# Inductor Voltage and Current Phase Delay on a DC Converter

We learn that inductors introduce phase delay between voltage and current for AC. On a DC-DC converter, such as boost, we have, at the inductor, a DC component superimposed with AC component with many harmonics (i.e. triangle). As the boost converter voltage, we have a square wave.

Many researchers discuss phase error between I and V, and that it is especially significant for low permeability cores. How would one go about measuring the phase between the two (in the context of a Boost converter)?

To help illustrate the question and why I am confused by this, I have attached an image of the voltage and current of the inductor of a boost converter. The converter is operating at 30% duty cycle. The inductor's core magnetic material is a low permeability sendust ($$\\mu_r = 75\$$). Is there even a phase shift here?

Edit: Thanks for the suggestion, here are some papers where phase delay is discussed:

https://ieeexplore.ieee.org/document/7930799 Addresses the error introduced by the phase delay https://ieeexplore.ieee.org/document/7846098 Addresses the error introduced by the phase delay https://ieeexplore.ieee.org/document/5542385 Talks about it in his article and adresses it https://ieeexplore.ieee.org/document/6559314 Also addresses phase delay (This one on a Boost converter as well) https://ieeexplore.ieee.org/document/4432686 Also addresses the issue.

• Could you add a citation or two for the researcher discussion on phase error? Aug 28, 2019 at 17:32
• I saw a paper called "Error analysis of high frequency core loss measurement for low-permeability low-loss magnetic cores" which talks about how phase error is significant when testing a core for loss using a small-signal sinusoidal excitation. This doesn't really have anything do to with the operation of a DC/DC converter, where you are applying a square wave to generate a linear ramp of current in the inductor over a finite time interval. That is to say, you're not expecting a phase-shifted square current wave - you are expecting current ramps. Aug 28, 2019 at 17:42

We learn that inductors introduce phase delay between voltage and current for AC.

And before that you should have learnt this: -

$$V=L\dfrac{di}{dt}$$

Because that is the fundamental property that governs the AC sinusoidal phase response AND the response in a circuit like a DC to DC converter.

How would one go about measuring the phase between the two (in the context of a Boost converter)?

It's irrelevant because the formula above (from Faraday) tells you directly all you need to know to understand the waveform shapes in a converter. You apply a voltage to an inductor and the current ramps up (or down) at a fixed rate determined by V/L.

Is there even a phase shift here?

You are asking the wrong question - you should be asking something more like this: are the ramp rates of current corresponding with what V/L tells us.