Series-Series Feedback Amplifier - Ideal Case

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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Voltage fedback to input


Series-Series Feedback Amplifier - Ideal Case

Gain (Transconductance Gain)

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* 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


* 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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* 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’



* 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


* 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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* 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)


Io



Ic3 ≈ Io



Input Loading Effects

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Output Loading Effects

Z-parameter equivalent circuit for feedback circuit



Io



Redrawn basic amplifier with loading effects,but not feedback.

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* 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)


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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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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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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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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:

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Correct voltage gain for the amplifier with feedback!

Wrong voltage gain!


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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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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Series-Series Feedback Amplifier - Ideal Case