Circuits with Feedback Assignment Example | Topics and Well Written Essays - 1500 words

Circuits with Feedback - Assignment Example 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 †¦Ã¢â‚¬ ¦(5) Similarly, if = ( vi ¯ – vo)/Rf †¦Ã¢â‚¬ ¦(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 †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦ (7) Substituting the values from equations (5) and (6) we have, (vin+ – vin ¯)/R1= (vi ¯ – vo)/Rf †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦ (8) Or vin+/R1 – vin ¯/R1= vi ¯/Rf – vo/Rf Solving for , = †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦ (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 ‘Î ², 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) Or vin+/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. (2i) (2ib) If 'Avf, be the gain