Shunt-Shunt 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 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

Shunt-Shunt Feedback Amplifier - Ideal Case

Rof

RoRfo A

AA

1

Rof

iif A

RR

1

Rof

oof A

RR

1

Rof

LLfHRofHf A

A

11


Shunt-Shunt Feedback Amplifier - Ideal Case

Gain

Rof

Ro

i

of

Ro

i

f

Ro

fi

iRo

s

oRfo A

A

I

VA

I

IA

II

IA

I

VA

111

Input Resistance

Rof

i

i

ofi

s

ofi

s

fi

s

s

sif

A

R

I

VI

V

VI

V

II

V

I

VR

11

Output Resistance

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offo

of

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1

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0

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'Io’

Vo’+_

Is = 0


* 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) !

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 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

Shunt-Shunt Feedback Amplifier - Practical Case

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f

VV

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V

Iy

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112

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Rof

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Rof

oof

Rof

iif

Rof

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AA

A

RR

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RR

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AA

y22

y21V1y11

y12V2

V1V2

I1I2


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’

y22

y21V1y11

y12V2

I1I2

V1V2


* Single stage CE amplifier

* Transistor parameters. Given: =100, rx= 0

* No coupling or emitter bypass capacitors

* DC analysis:

Example - Shunt-Shunt Feedback Amplifier

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rVmAV

mA

V

Ig

mAmAIIAmAK

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* 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)




Input Loading Effects Output Loading Effects

KRR F 471

R1= y11 R2= y22

KRR F 472

y22

y21V1y11

y12V2

I1

V1V2

I2

Equivalent circuit for feedback network



Modified Amplifier with Loading Effects, but Without Feedback

Note: We converted the signal source to a Norton equivalent current source since we need to calculate the gain

Original Feedback Amplifier

R1

R2

Rof

Ro

s

oRfo A

A

I

VA

1


* 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

oRo I

VA

s


Example - Shunt-Shunt Feedback AmplifierMidband Gain Analysis

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VA

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V

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oRo

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o

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Midband Gain with Feedback

* Determine the feedback factor f

* Calculate gain with feedback ARfo

* 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

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K

RRI

I

V

I

X

X

Fff

f

o

f

o

ff

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+_ Vo’

Note: The direction of If is always into the feedback network!


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.

KKKKrRRR FSi 3.16.14710

K

K

A

RR

Rof

iif

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Ri

Ro


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: dBdBA

VVK

K

R

A

I

V

RRI

V

V

VA

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s

Rfo

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wrong!are units and five offactor anearly by off is Magnitude

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1 fromfeedback gain with voltageCalculate

not! shouldit units; has thisNote/74.0/35/021.0

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VmAVVVmAACalculate

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A

RI

V

V

VAFind

A

AAAssume

Vof

VoVfo

Vof

s

Ro

ss

o

s

oVo

Vof

VoVfo

Correct voltage gain

Wrongvoltage gain!


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

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A

I

VA

Rof

Ro

fS

oRfo 42

1

VVR

AA

KA

AA

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S

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fRof

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Rof

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1

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A

RR

Rof

iif 15.0

4.8

3.1

1

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A

RR

Rof

oof 5.0

4.8

3.4

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Rif ARfoI i

Rof


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.

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Cof

LLfHCofHf A

A

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Shunt-Shunt Feedback Amplifier - Ideal Case