Hello friends, welcome to ELECTRICAL ENCYCLOPEDIA. In this article, we will study about the " Types of System ".
TYPES OF SYSTEM
Different types of system are:
1. Continuous & Discrete Time System
The system in which the variables are the function of continuous time variable 't' are called Continuous Time System. As shown in Fig a, here function x(t) is defined for every instant of time and value are changed at any instant.
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| Fig a. CONTINUOUS TIME SYSTEM |
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| Fig b. DISCRETE TIME FUNCTION |
Whereas the system in which variables are defined at only specified instants of time is called Discrete Time System.
2. Linear & Non-Linear System.
A system is said to be linear if it follows the rule of superposition i.e, additivity and homogeneity whereas a Non-Linear System does not follow at least one of these rules.
Mathematically, it can be written as:
Additivity- If the input signals x1(t) and x2(t) corresponds to output signals y1(t) and y2(t), then
x1(t) + x2(t) = y1(t) + y2(t) (mathematical expression for additivity)
Homogeneity- If the input signals x1(t) corresponds to output signal y1(t) , then
a.x1(t)=a.y1(t) (mathematical expression from Homogeneity)
Combining these two conditions we get that condition for linear system is :
ax1(t) + bx2(t) = ay1(t) + by2(t)
3. Instantaneous & Dynamic System
A instantaneous or static or memory less system is a system where the output signal at any specific time depends upon the input signal at that time.
This system has no memory. Memory in Electrical System means energy storing elements. So, static system does not contain any energy storing elements
Whereas, dynamic system is a system whose output depends upon present input as well as past or future values of input. Dynamic System contains energy storing elements.
4. Active & Passive System
A system that does not have any source of energy is called passive system. For eg- A circuit containing resistance , capacitance , inductance ,diode etc.
Active System consists of source of energy and passive elements. For eg- Electric Circuit containg voltage or current source including passive elements (like resistance, inductance, capacitance etc).
5. Stable & Unstable System
A stable system is one in which the output only diverges if the input diverges. A bounded input produces a bounded output. Therefore, this system is called bounded input-bounded output (BIBO) system. Mathematically,
If x(t) is the input and y(t) is the output, then output must follow this condition:
| y(t) | <= My < infinity ; for all t
Where input should satisfy this condition
| x(t) | <= Mx < infinity ; for all t
Here Mx & My both are the set of finite positive numbers.
If these conditions are not met then the output of the system grows or diverges without limit from the bounded input and such systems are called unstable system.
6. Invertible & Non-Invertible System
A system is said to invertible if:
* Distinct input leads to distinct output, and
* Input can be recovered from the output.
otherwise the system is non-invertible.
7. Time-Invariant (Fixed) or Time-Varying System
A system is called fixed or time-invariant if the behaviour or characteristics of the system does not changes with time. If x(t) input signal gives y(t) as output signal, then system is time-invariant if x(t-T) gives the output y(t-t) for any delay T. Hence, a time shift of Input gives the same time shift of Output.
Otherwise, the system is Time-Varying.
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