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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 ARo ARfo 1 f ARo Feedback changes input resistance from Ri to Rif Rif * 1 f ARo Feedback changes output resistance from Ro to Rof Rof * Ri 1 f ARo Feedback changes low and high frequency 3dB frequencies Hf 1 f ARo H ECE 352 Electronics II Winter 2003 Ro Ch. 8 Feedback Lf L 1 f ARo 1 Shunt-Shunt Feedback Amplifier - Ideal Case Gain ARfo Vo A I A ARo ARo Ro i Ro If f Vo 1 f ARo I s Ii I f 1 1 Ii Ii Input Resistance Rif Is = 0 Vs Vs Vs I s Ii I f I i f Vo Vs V I i 1 f o Ii Ri 1 f ARo Output Resistance Io ’ _ + Rof Vo’ Vo ' I o ' Ro ARo I i I Ro ARo i Io ' Io ' Io ' But I s 0 so I i I f and I f f Vo ' so I i f Vo ' f Vo ' Ii f Rof Io ' Io ' Rof Ro ARo f Rof so Rof ECE 352 Electronics II Winter 2003 Ch. 8 Feedback Ro 1 f ARo 2 Equivalent Network for Feedback Network * * * * * * * * ECE 352 Electronics II Winter 2003 Ch. 8 Feedback 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) ! 3 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 y12 I1 V2 V1 0 If f Vo 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 V1 y11 y12V2 V2 y22 * ARfo Rif ECE 352 Electronics II Winter 2003 Ch. 8 Feedback ARo ' 1 f ARo ' Ri Rof 1 f ARo ' Hf 1 f ARo ' H Ro 1 f ARo ' Lf L 1 f ARo ' 4 Shunt-Shunt Feedback Amplifier - Practical Case * * * * I2 I1 V1 y21V1 y11 y12V2 ECE 352 Electronics II Winter 2003 y22 V2 Ch. 8 Feedback 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’ 5 Example - Shunt-Shunt Feedback Amplifier * * * * Single stage CE amplifier Transistor parameters. Given: =100, rx= 0 No coupling or emitter bypass capacitors DC analysis: VBE ,active 0.7V 0.7V 0.07 mA 70A I 47 K I B 0.07 mA 10 K I C I B I 4.7 K I C ( I B 0.07 mA) 1I B 0.07 mA I10 K 12V I 4.7 K 4.7 K I B 0.07 mA47 K 0.7V 12V 1I B 0.07 mA4.7 K I B 0.07 mA47 K 0.7V 12V 0.33V 3.3V 1014.7 K 47 K I B 8.37V 0.016 mA 16 A I C I B 1000.016 mA 1.6 mA 522 K 1.6 mA I 100 gm C 63 mA / V r 1.6 K VT 0.0256 V g m 63 mA / V IB ECE 352 Electronics II Winter 2003 Ch. 8 Feedback 6 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) ECE 352 Electronics II Winter 2003 Ch. 8 Feedback 7 Example - Shunt-Shunt Feedback Amplifier Equivalent circuit for feedback network I1 I2 V1 y11 Input Loading Effects y21V1 y12V2 y22 V2 Output Loading Effects R1= y11 R2= y22 R1 RF 47 K ECE 352 Electronics II Winter 2003 R2 RF 47 K Ch. 8 Feedback 8 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 ARo since we need to calculate the gain A Vo Rfo I s 1 f ARo ECE 352 Electronics II Winter 2003 Ch. 8 Feedback 9 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 shuntshunt configuration) ARo Vo Is s ECE 352 Electronics II Winter 2003 Ch. 8 Feedback 10 Example - Shunt-Shunt Feedback Amplifier Midband Gain Analysis ARo Vo V Vo Vo V Is V I s g mV RC RF V g R m C RF 63 m A/ V 4.7 K 47K 269V / V V RS RF r 10K 47K 1.6 K 1.3K IS ARo Vo 2691.3K 350K Is ECE 352 Electronics II Winter 2003 Ch. 8 Feedback 11 Midband Gain with Feedback * * Determine the feedback factor f X I ' If ' 1 f f f X o Vo ' I f R f RF + _ Vo’ 1 0.021 mA / V 47 K Calculate gain with feedback ARfo f ARo 0.021mA / V (350 K ) 7.4 ARfo * ARo 350 K 42 K 1 f ARo 1 7.4 Note: The direction of If is always into the feedback network! Note f < 0 and 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 1 1 ARfo RF 47 K f (1 / RF ) ECE 352 Electronics II Winter 2003 Ch. 8 Feedback 12 Input and Output Resistances with Feedback Ro Ri * Determine input Ri and output Ro resistances with loading effects of feedback network. Ri RS RF r 10K 47K 1.6K 1.3K * Ro RC RF 4.7 K 47K 4.3K Calculate input Rif and output Rof resistances for the complete feedback amplifier. Rif Ri Rof 1 f ARo Ro (1 f ARo ) 4.3K 0.5K 8.4 1.3K 0.15K 8.4 ECE 352 Electronics II Winter 2003 Ch. 8 Feedback 13 Voltage Gain for Transresistance Feedback Amplifier * * Can calculate voltage gain after we calculate the transresistance gain! ARfo 42 K V V 1 V AVfo o o o 4.2 V / V V I R R I R 10 K s s f s s f s s f AVfo (dB) 20 log 4.2 12.5 dB Note - can’t calculate the voltage gain as follows: Assume AVfo Find AVo Correct voltage gain AVo 1 f AVo Vo V A 350 K o Ro 35 V / V Vs I s Rs Rs 10 K Calculate f AVo 0.021 mA / V 35 V / V 0.74 mA / V Note this has units; it should not! Calculate voltage gain with feedback from AVfo AVo 1 f AVo 35 V / V 1 0.74mA / V Magnitude is off by nearly a factor of five and units are wrong! ECE 352 Electronics II Winter 2003 Ch. 8 Feedback 20 V / V (?) Wrong voltage gain! 14 Equivalent Circuit for Shunt-Shunt Feedback Amplifier * * Rof Rif ARfoI i * V ARo ARfo o 42 K I 1 A f Ro S f Rif Rof Ri 1 f ARo f ARo 0.021mA / V (350 K ) 7.4 ARfo ARo 1 47 K 1 f ARo f AVfo ARfo 1.3K 0.15K 8.4 Ro 4.3K 0.5K (1 f ARo ) 8.4 ECE 352 Electronics II Winter 2003 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 Ch. 8 Feedback RS 4.2 V / V 15 Frequency Analysis * * * * * Hf 1 f ACo 'H Lf ECE 352 Electronics II Winter 2003 L 1 f ACo ' * * 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 16