# What does it mean, when an order of a system increase?

#### Sirbroccoli

Joined Feb 21, 2020
5
Talking about parasitic elements in an circuit.

#### Audioguru again

Joined Oct 21, 2019
3,513
An increase of an order is 10 times.

#### Papabravo

Joined Feb 24, 2006
16,783
The order of a system usually starts with the number of reactive elements. A system with a capacitor and an inductor is a second order system. Now imagine what would happen if the inductor had a parasitic capacitor in parallel with it. Now your second order system becomes a third order system.

#### MisterBill2

Joined Jan 23, 2018
9,266
The order of a system usually starts with the number of reactive elements. A system with a capacitor and an inductor is a second order system. Now imagine what would happen if the inductor had a parasitic capacitor in parallel with it. Now your second order system becomes a third order system.
This is the explanation that I would have given, as well. In this type of application "order" is talking about the exponent of the unknown in the math description of the circuit. So a circuit with only resistance is first order, with either capacitance or inductance would be second order, and if it has both capacitive and inductive reactance then it is third order.

#### Papabravo

Joined Feb 24, 2006
16,783
This is the explanation that I would have given, as well. In this type of application "order" is talking about the exponent of the unknown in the math description of the circuit. So a circuit with only resistance is first order, with either capacitance or inductance would be second order, and if it has both capacitive and inductive reactance then it is third order.
Circuits with only resistance are order 0, because there is no frequency dependence. Order 1 systems have either a capacitor or an inductor, but not both, The frequency dependence is 1st order. And so on.

#### crutschow

Joined Mar 14, 2008
27,714
From Wikibooks:
The order of the system is defined by the number of independent energy storage elements in the system, and intuitively by the highest order of the linear differential equation that describes the system. In a transfer function representation, the order is the highest exponent in the transfer function.

• TechWise

#### TechWise

Joined Aug 24, 2018
151
The OP may also find it useful to know that even a very complicated system of a high order, such as one with a resistance and inductance but with lots of stray capacitances and series resistances all over the place can often be approximated by a lower order system. This makes the analysis much easier.
Take the example of a DC-AC converter driving a motor. Yes, there are resistances in every switch, capacitances between every winding and inductances in every wire. So technically, it's probably a 15th order system or something ridiculous like that. However, we only actually consider the dominant elements in the system which are the resistance and inductance of the motor, so we analyse it as a first order system.

#### MisterBill2

Joined Jan 23, 2018
9,266
The exception being in designing switching mode power supplies, where it seems that everything matters. Not that every variable must be part of the calculations, but that the effect of all those variables must be considered when creating the physical arrangement of the supply.
This is why I do not encourage folks to create their own layouts of switchers: There is a lot more going on than a basic analysis shows.