# Ringing in inductively coupled coils

My circuit consists of two inductively coupled inductors. A 40 kHz 600 mV sine voltage is applied to the primary inductor. The induced voltage in the secondary inductor shows some ringing in the area of its own resonant frequency (1 MHz). A capacitor with 180 pF placed in parallel to the secondary inductor gets rid of most of the ringing. The voltage is measured with an active differential probe.

What exactely is causing this ringing? And how does the capacitor help to get rid of it? I see that the capacitor lowers the resonant frequency of the secondary circuit. But I don't exactely understand how it reduces the ringing.

Impedance of the primary inductor:

Impedance of the secondary inductor:

Impedance of the secondary inductor with 180 pF in parallel:

Voltage across the secondary inductor without capacitor:

Voltage across the secondary inductor with 180 pF parallel:

Schematic:

Spectrum of signal source:

• All inductors have distributed capacitance. So ringing is "logical". If you put another capacitor across, you increase this capacity and lower the frequency of ringing ... It is also a mean for measuring distributed capacitance, but there is another mean which is called a Q-meter.Be careful that the behavior of coupled tuned circuits is a little more complicated than that. Jul 15, 2021 at 7:41
• Are you sure that this is actually ringing? Jul 15, 2021 at 8:17
• @Antonio51 I get that the capacitor lowers the resonant frequency. I don't understand though, how the amplitude of the ringing voltage almost disappears then. Your graph is interesting, I will simulate it in LTSpice. Jul 15, 2021 at 8:33
• @Autistic I would call it ringing. It tested it with a signal generator and in a usb powered circuit. The behaviour is the same. I could not explain where it would come from otherwise. Jul 15, 2021 at 8:35
• Please, add a picture of your schematic, all included ? Do you use a rectangular wave ? USB is full of such waves. Jul 15, 2021 at 8:36

All inductors have distributed capacitance. So ringing is "logical". If you put another capacitor across, you increase this capacity and lower the frequency of ringing which can dissapear a little or be more amplified ... It is also a mean for measuring distributed capacitance, but there is another mean which is called a Q-meter.Be careful that the behavior of coupled tuned circuits is a little more complicated than that.

Please note also that the overall distortion in the frequency you use with Keysight Technologies 33500B generator (which use digital technology !) is about at -50 db. If you are "tuned" on one of these frequencies, you can "amplify" these and then see "garbage" ... So, filtering directly at output of generator would be necessary but probably difficult.

Here is a picture to illustrate what happens when you use coupled tuned inductors. It is an ac analysis at about "resonance frequency". Quality self (Q factor) are not really "good" ...

It's most likely caused by harmonic distortion in your oscillator but first; consider the bode plot of this circuit where CCAP is the parasitic capacitance of each coupled inductor. I've also chosen an inductor coupling factor of 0.35 but, you have have something a little different: -

The bode plot: -

As you can see there is a magnitude gain of 40 dB at 8 MHz. The ringing is probably just amplified distortion in your original sinewave. Certainly, some of the ringing appears to be around 1.25 MHz but there is higher frequency stuff in there.

So, determine how much distortion is coming from your sine wave source and factor that into your thinking.

• I thought about distortion in the signal source, too. But as I wrote, the circuit was supplied by two different sources. Jul 15, 2021 at 11:25
• You need to do more than that to rule it out. Jul 15, 2021 at 11:28
• I added a spectrum analysis of the source. There is not much going on in the 1 MHz region. Jul 15, 2021 at 11:44
• You didn't do this all the way past 8MHz and also, maybe your scope sampling is causing aliasing? Jul 15, 2021 at 11:47
• I meanwhile did a more accurate spectrum analysis of the signal generator and the usb powered DAC source. You where right. Both show harmonic distortion in the spectrum (Don't know why I didn't see it the first time). The DAC shows more distortion then the signal generator. After making more measurements it became clear that the problem was caused by harmonic distortion which was amplified by the coupled tuned circuit. So thanks a lot for your answer! Jul 26, 2021 at 10:51