# Tuned Amplifier – Common Emitter by hcj

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```									                                Tuned Amplifier – Common Emitter

Fig.1a Circuit of CE Tuned amplifier                       Fig. 1b Equivalent circuit (BJT and MOSFET)

The BJT is biased to give an ICQ and a corresponding gm = ICQ/VT.

Assumption: R1 and R2 are large. CE bypasses RE.
The inductance RFC (radio frequency choke) is large so it is open at signal frequencies.

From Fig. 1b, the output voltage is given by

Vo(s) = -gmViZ(s) where Z ( s)            1    .                                                          (1)
1 1
Cs    
Ls R
The voltage gain is given by

V ( s)                         gm          gm R
Av ( s)  o        g m Z ( s) =                           .                                             (2)
Vi ( s)                         1   1       R
Cs         1     RCs
Ls R       Ls
The frequency response (gain) of the amplifier will have the same shape as the frequency response of
a parallel resonant circuit. The following observations can be made:
a. The peak gain is gmR and it occurs at ω = ωo =       1    .                                             (3)
LC
b. The bandwidth of the amplifier will be the same as the bandwidth of the parallel resonant circuit.
It is given by

o                              R
BW           where Q p  o CR           .                                                      (4)
Qp                             o L
  o
c. For frequencies around resonance with small values for                 , the amplifier gain can be
o
expressed by a linear function as

 gmR
Av               .                                                                                        (5)
1 j 2Q p
The parasitic associated with the BJT (capacitances Cp, Cu) and the inductance (resistance Rc) are to
be included in calculating the equivalent values of C and R in equations (1) to (5).
Parasitic capacitors:

Cπ- - between base and emitter

Cμ - between base and collector

Input capacitance seen by Vi = Cin = Cπ+ Cμ(1+gmR)

Output capacitance ≈ Cμ

Including the parasitics:

R  R||Rt where
      
2
Rt  R c 1  Q s 
L
CRc
.

C  C + Cμ

In a multi-stage amplifier, a tapped capacitor may be used to match the two stages. The parameters of
the second stage have to be included in getting the loaded gain of the cascade. The parallel
combination of rπ and Cπ will appear across C2. The inductance L may be used instead of RFC.

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