Anti-resonance peak calculation of 2 capacitors in parallel - Page 1
Forum section: electronics / beginners

author: Freshman
author_rank: Regular Contributor
timestamp: March 24, 2025, 11:51:29 am
content: In this tool (https://pdntool.com/app/), I am using 2 capacitors in parallel. 1uF, 50mohm and 1uH. Capacitance, ESR and ESL respectively. The other caps values are 10uF, 50mohm and 1uH. The SRF of 1st capacitor lies around 50kHz and the second is 159kHz.However, there is an anti-resonance peak that occurs whose frequency is around 115kHz. Whats the formula to calculate the frequency of that anti-resonance peak?

author: jwet
author_rank: Frequent Contributor
timestamp: March 24, 2025, 08:32:01 pm
content: The quick answer for a rough estimate is the geometric mean = square root (f1 * f2). For your example, this gives 89 KHz vs your measured? 115K.This is way more complicated than it seems. Its a major rabbit hole. What really happens is that there is something called frequency splitting that goes on that you can google. It depends on the coupling between the two resonators. In your case, that might just be a short trace but it does have a small inductance does have some coupling factor.The weird thing is if you take 2 identical resonators and couple them together, you'll get this splitting. This is used to positive effect in RF filters mostly.If you do a complete analysis, you'll see that the circuits interact and you get cross products of the First L with the second C and Second L with the first C, these often create series resonances , etc. In this day and age, I would throw it all at spice and play with it.Edited later- formula shouldn't have squared values.

author: TimFox
author_rank: Super Contributor
timestamp: March 24, 2025, 08:56:21 pm
content: SPICE in .AC mode can handle this interesting question (overcoupled resonances) nicely.A good lab demonstration:I set up two physically large inductors on a wood table, one tuned with a variable capacitor and the other with a fixed capacitor. The free resonance of the fix-tuned coil was around 7 MHz (iirc). Both circuitQvalues were high.I connected a swept-frequency spectrum analyzer as a scalar analyzer, driving one coil from the tracking generator and connecting the second to the SA input (both through capacitive impedance matching).With the variable tuning coil far tuned below the fix-tuned resonance, the “double-hump” overall response showed the expected narrow peaks from the two resonant circuits, through the mutual-inductance coupling.Slowly tuning the variable circuit to higher frequency: the lower-frequency peak moved upward towards the second peak, but never reached it. The second peak started to move upward away from the lower peak, which stopped near the original frequency of the second peak, while the second peak continued to move away.I remembered an analogous effect in atomic scattering, called “avoided crossing”, where the atomic energy levels performed in a manner similar to these RLC resonances as the two nuclei approached each other and then flew apart.For a practical use of two nearby coils in MRI, I designed a capacitive network to counteract the mutual inductance and obtain a single peak response.

author: tszaboo
author_rank: Super Contributor
timestamp: March 24, 2025, 11:04:14 pm
content: Quote from: Freshman on March 24, 2025, 11:51:29 amNano Henry, right? Not Micro.Unless your capacitor is actually an inductor.

author: MathWizard
author_rank: Super Contributor
timestamp: March 26, 2025, 03:33:26 am
content: By hand I would try this type of stuff, with partial fractions and poles and zero's and maybe impedance graphs.I use a spreadsheet, and have automated a bunch of this stuff. Now some people would use a proper math program, but a spreadsheet can do it.