# time constant confusion of second order system

For first order systems, its easy to get the time constant by using thevenin concept.

Suppose i have a second order system ,for example consider a two stage cascaded LOW PASS FILTER with identical resistance and capacitor values. I am sure that this system will have more than 1 time constant.

However,

My guess is that the transfer function of desired output with respect to input voltage will have 2 poles and the reciprocal of these poles will give the time constants.

I am confused whether depending on the output of interest, will the poles change, i think it won't but i am not able to convince myself.

• Are you able to convince yourself that now is a good time to ask a question? – Andy aka Nov 30 '15 at 15:42
• yea :P i am able to – Ashik Anuvar Nov 30 '15 at 15:43
• So, feel free to ask one... – Brian Drummond Nov 30 '15 at 15:44
• please help me with how you evaluate the time constants in second order case – Ashik Anuvar Nov 30 '15 at 15:45
• If all components were impedances Z(f) would you be able to make an expression for this circuit ? Now fill in Z(f) = R for the resistors and Z(f) = 1/jwC for the capacitors. Then group the equation such that you have RC products. Since both RC influence each other you might not get "nice" timeconstants. For that you need to isolate them from each other. – Bimpelrekkie Nov 30 '15 at 15:52

$V_{OUT} = V_X \dfrac{1}{1+sCR}$