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# I will pay for the following essay Circuits with Feedback. The essay is to be 6 pages with three to five sources, with in-text citations and a reference page.Download file to see previous pages Deriva

I will pay for the following essay Circuits with Feedback. The essay is to be 6 pages with three to five sources, with in-text citations and a reference page.

Derivation of Feedback Equation for Inverting Amplifier

Let we consider an inverting amplifier as shown in fig. 2.

Then if ‘A, is the gain then, as vi+ = 0, there fore

vo = A(vin+ – vin¯)

vo = - A vin¯

Also from Ohm’s Law the current is simply the difference in the voltage across R1 divided R1,

i1 = (vin+ – vin¯)/R1 ……(5)

Similarly,if = ( vi¯ – vo)/Rf ……(6)

By Kerchief’s current Law at the inverting input,

i1 = if + i¯ where i¯ is the current entering the amplifier at

it’s inverting point, yet for an idea amplifier it reaches to zero hence,

i1 = if ……… (7)

Substituting the values from equations (5) and (6) we have,

(vin+ – vin¯)/R1= (vi¯ – vo)/Rf ……… (8)

Orvin+/R1 – vin¯/R1= vi¯/Rf – vo/Rf

Solving for ,

= ……… (9)

This is the required voltage gain expression for inverting amplifier with feedback in

terms of open loop gain.

Problem 2: Each of the amplifiers shown below incorporate series feedback. The

gains, input resistances

and output resistances are quoted without feedback. For each amplifier determine: -

a) The feedback fraction.

b) The gain with feedback.

c) The input impedance with feedback.

d) The output impedance with feedback.

Solution: (i) a) If we consider the given cct. then for feedback fraction ‘β, for

given cct. is defined as,

...

terms of open-loop gain A.

Derivation of Feedback Equation for Inverting Amplifier

Let we consider an inverting amplifier as shown in fig. 2 (Bogart, 1997, p. 670).

Then if 'A, is the gain then, as vi+ = 0, there fore

vo = A(vin+ - vin)

vo = - A vin

Fig. 2(a)

Also from Ohm's Law the current is simply the difference in the voltage

across R1 divided R1,

i1 = (vin+ - vin)/R1 (5)

Similarly,if = ( vi - vo)/Rf (6)

By Kerchief's current Law at the inverting input,

i1 = if + i where i is the current entering the amplifier at

it's inverting point, yet for an idea amplifier it reaches to zero hence,

i1 = if (7)

Substituting the values from equations (5) and (6) we have,

(vin+ - vin)/R1= (vi - vo)/Rf (8)

Orvin+/R1 - vin/R1= vi/Rf - vo/Rf

Solving for ,

= (9)

This is the required voltage gain expression for inverting amplifier with feedback in

terms of open loop gain.

Problem 2: Each of the amplifiers shown below incorporate series feedback. The

gains, input resistances

and output resistances are quoted without feedback. For each amplifier determine: -

a) The feedback fraction.

b) The gain with feedback.

c) The input impedance with feedback.

d) The output impedance with feedback.

Solution: (i) a) If we consider the given cct. then for feedback fraction ', for

given cct. is defined as,

= (2ia)

Substituting the values in equation (2ia) from given cct. we have,

=

= 0.175 2ia

Fig.