fdbkamps

# fdbkamps - c Copyright 2009 W Marshall Leach Jr Professor...

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c ° Copyright 2009. W. Marshall Leach, Jr., Professor, Georgia Institute of Technology, School of Electrical and Computer Engineering. Feedback Ampli f ers Co l lect iono fSo lvedProb lems A collection of solved feedback ampli f er problems can be found at the below link. The solutions are based on the use of the Mason Flow Graph described below. http://users.ece.gatech.edu/~mleach/ece3050/notes/feedback/FBExamples.pdf Basic Description of Feedback A feedback ampli f er is one in which the output signal is sampled and fed back to the input to form an error signal that drives the ampli f er. The basic block diagrams of non-inverting and inverting feedback ampli f ers are shown in Fig. 1. Depending on the type of feedback, the variables x , y , and z are voltages or currents. The diagram in Fig. 1(a) represents a non-inverting ampli f er. The summing junction at its input subtracts the feedback signal from the input signal to form the error signal z = x by which drives the ampli f er. If the ampli f er has an inverting gain, the feedback signal must be added to the input signal in order for the feedback to be negative. This is illustrated in Fig. 1(b). The summing junction at the input adds the feedback signal to the input signal to form the error signal z = x + by . In both diagrams, the gain around the loop is negative and equal to bA ,whe rebo th A and b are positive real constants. Because the loop-gain is negative, the feedback is said to be negative. If the gain around the loop is positive, the ampli f er is said to have positive feedback which causes it to be unstable. Figure 1: Feedback ampli f er block diagrams. (a) Non-inverting. (b) Inverting. In the non-inverting ampli f er of Fig. 1(a), the error signal is given by z = x by . The output signal can be written. y = Az = A ( x by ) (1) This can be solved for the gain to obtain y x = A 1+ bA (2) We see that the e f ect of the feedback is to reduce the gain by the factor (1 + bA ) . This factor is called the “amount of feedback”. It is often speci f ed in dB by the relation 20 log | bA | . In the inverting ampli f er of Fig. 1(b), the error signal is given by z = x + by .W h e n x goes positive, y goes negative, so that the error signal represents a di f erence signal. The output signal can be written y = Az = A ( x + by ) (3) 1

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This can be solved for the gain to obtain y x = A 1+ bA (4) We see that the amount of feedback for the inverting ampli f er is the same as for the non-inverting ampli f er. If A is large enough so that bA >> 1 , the gain of the non- inverting ampli f er given by Eq. (2) can be approximated by y x ' A bA = 1 b (5) The gain of the inverting ampli f er given by Eq. (4) can be approximated by y x ' A bA = 1 b (6) These are important results, for they show that the gain is set by the feedback network and not by the ampli f er. In practice, this means that an ampli f er without feedback can be designed without too much consideration of what its gain will be as long as the gain is high enough. When feedback is added, the gain can be reduced to any desired value by the feedback network.
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## This note was uploaded on 05/26/2011 for the course ECE 3050 taught by Professor Hollis during the Summer '08 term at Georgia Tech.

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fdbkamps - c Copyright 2009 W Marshall Leach Jr Professor...

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