1. ECE 352 Electronics II Winter 2003 Ch. 8 Feedback 1 *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 this configuration, the appropriate gain is the CURRENT GAIN A = A Io = I o /I i *For the feedback amplifier as a whole, feedback changes midband current gain from A Io to A Ifo *Feedback changes input resistance from R i to R if *Feedback changes output resistance from R o to R of *Feedback changes low and high frequency 3dB frequencies Shunt-Series Feedback Amplifier - Ideal Case Current samplingCurrent feedback

2. ECE 352 Electronics II Winter 2003 Ch. 8 Feedback 2 Shunt-Series Feedback Amplifier - Ideal Case Gain Input Resistance Output Resistance Io’Io’ Vo’Vo’ I s =0

3. ECE 352 Electronics II Winter 2003 Ch. 8 Feedback 3 *Feedback network is a two port network (input and output ports) *Can represent with g-parameter network (This is the best for this feedback amplifier configuration) *G-parameter equivalent network has FOUR parameters *G-parameters relate input and output currents and voltages *Two parameters chosen as independent variables. For G-parameter network, these are input voltages V 1 and the output current I 2 *Two equations relate other two quantities (input current I 1 and output V 2 ) to these independent variables *Knowing V 1 and I 2, can calculate I 1 and V 2 if you know the G-parameter values *G-parameters have various units of ohms, conductance (1/ohms=siemens) and no units ! Equivalent Network for Feedback Network

4. ECE 352 Electronics II Winter 2003 Ch. 8 Feedback 4 *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 g-parameter equivalent circuit for feedback network æ Feedback factor  f given by g 12 since æ Feedforward factor given by g 21 (neglected) æ g 22 gives feedback network loading on output æ g 11 gives feedback network loading on input *Can incorporate loading effects in a modified basic amplifier. Gain A Io becomes a new, modified gain A Io ’. *Can then use analysis from ideal case Shunt-Series Feedback Amplifier - Practical Case g 22 g 21 V 1 g 11 g 12 I 2 V1V1 V2V2 I1I1 I2I2

5. ECE 352 Electronics II Winter 2003 Ch. 8 Feedback 5 *How do we determine the g-parameters for the feedback network? *For the input loading term g 11 æ We turn off the feedback signal by setting I o = I 2 = 0. æ We then evaluate the resistance seen looking into port 1 of the feedback network. *For the output loading term g 22 æ We short circuit the connection to the input so V 1 = 0. æ We find the resistance seen looking into port 2 of the feedback network. *To obtain the feedback factor  f (also called g 12 ) æ We apply a test signal I o ’ to port 2 of the feedback network and evaluate the feedback current I f (also called I 1 here) for V 1 = 0. æ Find  f from  f = I f /I o ’ Shunt-Series Feedback Amplifier - Practical Case g 22 g 21 V 1 g 11 g 12 I 2 V2V2 I1I1 I2I2 V1V1

6. ECE 352 Electronics II Winter 2003 Ch. 8 Feedback 6 *Two stage [CE+CE] amplifier *Transistor parameters Given:  =100, r x = 0 *Input and output coupling and emitter bypass capacitors, but direct coupling between stages *Capacitor in feedback connection removes R f from DC bias *DC bias of two stages is coupled (bias of one affects the other) Example - Shunt-Series Feedback Amplifier

7. ECE 352 Electronics II Winter 2003 Ch. 8 Feedback 7 DC Bias Analysis V C1 V B2 (neglecting I B2 ) (<<I C1 =870  A)

8. ECE 352 Electronics II Winter 2003 Ch. 8 Feedback 8 Example - Shunt-Series Feedback Amplifier *Redraw circuit to show æ Feedback circuit æ Type of output sampling (current in this case = I o ) æ Type of feedback signal to input (current in this case = I f ) I out ’ Io’Io’

9. ECE 352 Electronics II Winter 2003 Ch. 8 Feedback 9 Example - Shunt-Series Feedback Amplifier Input Loading EffectsOutput Loading Effects R1R1 R2R2 Io’Io’ I o ’= 0 I out ’

10. ECE 352 Electronics II Winter 2003 Ch. 8 Feedback 10 Example - Shunt-Series Feedback Amplifier Amplifier with Loading Effects but Without Feedback

11. ECE 352 Electronics II Winter 2003 Ch. 8 Feedback 11 Example - Shunt-Series Feedback Amplifier Midband Gain Analysis IsIs V i2 R1R1 R2R2 R i2 I out ’ IC’IC’

12. ECE 352 Electronics II Winter 2003 Ch. 8 Feedback 12 Midband Gain with Feedback *Determine the feedback factor  f *Calculate gain with feedback A Ifo *Note æ  f < 0 and A Io < 0 æ  f A Io > 0 as necessary for negative feedback and dimensionless æ  f A Io is large so there is significant feedback. æ Can change  f and the amount of feedback by changing R F. æ Gain is determined by feedback resistance V E2 + -

13. ECE 352 Electronics II Winter 2003 Ch. 8 Feedback 13 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. RiRi RoRo

14. ECE 352 Electronics II Winter 2003 Ch. 8 Feedback 14 Voltage Gain for Current Gain Feedback Amplifier *Can calculate voltage gain *Note - can’t calculate the voltage gain as follows:

15. ECE 352 Electronics II Winter 2003 Ch. 8 Feedback 15 Equivalent Circuit for Shunt-Series Feedback Amplifier *Current gain amplifier A = I o /I s *Feedback modified gain, input and output resistances æ Included loading effects of feedback network æ Included feedback effects of feedback network *Significant feedback, i.e.  f A Io is large and positive R if A Ifo I i R of

16. ECE 352 Electronics II Winter 2003 Ch. 8 Feedback 16 Frequency Analysis *Low frequency analysis of poles for feedback amplifier follows Gray-Searle (short circuit) technique as before. *Low frequency zeroes found as before. *Dominant pole used to find new low 3dB frequency. *For high frequency poles and zeroes, substitute hybrid-pi model with C  and C  (transistor’s capacitors). æ Follow Gray-Searle (open circuit) technique to find poles *High frequency zeroes found as before. *Dominant pole used to find new high 3dB frequency.

17. ECE 352 Electronics II Winter 2003 Ch. 8 Feedback 17 Summary of Feedback Amplifier Analysis *Identify the amplifier configuration by: æ Output sampling ®I o = series configuration ®V o = shunt configuration æ Feedback to input ®I o = shunt configuration ®V o = series configuration *Calculate loading effects of feedback network æ On input æ On output *Calculate appropriate midband gain A’ (modified by loading effects of feedback network) *Calculate feedback factor  f. *Calculate midband gain with feedback A f. XoXo XiXi XfXf XsXs ff Calculate low frequency poles and zeroes. Determine dominant (highest) low frequency pole  L including loading effects of feedback network Calculate new dominant low frequency pole  Lf. Calculate high frequency poles and zeroes. Determine dominant (lowest) high frequency pole  H including loading effects of feedback network Calculate new dominant high frequency pole  Hf.

18. ECE 352 Electronics II Winter 2003 Ch. 8 Feedback 18 Summary of Feedback Amplifier Analysis