To calculate the small-signal input conductance (
g
m
) of a common-collector (CC) bipolar junction transistor (BJT) amplifier, you'll need to consider the small-signal model of the BJT. In the small-signal model, the BJT is represented by a linear equivalent circuit with small-signal parameters. The CC amplifier, also known as an emitter follower, has the emitter connected to the output and the base connected to the input. Here's how you can calculate the small-signal input conductance:
Step 1: Draw the Small-Signal Model
Start by drawing the small-signal model of the common-collector BJT amplifier. The small-signal model consists of the transistor itself and the relevant resistances, capacitances, and current sources. For the CC BJT amplifier, you will have:
r
π
: Base-emitter resistance.
g
m
: Transconductance of the transistor (small-signal current gain).
r
o
: Output resistance.
C
π
: Base-emitter capacitance.
C
mu
: Miller capacitance (collector-base capacitance effectively seen at the input).
C
o
: Output capacitance.
Step 2: Identify the Circuit Parameters
Determine the values of the resistances and capacitances in the small-signal model. These values are usually provided in the datasheet of the BJT or can be obtained from transistor parameters.
Step 3: Apply the Small-Signal Model
Replace the transistor in the small-signal model with its equivalent small-signal model, which involves replacing the transistor with a current source (
⋅
g
m
⋅V
be
) in parallel with
r
π
.
Step 4: Calculate
g
m
The transconductance (
g
m
) of the BJT is given by:
=
g
m
=
V
T
I
C
where:
I
C
= Collector current (in the DC operating point).
V
T
= Thermal voltage (approximately 26 mV at room temperature).
Step 5: Calculate the Input Conductance (
g
m
)
The small-signal input conductance (
g
m
) of the common-collector BJT amplifier can be calculated as follows:
=
1
g
m
=
r
π
1
Where
r
π
is the base-emitter resistance and is given by:
=
r
π
=
I
B
V
T
where:
I
B
= Base current (in the DC operating point).
So, the small-signal input conductance (
g
m
) is the reciprocal of the base-emitter resistance (
r
π
).
Keep in mind that this calculation assumes small-signal conditions and that the BJT is biased in its active region.