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 TRANSCONDUCTANCE GAIN A = A Co = I o /V i *For the feedback amplifier as a whole, feedback changes midband transconductance gain from A Co to A Cfo *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 Series-Series Feedback Amplifier - Ideal Case Output current sampling Voltage fedback to input

2. ECE 352 Electronics II Winter 2003 Ch. 8 Feedback 2 Series-Series Feedback Amplifier - Ideal Case Gain (Transconductance Gain) Input Resistance Output Resistance V V + -

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 Z-parameter network (This is the best for this feedback amplifier configuration) *Z-parameter equivalent network has FOUR parameters *Z-parameters relate input and output currents and voltages *Two parameters chosen as independent variables. For Z-parameter network, these are input and output currents I 1 and I 2 *Two equations relate other two quantities (input and output voltages V 1 and V 2 ) to these independent variables *Knowing I 1 and I 2, can calculate V 1 and V 2 if you know the Z-parameter values *Z-parameters have units of ohms ! 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 z-parameter equivalent circuit for feedback network æ Feedback factor  f given by z 12 since æ Feedforward factor given by z 21 (neglected) æ z 22 gives feedback network loading on output æ z 11 gives feedback network loading on input *Can incorporate loading effects in a modified basic amplifier. Gain A Co becomes a new, modified gain A Co ’. *Can then use analysis from ideal case Series-Series Feedback Amplifier - Practical Case

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

6. ECE 352 Electronics II Winter 2003 Ch. 8 Feedback 6 Series-Series Feedback Amplifier - Practical Case *Modified basic amplifier (including loading effects of feedback network) æ Including z 11 at input æ Including z 22 at output æ Including loading effects of source resistance æ Including load effects of load resistance *Now have an idealized feedback network, i.e. produces feedback effect, but without loading effects *Can now use feedback amplifier equations derived *Note æ A Co ’ is the modified transconductance gain including the loading effects of z 11, z 22, R S and R L. æ R i ’ and R o ’ are modified input and output resistances including loading effects. Original Amplifier Feedback Network Modified Amplifier Idealized Feedback Network

7. ECE 352 Electronics II Winter 2003 Ch. 8 Feedback 7 *Three stage amplifier *Each stage a CE amplifier *Transistor parameters Given:  1 =  2 =  3 =100, r x1 =r x2 =r x3 =0 *Coupled by capacitors, dc biased separately *DC analysis (given): Example - Series-Series Feedback Amplifier Note: Biasing resistors for each stage are not shown for simplicity in the analysis.

8. ECE 352 Electronics II Winter 2003 Ch. 8 Feedback 8 *Redraw circuit to show: æ Feedback circuit æ Type of output sampling (current in this case = I o ) ®Collector resistor constitutes the load so I o  I c ®Emitter current I e =(  +1) I b = {(  +1)/  } I c  I c = I o æ Type of feedback signal to input (voltage in this case = V f ) Example - Series-Series Feedback Amplifier IoIo Output current sampling Voltage fedback to input I c3 ≈ I o

9. ECE 352 Electronics II Winter 2003 Ch. 8 Feedback 9 Example - Series-Series Feedback Amplifier Input Loading Effects R1R1 R2R2 I 2 =0 I 1 =0 IoIo Output Loading Effects Z-parameter equivalent circuit for feedback circuit

10. ECE 352 Electronics II Winter 2003 Ch. 8 Feedback 10 Example - Series-Series Feedback Amplifier IoIo Output current sampling Voltage fedback to input Redrawn basic amplifier with loading effects, but not feedback. R1R1 R2R2

11. ECE 352 Electronics II Winter 2003 Ch. 8 Feedback 11 *Construct ac equivalent circuit at midband frequencies including loading effects of feedback network. *Analyze circuit to find MIDBAND GAIN (transconductance gain A Co for this series-series configuration) Example - Series-Series Feedback Amplifier IoIo I o = I E3 ≈ I C3 I C3 VSVS R1R1 R2R2

12. ECE 352 Electronics II Winter 2003 Ch. 8 Feedback 12 Example - Series-Series Feedback Amplifier Midband Gain Analysis R i3 R i1 V i1 V i3 IoIo VSVS Note convention on I o is into the output of the last stage of the amplifier. I3I3 I2I2 I1I1

13. ECE 352 Electronics II Winter 2003 Ch. 8 Feedback 13 Feedback Factor and Midband Gain with Feedback *Determine the feedback factor  f *Calculate gain with feedback A Cfo *Note æ  f A Co > 0 as necessary for negative feedback and dimensionless æ  f A Co is large so there is significant feedback. æ  f has units of resistance (ohms); A Co has units of conductance (1/ohms) æ Can change  f and the amount of feedback by changing R E1, R F and/or R E2. æ Gain is largely determined by ratio of feedback resistances I f1 V E2 Io’Io’

14. ECE 352 Electronics II Winter 2003 Ch. 8 Feedback 14 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. R i = R i1 V i1 RoRo I1I1 I  1 (1+g m1 r  1 ) IoIo

15. ECE 352 Electronics II Winter 2003 Ch. 8 Feedback 15 Voltage Gain for Transconductance Feedback Amplifier *Can calculate voltage gain after we calculate the transconductance gain! *Note - can’t calculate the voltage gain as follows: IoIo Correct voltage gain for the amplifier with feedback! Wrong voltage gain!

16. ECE 352 Electronics II Winter 2003 Ch. 8 Feedback 16 Equivalent Circuit for Series-Series Feedback Amplifier *Transconductance gain amplifier A = I o /V 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 Co is large and positive

17. ECE 352 Electronics II Winter 2003 Ch. 8 Feedback 17 Frequency Analysis *Simplified amplifier analyzed had biasing resistors omitted for simplicity. *For completeness, need to add biasing resistors. æ Coupling capacitors then need to be added to simplify biasing by isolating each stage. *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.