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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 - PowerPoint PPT Presentation
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Ch. 8 Feedback 1ECE 352 Electronics II Winter 2003
* 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
Series-Series Feedback Amplifier - Ideal Case
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Cofoof ARR 1
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11
Output current sampling
Voltage fedback to input
Ch. 8 Feedback 2ECE 352 Electronics II Winter 2003
Series-Series Feedback Amplifier - Ideal Case
Gain (Transconductance Gain)
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Ch. 8 Feedback 3ECE 352 Electronics II Winter 2003
* 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 !
Equivalent Network for Feedback Network
Ch. 8 Feedback 4ECE 352 Electronics II Winter 2003
* 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)
z22 gives feedback network loading on output
z11 gives feedback network loading on input
* Can incorporate loading effects in a modified basic amplifier. Gain ACo becomes a new, modified gain ACo’.
* Can then use analysis from ideal case
Series-Series Feedback Amplifier - Practical Case
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Ch. 8 Feedback 5ECE 352 Electronics II Winter 2003
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 6ECE 352 Electronics II Winter 2003
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.
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Original Amplifier
Feedback Network
Modified Amplifier
Idealized Feedback Network
Ch. 8 Feedback 7ECE 352 Electronics II Winter 2003
* 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):
Example - Series-Series Feedback Amplifier
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111
Note: Biasing resistors for each stage are not shown for simplicity in the analysis.
Ch. 8 Feedback 8ECE 352 Electronics II Winter 2003
* 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)
Example - Series-Series Feedback Amplifier
Io
Output current sampling
Voltage fedback to input
Ic3 ≈ Io
Ch. 8 Feedback 9ECE 352 Electronics II Winter 2003
Example - Series-Series Feedback Amplifier
Input Loading Effects
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Output Loading Effects
Z-parameter equivalent circuit for feedback circuit
Ch. 8 Feedback 10ECE 352 Electronics II Winter 2003
Example - Series-Series Feedback Amplifier
Io
Output current sampling
Voltage fedback to input
Redrawn basic amplifier with loading effects,but not feedback.
R1 R2
Ch. 8 Feedback 11ECE 352 Electronics II Winter 2003
* 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)
Example - Series-Series Feedback Amplifier
s
oCo V
IA
Io
Io= IE3 ≈ IC3
IC3
VS
R1 R2
Ch. 8 Feedback 12ECE 352 Electronics II Winter 2003
Example - Series-Series Feedback AmplifierMidband Gain Analysis
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Note convention on Io is into the output of the last stage of the amplifier.
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Ch. 8 Feedback 13ECE 352 Electronics II Winter 2003
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
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Ch. 8 Feedback 14ECE 352 Electronics II Winter 2003
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.
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Io
Ch. 8 Feedback 15ECE 352 Electronics II Winter 2003
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:
dBdBA
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Correct voltage gain for the amplifier with feedback!
Wrong voltage gain!
Ch. 8 Feedback 16ECE 352 Electronics II Winter 2003
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
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Ch. 8 Feedback 17ECE 352 Electronics II Winter 2003
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.
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LLfHCofHf A
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