Common collector amplifier and it’s equivalent AC and DC equivalent circuit

Common collector amplifier and it’s equivalent AC and DC equivalent circuit :

The small signal amplifier is common collector is as shown in figure. The input signal is given to the base of the transistor through coupling capacitor \(C_1\) whereas output signal is taken across load resistor \(R_L\) which is connected to emitter terminal through coupling capacitor \(C_2\) as in figure. This circuit is also called as emitter follower as the emitter signal is followed by the signal that appear in base in both magnitudes.The single dc supply ‘+’ve \(V_{CC}\) biases the transistor .

DC equivalent circuit :

To draw the dc equivalent circuit following steps should be adopted.

• Remove the ac-source i.e. ground ac source to ‘0’.
• Remove all coupling capacitor as they blocks the dc.
• Replace C\B junction by forward bias PN junction diode.
• Replace B\E junction by current source of base current \(I_B\).

In dc equivalent circuit

$$V_{EE}=I_BR_B+V_{BE}$$

$$I_B=\biggl(\frac{V_{EE}-V_{BE}}{R_B}\biggr)$$As we have ,

$$I_E=(1+\beta)I_B$$

$$V_{EE}=\frac{I_E}{(1+\beta)} R_B+I_E R_E$$

$$I_E=\frac{V_{EE}-V_{BE}}{R_E+\frac{R_B}{\beta}}({1+\beta \approx \beta})$$

AC equivalent circuit:

To draw ac-equivalent circuit, Let us adopt following steps as:

• All the dc series are shorted as they are treated as ground.
• All the coupling capacitor \(C_1\) and \(C_2\) mode closed as they allow as signal.
• The emitter base junction is replaced by ac emitter resistance of junction diode \(r_{ac}=(1+\beta) r_e’\) where \(r_e’=\frac{25mv}{I_C }\) and \(I_C\) is dc emitter current.
• The C\B junction is replaced by collectror current source of i_C.

In this ac equivalent circuit,E\B junction is replaced by \((1+ \beta )r_e’\) and C\B junction is replaced by collector current as in figure. Gradually, all dc source with shorting of coupling capacitor.

Principle of operating characteristics :

• Input characteristics(\(r_{in} or r_{in,stage}\):

It is the total resistance as seen from source region into in amplifier. Thus, \(r_{in}\) is the parallel combination of \(R_B\) and \(r_{in,base}\). \(r_{in,base}\) is the resistance as seen from base terminal i.e.

$$r_{in,base}=(1+\beta)(r_e’+r_l)$$

$$r_{in,stage}=R_B\parallel (1+ \beta){ r_e’+r_l}$$

$$r_{in,stage}=(1+\beta)(r_e’+r_l) if R_B>>r_l$$

$$=\beta(r_e+r_l) \rightarrow r_e’<<r_l$$

$$=\beta r_l$$ Which is large.

• ac- load resistance:

$$ r_{out}=R_E\parallel R_L$$

• Current gain(\(A_i\)):

$$A_i=\frac{emitter current }{base current}$$

Since \(i_e=(1+\beta) i_b\) $$A_i=\frac{(1+\beta) i_b}{i_b}=1+\beta$$

$$\therefore A_i=1+\beta$$ $$A_i \approx \beta$$ Current gain is large in CB-amplifier.

• Voltage gain(\(A_v\):

\(A_v\)=\(\frac{output voltage}{input voltage}\)

$$A_v=\frac{i_e.r_l}{i_b.r_{in}}$$

$$=A_i\biggl(\frac{r_l}{r_{in}}\biggr)$$

$$=\frac{\beta .r_l}{\beta .r_l}=1$$

There is no voltage gain .

• Power gain(\(A_v\)):

\(A_p\)=\(\frac{output power}{input power}\)

$$A_p=A_i \times A_v=\beta \times 1=\beta$$Therefore power gain is very large.

Circuit operation:

figure

During the positive going half cycle of input signal. The biases potential increases \(v_{BE}\) increases.

• The base current \(i_B\) also increases.
• Then the emitter current i.e. \(i_E\) also increases.
• Drop across emitter resistor increases.
• Then the output voltage across load resistor are \(R_L\) also increases.i.e

In increase decrease notation, the circuit action,

$$ v_{in}\uparrow, i_B\uparrow, v_{BE}\ uparrow , i_E\ uparrow, i_ER_E\uparrow$$ Since, the positive going input signal produces the amplitude positive going output signal. This means there is no phase inversion between input and output signal i.e. same phase.

Characteristics:

• The impedance is very high .
• The output impedance is low.
• current gain is very large i.e.(\(1+\beta\)).
• There is no voltage gain.
• The power gain is very large.
• There is no phase inversion in CC .

Uses:

• This amplifier is used as impedance matching circuit.
• It is used a switching circuit.
• It is also used as two amplifier as signal can flow either terminal.
• It is also used for circuit isolation.

References :

(1)Theraja, B.L. Basic Electronics. N.p.: S.Chand, n.d. Print.

(2)C.L.Arora. Refresher Course in Physics. Vol. II and III. N.p.: S.Chand, 2006. Print.

(3)Malvino. Electronic Principles. N.p.: Tata McGraw-Hill, n.d. Print.

(4)N.Nelkon and P.Parker. Advanced Level Physics. 5th ed. N.p.: Arnold Heinemann, n.d. Print.

(5)Priti Bhakta Adhikari,Diya Nidhi Chaatkuli, Ishowr Prasad Koirala. A Textbook of Physics (2nd Year). N.p.: Sukunda Pustak Bhawan, 2070. Prin