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Series-Series Feedback Amplifier - Ideal Case

Series-Series Feedback Amplifier - Ideal Case. Voltage fedback to input. 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

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Series-Series Feedback Amplifier - Ideal Case

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  1. Series-Series Feedback Amplifier - Ideal Case Voltage fedback to input • 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 TRANSCONDUCTANCE GAIN A = ACo = Io/Vi • For the feedback amplifier as a whole, feedback changes midband transconductance gain from ACo to ACfo • Feedback changes input resistance from Ri to Rif • Feedback changes output resistance from Ro to Rof • Feedback changes low and high frequency 3dB frequencies Output current sampling Ch. 8 Feedback

  2. Series-Series Feedback Amplifier - Ideal Case Gain (Transconductance Gain) Input Resistance Output Resistance + V - V Ch. 8 Feedback

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

  4. Series-Series 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 z-parameter equivalent circuit for feedback network • Feedback factor f given by z12 since • Feedforward factor given by z21 (neglected) • z22gives feedback network loading onoutput • z11gives feedback network loading oninput • Can incorporate loading effects in a modified basic amplifier. Gain ACo becomes a new, modified gain ACo’. • Can then use analysis from ideal case 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 z11 • We turn off the feedback signal by setting Io = 0 (I2 = 0 ). • We then evaluate the resistance seen looking into port 1 of the feedback network (R11 =z11). • For the output loading term z22 • We open circuit the connection to the input so I1 = 0. • We find the resistance seen looking into port 2 of the feedback network (R22 =z22). • To obtain the feedback factor f (also called z12 ) • We apply a test signal Io’ to port 2 of the feedback network and evaluate the feedback voltage Vf (also called V1 here) for I1 = 0. • Find f from f = Vf/Io’ Ch. 8 Feedback

  6. Series-Series Feedback Amplifier - Practical Case • Modified basic amplifier (including loading effects of feedback network) • Including z11 at input • Including z22 at output • Including loading effects of source resistance • 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 • ACo’ is the modified transconductance gain including the loading effects of z11 , z22 , RS and RL. • Ri’ and Ro’ are modified input and output resistances including loading effects. Original Amplifier Feedback Network Modified Amplifier Idealized Feedback Network Ch. 8 Feedback

  7. Example - Series-Series Feedback Amplifier • Three stage amplifier • Each stage a CE amplifier • Transistor parameters Given: 1= 2 = 3 =100, rx1=rx2=rx3=0 • Coupled by capacitors, dc biased separately • DC analysis (given): Note: Biasing resistors for each stage are not shown for simplicity in the analysis. Ch. 8 Feedback

  8. Example - Series-Series Feedback Amplifier • Redraw circuit to show: • Feedback circuit • Type of output sampling (current in this case = Io) • Collector resistor constitutes the load so Io Ic • Emitter current Ie=( +1) Ib = {( +1)/ } Ic Ic = Io • Type of feedback signal to input (voltage in this case = Vf) Ic3≈ Io Voltage fedback to input Io Output current sampling Ch. 8 Feedback

  9. Example - Series-Series Feedback Amplifier Z-parameter equivalent circuit for feedback circuit Io Input Loading Effects Output Loading Effects R1 I2=0 R2 I1=0 Ch. 8 Feedback

  10. Example - Series-Series Feedback Amplifier Voltage fedback to input Io Output current sampling Redrawn basic amplifier with loading effects, but not feedback. R1 R2 Ch. 8 Feedback

  11. Example - Series-Series Feedback Amplifier • Construct ac equivalent circuit at midband frequencies including loading effects of feedback network. • Analyze circuit to find MIDBAND GAIN (transconductance gain ACo for this series-series configuration) IC3 Io= IE3 ≈ IC3 Io VS R1 R2 Ch. 8 Feedback

  12. Example - Series-Series Feedback Amplifier Midband Gain Analysis Io I1 I2 I3 VS Vi1 Vi3 Note convention on Io is into the output of the last stage of the amplifier. Ri1 Ri3 Ch. 8 Feedback

  13. Feedback Factor and Midband Gain with Feedback • Determine the feedback factor f • Calculate gain with feedback ACfo • Note • f ACo > 0 as necessary for negative feedback and dimensionless • f ACo is large so there is significant feedback. • f has units of resistance (ohms); ACo has units of conductance (1/ohms) • Can change f and the amount of feedback by changing RE1 , RF and/or RE2. • Gain is largely determined by ratio of feedback resistances Io’ If1 VE2 Ch. 8 Feedback

  14. 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. I1 Io Vi1 I1(1+gm1r1) Ro Ri = Ri1 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: Io Correct voltage gain for the amplifier with feedback! Wrong voltage gain! Ch. 8 Feedback

  16. Equivalent Circuit for Series-Series Feedback Amplifier • Transconductance gain amplifier A = Io/Vs • Feedback modified gain, input and output resistances • Included loading effects of feedback network • Included feedback effects of feedback network • Significant feedback, i.e. f ACo is large and positive Ch. 8 Feedback

  17. Frequency Analysis • Simplified amplifier analyzed had biasing resistors omitted for simplicity. • For completeness, need to add biasing resistors. • 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). • 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

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