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 TRANSRESISTANCE GAIN A = A Ro = V o /I i *For the feedback amplifier as a whole, feedback changes midband transresistance gain from A Ro to A Rfo *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-Shunt Feedback Amplifier - Ideal Case

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

ECE 352 Electronics II Winter 2003 Ch. 8 Feedback 3 *Feedback network is a two port network (input and output ports) *Can represent with Y-parameter network (This is the best for this feedback amplifier configuration) *Y-parameter equivalent network has FOUR parameters *Y-parameters relate input and output currents and voltages *Two parameters chosen as independent variables. For Y-parameter network, these are input and output voltages V 1 and V 2 *Two equations relate other two quantities (input and output currents I 1 and I 2 ) to these independent variables *Knowing V 1 and V 2, can calculate I 1 and I 2 if you know the Y-parameter values *Y-parameters have units of conductance (1/ohms=siemens) ! Equivalent Network for Feedback Network

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

ECE 352 Electronics II Winter 2003 Ch. 8 Feedback 5 Shunt-Shunt Feedback Amplifier - Practical Case *How do we determine the y-parameters for the feedback network? *For the input loading term y 11 æ We turn off the feedback signal by setting V o = 0 (V 2 =0). æ We then evaluate the resistance seen looking into port 1 of the feedback network (R 11 = y 11 ). *For the output loading term y 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 y 12 ) æ We apply a test signal V 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 /V o ’ y 22 y 21 V 1 y 11 y 12 V 2 I1I1 I2I2 V1V1 V2V2

ECE 352 Electronics II Winter 2003 Ch. 8 Feedback 6 *Single stage CE amplifier *Transistor parameters. Given:  =100, r x = 0 *No coupling or emitter bypass capacitors *DC analysis: Example - Shunt-Shunt Feedback Amplifier

ECE 352 Electronics II Winter 2003 Ch. 8 Feedback 7 *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 (current in this case = I f ) Example - Shunt-Shunt Feedback Amplifier

ECE 352 Electronics II Winter 2003 Ch. 8 Feedback 8 Example - Shunt-Shunt Feedback Amplifier Input Loading EffectsOutput Loading Effects R 1 = y 11 R 2 = y 22 y 22 y 21 V 1 y 11 y 12 V 2 I1I1 V1V1 V2V2 I2I2 Equivalent circuit for feedback network

ECE 352 Electronics II Winter 2003 Ch. 8 Feedback 9 Example - Shunt-Shunt Feedback Amplifier Modified Amplifier with Loading Effects, but Without Feedback Note: We converted the signal source to a Norton equivalent current source since we need to calculate the gain Original Feedback Amplifier R1R1 R2R2

ECE 352 Electronics II Winter 2003 Ch. 8 Feedback 10 *Construct ac equivalent circuit at midband frequencies including loading effects of feedback network. *Analyze circuit to find midband gain (transresistance gain A Ro for this shunt- shunt configuration) Example - Shunt-Shunt Feedback Amplifier s

ECE 352 Electronics II Winter 2003 Ch. 8 Feedback 11 Example - Shunt-Shunt Feedback Amplifier Midband Gain Analysis

ECE 352 Electronics II Winter 2003 Ch. 8 Feedback 12 Midband Gain with Feedback *Determine the feedback factor  f *Calculate gain with feedback A Rfo *Note æ  f < 0 and has units of mA/V, A Ro < 0 and has units of K  æ  f A Co > 0 as necessary for negative feedback and dimensionless æ  f A Co is large so there is significant feedback. æ Can change  f and the amount of feedback by changing R F. æ Gain is determined primarily by feedback resistance + _Vo’Vo’ Note: The direction of I f is always into the feedback network!

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

ECE 352 Electronics II Winter 2003 Ch. 8 Feedback 14 Voltage Gain for Transresistance Feedback Amplifier *Can calculate voltage gain after we calculate the transresistance gain! *Note - can’t calculate the voltage gain as follows: Correct voltage gain Wrong voltage gain!

ECE 352 Electronics II Winter 2003 Ch. 8 Feedback 15 Equivalent Circuit for Shunt-Shunt Feedback Amplifier *Transresistance gain amplifier A = V 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 Ro is large and positive R if A Rfo I i R of

ECE 352 Electronics II Winter 2003 Ch. 8 Feedback 16 Frequency Analysis *For completeness, need to add coupling capacitors at the input and output. *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.