One very useful application of the transistor is an amplifier of time varying signals.
Consider the “conceptual BJT amplifier” circuit shown below:
The DC voltages provide the biasing. The input signal is vbe and the output signal is vc. We will assume the transistor is biased so that VC is greater than VB by an amount that llows for sufficient “signal swing” at the collector, but the transistor remains in the active mode at all times. That is, the transistor does not become saturated or cutoff during the cycle. From the circuit above, the total base-to-emitter voltage is
Correspondingly, the collector current is
or using (5.53) ic=Ice
For small vbe such that Vbe<<2VVr (i.e., the small-signal approximation), then (3) can be approximated by
This is a familiar result: We saw something very similar with small signals and diodes back in Lecture 4.The time varying current in (4)
Can be written as ic=gwVbe
is defined as the transistor small-signal transconductance. Its units are Siemens. Note that gmIc.
Significance of the BJT Small-Signal Transconductance
What is the physical significance of gm? First, gm is the slope of the iC-vBE characteristic curve at the Q point:
Consider the plot shown in Fig.
with ic= Ise from (2), the right-hand side of (8) becomes
therefore
as we defined in (6). Observe that:
• The small-signal vbe assumption restricts the operation of
the BJT to nearly linear portions of the iC-vBE characteristic
curve.
• From (6), the BJT behaves as a voltage controlled current
source for small signals: The small-signal be v controls the
small-signal ic
Signal Voltage Gain
Second, gm has an important relationship to the signal voltage gain in this circuit. Using KVL in Fig. 5.48a, the total collector voltage is
where VC is the DC voltage at the collector.
So from (11), the AC signal at the collector is
Vc=-IcRc
This result is negative, which means this circuit operates as an inverting amplifier for small, time varying signals.
From (6), c mbe ic= gm vbe = . Using this result in (12) gives
Vc=-gmVbeRc=-(gmRc)vbe
Consequently, the small-signal AC voltage gain Av is
In a broad sense, we can see that this transistor circuit can act an amplifier of the time varying input signal, provided this input voltage remains small enough.
gm is a very important amplifier parameter since the voltage gain in (14) is directly proportional to gm. BJTs have a relatively large gm compared to field effect transistors, which we will consider in the next chapter. Consequently, BJTs have better voltage gain in such circuits.
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