🚀 This week we’re going to check some interesting measurements about the 1kW DAB transformer we've designed in the previous newsletters, focusing in particular on parasitic elements.
⚙️ The manufactured sample
Figure 1. Manufactured sample
In Table 1 we can see again the very basic specs of the manufactured transformer. This one is simulated as a step-up transformer, as the turns ratio suggests.
☝️ Theoretically there is no gap between the cores, since we have chosen a no gap core set. However, in reality there are core surface finish imperfections, and usually these imperfections cause a 20-50um of distance between the core legs. Even that small gap between the cores causes the AL value and the magnetizing inductance to drop dramatically. Considering some gap in the micrometre range mentioned, we can get inductance values very close to the measured values minimizing iterations.
Tab 1. 1kW DAB transformer basic specs
Tab 2. Transformer Inductances
Table 2 shows the primary inductance, or magnetizing inductance, as we call it, as well as the secondary winding inductance and the leakage inductance.
So everything looks good right? Let's call it a day and go “home” 🍺!
😅 Ummm no, not so fast…
The best analogy that I can come up with is someone judging a movie from the trailer instead of watching it.
What I mean is that all the values in Table 2 are measured in a specific frequency (100kHz). Of course, if these values were out of range in the switching frequency, there would not be any chance of this being a successful design. But what about higher frequencies?
As Pablo mentioned in the last newsletter, the effect of leakage inductance can be detrimental in hard switched topologies. It can also be an advantage in resonant topologies saving us from the need of using an external inductor, but what about parasitic capacitances?
👩🏫 Self-resonance
Figure 2. A complete transformer model
Let's take a look at Figure 2. This is the equivalent transformer circuit including all parasitic elements to fully describe and simulate a transformer. As you can easily realize, all of these inductances and capacitances form resonant circuits that oscillate at specific frequencies. Self-resonance happens because of the primary or secondary magnetizing inductance and the effect of the lumped capacitance, as seen from the primary or secondary accordingly.
🔎 What I'm saying in fact is that if you take a transformer and you excite its primary winding leaving the secondary open, there is a certain self-resonance point. The same experiment can be duplicated exciting the secondary side while leaving the primary winding open (same resonant frequency).
Putting those ideas into writing we get:
Looking from the primary winding:
🤓 Using equation (2) errors of 1 to 4% are to be expected [1]. This is good enough for our purposes.
Measuring the lumped capacitance directly is not possible, but we can calculate it indirectly from (1) and (2):
💡 Measuring self-resonance:
The easiest way to measure the resonant frequency is to use a frequency response analyser like a bode100, a Cleverscope FRA or something similar. If the frequency response analyser is not available, Figure 3 shows an alternative way of measuring the self-resonance frequency.
Figure 3. Alternative way of measuring self-resonance
In Figure 3 when the voltage amplitude across resistor R1m is at its maximum, this is the frequency resonance point that we are looking for.
By using CS328A-FRA to measure the DAB transformer impedance, I got Figure 4.
Figure 4. Self-resonance measuring the DAB sample transformer impedance
Self-resonance happens around 315kHz. As you can see in Figure 4, the transformer is going through phase reversal at this frequency. In switching DC-DC converters, the transformer windings are excited with fast rising square waves. The bandwidth content of a 100 kHz square wave depends on the rising and falling edges, as we've seen in this newsletter.
Let's assume that we have a square wave with a rising edge of 20ns going from 0 to 400 volts. The bandwidth of this signal is about 17.5MHz. This is much higher than 315 kHz and some ringing is expected at the rising edge of the driving pulse. This of course is a general comment and whether or not ringing is going to be observed depends on the actual circuit topology and the mode of operation. If we're talking about soft switching, then no ringing will be seen, but when it comes to hard switching there will be ringing. Also clamping diodes and RC filters can be used to damp and clamp the oscillations to acceptable levels.
🤔 But what if the 315 kHz resonance frequency drops, somehow, down close to the fundamental switching frequency of the DCDC converter?
⚠️ This is a very real problem.
Actually, 315 kHz is a bit uncomfortably close to the 100 kilohertz switching frequency. The rule of thumb is for the self-resonant frequency to be 5-10 times more than the switching frequency to account for any changes due to things like extra circuit capacitances that will add up to the lumped capacitance causing a lower resonance frequency. If the new resonance frequency comes close to the switching frequency, then there is a chance that the circuit will burst into uncontrollable oscillations. And that is a recipe for disaster🔥.
In this specific transformer design, a foil winding was selected and x4 3T windings paralleled at the pins formed the primary winding. The problem with copper sheets is the large area between the paralleled windings. That increases the primary side capacitance considerably. As a reference evaluating an all-Litz wire transformer design that I had available, with similar inductances, a self-resonant frequency of over 1 MHz was observed.
📌 Interwinding capacitance
Looking at Figure 2 we can see the Cw capacitance between the secondary and the primary. This capacitance is called interwinding capacitance. That is also an important parasitic parameter when isolation between primary and secondary is needed, as is the case with most transformer designs.
The measured capacitance for the DAB transformer looks like this:
Figure 5. Interwinding capacitance
At 100kHz the interwinding capacitance is about 115pF, dropping down to 100pF above 1MHz, effectively staying constantly well into the 30MHz area. This is not an unusual capacitance for transformers of this power level and size, but it should be noted that this capacitance will inject current from the switching primary to the secondary side of the DCDC converter.
☝️ This current is injected into both terminals of the secondary winding and manifests itself as common mode noise. Mitigating common mode noise is a hard task and some effective solutions actually compromise the isolation between the sides. This is the reason why many off the self-low power converters specify the interwinding capacitance between the two isolated sides, trying to minimize this capacitance as much as possible in the range of 5 to 30pF.
⚡ Leakage inductance vs Frequency
Is the leakage inductance constant? Not in all frequencies!
Figure 6. Leakage inductance(reflected at the secondary) vs frequency
In Figure 6 we can observe how the leakage inductance drops from 10kHz up to 1MHz. In this specific example the inductance at 35 kHz it's only 7% higher than the inductance at 100 kHz, so there is not a really big fluctuation, but there are other transformer examples [3] like shown in Figure 7.
✅ The conclusion is that the leakage inductance should be defined in a frequency range close to the switching frequency of the power converter to account for the nonlinear behaviour of the leakage inductance versus frequency.
Figure 7. Forward 60W transformer primary leakage inductance vs frequency dependency
😎 Hope you liked it, and see you next week!
🚀 Have you heard about the Free Webinar on "How to design a DC Inductor"?
Read Dr. Molina's article on "How to design an inductor", and join the Free Webinar on November 28th, where he will discuss the practical process of designing an inductor, as well as showing examples of more complex design.
[1] Østergaard, C., Kjeldsen, C. S., & Nymand, M. (2020). Calculation of Planar Transformer Capacitance Based on the Applied Terminal Voltages. In 2020 IEEE 21st Workshop on Control and Modeling for Power Electronics (COMPEL) IEEE.
