# How does current flow in this circuit with multiple power regulators?

I have the following circuit:

simulate this circuit – Schematic created using CircuitLab

U1 contains two voltage regulators (Vo1=+10V, Vo2=-10V, input Vin=5V). (These could be buck, boost etc. but I think it is not important for the question)

Vo1 acts as voltage supply for the load (think of it as "VDD") and Vo2 as return path (think of it as "VSS"), so mostly Io1=Io2. (Note: I added D1 and GND just to show that there other other signals going into LOAD where (smaller) currents may flow, so Io1 may not be exactly Io2).

I am interested what Iin and Ignd current looks if I know Io1 and Io2.

Example: Say Io1, Io2 is a square wave with Ilow=0, Ihigh=1A and period 1kHz. Switching frequency is 10MHz. Conversion efficiencies 100% for simplicity. How would Iin/Ignd look like if I apply a 100kHz lowpass filter (so I can ignore switching/ripple)?

How is such a circuit analyzed?

• Ignoring switching ripple, that's just DC, is that what you expect? It would help writing a better answer if you would explain you own view. Dec 2, 2021 at 17:11
• It's like saying, ignoring the ingredients, how do I make a pizza. Dec 2, 2021 at 17:18
• @Justme Yes, that's the question I want to answer: Without ripple, Is Ignd/Iin just DC, even though ILoad has 1kHz frequency component? If I model Vo1/Vo2 with a voltage source, then this is the case but it doesn't sense to me: This current needs to come from somewhere (=Iin). If I do LTspice sim using ADP2503-5.0 as an example, I see the 1kHz in in the spectrum of Iin/Ignd (besides the switching harmonics).
– divB
Dec 2, 2021 at 17:58
• @Andyaka No that's not a good comparison. If you want, add in switching and ripple. Look at my example: ILoad draws 1A current at 1kHz. Switching is 1MHz. Then look at the spectrum of Ignd and Iin and and apply a lowpass filter with fc=100kHz. What does the spectrum look like? (EDIT: Changed the question to "How to make pizza with ingredients" if that's easier to understand)
– divB
Dec 2, 2021 at 18:00
• @divB Now you changed the specs. Of course if you specify that load takes current at 1 kHz frequency then it does so. For each DC current value out at any given time there is a matching DC current value in at any given time, no matter if the time frame is 1 hour or minute or 1 millisecond. Dec 2, 2021 at 18:03

Just think power in at any given moment matches power out. Including the losses that make the efficiency to be less than 100%. A first order assumption might ignore losses for simplicity.

If your load takes in power at 1 kHz rate, then the power supply must give out this power at 1kHz rate so there is constant voltage with current varying at 1 kHz rate. Which means the power supply will has to take in power at 1 kHz rate too.

Even simpler approximation could also ignore the 1 kHz and assume it's that some average DC power out equals to average DC power in.

• Great, I think this is exactly what I am looking for. Specific to the example, is this correct then? Given: ILoad (1kHz rect waveform 0A-1A) and all voltages (Vi=5V, V1=10V, V2=-10V). Po1=10*ILoad. Po2=-10*(-ILoad). Pin=Po1+Po2=5*Iin. --> Iin=4*ILoad ? So Ignd and Iin is 1kHz rect waveform between 0A and 5A (plus any switching noise added by the converter)?
– divB
Dec 2, 2021 at 18:26

The first step to this problem is to treat both outputs as two separate DC/DC regulators, connected in parallel.

Of course, contrary to what the comments suggest, it is possible to model each regulator with an ac/small signal model that ignores the switching. With a feedback loop, this concept is very similar to PLL modeling.

The book Fundamentals of Power Electronics by D. Erickson derives models to various degrees of accuracy, based on a canonical model (i.e., identical structure for different types of converters).

In the simplest case, the converter (open loop) can be modeled with a simple (DC) transformer (or, equivalently with controlled voltage/current sources). This model is sufficient for OPs question: A current in the secondary winding of a transformer (load current) results in a current in the primary winding based on winding ratio (here: duty cycle or voltage ratios).

The model can be extended to include losses (inductor and switch losses), dynamics and finally a feedback loop.

As to the numerical example with the square wave: With zero load current, there is no input current. With Io=1A, twice the current will flow in the primary winding of the first converter and with Io2=1A, 2A will flow in the primary winding of the second converter. So in total 4A.

Now we can confirm that power is conserved. At the input: Pin=5x4=20W. At the output: Pout=P1+P2=1x10 + (-1)x(-10)=20W.