# Input/Output Impedance of DC/DC converters and Impedance matching

I am interested in understanding how do DC/DC converters achieve impedance matching for maximum power transfer applications. After visiting this (historical) entry, you can see in the "impedance matching" paragraph some calculations that lead to $$\D = \sqrt{\eta \frac{Z_\textrm{out}}{Z_\textrm{in}}}\$$. What I would like to make clear is what exactly do we mean by input/output impedance, what the above $$\Z_\textrm{out}\$$, $$\Z_\textrm{in}\$$ are supposed to represent, and how can I achieve impedance matching with the source, when based on the above equation, by changing the duty cycle I can merely change the ratio of the converter's impedances.

• Note that impedance matching is usually not important since the source impedance is usually low. It can be important when the source impedance is high, such as photovoltaic cells. Feb 22, 2020 at 13:48
• They don't. They aim for maximum efficiency, because maximum power transfer is at only 50% efficiency.
– user16324
Feb 22, 2020 at 16:26

What I would like to make clear is what exactly do we mean by input/output impedance, what the above Z_out,Z_in are supposed to represent

• $$\Z_o\$$ is the external impedance connected to the buck converter's output.
• $$\Z_i\$$ is the impedance presented by the buck converts input to the power source.

how can I achieve impedance matching with the source, when based on the above equation, by changing the duty cycle I can merely change the ratio of the converter's impedances

The impedance seen by the source is the impedance presented by the buck converter, $$\Z_i\$$ and, in turn, that presented impedance is dependent on $$\Z_o\$$ and the duty cycle used by the buck converter.

In other words, the input impedance presented to the power source by the buck converter loaded with $$\Z_o\$$ is: -

$$Z_i =\dfrac{ηZ_0}{D^2}$$

• If the output impedance is just the external impedance of the load connected, that makes sense. What confused me though is that, if you take a look at this paper, in Fig.1, the output impedance is not just the load, but rather seems to refer to an intrinsic impedance of the converter. as seen from the load's side. Feb 22, 2020 at 14:52
• Well fig 1 shows two output impedances and that gives rise to uncertainty but, it's clear from the wiki article it can only mean the externally connected load impedance. Feb 22, 2020 at 14:55
• I agree that the wiki article does refer to the externally connected impedance. What really bothers me is whether the wiki calculations are correct, or there is an additional converter output impedance, like the one presented in the paper, that should be taken into account as well. In that case, Z_out would not be a constant value (i.e. just the external load), and I fail to see how one could achieve impedance matching. Feb 22, 2020 at 15:02
• The formula is correct; imagine that efficiency is 1 and think about the output voltage onto a 1 ohm resistor, remembering that the input voltage (say 10 volts) is square wave at the output with a duty cycle of D. Just do the math, calculate the power and realise that the same power goes into the input but, given that you know the input is (say) 10 volts, you can calculate the effective impedance of the input to the buck regulator. Feb 22, 2020 at 17:38