Download SMALL SIGNAL OPERATION AND MODEL

SMALL SIGNAL OPERATION
AND MODEL
Chapter 5.6
Micro Electronic Circuits,
Dr. Jagadish Nayak, Asst. Professor, BITS PILANI DUBAI
Base-Emitter Junction is
forward biased using VBE
(Battery)
Collector-Base junction is
reverse biased using power
supply VCC through RC
The input signal is vbe
Micro Electronic Circuits,
Dr. Jagadish Nayak, Asst. Professor, BITS PILANI DUBAI
Consider only the dc bias condition by letting vbe=0
The voltage and current relations are given by
IC
IE
IB
VC
ISe
VBE
VT
IC
IC
VCE
VCC
I C RC
For active mode operation VC should be greater than (VB-0.4)
Micro Electronic Circuits,
Dr. Jagadish Nayak, Asst. Professor, BITS PILANI DUBAI
COLLECTOR CURRENT AND
TRANSCONDUCTANCE
When vbe is applied, total instantaneous
base emitter voltage vBE becomes
vBE
VBE
vbe
The collector current becomes
iC
ISe
ISe
Micro Electronic Circuits,
VBE vbe
v BE
VT
VBE
VT
ISe
e
VT
vbe
VT
Dr. Jagadish Nayak, Asst. Professor, BITS PILANI DUBAI
Using I C I S e
VBE
VT
we get iC
IC e
vbe
VT
If vbe <<<< VT, we can approximate the above as
iC
vbe
I C (1
)
VT
This approximation which is valid only for vbe less than 10mV
is referred to as small signal approximation
Under this approximation , the total collector current is
given by
Signal Component ic
I v
iC
Micro Electronic Circuits,
IC
C be
VT
DC BIAS
Dr. Jagadish Nayak, Asst. Professor, BITS PILANI DUBAI
ic
IC
vbe
VT
The above relation relates signal current to the
corresponding base emitter signal voltage. This
can be written as
ic
g m vbe
Where gm is called as transconductance , g m
IC
VT
This is directly proportional to the collector bias current IC
BJTs have high transconductance. Eg IC=1mA, VT=25mV
gm≈40mA/V
Micro Electronic Circuits,
Dr. Jagadish Nayak, Asst. Professor, BITS PILANI DUBAI
gm
Micro Electronic Circuits,
iC
vbe
iC I C
Dr. Jagadish Nayak, Asst. Professor, BITS PILANI DUBAI
The Small signal approximation implies keeping the signal
amplitude sufficiently small, so that operation is restricted to
an almost linear segment of the iC-vBE exponential curve.
This analysis shows that transistor behaves as a voltage
controlled current source.
Micro Electronic Circuits,
Dr. Jagadish Nayak, Asst. Professor, BITS PILANI DUBAI
The BASE CURRENT AND
INPUT RESISTANCE AT BASE
In this circuit , what is the resistance seen
by vbe
Let is evaluate base current iB
iB
iB
iC
and we know iC
IC
1 IC
vbe
VT
total base current iB
where I B
Micro Electronic Circuits,
IC
IC
vbe
VT
IC
I B ib
and ib is signal component
Dr. Jagadish Nayak, Asst. Professor, BITS PILANI DUBAI
ib
1 IC
vbe
VT
IC
Substitute
VT
g m , we get ib
gm
vbe
The small signal input resistance between base and emitter
looking into base is defined by
r
Micro Electronic Circuits,
vbe
ib
gm
Dr. Jagadish Nayak, Asst. Professor, BITS PILANI DUBAI
EMITTER CURRENT AND INPUT
RESISTANCE AT EMMITER
The total emitter current is
iE
iC
IC
ic
total emitter current
We know that ic
iE
IC
iE
IE
ie
IC
vbe
VT
1 IC
vbe
VT
comparing the equations for iE , we get
IE
Micro Electronic Circuits,
IC
and Signal current ie
1 IC
vbe
VT
Dr. Jagadish Nayak, Asst. Professor, BITS PILANI DUBAI
We can write
ie
IE
vbe
VT
 IE
IC
If we denote small signal resistance between base and emitter
looking onto emitter by re
re
vbe
ie
VT
IE
IC
We know that g m
and I C
VT
using above we can write re
Micro Electronic Circuits,
IE
gm
1
gm
Dr. Jagadish Nayak, Asst. Professor, BITS PILANI DUBAI
What is the relation between rπ and re
vbe
ib r
r
ie
re
ib
Micro Electronic Circuits,
ie re
i.e r
(
1) re
Dr. Jagadish Nayak, Asst. Professor, BITS PILANI DUBAI
VOLTAGE GAIN
Transistor is acting as a voltage controlled current source. To
obtain output voltage signal , current has to be flown through
the resistor. Considering the circuit below
The total collector voltage vC
vC
VCC
iC RC
VCC
(IC
VCC
I C RC
VC
Micro Electronic Circuits,
ic ) RC
ic RC
ic RC
Dr. Jagadish Nayak, Asst. Professor, BITS PILANI DUBAI
We know that total collector current is equal to dc
component plus signal component, accordingly we can
write v
V v
C
C
c
Comparing above with vC
VC
ic RC
DC BIAS VOLTAGE AT THE
COLLECTOR
vc
vc
ic RC using relation ic
g m vbe we get
( g m RC )vbe
vc
Thus voltage gain of the amplifier is
vbe
Micro Electronic Circuits,
g m RC
Av
Dr. Jagadish Nayak, Asst. Professor, BITS PILANI DUBAI
Substituting for, g m
IC
VT
we get
Av
I C RC
VT
E.g.
A BJT having β=100 is biased at a dc collector current of
1mA. Find the value of gm , re and rπ at the bias point
Ans: gm=40mA/V
Micro Electronic Circuits,
re=25Ω
rπ=2.5KΩ
Dr. Jagadish Nayak, Asst. Professor, BITS PILANI DUBAI
E.g.
In the circuit shown below, VBE is adjusted to yield a dc
collector current of 1mA. Let VCC=15V, RC=10KΩ and
β=100. Find the voltage gain vc/vbe
If vbe = 0.005 sin wt volts find vC(t) and iB(t)
Ans : Av=-400 V/V
Micro Electronic Circuits,
Dr. Jagadish Nayak, Asst. Professor, BITS PILANI DUBAI
SEPERATING SIGNAL FROM
THE DC QUANTITIES
The analysis we have seen consist of two components ,
i. e dc component and the signal component
iC
I C ic
and
vBE
VBE vbe
Signal operation can also be represented by eliminating
the dc sources as shown
This is only the
representation as it is
not an amplifier due
to no dc bias
Micro Electronic Circuits,
Dr. Jagadish Nayak, Asst. Professor, BITS PILANI DUBAI
THE HYBIRD π MODEL
This model represents the BJT as a voltage controlled current
source and explicitly includes the input resistance looking into
the base , rπ
Micro Electronic Circuits,
Dr. Jagadish Nayak, Asst. Professor, BITS PILANI DUBAI
In this model ic
ib
g m vbe
vbe
r
The current ie
vbe
vbe
g m vbe
1 gmr
r
r
vbe
But g m r
, we get ie
1
r
We can rearrange the above equation as
ie
vbe
r
vbe
re
1
Micro Electronic Circuits,
Dr. Jagadish Nayak, Asst. Professor, BITS PILANI DUBAI
Slightly different model can be obtained by expressing
the current of the controlled source (gmvbe) interms of
base current ib
gmvbe
gm (ib r )
gmr ib
ib
Equivalent circuit model is
Now the transistor circuit is
modeled as current controlled
current source.
Micro Electronic Circuits,
Dr. Jagadish Nayak, Asst. Professor, BITS PILANI DUBAI
THE T MODEL
The resistance between base and
emitter is shown. This model will
yield current expressions for ic
and ie
We note that
ib
vbe
re
g m vbe
vbe
(1
re
vbe
( 1)re
Micro Electronic Circuits,
)
vbe
(1 g m re )
re
vbe
(1
re
1
)
vbe
r
Dr. Jagadish Nayak, Asst. Professor, BITS PILANI DUBAI
The current of the controlled source can be expressed in
terms of the emitter current.
gmvbe
gm (ie re )
gm re ie
ie
This will yield an alternative T model, represented as a
current controlled current source.
Micro Electronic Circuits,
Dr. Jagadish Nayak, Asst. Professor, BITS PILANI DUBAI
APPLICATION OF THE SMALL
SIGNAL EQUIVALENT CIRCUIT
To analyze the transistor amplifier circuits in
systematic process
The Process consist of following steps
1. Determine the DC operating point of the BJT and
in particular dc collector current IC
2. Calculate the values of the small signal model
parameters such as
gm
Micro Electronic Circuits,
IC
,r
VT
gm
, and re
VT
IE
gm
Dr. Jagadish Nayak, Asst. Professor, BITS PILANI DUBAI
3. Eliminating the dc sources by replacing each dc
voltage sources with short circuit and each dc current
source with an open circuit.
4. Replace the BJT with one of its small signal
equivalent model
5. Analyze the resulting circuit to determine the
required quantities. (e.g. voltage gain input
resistance)
Micro Electronic Circuits,
Dr. Jagadish Nayak, Asst. Professor, BITS PILANI DUBAI