Input impedance of a buck converter

Question

Is there an approximate formula for calculating the minimum value of the input resistance (or impedance) of a switching regulator? I found several formulas but can't figure out which one to choose. I would need it to understand how to calculate an input filter so that it has an output resistance much smaller than the input resistance of the buck. Otherwise can i calculate through efficiency and power informations? Thanks

Answer 1

I have determined the open-loop input impedance of the buck converter operated in voltage-mode (VM) and current-mode control (CM) in my last book on transfer functions. When operated in VM, the incremental input resistance is positive but it becomes negative in closed-loop operations. On the contrary, in CM, the incremental input resistance is natively negative in open loop.

For a buck converter, you have several options:

1. plot \$Z_{in}\$ in closed-loop using the formula I derived in my APEC 2017 presentation. Needless to say, it is quite complex to handle:

On this graph, you should now superimpose the output impedance magnitude of your EMI filter and check for any overlaps. If there are some, damp the filter to offer a 10-dB margin at least.

2. consider the closed-loop input impedance as a flat magnitude across frequency. In this case, you derive the incremental resistance by \$R_{in}=\frac{V_{in}^2}{P_{in}}\$:

With this approach, you ignore any notch in the input impedance and need to ensure sufficient margin with the peaking of the EMI filter impedance. I've seen many high-power converters designers successfully applying this method.

3. Use a simulator to plot this closed-loop input impedance in worst-case conditions and that is probably the fastest way to obtain an accurate picture:

I used one of my free 120+ SIMPLIS templates but an averaged model in LTspice or other SPICE-based engine would produce a close plot.

For more information, you can see my answer on SE for instabilities linked to the EMI filter but also some basic guidance on how to design the filter here.

Answer 2

For DC it's negative since, for constant output, input voltage and input current have an inverse relationship. That can destabilize an LC filter: you may need to add damping.

At higher frequencies there's no general formula. God is in the details...

Answer 3

Is there an approximate formula for calculating the minimum value of the input resistance (or impedance) of a switching regulator?

Within the input supply range that it operates over, you can regard it as a constant power input device (where the power input equals the load power output) plus an offset power that remains roughly constant (representing the power overhead needed to keep the converter functioning).

I would need it to understand how to calculate an input filter so that it has an output resistance much smaller than the input resistance of the buck

I strongly advise you to check any filter design using a simulator; they are free and accurate. I use micro-cap but, many other use LTspice. A constant power load can be created or, just use your buck converter circuit to get a more accurate result.