Closed Loop Amplifier

Input Resistance with Feedback:

fig. 1, shows a voltage series feedback with the OPAMP equivalent circuit.

Fig. 1

In this circuit R_i is the input resistance (open loop) of the OPAMP and R_if is the input resistance of the feedback amplifier. The input resistance with feedback is defined as

Since AB is much larger than 1, which means that R_if is much larger that R_i. Thus R_if approaches infinity and therefore, this amplifier approximates an ideal voltage amplifier.

Output Resistance with Feedback:

Output resistance is the resistance determined looking back into the feedback amplifier from the output terminal. To find output resistance with feedback R_f, input v_in is reduced to zero, an external voltage V_o is applied as shown in fig. 2.

Fig. 2

The output resistance (R_of ) is defined as

This shows that the output resistance of the voltage series feedback amplifier is ( 1 / 1+AB ) times the output resistance R_o of the op-amp. It is very small because (1+AB) is very large. It approaches to zero for an ideal voltage amplifier.Reduced Non-linear Distortion:

 The final stage of an OPAMP has non-linear distortion when the signal swings over most of the ac load line. Large swings in current cause the r'_e of a transistor to change during the cycle. In other words, the open loop gain varies throughout the cycle of when a large signal is being applied. It is this changing voltage gain that is a source of the non-linear distortion.

Noninverting voltage feedback reduces non-linear distortion because the feedback stabilizes the closed loop voltage gain, making it almost independent of the changes in open loop voltage gain. As long as loop gain, is much greater than 1, the output voltage equals 1/B times the input voltage. This implies that output will be a more faithful reproduction of the input .

Consider, under large signal conditions, the open loop OPAMP circuit produces a distortion voltage, designated v_dist. It can be represented by connecting a source v_dist in series with Av_d. Without negative feedback all the distortion voltage v_dist appears at the output. But with negative feedback, a fraction of v_dist is feedback to inverting input. This is amplified and arrives at the output with inverted phase almost completely canceling the original distortion produced by the output stage.

The first term is the amplified output voltage. The second term in the distortion that appears at the final output. The distortion voltage is very much, reduced because AB>>1

Bandwidth with Feedback:

The bandwidth of an amplifier is defined as the band of frequencies for which the gain remains constant. Fig. 3, shows the open loop gain vs frequency curve of 741C OPAMP. From this curve for a gain of 2 x 10⁵ the bandwidth is approximately 5Hz. On the other hand, the bandwidth is approximately 1MHz when the gain is unity.

Fig. 3

The frequency at which gain equals 1 is known as the unity gain bandwidth. It is the maximum frequency the OPAMP can be used for.
Furthermore, the gain bandwidth product obtained from the open loop gain vs frequency curve is equal to the unity gain bandwidth of the OPAMP.
Since the gain bandwidth product is constant obviously the higher the gain the smaller the bandwidth and vice versa. If negative feedback is used gain decrease from A to A / (1+AB). Therefore the closed loop bandwidth increases by (1+AB).

Bandwidth with feedback = (1+ A B) x (B.W. without feedback)

f_f= f_o (1+A B)

 Output Offset Voltage:

In an OPAMP even if the input voltage is zero an output voltage can exist. There are three cause of this unwanted offset voltage. Input offset voltage. Input bias voltage. Input offset current. Fig. 4, shows a feedback amplifier with an output offset voltage source in series with the open loop output AVd. The actual output offset voltage with negative feedback is smaller. The reasoning is similar to that given for distortion. Some of the output offset voltage is fed back to the inverting input. After amplification an out of phase voltage arrives at the output canceling most of the original output offset voltage. When loop gain AB is much greater than 1, the closed loop output offset voltage is much smaller than the open loop output offset voltage.

Fig. 4

Voltage Follower:

The lowest gain that can be obtained from a non-inverting amplifier with feedback is 1. When the non-inverting amplifier gives unity gain, it is called voltage follower because the output voltage is equal to the input voltage and in phase with the input voltage. In other words the output voltage follows the input voltage.

To obtain voltage follower, R₁ is open circuited and R_f is shorted in a negative feedback amplifier of fig. 4. The resultant circuit is shown in fig. 5.

vout = Avd= A (v1 – v2) v1 = vin v2 =vout v1 = v2 if A >> 1 vout = vin. The gain of the feedback circuit (B) is 1. Therefore Af = 1 / B = 1

Fig. 5