# LINEAR AND NONLINEAR SYSTEMS

#### ahsan

Joined Jun 26, 2005
5
Can anybody differentiate b/w Linear and NonLinear systems?

#### mozikluv

Joined Jan 22, 2004
1,437
hi,

what do you mean by challenging us members to come to it? are you trying to test our capabilities just for the heck of it? :angry: :angry:

#### n9xv

Joined Jan 18, 2005
329
Linear or Non-linear in regaurds to what specific area.

#### ahsan

Joined Jun 26, 2005
5
No A ctually I don't mean it. This argument was put forth by one of my friends who claimed a very different definition of Linear systems.So I just wanted to have some discussion on this issue. Linear and Non-Linear electric systems etc.

#### thingmaker3

Joined May 16, 2005
5,084
Originally posted by ahsan@Jun 27 2005, 12:50 PM
No A ctually I don't mean it. This argument was put forth by one of my friends who claimed a very different definition of Linear systems.So I just wanted to have some discussion on this issue. Linear and Non-Linear electric systems etc.
[post=8775]Quoted post[/post]​
Different from what?

If you are trying to settle a bet, how about giving us your definition as well as your friend's definition?

#### mozikluv

Joined Jan 22, 2004
1,437
Originally posted by ahsan@Jun 27 2005, 02:50 PM
No A ctually I don't mean it. This argument was put forth by one of my friends who claimed a very different definition of Linear systems.So I just wanted to have some discussion on this issue. Linear and Non-Linear electric systems etc.
[post=8775]Quoted post[/post]​
hi ahsan,

then you should have not used the term "i challenge" because that is confrontational in nature. you could have simply ask for more information on that topic.

#### aac

Joined Jun 13, 2005
35
Originally posted by ahsan@Jun 26 2005, 06:41 PM
Can anybody differentiate b/w Linear and NonLinear systems?
[post=8754]Quoted post[/post]​
In functional form; F(v1+v2)=F(v1)+F(v2) for a linear circuit.

In a linear system the response to an input sum is the same as the sum of the responces. If a voltage divder divides by 3 with a 1.5V battery as the input, the output would be 0.5V. Now if a second battery is added, to get a 3.0V input, the output is 1.0V which is the same as 0.5V from the first battery added to 0.5V from the second.

This would not be true with a non-linear circuit. An example of this would be a resistor in series with a diode so the diode is forward biased. With one battery the voltage across the diode would be about 0.7V. Adding a second battery would not give 1.4V across the diode it would still be about 0.7V, very non-linear.

#### Dave

Joined Nov 17, 2003
6,970
Further to the above posts:

From a strict Signals and Systems perspective, a linear system, whether in continuous or discrete time, is a system that possesses the property of superposition. If an input consists of the weighted sum of several signals the the output is the superposition, or weighted sum, of the responses of the system to each of those signals. This can be classified by two properties:

The Scaling Property:

Response to x1(t) + x2(t) is y1(t) + y2(t)

The Scaling or Homogeneity Property:

Response to ax1(t) is ay1(t)

Not this is written in terms of continuous time signals but is equally applicable to discrete time signals.

The property of linearity (from a strict mathemetical sense):

Continuous time:

ax1(t) + bx2(t) → ay1(t) + by2(t)

Discrete time:

ax1[n] + bx2[n] → ay1[n] + by2[n]

Further to the basic concepts of linearity, above, there is a special class of linear system which has the property of time-invariance. These systems are known as Linear-Time Invariant (LTI) Systems. LTI systems have a significant use in Control Theory and design as well as Communication Engineering.

Non-linear systems are systems that can be algebraic equations, ordinary differential equations or partial differential equations, which do not follow one of the properties of the superposition principle. In the example stated above, we can see that the use of a diode in a electrical circuit will introduce non-linear system characteristics due to the Ebers-Moll characterisation of the diode introducing an expontial factor at the system output. It is common when analysing non-linear systems to linearise the system around a small area - this produces a good estimate of the system response.

#### _Raven_

Joined Jun 3, 2005
10
Look at this.... A circuit that process signal corresponding to time is linear I mean If you have a circuit solving for f(t) = ASIN(Bt+C) this is linear. on the contrary a non linear circuit or system solves for a non continious signal say DSP functions, which solves for integral or diferential functions.