Shunt-Shunt Feedback Amplifier - Ideal Case

1. Shunt-Shunt Feedback Amplifier - Ideal Case • 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 this configuration, the appropriate gain is the TRANSRESISTANCE GAIN A = ARo = Vo/Ii • For the feedback amplifier as a whole, feedback changes midband transresistance gain from ARo to ARfo • Feedback changes input resistance from Ri to Rif • Feedback changes output resistance from Ro to Rof • Feedback changes low and high frequency 3dB frequencies Ch. 8 Feedback

2. Shunt-Shunt Feedback Amplifier - Ideal Case Gain Input Resistance Output Resistance Is = 0 Io’ + _ Vo’ Ch. 8 Feedback

3. Equivalent Network for Feedback Network • 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 V1 and V2 • Two equations relate other two quantities (input and output currents I1 and I2) to these independent variables • Knowing V1 and V2, can calculate I1 and I2 if you know the Y-parameter values • Y-parameters have units of conductance (1/ohms=siemens) ! Ch. 8 Feedback

4. Shunt-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 y-parameter equivalent circuit for feedback network • Feedback factor f given by y12 since • Feedforward factor given by y21 (neglected) • y22 gives feedback network loading on output • y11 gives feedback network loading on input • Can incorporate loading effects in a modified basic amplifier. Gain ARo becomes a new, modified gain ARo’. • Can then use analysis from ideal case I2 I1 y21V1 V2 V1 y11 y22 y12V2 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 y11 • We turn off the feedback signal by setting Vo = 0 (V2 =0). • We then evaluate the resistance seen looking into port 1 of the feedback network (R11 = y11). • For the output loading term y22 • We short circuit the connection to the input so V1 = 0. • We find the resistance seen looking into port 2 of the feedback network. • To obtain the feedback factor f (also called y12 ) • We apply a test signal Vo’ to port 2 of the feedback network and evaluate the feedback current If (also called I1 here) for V1 = 0. • Find f from f = If/Vo’ I2 I1 y21V1 y11 V2 V1 y22 y12V2 Ch. 8 Feedback

6. Example - Shunt-Shunt Feedback Amplifier • Single stage CE amplifier • Transistor parameters. Given:  =100, rx= 0 • No coupling or emitter bypass capacitors • DC analysis: Ch. 8 Feedback

7. Example - Shunt-Shunt Feedback Amplifier • Redraw circuit to show • Feedback circuit • Type of output sampling (voltage in this case = Vo) • Type of feedback signal to input (current in this case = If) Ch. 8 Feedback

8. Example - Shunt-Shunt Feedback Amplifier Equivalent circuit for feedback network I1 I2 y21V1 y11 V2 V1 y22 y12V2 Input Loading Effects Output Loading Effects R1= y11 R2= y22 Ch. 8 Feedback

9. Example - Shunt-Shunt Feedback Amplifier Modified Amplifier with Loading Effects, but Without Feedback Original Feedback Amplifier R2 R1 Note: We converted the signal source to a Norton equivalent current source since we need to calculate the gain Ch. 8 Feedback

10. Example - Shunt-Shunt Feedback Amplifier • Construct ac equivalent circuit at midband frequencies including loading effects of feedback network. • Analyze circuit to find midband gain (transresistance gain ARo for this shunt-shunt configuration) s Ch. 8 Feedback

11. Example - Shunt-Shunt Feedback Amplifier Midband Gain Analysis Ch. 8 Feedback

12. Midband Gain with Feedback • Determine the feedback factor f • Calculate gain with feedback ARfo • Note • f < 0and has units of mA/V, ARo < 0 and has units of K • f ACo > 0 as necessary for negative feedback and dimensionless • f ACo is large so there is significant feedback. • Can change f and the amount of feedback by changing RF. • Gain is determined primarily by feedback resistance + _ Vo’ Note: The direction of If is always into the feedback network! Ch. 8 Feedback

13. 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. Ro Ri 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! Ch. 8 Feedback

15. Equivalent Circuit for Shunt-Shunt Feedback Amplifier • Transresistance gain amplifier A = Vo/Is • Feedback modified gain, input and output resistances • Included loading effects of feedback network • Included feedback effects of feedback network • Significant feedback, i.e. f ARo is large and positive Rof Rif ARfoI i 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). • Follow Gray-Searle (open circuit) technique to find poles • High frequency zeroes found as before. • Dominant pole used to find new high 3dB frequency. Ch. 8 Feedback