Input impedance of an SMPS?

[treez]

Hello,
What is the equation for the dynamic input impedance of an smps?

The following , and many others, do not state it...
http://www.intusoft.com/lit/psbook.pdf

The following seems to state it...
**broken link removed**
...according to this, for a buck converter, dynamic input impedance (dVin/dIin) = -((1/D)^2) * Vout/Iout
..but surely that can't be right?..it doesn't take into account the feedback loop bandwidth?


We are cascading SMPS's, and as you know, if the 'downstream' smps has an input impedance less than the output impedance of its input filter, then it will oscillate. Though what is the equation for dynamic input impedance of an SMPS?

The DC value of the smps input impedance is given on page 11 of the above , but its the dynamic input impedance that is needed.
Does SMPS input impedance decrease with increasing feedback loop bandwidth?

Also, regarding the rule that the input impedance of an smps must be higher than the output impedance of its own input filter.....does that mean, "bigger negatively"?....because as you know, the dynamic input impedance of an smps is negative.

 

[KlausST]

Hi,

dynamic input impedance (dVin/dIin) = -((1/D)^2) * Vout/Iout

thisis for low frequency. just the power transfer characteristic of the SMPS.

For higher frequency you have to take the input Cs into account.

It is an optimized calculation, it does not take efficiency (and it´s variation with input voltage) into account.

I think the feedback loop has minor influence on the input impedance. I expect 0.1% influence for a open loop gain of 1000.

To calculate the input impedance of a smps with_variable_output_voltage i think the output capacitor i must be added to the input capacitor with Ci_tot = C_in + C_out * (V_out / V_in)^2.

But to be true these are my estimations, but not my knowledge.

Klaus

 

[mtwieg]

There's not a general formula for the AC impedance. It can be solved for, but only given a detailed model of the converter and feedback loop, and biasing conditions.

 

[D.A.(Tony)Stewart]

Every circuit type of SMPS has a unique input voltage V1(f,t), Z1(f,t) and unique output V2(f,t), Z2(f,t) in s parameters these can either all voltage or current or all impedances where s11 is input and s22 is output for a 2 port device. The forward transfer function is s12 and reverse is s21. Load regulation is due to the ratio of dynamic and static load to output impedance. The dynamic ratio of voltage tends to be dominated by ESR of load / source as well as capacitance load switch ratios and how well feedback is regulated.


One method of testing requires measuring the ratio of source voltage on either side of a series shunt resistor with current being sensed.

Another method uses a variable known series switch and series resistance to inject a noise current and measure the voltage from that source to measure that node impedance, which is the output and input in parallel. Then testing each independently you can correlate the node response with each output and input. to measure the net lump impedance of both source voltages.

For good load regulation the dynamic source impedance or usually ESR of cap & ZL (ESL of inductance impedance) is less than 10% of dynamic load impedance. A great design will be less than 2% of load dynamic impedance. An unstable one may be >30% of dynamic load.

Without schematic, layout details and all component specs, one cannot say much more precisely than these " hand-waving" discussions.