Discuss the advantages of transforming timedomain circuits i

Discuss the advantages of transforming time-domain circuits into the corresponding frequency domain. How does this change the way circuits are analyzed?

Discuss what is meant by instantaneous, average and apparent power with the help of mathematical expressions. Also, Discuss how to define power factor from these quantities and what methods are used to improve it?

Solution

advantages of frequency domain approach:

1) with out the knowledge of the transfer function,the frequency responsse of stable open loop system can be obtained experimentally.

2) these methods are easy to use for design of control systems and for finding absolute as well as relative stability of the system.

3)when it is difficult to find transsfer function of a given system by writing differential equations, the transfer function of the system can be determined practically in the lobarotary by obtaining the frequency response of the sysstem.

4) frequency responsse tests are simple and can be made accurately by use of readily available signal generators and the precise measuring insstruments.

5) the apparatus required for obtaining frequency response is simple and inexpensive, and eassy to use.

6) for difficult cases,such as conditionally stable systems, nyquist plot is probabily the only method to analyse stability.

instantaneous power:

consider a circuit having complex impedance. let v(t)=vm.coswt be the voltage applied to the circuit and let i(t)=im.cos(wt+q) be the corresponding current flowing through the circuit. then the power at any instant of time is

p(t)=v(t).i(t)=vm.coswt.im.cos(wt+q)

we get

p(t)=[(vm.im)/2].[cos(2wt+q)+cosq]

the above equation represents instantaneous power.

average power:

if we conssider a purely resistive circuit, the phase angle between voltage and current is zero. hence the average power i

pav=(1/2).vm.im

if we conider a purely reactive circuit, the phase angle between voltage and current is 90 degrees. hence the average power is zero.

apparent power:

in case of sinusoidal voltage applied to the circuit,the product of voltage and current is not the true power or average power. this product is called apparent power. the apparent power is expressed in volt-amperes

apparent power=veff.Ieff