Question

How can you calculate the small-signal input conductance of a common-collector BJT amplifier?

Answer 1

To calculate the small-signal input conductance (


g
m
    ​

) of a common-collector (CC) bipolar junction transistor (BJT) amplifier, also known as an emitter follower, you can follow these steps:

Draw the small-signal equivalent circuit: Begin by drawing the small-signal equivalent circuit of the common-collector amplifier. In this small-signal model, you represent the BJT as a small-signal equivalent circuit with its base-emitter junction represented as a small resistor (


r
π
    ​

) in series with a voltage source (


v
π
    ​

), and the base-collector junction represented as a small resistor (


r
o
    ​

) in parallel with a current source (


i
o
    ​

).

Identify the transistor parameters: You will need the small-signal model parameters of the BJT, which are typically given in the datasheet. The parameters required for this calculation are:

ℎ


h
fe
    ​

: The small-signal current gain or common-emitter current transfer ratio.


r
π
    ​

: The small-signal base-emitter resistance (also known as dynamic or small-signal input resistance).


r
o
    ​

: The small-signal output resistance (also known as dynamic or small-signal output resistance).

Find the expression for small-signal input conductance: The small-signal input conductance (


g
m
    ​

) is the ratio of the small-signal base current (


i
b
    ​

) to the small-signal input voltage (



v
in
    ​

).



=





g
m
    ​

=
v
in
    ​

i
b
    ​

    ​


Calculate


i
b
    ​

 and



v
in
    ​

: In a common-collector configuration, the emitter current (


i
e
    ​

) is equal to the collector current (


i
c
    ​

). Since the base current (


i
b
    ​

) is the difference between


i
e
    ​

 and


i
c
    ​

, we can calculate


i
b
    ​

:



=


−


i
b
    ​

=i
e
    ​

−i
c
    ​


The small-signal input voltage (



v
in
    ​

) is the voltage across


r
π
    ​

, which is the voltage difference between the base and emitter terminals.

Express


i
b
    ​

 in terms of



v
in
    ​

: Use the small-signal model equation for


i
e
    ​

 and


i
c
    ​

 in terms of



v
in
    ​

 to express


i
b
    ​

 solely in terms of



v
in
    ​

.

Calculate


g
m
    ​

: Substitute the expression for


i
b
    ​

 in terms of



v
in
    ​

 into the


g
m
    ​

 equation from step 3. Simplify to obtain the final expression for


g
m
    ​

 in terms of



v
in
    ​

.

(Optional) If you have measured or been given



v
in
    ​

, plug it into the expression to get the value of


g
m
    ​

.

Keep in mind that the above steps are based on the small-signal model, which is valid for analyzing small variations around the DC operating point. Also, transistor parameters might vary with temperature and biasing conditions, so it's essential to use appropriate values for accurate calculations.