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# GAIN, EFFICIENCY, TRANSFER FUNCTION

can anyone say the difference between gain, efficiency and transfer function! with correct definitions?

I will explain the concepts in signal and systems terminology (which you can also import easily into control systems and communications).

Most of the systems which are picked up for study are LTI , i.e Linear Time Invariant. Various signals can be applied to these systems. A special class of signals if applied as input to such a system will have it's shape retained at the output, i.e their amplitude may change and their phase may change.But other than that there is no difference between input and output signals. (Such an input signal is an eigen function to the system and the amount by which it's amplitude changes is the eigen value of the system for that eigen function). For LTI systems a complex exponential signal is a typical signal which retains it's shape at the output i.e only the amplitude and phase may change. The 'transfer function' basically gives you an idea how the amplitude and phase may change for a particular exponential.

Suppose the 'transfer function' is H(s) and the complex exponential at the input is e^(s1t) (here s = s1) . The output is

|H(s1)| * e^(s1t - arg(H(s1))).

H(s) is complex function of s, so |H(s)| is its magnitude and arg(H(s)) is argument.

You can say that the 'gain' of the system is |H(s)|. As you will observe for different values of s (i.e for different complex exponentials) we get different gains.

Arg(H(s)) will be the 'phase change'.

We can't speak of gain as such for more general input signals as their shape is not conserved at the output of the system as is the case for exponential signals.

I Hope that some of your queries are cleared.

Most of the systems which are picked up for study are LTI , i.e Linear Time Invariant. Various signals can be applied to these systems. A special class of signals if applied as input to such a system will have it's shape retained at the output, i.e their amplitude may change and their phase may change.But other than that there is no difference between input and output signals. (Such an input signal is an eigen function to the system and the amount by which it's amplitude changes is the eigen value of the system for that eigen function). For LTI systems a complex exponential signal is a typical signal which retains it's shape at the output i.e only the amplitude and phase may change. The 'transfer function' basically gives you an idea how the amplitude and phase may change for a particular exponential.

Suppose the 'transfer function' is H(s) and the complex exponential at the input is e^(s1t) (here s = s1) . The output is

|H(s1)| * e^(s1t - arg(H(s1))).

H(s) is complex function of s, so |H(s)| is its magnitude and arg(H(s)) is argument.

You can say that the 'gain' of the system is |H(s)|. As you will observe for different values of s (i.e for different complex exponentials) we get different gains.

Arg(H(s)) will be the 'phase change'.

We can't speak of gain as such for more general input signals as their shape is not conserved at the output of the system as is the case for exponential signals.

I Hope that some of your queries are cleared.

Gain is the ratio of output to input and is represented by a real number between negative infinity and positive infinity.

Efficiency is the ratio of output power to input power and is represented by a real number between zero and the whole number one

Transfer function is the ratio of output to input and it is represented by a function who`s value may vary with time and the frequency of the input.

Efficiency is the ratio of output power to input power and is represented by a real number between zero and the whole number one

Transfer function is the ratio of output to input and it is represented by a function who`s value may vary with time and the frequency of the input.

GAIN :

In analog signals, gain is the basic measure of how much an amplifier, 'amplifies' the input signal.

let the gain is denoted as 'A'

A= ratio of output signal to input signal, where as the output signal is always greater than the input signal.

Suppose the output signal's value is less than the input, then their ratio results in 'attenuation'.

Amplifier Gain is of three types

1) Voltage Gain (Av)

2) Current Gain (Ai)

3) Power Gain (Ap)

where Av= output voltage/ input voltage

Ai= output current/ input current

Ap = Av * Ai

In analog signals, gain is the basic measure of how much an amplifier, 'amplifies' the input signal.

let the gain is denoted as 'A'

A= ratio of output signal to input signal, where as the output signal is always greater than the input signal.

Suppose the output signal's value is less than the input, then their ratio results in 'attenuation'.

Amplifier Gain is of three types

1) Voltage Gain (Av)

2) Current Gain (Ai)

3) Power Gain (Ap)

where Av= output voltage/ input voltage

Ai= output current/ input current

Ap = Av * Ai