What do you mean by superposition and linearity, Electrical Engineering

Assignment Help:

Q. What do you mean by Superposition and linearity?

Mathematically a function is said to be linear if it satisfies two properties: homogeneity (proportionality or scaling) and additivity (superposition),

f (Kx) = Kf (x) (homogeneity)

where K is a scalar constant, and

f (x1 + x2) = f (x1) + f (x2) (additivity)

Linearity requires both additivity and homogeneity. For a linear circuit or system in which excitations x1 and x2 produce responses y1 and y2, respectively, the application of K1x1 and K2x2 together (i.e., K1x1 + K2x2) results in a response of (K1y1 + K2y2), where K1 and K2 are constants. With the cause-and-effect relation between the excitation and the response, all linear systems satisfy the principle of superposition. A circuit consisting of independent sources, linear dependent sources, and linear elements is said to be a linear circuit. Note that a resistive element is linear. Capacitors and inductors are also circuit elements that have a linear input-output relationship provided that their initial stored energy is zero. Nonzero initial conditions are to be treated as independent sources.


Related Discussions:- What do you mean by superposition and linearity

Describe the meaning of standing wave ratio, a. Describe the meaning of sta...

a. Describe the meaning of standing wave ratio. What is the formula for it, if the load is purely resistive? Why is a high value of SWR often undesirable? b. Determine how the c

Determine the 60-hz resistance of line, Q A handbook lists the 60-Hz resist...

Q A handbook lists the 60-Hz resistance at 50°C of a 900-kcmil aluminumconductor as 0.1185/mile. If four such conductors are used in parallel to form a line, determine the 60-Hz r

Differences between a timer and a counter, Question : a) Embedded Syste...

Question : a) Embedded Systems will be Hard Real-Time Systems, Soft Real-Time Systems and Hybrid Real-Time Systems. Briefly explain all three types of Real-Time Systems, using

Explain public mode, Explain PUBLIC For large programs several small mo...

Explain PUBLIC For large programs several small modules are linked together. In order that the modules link together correctly any variable name or label referred to in other m

System of forces.., Example of unlike coplaner parallel force''

Example of unlike coplaner parallel force''

Partial derivatives - transistor hybrid model, Partial derivatives - Transi...

Partial derivatives - Transistor hybrid model: The partial derivatives are taken by keeping the collector voltage or base current constant as pointed out by the subscript atta

Power control - motor control , Power Control A chopper converts  fix...

Power Control A chopper converts  fixed  de input voltage to a controllable dc output voltage. It is  the single  stage dc to dc conversion device. It is a high  speed  on/ of

Obtain the node voltages and current through each element, Q. For the circu...

Q. For the circuit shown in Figure, develop and execute a PSpice program to obtain the node voltages and the current through each element.

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd