In design of DC-DC converters (buck, boost, buck-boost), selecting proper values of inductor and capacitor of power stage are important for determining the performance of overall system. In the simulation (I am using Cadence), the parasitic (Equivalent Series Resistance) of output capacitor Cout as well as of Inductor L should be calculated for many spec such as inductor current ripple, compensation.
But the problem here is the calculated value (ideal case) and the real value of the L and C.
On the market, there are many types of high quality capacitor and inductor with small tolerance and information of ESR. However, C, L and their ESR values seem to vary much according to the frequency.
Please refer to the attached figure below that I measured the Inductor and its ESR value) from a norminal 100 uH on the market. the measured results show a frequency-dependent (I took 2 points for examples: L = 119uH and ESR = 112 mOhm where L = 85.888uH at f = 1MHz)
My question is, should we measure the real inductor and use this value in the simulation?
Thank you!
The answer substantially depends on what you expect from the simulation. As far as your goal is to perform a coarse analysis intended just to check a pen-and-paper design and/or to assist you in the choice of the order of magnitude of the components, simulations with ideal components (L, C, switches) can be sufficient. If your goal is to achieve an accurate estimate of losses, residual ripple,.. more accurate models are needed. Extracting the models from real-world measured is surely the best, nonetheless several things should be considered:
- the model should match the measured data over the whole bandwidth and current/voltage range of interest in your simulations. In your example, the inductor model (lumped ESR, L and C or possibly black box) should match the whole measured impedance frequency response of the component up to about 10 times the switching frequency (i.e. up to the higher frequency at which a square wave or a triangular wave have relevant spectral content), not just at a single frequency. Moreover, inductors undergo core saturation under high current operation and this should be also taken into account in the model.
- the fabrication tollerance of real world components should be accounted for.
- when the RF behaviour of components for EMC/EMI analysis is to be investigated, an accurate RF electromagnetic characterization/simulation not just of the components, but also of the PCBs, package,... is often important.
Having said that, accurate component modelling from measurements is not straightforward and one should carefully consider case by case if this is really needed and/or if it is more convenient to introduce approximations (e.g. just a "best fit" LR model for an inductor) and to verify the perfromance on a prototype.
Dear Prof., Paolo Stefano Crovetti,
Thank you for your detail explanation. As you mentioned that the inductor value should match the measured data over the whole bandwidth of interest in your simulations. So I am still wondering that, when I design the buck converter (for example), the inductor value I should inserted in the simulation must be the real inductance at that frequency. For example, I picked up an inductor with the norminal value is 120uH (and the measured value is also approximately 120uH at low frequency as in the Figure I attached before). But the switching frequency in my design was 1 MHz, so should I use the measured value (85.88uH) for the simulation?
Also the same case for the ESR, should I use the value at 1MHz instead of low frequency value?
Really appreciate your discussion.
Sincerely,
Dear Van Ha Nguyen,
based on what I have said before, provided that you model a real inductor as an ideal inductor (L) in series with a small resistor (ESR), the best values of L and ESR to be used in the simulation are those which provide the best fit of the impedance Z(omega)=j*omega*L+ ESR with the measured impedance over the frequency bandwidth of interest (let's say from DC up to 10MHz or more, if your switching frequency is 1MHz.) Possibly these L and ESR values achieving the best fit are different compared to the low frequency and to the high frequency measured values and probably they will be in between them. Using either the high frequency or the low frequency L and ESR measured values, the simulation will give rise to different but possibly equally relevant errors, since the operation of the DC-DC converter involves inductor voltages and currents with low-frequency and high-frequency components. If you really need to get a better approximation, you should introduce more parasitic elements in the inductor equivalent circuit so that its impedance matches the measured one. Having said that, in most cases the improvement in terms of accuracy that can be achieved in the simulation of the DC-DC converter is relatively modest compared with the modeling effort and the estimate that can be obtained using the nominal (low frequency) L and ESR values is satisfactory.
Thank you very much dear Prof. Paolo Stefano Crovetti,
I got the answer.
Sincerely,
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