Download 3 Static Characteristics III

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Static Characteristics III
3.1 Inverter Design
VCC

IC
RC
IB
F
C
B
RB
T
VO
E
Vi
IC
Maximum gain
Fig. 3.1 Bipolar Transistor Inverter Circuit
Generally choose IC mid range for a high value of F.
Consider a supply VCC = 5V.
A typical mid-range value of IC would be 3 - 5 mA.
For IC = 5mA,
RC 
VCC
5V

 1kΩ
ICMAX 5mA
A typical F = 50 for an integrated transistor.
If we use a base overdrive factor of σ u  5
Then,
σu 
βFR C
RB

5
50  1kΩ
RB
 RB 
50kΩ
 10kΩ
5
The idea is simply to make sure that RB provides sufficient current to
overdrive the transistor. Rewriting the relationship, the choice is
really:
RB 
F
RC .
σu
1
3.2 Operation and Output Characteristic
IC
IC
The collector current that flows
through the transistor depends on the
bias applied to the base-emitter
junction according to the normal
exponential law for the p-n junction.
MAX
Typically:
VBE cut - in = 0.6V
VBE on = 0.7V
IC
Forward
active
mode
VBE sat = 0.8V
VBE
CUT - IN
VBE
Figure 3.2
VBE
SAT
ON
Collector Current as a Function of Base-Emitter Bias
Referring to the output characteristic of Fig. 3.3, which shows an
operating load line, the following can be seen. At very low input
voltages, VBE is small and no current flows in the collector of the
transistor, apart from some small leakage current. Hence, the output
voltage is at VO  VCE  VCC . If the input voltage to the inverter is
slowly increased, eventually the base-emitter junction reaches the
point of cut-in when Vi  VBE CUT IN at point A on the characteristic in Fig.
3.3. Here, IC  0 so that VO  VCE  VCC still. As the input voltage is
further increased, base current starts to flow and the transistor enters
the forward active mode where I C   F IB and the operating point
travels upward along the load line. Eventually, the point B is reached
where IB  ICMAX /F and the transistor arrives at the edge of saturation.
In this case, the collector current reaches its maximum value and the
output voltage falls to its minimum of VO  VCE SAT  0.1  0.2V . Further
increase in the input voltage overdrives the transistor deeper into
saturation but has little effect on the collector current or the output
voltage.
2
saturation
VO  VCE
cut-off
forward active mode
IC   F IB
SAT
Vi  VBE
CUT - IN
IC
mA
IC
MAX
5
IB
edge of saturation
90 A
B
80 A
4
load line
70 A
RC  1k
60 A
3
50 A
V i increasing
40 A
2
30 A
20 A
1
10 A
A IB
edge of conduction
=0
ICE0
VCE
0
VO  VCE
Fig. 3.3
1
3
2
VCE  VCC - ICRC
SAT
4
5
VO  VCC
Output IC vs VCE Characteristic for Single Transistor Inverter
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3.3 Transfer Characteristic
The transfer characteristic of a logic gate is simply a plot of the
steady-state output voltage vs input voltage over its range of
operation such as that shown in Fig. 3.4. Initially if Vi = 0, T is OFF so
that IC = 0 and VO = VCC. As Vi is slowly increased, a point is eventually
reached at A, where the transistor begins to turn ON. This is referred
to as the cut-in point for the transistor or the “edge of conduction”. As
Vi is further increased, the transistor becomes fully conducting and
enters the forward active mode between the points A and B on the
characteristic. As the collector current increases, the output voltage
falls from VCC towards ground until the transistor reaches the edge of
saturation at point B. The slope of the characteristic between points A
and B is essentially determined by the gain of the circuit. Finally, as
the transistor is driven well into saturation, the output voltage levels
off at VO  VCE SAT . The critical points on the characteristic are points A
and B as these are the points which define the transition region in the
output between a high and low logic level. They also define the
boundaries of operation between, the Cut-off, Forward Active and
Saturation modes of operation of the transistor.
3.4 Logic Voltages
(a) Output Levels
From the transfer characteristic for the single transistor inverter,
it can be seen that the output LO and HI logic voltages are well
defined.
VOL  VCE SAT
;
VOH  VCC
(b) Input Levels
The input logic voltages are not as clearly defined and can occupy
ranges where the output remains at the correct logic level. The
critical points, A and B, on the characteristic can be used as
critical points to define the limiting values for these ranges.
Point A defines the input voltage which just begins to turn on the
transistor and is, hence, the maximum input LO voltage. Hence:
ViL MAX  VBECUT-IN
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typically 0.6V
Point B defines the minimum input voltage which will just keep the
transistor at the edge of the saturation region and hence also at the
edge of the linear forward active region. At this point:
Vi  ViHMIN
ICMAX  FIB
V
 VBE SAT
VCC  VCE SAT
 F iHMIN
RC
RB
(VCC  VCE SAT )R B
 ViHMIN  VBE SAT
FR C
ViHMIN  VBE SAT 
RB
1
(VCC  VCE SAT )  VBE SAT 
(VCC  VCE SAT )
FR C
σu
For the component values established above:
ViHMIN  0.8 
1
5  0.2  0.8  0.2  4.8  0.8  0.96  1.76 V
5
5
VO
CUTOFF
VOH 5
SATURATION
FORWARD
ACTIVE
A
4
3
2
1
B
VOL
Vi
0
Fig. 3.4
ViLMAX 1
ViHMIN
2
3
4
5
Transfer Characteristic of the Bipolar Transistor Inverter
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