# To return a voltage or current to the input we must

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remains unaffected. To return a voltage or current to the input, we must employ a mechanism for adding or sub- tracting such quantities. To add two voltage sources, we place them in series [Fig. 12.21(a)]. Thus, a feedback network returning a voltage must appear in series with the input signal, [Fig. (a) 1 2 Feedforward System Feedback (b) in F v v v v v e in F v v F v in v M 1 (c) (d) 0 Network M F in 1 v v Figure 12.21 (a) Addition of two voltages, (b) addition of feedback and input voltages, (c) differential pair as a voltage subtractor, (d) single transistor as a voltage subtractor. 12.21(b)], so that (12.47) For example, as shown in Fig. 12.21(c), a differential pair can subtract the feedback voltage from the input. Alternatively, as mentioned in Example 12.7, a single transistor can operate as a voltage subtractor [Fig. 12.21(d)]. To add two current sources, we place them in parallel [Fig. 12.22(a)]. Thus, a feedback net- work returning a current must appear in parallel with the input signal, Fig. 12.22(b), so that (12.48) For example, a transistor can return a current to the input [Fig. 12.22(c)]. So can a resistor if it is large enough to approximate a current source [Fig. 12.22(d)]. Example 12.10 Determine the types of sensed and returned signals in the circuit of Fig. 12.23. Solution This circuit is an implementation of the noninverting amplifier shown in Fig. 12.2. Here, the differential pair with the active load plays the role of an op amp. The resistive divider senses the output voltage and serves as the feedback network, producing . Also, Of course, only quantities having the same dimension can be added or subtracted. That is, a voltage cannot be added to a current.

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BR Wiley/Razavi/ Fundamentals of Microelectronics [Razavi.cls v. 2006] June 30, 2007 at 13:42 620 (1) 620 Chap. 12 Feedback i 1 i 2 (a) Feedforward System Feedback (b) (c) (d) in i e i i F in i M 1 e i F i in i e i F i R F Network Figure 12.22 (a) Addition of two currents, (b) addition of feedback current and input current, (c) circuit realization, (d) another realization. M 1 I SS DD M 2 V M 3 M 4 R 1 R 2 out in v v v F Figure 12.23 and operate as both part of the op amp (the forward system) and a voltage subtractor. The amplifier therefore combines the topologies in Figs. 12.19(c) and 12.21(c). Exercise Repeat the above example if . Example 12.11 Compute the feedback factor, , for the circuit depicted in Fig. 12.24. Assume . Solution Transistor both senses the output voltage and returns a current to the input. The feedback factor is thus given by (12.49) where denotes the transconductance of .
BR Wiley/Razavi/ Fundamentals of Microelectronics [Razavi.cls v. 2006] June 30, 2007 at 13:42 621 (1) Sec. 12.5 Polarity of Feedback 621 M 1 V DD R I in M 2 R D1 D2 out V M F i F Figure 12.24 Exercise Calculate the feedback factor if is degenerated by a resistor of value . Let us summarize the properties of the “ideal” feedback network. As illustrated in Fig. 12.25(a), we expect such a network to exhibit an infinite input impedance if sensing a volt- K out V K 0 I out K F V in V 0 K I in I F (a) (b) Figure 12.25 (a) Input impedance of ideal feedback networks for sensing voltage and current quantities, (b) output impedance of ideal feedback networks for producing voltage and current quantities.

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