Mumbai University > Electronics Engineering > Sem 4 > Discrete Electronic Circuits

Marks: 10M

Year: May 2016

Feedback is a network which take samples of output which may voltage or current and feeds back to the input. If the feedback signal is out of phase with the input signal then it is called as Negative Feedback.

Advantages of Negative Feedback :

• Bandwidth of amplifier increases.
• Noise gets reduced.
• Stability of amplifier increases.
• Decreases frequency distortion.

Current Series Negative Feedback :

Figure 1 shows the block diagram of current series negative feedback. Since current series is mentioned, output is connected in series configuration because of current sampling and input is connected in series mixing. It increases both the input and output impedance.

Figure 1 : Current Series Negative Feedback Block diagram

• The input signal $V_S$ is applied as a input, $V_f$ is the feedback voltage and $I_O$ is the output current.
• $A_f$ indicate relationship between $I_O$ and input voltage $V_S$. The feedback voltage is given by $V_f$ = β $I_O$.
• Transconductance amplifier is called so because output is current and input is voltage, hence ratio gives us transconductance.
• The sample of output current is applied as a input to feedback network which feeds back the output signal to the input.
• The difference of input signal and feedback signal gets amplified by the transconductance amplifier.

Derivation for Rif, Rof and Af :

1) Rif ( Input Resistance with feedback) :

Rif = $\frac{Vs}{Iin}$

Rif = $\frac{Vs}{Iin}$ = $\frac{Vin+ βIo}{Iin}$ ….(1)

Since, Vs = Vin+βIo and A= $g_m$ = $\frac{Io}{Vin}$

Io=AVin

Substituting in equation (1),

Rif = $\frac{Vs}{Iin}$ = $\frac{Vin+ βAVin}{Iin}$

Hence, Rin= $\frac{Vin}{Iin}$

Rif=Rin(1+Aβ)

Input impedance increases by a factor 1+Aβ.

2) Rof (Output Impedance with feedback) :

Figure 2 : Equivalent Circuit of Current Series Negative Feedback

Figure 2 shows the equaivalent circuit for Rof.

For Rof :

1. Short the input voltage source.
2. Remove output load resistance.
3. Connect an imaginary current source that delivers current Io.

Rof = $\frac{Vo}{Io}$ …..(2)

From Figure 2,

Io = $\frac{Vo}{Ro}$ - $g_m$Vin …..(3)

Vin = -Vf = -βIo

since, Io=-Io, refer Figure 2 which shows that current through load resistance is opposite to the current through voltage source.

Hence,

Vin = -βIo

Substitute in equation (3),

Io = $\frac{Vo}{Ro}$ - $g_m$βIo

Since, $g_m$ = A

Io = $\frac{Vo}{Ro}$ - AβIo

$\frac{Vo}{Ro}$ = Io(1+Aβ)

Rof = $\frac{Vo}{Io}$ = Ro(1+Aβ)

Output impedance increases by factor (1+Aβ).

3) Af( Voltage gain with feedback ):

Af = $\frac{Io}{Vs}$ = Aif …………(4)

Vin = Vs - Vf

Vs = Vin + Vf

But, Vf = βIo,

Vs=Vin+βIo

Substitute Vs in equation (4),

Af = $\frac{Io}{Vs}$ = $\frac{Io}{Vin+βIo}$

Divide numerator and denominator by Vin,

Af= $\frac{\frac{Io}{Vin}}{\frac{Vin}{Vin} + β \frac{Io}{Vin}}$

Af = $\frac{A}{1+Aβ}$

Voltage Gain decrease by a factor (1+Aβ).