The Importance of LCR Meter Sweeping Resonant Frequency
Author: Sean Chen
Product Marketing Department
The formula of impedance is as shown in formula 1. From this formula, we can know the role of three passive components played in impedance. The real part of impedance is resistance, and the imaginary part is reactance that includes capacitance and inductance. Passive components in the real environment all have unideal situations. Pure resistance, pure inductance, and pure capacitance only appear when discussing ideal conditions in textbooks. Practical applications must consider the unideal conditions caused by parasitic components, because parasitic components cause inductance to be existed in capacitance and inductance in capacitance. The reactance characteristics will be changed after the resonant frequency occurs. Hence, it is important to understand and measure the resonant frequency.
The reactance formula of capacitance is as shown in formula 2. As the frequency f increases, the XC reactance will become smaller. Capacitance allows high frequencies to pass and blocks low frequencies. For DC, capacitor is an open circuit.
The reactance formula of inductance is as shown in formula 3. As the frequency f increases, the XL reactance will become larger. Inductance allows low frequencies to pass and blocks high frequencies. For DC, inductor is a short circuit.
1. What is resonance and resonant frequency?
There are capacitance and inductance in the circuit. When the inductive reactance is equal to the capacitive reactance, it is called resonance (Formula 4). Through this definition, the resonant frequency can be calculated (Formula 5):
*The derivation process is as follows:
2. Why is this resonant frequency important for measuring passive component characteristics?
We can say that when the frequency applied to this component is lower than the resonant frequency, it generally responds in accordance with the ideal component characteristics. However, once the frequency applied is higher than the resonant frequency, it will show the opposite characteristics, that is, the capacitive reactance will become inductive reactance and vice versa.
Take Figure A as an example, which is the frequency response diagram of a capacitor. The horizontal axis is the applied frequency, and the vertical axis is the reactance corresponding to the component. The red straight diagonal line is the ideal component characteristic. The higher the frequency, the smaller the reactance (can be obtained from Formula 2). But in fact, when the frequency is higher than the resonant frequency, the reactance rises instead of falling as the frequency increases, that is, it begins to show reversal characteristics.
Figure A: Comparison of the impedance curve of an ideal capacitor and the actual characteristics before and after the resonance frequency
Then why does the reactance rise instead of falling? In Figure B/C, you can see the parasitic inductance connected in series on a capacitor. When it is higher than the resonant frequency, the reactance produced by the parasitic inductance is greater than the reactance of the capacitance. Because it is a series connected parasitic inductance, the equivalent reactance will increase. In other words, the parasitic inductance at this time becomes the main player, so the frequency response characteristics of the inductance will appear.
Figure B: Equivalent circuit of a SMD capacitor
Figure C: Equivalent circuit of a lead capacitor
Taking Figure D as an example, it is the frequency response of the inductive component. The red straight diagonal line is the ideal inductor characteristic. The higher the frequency, the greater the reactance (can be obtained from Formula 3). But in fact, when the frequency increases to the resonant frequency, the reactance does not increase but decreases as the frequency increases, that is, it begins to show reversal characteristics.
Figure D: Comparison of the impedance curve of an ideal inductor and the actual characteristics before and after the resonance frequency
Why does the reactance begin to decrease instead of rising? The reason is the same as above-mentioned. You can see the parasitic capacitance on the inductor in Figure E. When it is higher than the resonant frequency, the reactance generated by the parasitic capacitance is smaller than the reactance of the inductor, and the current will flow to the place with the least resistance, so the current is diverted to the path of the parasitic capacitance. In short, the parasitic capacitance at this time becomes the major player, so the frequency response characteristics of the capacitor will appear.
Figure E: Equivalent circuit of inductor (without core)
3. How to analyze resonant frequency?
Component characteristics refer to the performance of components under specific conditions (commercial specifications, automotive specifications, military specifications), so the measurement conditions must be greater than or equal to the actual application conditions. The reactance characteristics of inductors and capacitors at different frequencies are different. Although the production process of components from the same batch is highly consistent, there are still slight differences in the values of parasitic components. It is also necessary to confirm whether the components are operating after the resonant frequency (due to the change in reactance characteristics). For the above requirement, the conventional LCR meter for single point frequency measurement cannot meet the demand. In the past, measurements that could be performed through frequency sweep were only available on expensive impedance analyzers.
The current LCR meter has evolved to have the capability of frequency sweep and parasitic component evaluation of an impedance analyzer. Figure F is the frequency sweep result of a capacitive component measured by GW Instek LCR-8200A. The sweep frequency range is from 1MHz to 27.5MHz. The result of the sweep shows the corresponding impedance value Z and phase change within the frequency range. The horizontal axis is the applied frequency.
It should be noted that the log scale is usually used here. The vertical axis is the impedance and phase corresponding to the component; the yellow line is the impedance value change on the logarithmic scale, while the green line is the phase change on the linear scale. From the impedance value at the reversal of the change, it can be seen that the resonant frequency of this component is about 18MHz. That is, the component characteristics of the capacitor are maintained under the frequency of 18MHz. Beyond 18MHz, it will switch to the inductive characteristic (changed to be dominated by parasitic inductance).
Figure F: Application example of characteristic curve sweeping
If you want to analyze further, you can use the equivalent circuit model analysis function (Equivalent Circuit Analysis). The equivalent circuit model analysis function is to call out the model derived from the theoretical value and compare it through curve fitting. When the measured value approaches the theoretical value, the value of the parasitic component can be obtained.
As shown in Figure G, you can first call out the close equivalent circuit model D (L1 C1 R1 are connected in series), and the theoretically derived model curve will appear. Then you can slowly adjust the parameters of the equivalent circuit model L1 C1 R1 to approximate the actual measurement value. When the theoretical curve is almost identical to the real result curve, L1 R1 at this time are closest to the value of the parasitic element. This is close to the function of the impedance analyzer.
Figure G: Parasitic component evaluation
GW Instek LCR-8200A series provides a sweeping frequency of up to 50MHz and seven equivalent circuit models to assist in the analysis of parasitic components. For more product information, please click on the following link:
https://www.gwinstek.com/en-global/products/detail/LCR-8200
Contact us:
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Good Will Instrument Co., Ltd
No. 7-1, Jhongsing Road, Tucheng Dist.,
New Taipei City 23678, Taiwan R.O.C
Email: marketing@goodwill.com.tw