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

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

The small signal amplifier is common emitter 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 collector terminal through coupling capacitor \(C_2\) as in figure. 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 B\E junction by forward bias PN junction diode.
• Replace B\C junction by current source of base current \(I_B\).

In dc equivalent circuit

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

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

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

$$\sim \beta I_B=\beta \biggl(\frac{V_{CC}-V_{BE}}{R_B}\biggr)$$

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 \(r_{ac}=\beta r_e’\) where \(r_e’=\frac{25mv}{I_B }\) and \(I_B\) is dc emitter current.
• The C\E junction is replaced by collectror current source of\( i_C\). As seen from input as source , it is shared by \(R_B\) and \( \beta r_e’\) and then seen from output side, collector current \(i_C\) is shorted by \(R_C\) and \(R_L\) i.e. \(\frac{R_B}{\beta r_e’}\) and \(R_C \shortparallel R_L\)

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

Principle of operating characteristics :

• Input characteristics(\(r_{in}\):

$$r_{in}=R_B\shortparallel \beta r_e’$$

$$r_{in}=\frac{R_B.\beta r_e’}{R_B+\beta r_e’}$$ Since, \(R_B>>\beta r_e’\) then $$ r_{in}=\beta r_e’$$

• Output resistance(or load resistance):

$$ r_{out}=R_C\shortparallel R_L$$

$$ r_{out}=\frac{R_c.R_L}{R_C+R_L}$$

• Current gain(\(A_i\)):

\(A_i\)=\(\frac{collector current }{base current}\)

Since \(i_C=\beta i_b\) $$A_i=\frac{\beta i_b}{i_b}$$

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

• Voltage gain(\(A_v\):

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

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

$$=\frac{(\beta i_b).r_L}{i_b . r_{in}}$$

$$=\frac{\beta . R_C\shortparallel R_L}{\beta r_e’}$$

$$=\frac{R_C\shortparallel R_L}{r_e’}$$

\(\therefore\) voltage gain is very large.

• Power gain(\(A_v\)):

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

$$A_p=\beta \biggl(\frac{R_C\shortparallel R_L}{r_e’}\biggr)$$Therefore power gain is very large.

Circuit operation:

During ‘+’ve half cycle or input ac signal, the net base current (\(i_B\)) is increases due to same direction of flow of ac signal as well as dc base current (\(I_B\)). This increase biasing potential \(v_{BE}\) due to increases in (\(i_B\)). This causes increases in emitter current which causes the further increase in collector current as \(i_c=\alpha i_e\). Now increase in collector current \(i_{cd}\) the increase in drop of potential across (\(R_c\)) reduces the output voltage \(v_{CE}\).

In increase decrease notation, the circuit action,

$$ v_{in}\uparrow, i_B\uparrow, v_{BE}\ uparrow , i_E\ uparrow, i_C\ uparrow, i_CR_C \ uparrow v­_{CE}\downarrow$$ Since, the positive going input signal produces the amplitude negative going output signal. This means there is phase inversion input and output signal. Thus CE amplifier is called as inverting amplifier.

Characteristics:

• Low input resistance.
• Very high output impedance.
• Large current gain.
• Large voltage gain.
• Very large power gain.
• Phase inversion between output and input.

Uses:

• This amplifier used as power amplifier /voltage/current.
• This amplifier are made for oscillator circuit.

Reference:

(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. Print.