Negative Feedback Amplifier PDF

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UNIT 4 FEEDBACK AMPLIFIERS PART I

Analog Electronic Circuit I

Outline         

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Introduction to Feedback  





Feedback is used in virtually all amplifier system. Invented in 1928 by Harold Black – engineer in Western Electric Company  methods to stabilize the gain of amplifier for use in telephone repeaters. In feedback system, a signal that is proportional to the output is fed back to the input and combined with the input signal to produce a desired system response. However, unintentional and undesired system response may be produced.

Feedback Amplifier 

Feedback is a technique where a proportion of the output of a system (amplifier) is fed back and recombined with input

input

A

output

b 

There are 2 types of feedback amplifier: Positive feedback  Negative feedback 

Positive Feedback 

Positive feedback is the process when the output is added to the input, amplified again, and this process continues.

A

input

output

+

b 

Positive feedback is used in the design of oscillator and other application.

Positive Feedback - Example 

In a PA system get feedback when you put the microphone in front of a speaker and the sound gets uncontrollably loud (you have probably heard this unpleasant effect).

Negative Feedback 

Negative feedback is when the output is subtracted from the input.

input

A

output

b 

The use of negative feedback reduces the gain. Part of the output signal is taken back to the input with a negative sign.

Negative Feedback - Example 

Speed control If the car starts to speed up above the desired setpoint speed, negative feedback causes the throttle to close, thereby reducing speed; similarly, if the car slows, negative feedback acts to open the throttle

Feedback Amplifier - Concept

Basic structure of a single - loop feedback amplifier

Advantages of Negative Feedback 1. 2.

3. 4. 5.

Gain Sensitivity – variations in gain is reduced. Bandwidth Extension – larger than that of basic amplified. Noise Sensitivity – may increase S-N ratio. Reduction of Nonlinear Distortion Control of Impedance Levels – input and output impedances can be increased or decreased.

Disadvantages of Negative Feedback 1.

2.

Circuit Gain – overall amplifier gain is reduced compared to that of basic amplifier. Stability – possibility that feedback circuit will become unstable and oscillate at high frequencies.

Basic Feedback Concept

Basic configuration of a feedback amplifier

Basic Feedback Concept 



 

The output signal is: So  AS where A is the amplification factor Feedback signal is S fb  b S o where ß is the feedback transfer function At summing node: S  Si  S fb Closed-loop transfer function or gain is S A Af  o  S i 1  bA A 1 if b A  1 then A f   bA b

Classification of Amplifiers Classify amplifiers into 4 basic categories based on their input (parameter to be amplified; voltage or current) & output signal relationships:    

Voltage amplifier (series-shunt) Current amplifier (shunt-series) Transconductance amplifier (series-series) Transresistance amplifier (shunt-shunt)

Feedback Configuration Series: connecting the feedback signal in series with the input signal voltage.

Shunt: connecting the feedback signal in shunt (parallel) with an input current source

Series - Shunt Configuration

Avf 

Av 1  b v Av

Series - Shunt Configuration if

Ro  RL

then the output of feedback network is an open circuit; Output voltage is:

Vo  AvV feedback voltage is:

V fb  b vVo

where ßv is closed-loop voltage transfer function

By neglecting Rs due to Ri  Rs ; error voltage is:

V  Vi  V fb

Vo Av  Avf   Vi 1  b v Av

Series - Shunt Configuration Input Resistance, Rif

Output Resistance, Rof

Vi  V  V fb  V  b v ( AvV ) Or Vi V  (1  bv Av )  Input current V Vi Ii    Ri Ri (1  b v Av )

Assume Vi=0 and Vx applied to output terminal. V  V fb  V  bvVx  0



Rif with feedback

Rif 

Vi  Ri (1  b v Av ) Ii

Or V  b vVx  Input current V  AvV Vx (1  b v Av ) Ii  x  Ro Ro  Rof with feedback V Ro Rof  x  I x (1  b v Av )

Series - Shunt Configuration 



Series input connection increase input resistance – avoid loading effects on the input signal source. Shunt output connection decrease the output resistance - avoid loading effects on the output signal when output load is connected.

Equivalent circuit of shunt - series feedback circuit or voltage amplifier

Series - Shunt Configuration 

Non-inverting op-amp is an example of the seriesshunt configuration. For ideal non-inverting opamp amplifier

Vo  R2  Avf   1   Vi  R1  Feedback transfer function;

b

1  R2   1   R1  

Series - Shunt Configuration (ok) V o  AvV  V   V i  V fb  R1 V fb    R1  R 2 V Avf  o  Vi 1 

 V o  Av Av  R1   R1  R 2

 R1 V i  V    R1  R 2

Equivalent circuit

R if 



Av 1  b Av

  

 AvV Vo  V   R   1  2 R1 

Vi Vi   R i (1  b Av ) I i V / R i

  

Series - Shunt Configuration Example: Calculate the feedback amplifier gain of the circuit below for op-amp gain, A=100,000; R1=200 Ω and R2=1.8 kΩ.

Solution: Avf = 9.999 or 10

Series - Shunt Configuration 

Basic emitter-follower and source-follower circuit are examples of discrete-circuit series-shunt feedback topologies. • vi is the input signal • error signal is baseemitter/gate-source voltage. • feedback voltage = output voltage  feedback transfer function, ßv = 1

Series - Shunt Configuration 

Small-signal voltage gain: 1  RE   g m R E r V re  Avf  o     RE Vi  1 1    g m  RE 1  re   r



Open-loop voltage gain:



Closed-loop input resistance:



Output resistance:

1  R Av    g m R E  E re  r 

 1   Rif  r  (1 g m r )RE  r 1   g m RE      r Rof  R E

r  (1  g m r )

RE 1  1    gm  RE  r 

Shunt – Series Configuration

Aif 

Ai 1  b i Ai

Shunt – Series Configuration 









Basic current amplifier with input resistance, Ri and an open-loop current gain, Ai. Current IE is the difference between input signal current and feedback current. Feedback circuit samples the output current – provide feedback signal in shunt with signal current. Increase in output current – increase feedback current – decrease error current. Smaller error current – small output current – stabilize output signal.

Shunt – Series Configuration if

Ri  Rs

then

I i  I

then the output is a short circuit; output current is:

I o  Ai I  feedback current is:

I fb  b i I o

where ßi is closed-loop current transfer function

Input signal current:

I i  I   I fb  Aif 

Io Ai  I i 1  b i Ai

Shunt – Series Configuration Input Resistance, Rif

Output Resistance, Rof

I i  I   I fb  I   b i ( Ai I  ) Or Ii I  (1  b i Ai )  Input current Ii Ri Vi  I  Ri  (1  bi Ai )

Assume Ii=0 and Ix applied to output terminal. I   I fb  I   b i I x  0



I   b i I x V x  ( I x Ai I  ) Ro

Vx  I x  Ai ( bi I x )Ro Vx  I x (1  bi Ai ) Ro

Rif with feedback

V Ri Rif  i  I i (1  b i Ai )



Rof with feedback Rof 

Vx  Ro 1  bi Ai  Ix

Shunt - Series Configuration 



Shunt input connection decrease input resistance – avoid loading effects on the input signal current source. Series output connection increase the output resistance - avoid loading effects on the output signal due to load connected to the amplifier output.

Equivalent circuit of shunt - series feedback circuit or voltage amplifier

Shunt - Series Configuration  

Op-amp current amplifier – shunt-series configuration. Ii’ from equivalent source of Ii and Rs. • I is negligible and Rs>>Ri; I i  I i '  I fb • assume V1 virtually ground; Vo   I fb RF   I i RF • Current I1: I 1  Vo / R1 • Output current:   R I o  I fb  I1  I i 1  F  R1  • Ideal current gain:   R  I Ai  o  1  F  Ii  R1 

Shunt - Series Configuration 

Ai is open-loop current gain I   I i ' I fb  I i  I fb

and I o  Ai I   Ai ( I i  I fb )  Assume V1 is virtually ground: Vo   I fb RF 

Closed-loop current gain: I Ai Aif  o  Ai Ii 1   RF  1   R1  



I1 current:

I1  

Output current

R Vo  I fb  F R1  R1

R Io  I fb  I1  I fb  I fb  F  R1

  

  

Shunt - Series Configuration 

Common-base circuit is example of discrete shuntseries configuration. I Io Ii



I

Amplifier gain: I o / I   Ai  b

Io

RL

Ifb Ii

Closed-loop current gain: Aif 

Io Ai b   I i 1  b 1  Ai

RL

Shunt - Series Configuration 

Common-base circuit with RE and RC

Ii RC

Ii RE

Io

RE

V-

V+

Aif 

Ai Io g m r   Ii   r  r   1     g m r 1     Ai  RE   RE 

Io

RC

Series – Series Configuration

Agf 

Ag 1  b g Ag

Series – Series Configuration 





The feedback samples a portion of the output current and converts it to a voltage – voltage-tocurrent amplifier. The circuit consist of a basic amplifier that converts the error voltage to an output current with a gain factor, Ag and that has an input resistance, Ri. The feedback circuit samples the output current and produces a feedback voltage, Vfb, which is in series with the input voltage, Vi.

Series – Series Configuration (ok) Assume the output is a short circuit, the output current:

I o  AgV feedback voltage is:

V fb  b z I o

where ßz is a resistance feedback transfer function

Input signal voltage (neglect Rs=∞):

Vi  V  V fb Ag Io  Agf   Vi 1  b z Ag

Series – Series Configuration Input Resistance, Rif

Output Resistance, Rof

Vi  V  V fb  V  b z ( AgV ) Or Vi V  (1  b z Ag )  Input current V Vi Ii    Ri Ri (1  b z Ag )

Assume Ii=0 and Ix applied to output terminal. I   I fb  I   b z I x  0



I   bz I x Vx  ( I x  Ag I  ) Ro



Rif with feedback

V Rif  i  Ri (1  b z Ag ) Ii



V x  I x  Ag (  b z I x ) Ro 

Vx  I x (1  b z Ag ) Ro Rof with feedback Rof 

Vx  Ro 1  bz Ag  Ix

Series – Series Configuration  

Series input connection increase input resistance Series output connection increase the output resistance

Equivalent circuit of series - series feedback circuit or voltage amplifier

Series – Series Configuration 



The series output connection samples the output current  feedback voltage is a function of output current. Assume ideal op-amp circuit and neglect transistor basecurrent:

Vi  V fb  I o RE Io 1 Agf   Vi RE

Series – Series Configuration 

Assume IEIC and Ri

Io 

V fb

 gmr I b  gmr AgV

RE V  Vi  Vfb  Vi  Io RE Io  gm r Ag Vi  Io RE 

gmr Ag Io Agf   Vi 1  gmr Ag RE

Series – Series Configuration

Series – Series Configuration  RC   Io  ( gmV )  RC  RL    V  Vfb    gmV  RE   r  1   Vi  V Vfb  V 1    gm  RE      r  RC    gm I  RC  RL  Agf  o  Vi  1 1   g m RE   r

Shunt – Shunt Configuration

Azf 

Az 1  b z Az

Shunt – Shunt Configuration 





The feedback samples a portion of the output voltage and converts it to a current – current-tovoltage amplifier. The circuit consist of a basic amplifier that converts the error current to an output voltage with a gain factor, Az and that has an input resistance, Ri. The feedback circuit samples the output voltage and produces a feedback current, Ifb, which is in shunt with the input current, Ii.

Shunt – Shunt Configuration Assume the output is a open circuit, the output voltage:

Vo  Az I  feedback voltage is: I fb  b gVo where ßg is a conductance feedback transfer function Input signal voltage (neglect Rs=∞):

I i  I   I fb Vo Az  Azf   Ii 1  b g Az

Shunt – Shunt Configuration Input Resistance, Rif

Output Resistance, Rof

Ii  I   I fb  I   b g ( Az I  ) Or Ii I  (1  b g Az )  Input current I i Ri Vi  I Ri  (1  b g Az )

Assume Vi=0 and Vx applied to output terminal. V  V fb  V  b gVx  0 Or V   b gVx



Rif with feedback

Rif 

Vi Ri  I i (1 b g Az )





Input current V  AzV V x (1 b g Az )  Ii  x Ro Ro Rof with feedback V Ro Rof  x  I x (1  b g Az )

Shunt – Shunt Configuration

Equivalent circuit of shunt - shunt feedback circuit or voltage amplifier

Shunt – Shunt Configuration 

Basic inverting op-amp circuit is an example of shuntshunt configuration. Vo  I fb R 2 where I fb  I i Azf 





Vo   R2 Ii

Input current splits between feedback current and error current. Shunt output connection samples the output voltage  feedback current is function of output voltage.

Shunt – Shunt Configuration 

Az is open-loop transresistance gain factor (-ve value)

Vo  Az I   Az  Ii  I fb  where I fb  Vo / R2  Az Vo Azf   Az Ii 1 R2

Shunt – Shunt Configuration

Shunt – Shunt Configuration Vo V V  g mV  o   0 RC RF Ii 

V V  Vo  r RF

 1 1  1 1   1  V   Ii  o   0    g m    Vo   R F  RF   RC R F  r R F    1    g m   R V F   Azf  o  Ii  1 1  1 1   1  1          g m    RF   RC RF   r RF   RF 

Shunt – Shunt Configuration 

Open-loop transresistance gain factor Az is found by setting RF=  g m  Az 



 1  1    RC  r

Multiply by (rπRC) Azf 

Vo Ii

Assume RC...