1. Feedback Amplifiers

2. Todays Agenda Feedback Concepts The Four Basic Feedback Topologies
Series - Shunt Feedback or Voltage Amplifiers
shunt-series feedback or Current Amplifiers
Series-Series Feedback or Transconductance Amplifiers
Shunt - Shunt Feedback or Transresistance Amplifiers
Summary of Feedback Topologies
Negative Feedback Voltage Amplifiers
Gain Calculation
Bandwidth Extension
Input and output Impedance
Noise Reduction
Advantages and Disadvantages of negative feedback
Stability Problems in negative Feedback

4. Feedback Concepts
Most physical systems incorporate some form of feedback. A typical feedback connection is shown in Fig.1. The input signal, Vs, is applied to a mixer network, where it is combined with a feedback signal, Vf. The sum or difference of these signals, Vi, is then the input voltage to the amplifier. A portion of the amplifier output, Vo, is connected to the feedback network (), which provides a reduced portion of the output as feedback signal to the input mixer network.
(a)
(b)
Fig. 1 Block diagram (a) Positive feedback (b) Negative feedback amplifier.

5. Feedback Concepts (Continued)
Depending on the relative polarity of the signal being fed back into a circuit, one may have negative or positive feedback.
Negative feedback results in decreased voltage gain, for which a number of circuit features are improved as summarized below.
Positive feedback drives a circuit into oscillation as in various types of oscillator circuits that will be discussed in The next chapters.
Negative feedback results in reduced overall voltage gain, a number of improvements are obtained, among them being:
Better stabilized voltage gain or desensitize the gain: that is, make the value of the gain less sensitive to variations in the value of circuit components, such as might be caused by changes in temperature.
Improved frequency response or extend the bandwidth of the amplifier.
Control the input and output impedances or higher input impedance and lower output impedance.
Reduce the effect of noise: that is, minimize the contribution to the output of unwanted electric signals generated, either by the circuit components themselves, or by extraneous interference.
More linear operation or Reduce nonlinear distortion: that is, make the output proportional to the input (in other words, make the gain constant, independent of signal level).

6. The Four Basic Feedback Topologies
1. Series-Shunt Feedback (Voltage amplifiers)
i/p mixing o/p sampling
Shunt- Series Feedback (Current amplifiers)
Series-Series Feedback (Transconductance amplifiers)
Shunt-Shunt Feedback (Transresistance amplifiers)

7. The Four Basic Feedback Topologies
Based on the quantity to be amplified (voltage or current) and on the desired form of output (voltage or current), amplifiers can be classified into four categories. These categories Classified as follows:
Series - Shunt Feedback or Voltage Amplifiers
Voltage amplifiers are intended to amplify an input voltage signal and provide an output voltage signal. The voltage amplifier is essentially a voltage-controlled voltage source. A suitable feedback topology is the voltage-mixing (series connection at the input ) and voltage sampling (parallel or shunt connection at the output) as shown in Fig. 2.2.
Because of the Thevenin representation of the source, the feedback signal Vf should be a voltage that can be mixed with the source voltage in series.
This topology not only stabilizes the voltage gain but also results in a higher input resistance (intuitively, a result of the series connection at the input) and a lower output resistance (intuitively, a result of the parallel connection at the output), which are desirable properties for a voltage amplifier.
Fig. 2.2 Series - shunt feedback or voltage amplifier topology.

8. The Four Basic Feedback Topologies (Continued)
shunt-series feedback or Current Amplifiers
The input signal in a current amplifier is essentially a current, and thus the signal source is most conveniently represented by its Norton equivalent.
The output quantity of interest is current; hence the feedback network should sample the output current.
The feedback signal should be in current form so that it may be mixed in shunt with the source current.
Thus the feedback topology suitable for a current amplifier is the current- mixing current-sampling topology, illustrated in Fig. 2.3.
Because of the parallel (or shunt) connection at the input, and the series connection at the output, this feedback topology is also known as shunt series feedback.
This topology not only stabilizes the current gain but also results in a lower input resistance, and a higher output resistance, both desirable properties for a current amplifier.
Fig. 2.3 shunt-series feedback or Current amplifier topology.

9. EXAMPLE of Current Amplifier

10. The Four Basic Feedback Topologies (Continued)
Series-Series Feedback or Transconductance Amplifiers
In transconductance amplifiers the input signal is a voltage and the output signal is a current.
It follows that the appropriate feedback topology is the voltage-mixing current-sampling topology, illustrated in Fig. 2.4.
Fig. 2.4 Series-series feedback or transconductance amplifier topology.

11. Series-Series Feedback or Trans-conductance Amplifiers

12. The Four Basic Feedback Topologies (Continued)
Shunt - Shunt Feedback or Transresistance Amplifiers
In Transresistance amplifiers the input signal is current and the output signal is voltage.
It follows that the appropriate feedback topology is of the current - mixing voltage-sampling type, shown in Fig The presence of the parallel (or shunt) connection at both the input and the output makes this feedback topology also known as shunt - shunt feedback.
Fig. 2.5 Shunt - shunt feedback or Transresistance amplifier topology.

13. Shunt - Shunt Feedback or Transresistance Amplifiers

14. The Four Basic Feedback Topologies (Continued)
Summary of Feedback Topologies
A summary of the gain, feedback factor, and gain with feedback of Figs. 2.2 to 2,5 is provided for reference in Table 2.1.

15. 2.3 Negative Feedback Voltage Amplifiers
2.3.1 Gain Calculation
Fig shows the basic structure or signal-flow diagram of a negative feedback amplifier. Ao is the Gain of the open-loop amplifier and  is the feedback factor.
Thus its output voltage Vo is related to the input voltage Vi by:
Vo  AoVi
(2.1)
The output Vo is fed to the load as well as to a feedback network, which produces a sample of the output.
Fig. 2.6 General structure of negative feedback amplifier

16. 2.3 Negative Feedback Voltage Amplifiers (Continued)
2.3.1 Gain Calculation
This sample Vf is related to Vo by the feedback factor  as:
Vf  Vo
(2.2)
The feedback signal Vf subtracted from the source signal Vs, which is the input to the complete feedback amplifier, to produce the signal Vi which is the input to the basic amplifier which is given by:
Vi  Vs Vf
(2.3)
Here we note that it is this subtraction that makes the feedback negative. In essence, negative feedback reduces the signal that appears at the input of the basic amplifier.
The gain of the feedback amplifier can be obtained by combining Eqs. (2.1) through (2.3) as:
V A A
A  o
 
o o f
(2.4)
Vs 1 A0 1 T
The quantity Af is called the feedback gain or closed loop gain, a name that follows from Fig. 2.6, A0 is the open loop gain or gain without feedback, T = A0 is the loop gain, and (1+ A0) is the amount of feedback.

17. 2.3 Negative Feedback Voltage Amplifiers (Continued)
2.3.1 Gain Calculation
For the feedback to be negative, the loop gain Ao should be positive; that is, the feedback signal Vf should have the same sign as Vs .
Thus this resulting in a smaller difference signal Vi. Equation (2.4) indicates
that for positive Ao the gain-with-feedback, Af will be smaller than the open- loop gain Ao by the quantity 1+ Ao, which is called the amount of feedback.
In other words, the overall gain will have very little dependence on the gain of the basic amplifier, Ao, a desirable property because the gain Ao is usually a function of many manufacturing and application parameters, some of which might have wide tolerances.
Therefore, the closed-loop gain is almost entirely determined by the feedback elements.

18. 2.3 Negative Feedback Voltage Amplifiers (Continued)
2.3.1 Gain Calculation
Gain Desensitivity
The gain of the closed-loop amplifier is less sensitive to variation of the gain of the basic amplifier this property can be analytically established as follows: Assume that  is constant. Taking differentials of both sides of Eq. (2.4)
which says that the percentage change in Af (due to variations in some circuit parameter) is smaller than the percentage change in Ao by the amount of feedback.
For this reason the amount of feedback, (1 +  Ao) or (1 + T), is also known as the Desensitivity factor.
Sensitivity 1/ ((1 +  Ao) )

19. 2.3 Negative Feedback Voltage Amplifiers (Continued)
Gain Calculation
Example 2.1:
For the Op Amp circuit shown in Fig. 2.7, if the op amp has infinite input resistance (Ri = ), zero output resistance (Ro = o) and the open-loop voltage gain Ao = 100 .
Find an expression for the feedback factor .
Find the ratio R2/R1 to obtain a closed loop voltage gain Af of 10.
What is the amount of feedback in decibels?
If the source voltage, Vs = 1 V, find the output voltage, Vo, the feedback voltage Vf, and the input voltage Vi.
If Ao decreases by 20%, what is the corresponding decrease in Af ?
Solution
(a) The feedback factor,  is given by: V
B = f  R1
Vo R1  R2
(b) From (2.4), closed loop voltage gain Af is:
 Vo Ao Ao A
  f
Vs 1  Ao 1 T
Fig. 2.7 An Op Amp circuit

20. 2.3 Negative Feedback Voltage Amplifiers (Continued)
2.3.1 Gain Calculation
Example 2.1 Solution
The amount of feedback =1 +Ao = x 9x10-2 = 10 = 20 dB.
The output voltage, Vo = Af x Vs = 10 x 1 = 10 V.
The feedback voltage Vf =  x Vo = 9x10-2 x 10 = 0.9 V.
The input voltage, Vi = Vs - Vf = 1 – 0.9 V = 0.1 V
(b) From (2.8), the percentage change in Af is given by:
dAf
1 dAo 1
 20%  2.44%  
A (1 Ao ) A
(1 9x102 x80) 80 f o

22. 2.3 Negative Feedback Voltage Amplifiers (Continued)
Bandwidth Extension
Example 2.2:
Consider the noninverting op-amp circuit of Fig.2.8. Let the open-loop gain, Ao has a low-frequency value of 104 and a uniform 20 dB/decade rolloff at high frequencies with a 3-dB frequency, fb of 100 Hz. If R1 = 1 kΩ and R2 = 9 kΩ, for the closed-loop amplifier find:
The low-frequency gain Af.
The upper 3-dB frequency, fbf .
Solution
R 1
    0.1 1
R1  R2 1 9
The amount of FB  (1 Ao )  (1 T )  1001
(a) From Eq. (2.12a) Af , is given by: 4
Af  A /(1 Ao )  A /(1 T )  10 /1001  9.99 V /V
Fig. 2.8 An Op Amp circuit
(b) From Eq. (2.12a) fbf ) is given by:
fbf
 fb (1 Ao )  fb (1 T )  100x1001  kHz

23. 2.3 Negative Feedback Voltage Amplifiers (Continued)
2.3.3 Input and output Impedances Input Impedance
Consider the series-shunt feedback amplifier connection shown in Fig. 2.9, the input impedance can be determined as follows:
The input impedance with series feedback is increased and has the value of the input impedance without feedback multiplied by a factor equal to the amount of feedback (1 +  Ao) = (1 + T).

24. 2.3 Negative Feedback Voltage Amplifiers (Continued)
Fig. 2.9 Voltage amplifier feedback connection model

25. 2.3 Negative Feedback Voltage Amplifiers (Continued)
2.3.3 Input and output Impedances Output Impedance
The series-shunt feedback amplifier connection shown in Fig. 2.9, provides sufficient circuit detail to determine the output impedance with feedback. The output impedance is determined by applying a voltage, V, resulting in a current, I, with Vs shorted out (Vs = 0). The voltage V is then given by:
The output impedance with series feedback is reduced and has the value of the output impedance without feedback divided by a factor equal to the amount of feedback (1 +  Ao) or (1 +T).

26. 2.3 Negative Feedback Voltage Amplifiers (Continued)
2.3.3 Input and output Impedances
Example 2.3:
Determine the voltage gain, Af, breakdown frequency, fbf, input impedance Zi and output impedance, Zo with feedback for voltage amplifier, shown in Fig. 2.9, having Ao = 100, fb = 200 Hz, Ri = 10 kΩ and Ro = 20 kΩ for:(a)  = 0.1 (b)  = 0.5

27. 2.3 Negative Feedback Voltage Amplifiers
2.3.4 Noise Reduction
Negative feedback can be employed to reduce the noise or interference in an amplifier or, more precisely, to increase the ratio of signal to noise.
From Fig (a),the output voltage Vo is related to the input voltage Vi by:
Vo  AoVi  D
where D is the distortion generated by the amplifier.
With the negative feedback amplifier of Fig (b), when Vs =0, to study
the effect of noise, the output voltage Vo is related to the input voltage Vi by:
D D
d  AoVi  D    Ao d  D  d  
(2.15)
(1  Ao)
(1 T )
Feedback distortion < open loop distortion
The distortion with feedback is reduced and has the value of distortion without feedback, D, divided by a factor equal to the amount of feedback (1 +  Ao) or (1 + T).
(a)
(b)
Fig Voltage amplifier noise model: (a) Open loop; (b) With feedback

28. 2.3 Negative Feedback Voltage Amplifiers (Continued)
2.3.5 Advantages and Disadvantages of negative feedback

29. THE STABILITY PROBLEM Transfer Function of the Feedback Amplifier
The Nyquist Plot
Effect Of Feedback On The Amplifier Poles
STABILITY STUDY USING BODE PLOTS

30. Stability

31. Relationship between pole location and transient response.