1. ECE 352 Electronics II Winter 2003 Ch. 8 Feedback 1 Feedback *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. XoXo XiXi XfXf XsXs + - βfβf

2. ECE 352 Electronics II Winter 2003 Ch. 8 Feedback 2 Feedback Amplifier Analysis XoXo XiXi XfXf XsXs + - βfβf

3. ECE 352 Electronics II Winter 2003 Ch. 8 Feedback 3 *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: æ Loss of gain, may require an added gain stage to compensate. æ Added complexity in design Advantages of Negative Feedback

4. ECE 352 Electronics II Winter 2003 Ch. 8 Feedback 4 *There are four types of feedback amplifiers. Why? æ Output sampled can be a current or a voltage æ Quantity fed back to input can be a current or a voltage æ 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 æ First term refers to nature of feedback connection at the input. æ Second term refers to nature of sampling connection at the output. Basic Types of Feedback Amplifiers

5. ECE 352 Electronics II Winter 2003 Ch. 8 Feedback 5 Basic Types of Feedback Amplifiers Series - ShuntShunt - Series Series - SeriesShunt - Shunt

6. ECE 352 Electronics II Winter 2003 Ch. 8 Feedback 6 *Recognize the feedback amplifier’s configuration, e.g. Series-shunt *Calculate the appropriate gain A for the amplifier, e.g. voltage gain. æ 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 A f 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 Method of Feedback Amplifier Analysis

7. ECE 352 Electronics II Winter 2003 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 R i and R o *For the feedback amplifier as a whole, feedback does change the midband voltage gain from A to A f *Does change input resistance from R i to R if *Does change output resistance from R o to R of *Does change low and high frequency 3dB frequencies Basic Amplifier Feedback Circuit Equivalent Circuit for Feedback Amplifier

8. ECE 352 Electronics II Winter 2003 Ch. 8 Feedback 8 Series-Shunt Feedback Amplifier - Ideal Case Midband Gain Input Resistance Output Resistance VtVt ItIt

9. ECE 352 Electronics II Winter 2003 Ch. 8 Feedback 9 Series-Shunt Feedback Amplifier - Ideal Case Low Frequency Pole High Frequency Pole Low 3dB frequency lowered by feedback. Upper 3dB frequency raised by feedback.

10. ECE 352 Electronics II Winter 2003 Ch. 8 Feedback 10 *Feedback networks consist of a set of resistors æ Simplest case (only case considered here) æ In general, can include C’s and L’s (not considered here) æ Transistors sometimes used (gives variable amount of feedback) (not considered here) *Feedback network needed to create V f feedback signal at input (desirable) *Feedback network has parasitic (loading) effects including: *Feedback network loads down amplifier input æ Adds a finite series resistance æ Part of input signal V s lost across this series resistance (undesirable), so V i reduced *Feedback network loads down amplifier output æ Adds a finite shunt resistance æ Part of output current lost through this shunt resistance so not all output current delivered to load R L (undesirable) Practical Feedback Networks ViVi VfVf VoVo * How do we take these loading effects into account?

11. ECE 352 Electronics II Winter 2003 Ch. 8 Feedback 11 *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 I 1 and output voltage V 2 *Two equations relate other two quantities (output current I 2 and input voltage V 1 ) to these independent variables *Knowing I 1 and V 2, can calculate I 2 and V 1 if you know the h-parameter values *h-parameters can have units of ohms, 1/ohms or no units (depends on which parameter) Equivalent Network for Feedback Network

12. ECE 352 Electronics II Winter 2003 Ch. 8 Feedback 12 *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 æ Feedback factor  f given by h 12 since æ Feedforward factor given by h 21 (neglected) æ h 22 gives feedback network loading on output æ h 11 gives feedback network loading on input *Can incorporate loading effects in a modified basic amplifier. Basic gain of amplifier A V becomes a new, modified gain A V ’ (incorporates loading effects). *Can then use feedback analysis from the ideal case. Series-Shunt Feedback Amplifier - Practical Case

13. ECE 352 Electronics II Winter 2003 Ch. 8 Feedback 13 Series-Shunt Feedback Amplifier - Practical Case *How do we determine the h-parameters for the feedback network? *For the input loading term h 11 æ Turn off the feedback signal by setting V o = 0. æ Then evaluate the resistance seen looking into port 1 of the feedback network (also called R 11 here). *For the output loading term h 22 æ Open circuit the connection to the input so I 1 = 0. æ Find the resistance seen looking into port 2 of the feedback network (also called R 22 here). *To obtain the feedback factor  f (also called h 12 ) æ Apply a test signal V o ’ to port 2 of the feedback network and evaluate the feedback voltage V f (also called V 1 here) for I 1 = 0. æ Find  f from  f = V f /V o ’ Summary of Feedback Network Analysis

14. ECE 352 Electronics II Winter 2003 Ch. 8 Feedback 14 *Evaluate modified basic amplifier (including loading effects of feedback network) æ Including h 11 at input æ Including h 22 at output æ Including loading effects of source resistance æ Including load effects of load resistance *Analyze effects of idealized feedback network using feedback amplifier equations derived *Note æ A v ’ is the modified voltage gain including the effects of h 11, h 22, R S and R L. æ R i ’, R o ’ are the modified input and output resistances including the effects of h 11, h 22, R S and R L. Series-Shunt Feedback Amplifier - Practical Case Summary of Approach to Analysis Modified Basic Amplifier Idealized Feedback Network Practical Feedback Network Basic Amplifier

15. ECE 352 Electronics II Winter 2003 Ch. 8 Feedback 15 *Two stage amplifier *Each stage a CE amplifier *Transistor parameters Given:  1 =  2 =50, r x1 =r x2 =0 *Coupled by capacitors, dc biased separately *DC analysis: Example - Series-Shunt Feedback Amplifier DC analysis for each stage can be done separately since stages are isolated (dc wise) by coupling capacitors.

16. ECE 352 Electronics II Winter 2003 Ch. 8 Feedback 16 Example - Series-Shunt Feedback Amplifier ViVi + _ *Redraw circuit to show æ Feedback circuit æ Type of output sampling (voltage in this case = V o ) æ Type of feedback signal to input (voltage in this case = V f ) VfVf + _ VoVo + _

17. ECE 352 Electronics II Winter 2003 Ch. 8 Feedback 17 Example - Series-Shunt Feedback Amplifier Input Loading Effects Output Loading Effects Amplifier with Loading Effects I 1 =0 V o =0 R1R1 R2R2

18. ECE 352 Electronics II Winter 2003 Ch. 8 Feedback 18 *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) Example - Series-Shunt Feedback Amplifier R1R1 R2R2 R1R1 R2R2

19. ECE 352 Electronics II Winter 2003 Ch. 8 Feedback 19 Example - Series-Shunt Feedback Amplifier Midband Gain Analysis

20. ECE 352 Electronics II Winter 2003 Ch. 8 Feedback 20 Midband Gain with Feedback *Determine the feedback factor  f *Calculate gain with feedback A vf *Note æ  f A vo > 0 as necessary for negative feedback æ  f A vo is large so there is significant feedback. For  f A vo  0, there is almost no feedback. æ Can change  f and the amount of feedback by changing R f1 and/or R f2. æ NOTE: Since  f A vo >> 0

21. ECE 352 Electronics II Winter 2003 Ch. 8 Feedback 21 Input and Output Resistances with Feedback *Determine input R i and output R o resistances with loading effects of feedback network. *Calculate input R if and output R of resistances for the complete feedback amplifier.

22. ECE 352 Electronics II Winter 2003 Ch. 8 Feedback 22 Equivalent Circuit for Series-Shunt Feedback Amplifier *Voltage gain amplifier *Modified voltage gain, input and output resistances æ Included loading effects of feedback network æ Included feedback effects of feedback network æ Include source resistance effects *Significant feedback, i.e.  f A vo is large and positive

23. ECE 352 Electronics II Winter 2003 Ch. 8 Feedback 23 Low Frequency Poles and Zeros for Series-Shunt Feedback Amplifier *Six capacitors: æ Input and output coupling capacitors C 1 and C 5 æ Emitter bypass capacitors C 3 and C 4 æ Interstage coupling capacitors C 2 æ Feedback coupling capacitor C 6 *Analyze using Gray-Searle (Short Circuit) Technique one capacitor at a time *Find dominant low frequency pole (highest frequency one)

24. ECE 352 Electronics II Winter 2003 Ch. 8 Feedback 24 Example - Input Coupling Capacitor’s Pole Frequency Equivalent circuit for C 1 Note that there are some loading effects of the feedback network on this pole frequency. In R i1 the feedback resistors determine R 1

25. ECE 352 Electronics II Winter 2003 Ch. 8 Feedback 25 Example - Interstage Coupling Capacitor’s Pole Frequency Equivalent circuit for C 2 Note: No R E2 since C 4 shorts it out.

26. ECE 352 Electronics II Winter 2003 Ch. 8 Feedback 26 Example - Feedback Coupling Capacitor’s Pole Frequency Equivalent circuit for C 6

27. ECE 352 Electronics II Winter 2003 Ch. 8 Feedback 27 Example - Emitter Bypass Capacitor’s Pole Frequency Equivalent circuit for C 3 I E1

28. ECE 352 Electronics II Winter 2003 Ch. 8 Feedback 28 Example - Emitter Bypass Capacitor’s Pole Frequency Equivalent circuit for C 4 I E2

29. ECE 352 Electronics II Winter 2003 Ch. 8 Feedback 29 Example - Output Coupling Capacitor’s Pole Frequency Equivalent circuit for C 5

30. ECE 352 Electronics II Winter 2003 Ch. 8 Feedback 30 Zeros for Series-Shunt Feedback Amplifier Example *Coupling capacitors C 1, C 2 and C 5 give zeros at  = 0 since Z C = 1/sC and they are in the signal line. *Emitter bypass capacitors C 3 and C 4 give a zero when the impedance Z CE || R E . *Feedback capacitor C 6 gives a zero when [Z C6 +R 2 ] || R C2  when

31. ECE 352 Electronics II Winter 2003 Ch. 8 Feedback 31 *Midband Gain Low Frequency Poles Low Frequency Zeros Series-Shunt Example - Low Frequency Low 3dB Frequency

32. ECE 352 Electronics II Winter 2003 Ch. 8 Feedback 32 *Substitute hybrid-pi model for transistor with C  and C  *Short all coupling capacitors and emitter bypass capacitors *Include loading effects of feedback network R 1 and R 2 *Find high frequency poles and zeros using Gray-Searle (Open Circuit) Method Series-Shunt Example - High Frequency

33. ECE 352 Electronics II Winter 2003 Ch. 8 Feedback 33 Series-Shunt Example - High Frequency Pole - C  1 Given: C  1 = 15 pF I1I1 ISIS

34. ECE 352 Electronics II Winter 2003 Ch. 8 Feedback 34 Series-Shunt Example - High Frequency Pole - C  1 Given: C  1 = 1.2 pF

35. ECE 352 Electronics II Winter 2003 Ch. 8 Feedback 35 Given: C  2 = 12 pF Series-Shunt Example - High Frequency Pole - C  2

36. ECE 352 Electronics II Winter 2003 Ch. 8 Feedback 36 Series-Shunt Example - High Frequency Pole - C  2 Given: C  2 = 1.4 pF

37. ECE 352 Electronics II Winter 2003 Ch. 8 Feedback 37 Series-Shunt Example - High Frequency Zeros - C  1 & C  2 For CE amplifier, a high frequency zero occurs when  ZH = g m /C  I2I2

38. ECE 352 Electronics II Winter 2003 Ch. 8 Feedback 38 *Midband Gain High Frequency Poles High Frequency Zeros Series-Shunt Example - High Frequency High 3dB Frequency