# Determining the order of a system

Discussion in 'Homework Help' started by rsashwinkumar, Dec 11, 2013.

1. ### rsashwinkumar Thread Starter New Member

Feb 15, 2011
23
2
Consider a series combination of a resistor R1, and two capacitors C1 and C2, driven by a voltage source. The series capacitor combination can be reduced to one single effective capacitor, and so the order of the system is one.

But order of a system is also equal to the number of independent initial conditions that can be assigned to state variables. Here both voltages across C1 and C2 can be independently assigned initial conditions. This predicts an order of 2 for the system. But still the transfer function (considering current as the output variable), has a denominator which is a first order polynomial in 's'. So what is the catch here? Is the system really a first order or a second order? Please help me out...

2. ### LvW Active Member

Jun 13, 2013
674
100
According to my knowledge the order of a system is defined as the order of the corresponding transfer function - in particular the order of the denominator.
Can you give a reference for the definition mentioned by you above?

Feb 15, 2011
23
2
4. ### LvW Active Member

Jun 13, 2013
674
100
I wouldn`t trust too much you tube lessons.
There are more serious knowledge sources .
Perhaps I should add to my last post that the order of the transfer function equals the order of the corresponding diff. equation in the time domain.

5. ### rsashwinkumar Thread Starter New Member

Feb 15, 2011
23
2
FYI That was a lecture by a professor from Indian Institute of Technology (IIT). (one of the best institutes in India). So I would very much trust that lecture, than some random google searches. Also state space method of analysis represents an nth order diff equation as a system of 'n' coupled 1st order differential equations. So it is very much possible to relate the order of a system to the number of independent state variables. My question was whether my statement regarding the mentioned system comes with some catch.
(Even in a miller compensated 2 stage OTA, we have a loop of capacitors (Compensatoin cap, input cap of 2nd stage and output cap of first stage), but still the overall order of the system is two, since only two state variables are independent there).

6. ### LvW Active Member

Jun 13, 2013
674
100
OK - it was not my intention to critisize ALL youtube video lectures. How could I ?
I suppose, in this case you are right.

7. ### rsashwinkumar Thread Starter New Member

Feb 15, 2011
23
2
I think I caught the 'catch' in the prediction of order 2 for the above system by the number of independent state variables. If the transfer function is solved for in state space, there occurs a pole zero cancellation (A pole at zero is cancelled by a zero at zero). The system when considered to have two independent state variables will be uncontrollable. And when a system is uncontrollable a pole zero cancellation occurs. I figured this by considering a simpler network, a capacitive divider. The transfer function is of zeroth order, but it is possible to assign one single independent initial condition, and it can be viewed as a first order system. But the transfer function is 1/sC/(1/sC+1/sC) = s/(2*s). Thus a pole-zero cancellation occurs at 0 complex frequency. The system is again uncontrollable.