Ch_4prob_0006

# Ch_4prob_0006 - Problem 4.6 The inverting ampliﬁer...

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Unformatted text preview: Problem 4.6 The inverting ampliﬁer circuit shown in Fig. P4.6 uses a resistor Rf to provide feedback from the output terminal to the inverting-input terminal. (a) Use the equivalent-circuit model of Fig. 4-4 to obtain an expression for the closed-loop gain G = vo /vs , in terms of Rs , Ri , Ro , RL , Rf , and A. (b) Determine the value of G for Rs = 10 Ω, Ri = 10 MΩ, Rf = 1 kΩ, Ro = 50 Ω, RL = 1 kΩ, and A = 106 . (c) Simplify the expression for G obtained in (a) by letting A → ∞, Ri → ∞, and Ro → 0 (ideal op-amp model). (d) Evaluate the approximate expression obtained in (c) and compare the result with the value obtained in (b). vp vn Rs vs _ + + _ Rf vo RL Figure P4.6: Circuit for Problem 4.6. Solution: (a) Upon replacing the op amp with its equivalent circuit model, we have: vp Ro + _ A(vp − vn) Rf i3 vo i4 RL vo Ri vn i2 Rs vs _ + in i1 At node vn : i1 + i2 + in = 0, or vn − vo vn − vs vn + + =0 Rf Rs Ri i3 + i4 − i1 = 0, or vo − A(vp − vn ) vo (vn − vo ) + − =0 Ro RL Rf (2) (1) At node vo : All rights reserved. Do not reproduce or distribute. ©2009 National Technology and Science Press Additionally, vp = 0. Simplifying and rearranging Eqs. (1) and (2), we have: vn vn 1 A − Ro Rf 1 1 1 ++ Rf Rs Ri + vo − vo vs = Rf Rs =0 (3) (4) 1 1 1 + + Rf RL Ro Solving Eqs. (3) and (4) simultaneously for vo leads to G= −(ARf − Ro )Rf Ri RL vo = vs Rs Ri RL (ARf − Ro ) + (Rs Ri + Rf Ri + Rf Rs )(Ro RL + Ro Rf + RLRf ) (3) (b) For Rs = 10 Ω, Ri = 10 MΩ, Rf = 1 kΩ, Ro = 50 Ω, RL = 1 kΩ, and A = 106 , G= ≃ −(106 × 103 − 50) × 103 × 107 × 103 10 × 107 × 103 (106 × 103 − 50) + (107 + 1010 + 104 )(5 × 104 + 5 × 104 + 106 ) −1022 = −99.9889 ≃ −100. 1020 + 1016 + · · · (c) For A → ∞, Ri → ∞, and Ro → 0, the expression in (5) reduces to G≃ (d) G=− 103 = −100. 10 −R f Rs All rights reserved. Do not reproduce or distribute. ©2009 National Technology and Science Press ...
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## This note was uploaded on 04/19/2010 for the course EE 220 taught by Professor Rawat during the Spring '09 term at Nevada.

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Ch_4prob_0006 - Problem 4.6 The inverting ampliﬁer...

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