Properties of Negative Feedback: An Explanation

What is Negative Feedback?

When the feedback energy is out of phase with the input signal, it is called negative feedback. Negative feedback reduces the gain of the amplifier. That is why, it is sometimes called degenerative or inverse feedback. However, the advantages of negative feedback are:

• Higher input impedance
• Lower output impedance
• Better stabilized gain
• Reduction of noise
• Improved frequency response

Properties negative voltage series feedback: 

Considering the following feedback circuit, we will explain the mentioned properties of a negative feedback circuit.

Fig: Negative Feedback

Decreased Gain & increased Stability:

The gain of the amplifier without feedback is A_v . Negative feedback is then applied by feeding a fraction m_v of the output voltage e_o back to amplifier circuit.

Therefore, the actual input to amplifier = e_g -m_ve_o

The output e_o must be equal to the input voltage multiplied by gain A_v of the amplifier.

                           ( e_g – m_ve_o ) A_v = e_o

                 Or,   e_g A_v  - m_vA_ve_o = e_o

                Or,   e_o ( 1 + m_vA_v ) = e_gA_v

                Or,   e_{o /} e_g  = A_v /( 1 + m_vA_v )

But   e_o |e_g   is the gain of the amplifier with feedback. Therefore-

                           A_vf = A_v /( 1 + m_vA_v )

So due to negative voltage feedback, the gain is reduced by a factor  ( 1 + m_vA_v )

For effective design  m_vA_v >> 1   

 then  A_vf = A_v / m_vA_v  =1/m_v

As the gain of the negative feedback depends on only feedback ratio or feedback circuit which is actually a resistive network that is why the negative feedback gain is unaffected from the variations of transistor parameters, temperature, frequency. Therefore it will be extremely stable.

Increased in Input Impedance: 

Consider the above circuit parameters. We also assume that:

                       Z_in  = input impedance without feedback

                       Z_in^/ = input impedance with feedback

                       i₁  = input current

So from above fig we get,   e_g – m_ve_o = i₁Z_in     --- (1)

Now,         e_g = e_g – m_ve_o + m_ve_o

                        = (e_g – m_ve_o) + (e_g – m_ve_o)m_vA_v         
                                                [ as ( e_g – m_ve_o ) A_v = e_o ]

                    = (e_g – m_ve_o) ( 1 + m_vA_v )

                    = i₁Z_in ( 1 + m_vA_v )       [ From 1]

             Or, e_{g /} i₁ =  Z_in ( 1 + m_vA_v )      

But   e_g|i₁  is the input impedance with feedback.

             So,    Z_in^/ = Z_in ( 1 + m_vA_v )      

Therefore the input impedance of the negative feedback is increased by a factor ( 1 + m_vA_v ). This is an advantage, the amplifier will now present less of a load to its source circuit.

Reduction in Output Impedance: 

Apply an voltage  e  at the output circuit which causes to flow current I and short the input voltage e_g .

Now consider,     Z_o  = output impedance without feedback

                           Z_o^/ = output impedance with feedback

We get,       e = Z_oI + A_vV_i     

       where V_i = input voltage across the amplifier

But,           V_i = e_g - e_f                      

       where  e_f = voltage across the feedback

                     =  - e_f

                     =  - m_ve                 Here  e = e_o

Putting this into above relation we get,

                  e = Z_oI - A_vm_ve  

            or, e( 1 + m_vA_v ) = Z_oI 

            or, e/I  =  Z_{o  /}( 1 + m_vA_v )     
      

Therefore output impedance with feedback, 
             Z_o^/ = e/I  =  Z_{o /}( 1 + m_vA_v )   

So the output impedance is reduced by a factor   ( 1 + m_vA_v ) .

Improved Frequency Response:

The gain of the negative feedback depends on only feedback ratio or feedback circuit which is actually a resistive network. That is why the gain is independent of signal frequency. The result is that voltage gain of the amplifier will be constant over a wide range of signal frequency. The negative voltage feedback therefore improves the frequency response of the amplifier.

Increase in the Bandwidth: 

When the gain decreases by a factor  ( 1 + m_vA_v ) by providing negative feedback. It is seen that the lower cut off frequency is also lowered by this factor  ( 1 + m_vA_v ) and upper cut off frequency is raised by the same factor. As a result the difference between the frequencies means bandwidth is increased.

Fig: Bandwidth Increased by Negative Feedback

 

Decreased distortion: 

Let the harmonic distortion voltage generated within in the amplifier change from D to D^/ , when negative feedback is applied to the amplifier.

Suppose     D^/ = xD

The fraction of the output distortion voltage which is feedback to the input is:   m_vD^/ = m_vxD

After amplification, it becomes m_vxDA_v and is antiphase(due to negative feedback) with orginal distortion voltage D.

Hence the new distortion voltage D/ which appears in the output is:

               D^/ = D – m_vxDA_v

       Or,  xD = D – m_vxDA_v

      Or,  x = 1 -  xm_vA_v

      Or, x ( 1 + m_vA_v ) = 1

      Or, x = 1/  ( 1 + m_vA_v )

      Or, xD = D/( 1 + m_vA_v )

     Or, D^/ = D/( 1 + m_vA_v )

Therefore, the negative feedback reduces the distortion.

Reduce Noise Effect:

Negative feedback can help reduce the impact of noise on electronic circuits by reducing the gain of the amplifier and increasing the signal-to-noise ratio. This makes negative feedback a useful tool in designing circuits that are stable, reliable, and perform optimally in the presence of noise.