ANALOG CIRCUITS
18EC42
Biasing Using a Collector-to-Base
Feedback Resistor
• Figure shows a simple Biasing Using a
Collector-to-Base Feedback Resistor
Biasing Using a Collector-to-Base
Feedback Resistor
• The circuit employs a
resistor RB connected
between the collector
and the base
• Resistor RB provides
negative feedback, which
helps to stabilize the bias
point of the BJT.
Biasing Using a Collector-to-Base
Feedback Resistor
• Analysis of the circuit
is shown in Fig., from
which we can write
Summary of the BJT Current–Voltage
Relationships in the Active Mode
Small-Signal Operation and Models
• conceptual amplifier circuit shown in Fig.
Cont…
• Here the base–emitter junction is forward
biased by a dc voltage VBE (battery).
• The reverse bias of the collector–base junction
is established by connecting the collector to
another power supply of voltage VCC through a
resistor RC.
• The input signal to be amplified is represented
by the voltage source vbe that is
superimposed on VBE.
Cont..
• We consider first the dc bias conditions by
setting the signal vbe to zero.
Cont..
•
•
•
•
IC = ISeVBE ⁄ VT
IE = IC ⁄α
IB = IC ⁄ β
VCE = VCC – ICRC
The Collector Current and the
Transconductance
• If a signal vbe is applied as shown in Fig. (a),
the total instantaneous base–emitter voltage
vBE becomes
vBE = VBE + vbe
• Correspondingly, the collector current
becomes
iC = IS evBE ⁄ VT =IS e (VBE + vbe) ⁄ VT
‫؞‬iC =ISeVBE ⁄ VT evbe ⁄ VT
• Use of Eq. IC = IS eVBE ⁄ VT in iC =IS eVBE ⁄ VT evbe ⁄ VT yields
iC = IC evbe ⁄ VT
• Now, if vbe<<VT, we may approximate the above Eq.
as
Here we have expanded the exponential in Eq. iC = IC evbe ⁄ VT in a series and
retained only the first two terms. This approximation, which is valid only for
vbe less than approximately 10 mV, is referred to as the small-signal
approximation. Under this approximation, the total collector current is given
by the above Eq. and can be rewritten
• Thus the collector current is composed of the
dc bias value IC and a signal component ic ,
• This equation relates the signal current in the
collector to the corresponding base–emitter
signal voltage. It can be rewritten as
where gm is called the transconductance
The Base Current and the Input
Resistance at the Base
• To determine the resistance seen by vbe, we
first evaluate the total base current iB using
Eq.
as follows:
Thus,
Base Current
• where IB is equal to and the signal component
ib is given by
• The small-signal input resistance between base and
emitter, looking into the base, is denoted by rπ and is
defined as
the Input Resistance at the Base
• Using Eq.
gives
•Thus rπ is directly dependent on β and is inversely proportional
to the bias current IC.
•Substituting for gm in Eq.
from Eq.
and
replacing IC /β by IB gives an alternative expression for rπ ,