Electrical Engineering ⇒ Topic : Practical Inverting Op Amp

PRACTICAL INVERTING OP AMP

In this case,

                                Ri ≠ ∞, A_v ≠ ∞, and R₀ ≠ 0

The practical OP Amp is shown in Figure (a)

                         Figure (a) Practical equivalent circuit.

The equivalent circuit of Figure (a) is shown in Figure 1 (a) and its Thevenin's equivalent is shown in Figure 1 (b).

                                                  Figure (1) Practical OP Amp.

V'_S and R'₁ are given as:

                                          ............ (1)

                                         .............. (2)

Since R_i ≠ ∞ , R_i. connected between inverting and non-inverting terminals. Since R₀ ≠ 0,R₀ is connected in series with the voltage source (A_vV_i). The equivalent circuit of Figure (a) is redrawn in Figure 1 (a). Let us replace the components to the left of the terminals 2 and 4 of Figure 1 (a) by the Thevenin's voltage V's and Thevenin's equivalent resistance R'1 as shown in Figure 1 (b).

V'_S and R'₁ are given by

                                         ................. (3)

                                     ........... (4)

Closed loop voltage gain A_V

The voltage between terminals 2 and 4 is V₂₄. Let V₂₄ = V. Therefore, it can be written as:

                            V_i = IR₂ + V_{0               ................ (5)}

                  Also V₀ = A_vV_i + IR₀,               ............... (6)

Applying KVL to the loop of Figure  1 (b), it can be written as:

             -V'_S; +  IR'1 + R₂ + R₀) A_vV_i = 0             ............ (7)

Using Eqs. (5) and (6), we obtain

                           ................ (8)

Using Eq. (7), Eq. (6) can be written as:

      [Using Eq. (8)]

                                    ............. (9)

Since R_i ≥ R₁, the following approximations can be made:

With approximations, Eq. (9) can be written as:

                    ............ (10)

where A, is gain of circuit with feedback or closed loop gain. If A_v ≥₁ and R₁ ≥(R₂ + R₀),A_v → R_2/R₁ Therefore, A_V, has the same value as in ideal case.