed up with the self-capacitance of the coil. The mutual induction of the measuring equipment with the coil may also have an effect.
• Large self-loss of the coil (large ESR value or, correspondingly, low Q-factor), as well as large insertion losses from the measuring circuit lead to unreliable results.
• The value of the coil's self-capacitance is not constant and, as we noted above, depends on the frequency. To reduce the influence of this factor, we should to select measurement frequencies an order of magnitude lower than the coil's self-resonance frequency.
• The accuracy of measurements has a great influence. Especially at points where the small value of the capacitance of the oscillating circuit capacitor is comparable to the coil's self-capacitance. Hence, the conclusion that you cannot do without good capacitance and frequency meters. If you simply take the nominal value on the capacitor label with a tolerance of ±20%, the calculation result will most likely be unreliable.
• The veracity of the self-inductance calculation is always much greater than the veracity of the calculation of the coil's self-capacitance.
• The greatest reliability and accuracy can be achieved by using higher quality measuring instruments, such as a Q-meter.

More about the calculation algorithm. The old Radio-Engineers Handbooks offer a graphical method to looking for the value of the coil's self-capacitance based on multiply measurements. The X axis shows the value of the oscillating circuit capacitor capacitance C, and the Y axis shows the corresponding value proportional to 1 / f². A straight line connects the resulting points. The point of intersection of this line with the X axis in the negative area shows the value of the coil's self-capacitance. Below is an example graph based on the default data from our calculator:

By drawing a straight line through approximately all measurement points, we can estimate the coil's self-capacitance of slightly more than 5 pF. If we do the same for two points (C4, C5), we will get a result of approximately 20 pF. It is obvious from the graph that the second result is far from the truth, i.e., unreliable. The same result when using these two measurement points you will get in the calculator based on the dual frequency method. Therefore, using multiply measurement points is preferable. This calculator uses a numerical algorithm based on the mathematical “least squares method” designed to process data arrays, and does approximately the same as a line on the graph. However, if we see on a graph that someone point has deviated greatly from the general line, we can recognize such a measurement as untrusted and exclude it. The calculator does not do this, so a single erroneous measurement can lead to a failed solution or to an unreliable result. This circumstance should be kept in mind. Although this is simply an exceptional case of a gross error, from which the dual-frequency method is also not insured. At the same time, the multi-frequency method allows leveling out small measurement inaccuracies, which is illustrated in the graph above.

References:

1. Measurement of Coil Self Capacitance, Terman's method: Music Electronics Forum
2. Coil Distributed Capacitance, VK2ZAY: One example of a coil self-capacitance calculator based on the dual-frequency measurement method.
3. Measurement/calculation of self-capacitance and inductance of a medium-wave loop antenna: Copyright 2013, 2023 Robert Weaver;