Switchmode Dynamic Input Impedance - John Dunn, Consultant, Ambertec, P.E., P.C.

Let's assume an ideal, one hundred efficient switchmode power supply passing one hundred watts to its load and drawing its input power from an input line of one hundred volts. That ideal case would look like this:  

 

If we then vary the input line voltage up and down just a little bit, the input current responds by going down and up just a little bit:  

     

With a little calculus, we can look at the first derivative of the input line voltage with respect to the input line current as follows. That first derivative value is the dynamic impedance at the input:    

 
For this negative value of dynamic input impedance, we can get into trouble with power supply instability if the power line source impedance is too large:     

We need to make sure than the source impedance of the power line is smaller than the absolute value of the dynamic input impedance of the power supply or there will be an intractable instability problem.

Please bear in mind that even though this example posits an ideal 100% efficiency value, the dynamic input impedance of a real-world high-efficiency power supply will still be negative and the same cautionary tale will still apply regarding the source impedance of the power line.

 

 

Comments

[Bruce Baker]

John, I think this is according to the rule that amplifiers will, oscillators won't. What happens if you put a smoking big cap across the input? Does that fix the problem?

[John Dunn]

Hi, Bruce.

That really big capacitor would not solve the oscillation problem. It would only make the oscillation happen at a lower frequency.

John

[Saieb AlRawi]

Nice artical, thank you, but your first value for V=1.01 Volts, you stated the current is ).0990099A, I think you meant 0.99 right?

Thank you,

Saieb,

[John Dunn]

You're right, Saleb. I never noticed the error before.