1. Feedback Xs Xi Xo + - Xf βf
What is feedback? Taking a portion of the signal arriving at the load and feeding it back to the input.
What is negative feedback? Adding the feedback signal to the input so as to partially cancel the input signal to the amplifier.
Doesn’t this reduce the gain? Yes, this is the price we pay for using feedback.
Why use feedback? Provides a series of benefits, such as improved bandwidth, that outweigh the costs in lost gain and increased complexity in amplifier design.
Ch. 8 Feedback

2. Feedback Amplifier AnalysisXs Xi Xo + - Xf βf
Ch. 8 Feedback

3. Advantages of Negative Feedback
Gain desensitivity - less variation in amplifier gain with changes in  (current gain) of transistors due to dc bias, temperature, fabrication process variations, etc.
Bandwidth extension - extends dominant high and low frequency poles to higher and lower frequencies, respectively.
Noise reduction - improves signal-to-noise ratio
Improves amplifier linearity - reduces distortion in signal due to gain variations due to transistors
Cost of these advantages:
Loss of gain, may require an added gain stage to compensate.
Added complexity in design
Ch. 8 Feedback

4. Basic Types of Feedback Amplifiers
There are four types of feedback amplifiers. Why?
Output sampled can be a current or a voltage
Quantity fed back to input can be a current or a voltage
Four possible combinations of the type of output sampling and input feedback
One particular type of amplifier, e.g. voltage amplifier, current amplifier, etc. is used for each one of the four types of feedback amplifiers.
Feedback factor f is a different type of quantity, e.g. voltage ratio, resistance, current ratio or conductance, for each feedback configuration.
Before analyzing the feedback amplifier’s performance, need to start by recognizing the type or configuration.
Terminology used to name types of feedback amplifier, e.g. Series-shunt
First term refers to nature of feedback connection at the input.
Second term refers to nature of sampling connection at the output.
Ch. 8 Feedback

5. Basic Types of Feedback Amplifiers
Series - Shunt
Shunt - Series
Series - Series
Shunt - Shunt
Ch. 8 Feedback

6. Method of Feedback Amplifier Analysis
Recognize the feedback amplifier’s configuration, e.g. Series-shunt
Calculate the appropriate gain A for the amplifier, e.g. voltage gain.
This includes the loading effects of the feedback circuit (some combination of resistors) on the amplifier input and output.
Calculate the feedback factor f
Calculate the factor f A and make sure that it is: 1) positive and 2) dimensionless
Calculate the feedback amplifier’s gain with feedback Af using
Calculate the final gain of interest if different from the gain calculated, e.g. Current gain if voltage gain originally determined.
Determine the dominant low and high frequency poles for the original amplifier, but taking into account the loading effects of the feedback network.
Determine the final dominant low and high frequency poles of the amplifier with feedback using
Ch. 8 Feedback

7. Series-Shunt Feedback Amplifier - Ideal Case
Assumes feedback circuit does not load down the basic amplifier A, i.e. doesn’t change its characteristics
Doesn’t change gain A
Doesn’t change pole frequencies of basic amplifier A
Doesn’t change Ri and Ro
For the feedback amplifier as a whole, feedback does change the midband voltage gain from A to Af
Does change input resistance from Ri to Rif
Does change output resistance from Ro to Rof
Does change low and high frequency 3dB frequencies
Basic Amplifier
Feedback Circuit
Equivalent Circuit for Feedback Amplifier
Ch. 8 Feedback

8. Series-Shunt Feedback Amplifier - Ideal Case
Midband Gain
Input Resistance
Output Resistance It Vt
Ch. 8 Feedback

9. Series-Shunt Feedback Amplifier - Ideal Case
Low Frequency Pole
Low 3dB frequency lowered by feedback.
High Frequency Pole
Upper 3dB frequency raised by feedback.
Ch. 8 Feedback

10. Practical Feedback Networks
Feedback networks consist of a set of resistors
Simplest case (only case considered here)
In general, can include C’s and L’s (not considered here)
Transistors sometimes used (gives variable amount of feedback) (not considered here)
Feedback network needed to create Vf feedback signal at input (desirable)
Feedback network has parasitic (loading) effects including:
Feedback network loads down amplifier input
Adds a finite series resistance
Part of input signal Vs lost across this series resistance (undesirable), so Vi reduced
Feedback network loads down amplifier output
Adds a finite shunt resistance
Part of output current lost through this shunt resistance so not all output current delivered to load RL (undesirable) Vi Vo Vf
How do we take these
loading effects into account?
Ch. 8 Feedback

11. Equivalent Network for Feedback Network
Need to find an equivalent network for the feedback network including feedback effect and loading effects.
Feedback network is a two port network (input and output ports)
Can represent with h-parameter network (This is the best for this particular feedback amplifier configuration)
h-parameter equivalent network has FOUR parameters
h-parameters relate input and output currents and voltages
Two parameters chosen as independent variables. For h-parameter network, these are input current I1 and output voltage V2
Two equations relate other two quantities (output current I2 and input voltage V1) to these independent variables
Knowing I1 and V2, can calculate I2 and V1 if you know the h-parameter values
h-parameters can have units of ohms, 1/ohms or no units (depends on which parameter)
Ch. 8 Feedback

12. Series-Shunt Feedback Amplifier - Practical Case
Feedback network consists of a set of resistors
These resistors have loading effects on the basic amplifier, i.e they change its characteristics, such as the gain
Can use h-parameter equivalent circuit for feedback network
Feedback factor f given by h12 since
Feedforward factor given by h21 (neglected)
h22 gives feedback network loading on output
h11 gives feedback network loading on input
Can incorporate loading effects in a modified basic amplifier. Basic gain of amplifier AV becomes a new, modified gain AV’ (incorporates loading effects).
Can then use feedback analysis from the ideal case.
Ch. 8 Feedback

13. Series-Shunt Feedback Amplifier - Practical Case
Summary of Feedback Network Analysis
How do we determine the h-parameters for the feedback network?
For the input loading term h11
Turn off the feedback signal by setting Vo = 0.
Then evaluate the resistance seen looking into port 1 of the feedback network (also called R11 here).
For the output loading term h22
Open circuit the connection to the input so I1 = 0.
Find the resistance seen looking into port 2 of the feedback network (also called R22 here).
To obtain the feedback factor f (also called h12 )
Apply a test signal Vo’ to port 2 of the feedback network and evaluate the feedback voltage Vf (also called V1 here) for I1 = 0.
Find f from f = Vf/Vo’
Ch. 8 Feedback

14. Series-Shunt Feedback Amplifier - Practical Case Summary of Approach to Analysis
Evaluate modified basic amplifier (including loading effects of feedback network)
Including h11 at input
Including h22 at output
Including loading effects of source resistance
Including load effects of load resistance
Analyze effects of idealized feedback network using feedback amplifier equations derived
Note
Av’ is the modified voltage gain including the effects of h11 , h22 , RS and RL.
Ri’, Ro’ are the modified input and output resistances including the effects of h11 , h22 , RS and RL.
Basic Amplifier
Practical Feedback Network
Modified Basic Amplifier
Idealized Feedback Network
Ch. 8 Feedback

15. Example - Series-Shunt Feedback Amplifier
Two stage amplifier
Each stage a CE amplifier
Transistor parameters Given: 1= 2 =50, rx1=rx2=0
Coupled by capacitors, dc biased separately
DC analysis:
DC analysis for each stage can be done separately
since stages are isolated (dc wise) by coupling capacitors.
Ch. 8 Feedback

16. Example - Series-Shunt Feedback Amplifier
Redraw circuit to show
Feedback circuit
Type of output sampling
(voltage in this case = Vo)
Type of feedback signal to input (voltage in this case = Vf) + _ Vi + + Vf Vo _ _
Ch. 8 Feedback

17. Example - Series-Shunt Feedback Amplifier
Input Loading Effects
Vo=0
Output Loading Effects
I1=0
Amplifier with Loading Effects R1 R2
Ch. 8 Feedback

18. Example - Series-Shunt Feedback Amplifier
Construct ac equivalent circuit at midband frequencies including loading effects of feedback network.
Analyze circuit to find midband gain
(voltage gain for this series-shunt configuration) R1 R2 R2 R1
Ch. 8 Feedback

19. Example - Series-Shunt Feedback Amplifier
Midband Gain Analysis
Ch. 8 Feedback

20. Midband Gain with Feedback
Determine the feedback factor f
Calculate gain with feedback Avf
Note
f Avo > 0 as necessary for negative feedback
f Avo is large so there is significant feedback. For f Avo  0, there is almost no feedback.
Can change f and the amount of feedback by changing Rf1 and/or Rf2.
NOTE: Since f Avo >> 0
Ch. 8 Feedback

21. Input and Output Resistances with Feedback
Determine input Ri and output Ro resistances with loading effects of feedback network.
Calculate input Rif and output Rof resistances for the complete feedback amplifier.
Ch. 8 Feedback

22. Equivalent Circuit for Series-Shunt Feedback Amplifier
Voltage gain amplifier
Modified voltage gain, input and output resistances
Included loading effects of feedback network
Included feedback effects of feedback network
Include source resistance effects
Significant feedback, i.e f Avo is large and positive
Ch. 8 Feedback

23. Low Frequency Poles and Zeros for Series-Shunt Feedback Amplifier
Six capacitors:
Input and output coupling capacitors C1 and C5
Emitter bypass capacitors C3 and C4
Interstage coupling capacitors C2
Feedback coupling capacitor C6
Analyze using Gray-Searle (Short Circuit) Technique one capacitor at a time
Find dominant low frequency pole (highest frequency one)
Ch. 8 Feedback

24. Example - Input Coupling Capacitor’s Pole Frequency
Equivalent circuit for C1
Note that there are some loading effects of the feedback network on this pole frequency. In Ri1 the feedback resistors determine R1
Ch. 8 Feedback

25. Example - Interstage Coupling Capacitor’s Pole Frequency
Equivalent circuit for C2
Note: No RE2 since
C4 shorts it out.
Ch. 8 Feedback

26. Example - Feedback Coupling Capacitor’s Pole Frequency
Equivalent circuit for C6
Ch. 8 Feedback

27. Example - Emitter Bypass Capacitor’s Pole Frequency
Equivalent circuit for C3
IE1
Ch. 8 Feedback

28. Example - Emitter Bypass Capacitor’s Pole Frequency
Equivalent circuit for C4
IE2
Ch. 8 Feedback

29. Example - Output Coupling Capacitor’s Pole Frequency
Equivalent circuit for C5
Ch. 8 Feedback

30. Zeros for Series-Shunt Feedback Amplifier Example
Coupling capacitors C1, C2 and C5 give zeros at  = 0 since ZC = 1/sC and they are in the signal line.
Emitter bypass capacitors C3 and C4 give a zero when the impedance ZCE || RE.
Feedback capacitor C6 gives a zero when [ZC6 +R2] || RC2 when
Ch. 8 Feedback

31. Series-Shunt Example - Low Frequency
Midband Gain Low Frequency Poles Low Frequency Zeros
Low 3dB Frequency
Ch. 8 Feedback

32. Series-Shunt Example - High Frequency
Substitute hybrid-pi model for transistor with C and C
Short all coupling capacitors and emitter bypass capacitors
Include loading effects of feedback network R1 and R2
Find high frequency poles and zeros using Gray-Searle (Open Circuit) Method
Ch. 8 Feedback

33. Series-Shunt Example - High Frequency Pole - C1
Given: C1 = 15 pF IS I1
Ch. 8 Feedback

34. Series-Shunt Example - High Frequency Pole - C1
Given: C1 = 1.2 pF
Ch. 8 Feedback

35. Series-Shunt Example - High Frequency Pole - C2
Given: C2 = 12 pF
Ch. 8 Feedback

36. Series-Shunt Example - High Frequency Pole - C2
Given: C2 = 1.4 pF
Ch. 8 Feedback

37. Series-Shunt Example - High Frequency Zeros - C1 & C2
For CE amplifier, a high frequency zero
occurs when ZH = gm/C
Ch. 8 Feedback

38. Series-Shunt Example - High Frequency
Midband Gain High Frequency Poles High Frequency Zeros
High 3dB Frequency
Ch. 8 Feedback