User manual

page 24
Analog System Lab Kit PRO
experiment 2
The goal of this experiment is to understand the basics of hysteresis and
the need of hysteresis in the switching circuits.
In the earlier experiment we had discussed the use of only negative feedback. Let
us now introduce the case of regenerative positive feedback as shown in Figure 2.1.
Thereaderwillbenetbylisteningtotherecordedlectureat[20].
2.1 Brief theory and motivation
2.1.1 Inverting Regenerative Comparator
2.1.2 Astable Multivibrator
Figure 2.1: Inverting Schmitt-Trigger and its Hysteresis Characteristic
Figure 2.3: Non-inverting Schmitt Trigger and its Hysteresis Curve
Goal of the experiment
- -
V
bV
= =
1
1
1
1
1
2
2
1
1
1
1
1,5
4
ln
ln
ln
V A
V
V
A
A
R R
R
A
A
A
V
V
V
V
V
T RC
RC
t
RC
V
R R
R
R
R
R
f
T
kHz
ms
RC
1
1
1
1 2
1
0
1 2
1
1
i
i
ss
ss
ss
ss
ss
0 0 0
0
0
0
0
0
2
$
$
$
$
$
$
$
$
$
$ $
$
$
!
1
b
b
b
b
b
b
b
b
b
b
b
b
b
x
&
=
=
=
+
=
+
=
+
=
+
=
=
x
x
x
=-
-
+
-
-
-
+
_
d
d
d
i
n
n
n
- -
V
bV
= =
1
1
1
1
1
2
2
1
1
1
1
1,5
4
ln
ln
ln
V A
V
V
A
A
R R
R
A
A
A
V
V
V
V
V
T RC
RC
t
RC
V
R R
R
R
R
R
f
T
kHz
ms
RC
1
1
1
1 2
1
0
1 2
1
1
i
i
ss
ss
ss
ss
ss
0 0 0
0
0
0
0
0
2
$
$
$
$
$
$
$
$
$
$ $
$
$
!
1
b
b
b
b
b
b
b
b
b
b
b
b
b
x
&
=
=
=
+
=
+
=
+
=
+
=
=
x
x
x
=-
-
+
-
-
-
+
_
d
d
d
i
n
n
n
- -
V
bV
= =
1
1
1
1
1
2
2
1
1
1
1
1,5
4
ln
ln
ln
V A
V
V
A
A
R R
R
A
A
A
V
V
V
V
V
T RC
RC
t
RC
V
R R
R
R
R
R
f
T
kHz
ms
RC
1
1
1
1 2
1
0
1 2
1
1
i
i
ss
ss
ss
ss
ss
0 0 0
0
0
0
0
0
2
$
$
$
$
$
$
$
$
$
$ $
$
$
!
1
b
b
b
b
b
b
b
b
b
b
b
b
b
x
&
=
=
=
+
=
+
=
+
=
+
=
=
x
x
x
=-
-
+
-
-
-
+
_
d
d
d
i
n
n
n
- -
V
bV
= =
1
1
1
1
1
2
2
1
1
1
1
1,5
4
ln
ln
ln
V A
V
V
A
A
R R
R
A
A
A
V
V
V
V
V
T RC
RC
t
RC
V
R R
R
R
R
R
f
T
kHz
ms
RC
1
1
1
1 2
1
0
1 2
1
1
i
i
ss
ss
ss
ss
ss
0 0 0
0
0
0
0
0
2
$
$
$
$
$
$
$
$
$
$ $
$
$
!
1
b
b
b
b
b
b
b
b
b
b
b
b
b
x
&
=
=
=
+
=
+
=
+
=
+
=
=
x
x
x
=-
-
+
-
-
-
+
_
d
d
d
i
n
n
n
(2.1)
(2.4)
(2.2)
(2.3)
+
R2
R1
VI
VO
+VSS
-VSS
However, when
--
V
bV
==
1
1
1
1
1
2
2
1
1
1
1
1,5
4
ln
ln
ln
VA
V
V
A
A
RR
R
A
A
A
V
V
V
V
V
TRC
RC
t
RC
V
RR
R
R
R
R
f
T
kHz
ms
RC
1
1
1
12
1
0
12
1
1
i
i
ss
ss
ss
ss
ss
00 0
0
0
0
0
0
2
$
$
$
$
$
$
$
$
$
$$
$
$
!
1
b
b
b
b
b
b
b
b
b
b
b
b
b
x
&
=
=
=
+
=
+
=
+
=
+
=
=
x
x
x
=-
-
+
-
-
-
+
_
d
d
d
i
n
n
n
, it becomes
unstable as amplier as output satu-
rates. When
--
V
bV
==
1
1
1
1
1
2
2
1
1
1
1
1,5
4
ln
ln
ln
VA
V
V
A
A
RR
R
A
A
A
V
V
V
V
V
TRC
RC
t
RC
V
RR
R
R
R
R
f
T
kHz
ms
RC
1
1
1
12
1
0
12
1
1
i
i
ss
ss
ss
ss
ss
00 0
0
0
0
0
0
2
$
$
$
$
$
$
$
$
$
$$
$
$
!
1
b
b
b
b
b
b
b
b
b
b
b
b
b
x
&
=
=
=
+
=
+
=
+
=
+
=
=
x
x
x
=-
-
+
-
-
-
+
_
d
d
d
i
n
n
n
the region of
operation of this circuit is regenerative
comparator. This is the mixed-mode
circuit. Output is stable only in two
stages
--
V
bV
==
1
1
1
1
1
2
2
1
1
1
1
1,5
4
ln
ln
ln
VA
V
V
A
A
RR
R
A
A
A
V
V
V
V
V
TRC
RC
t
RC
V
RR
R
R
R
R
f
T
kHz
ms
RC
1
1
1
12
1
0
12
1
1
i
i
ss
ss
ss
ss
ss
00 0
0
0
0
0
0
2
$
$
$
$
$
$
$
$
$
$$
$
$
!
1
b
b
b
b
b
b
b
b
b
b
b
b
b
x
&
=
=
=
+
=
+
=
+
=
+
=
=
x
x
x
=-
-
+
-
-
-
+
_
d
d
d
i
n
n
n
and
--
V
bV
==
1
1
1
1
1
2
2
1
1
1
1
1,5
4
ln
ln
ln
VA
V
V
A
A
RR
R
A
A
A
V
V
V
V
V
TRC
RC
t
RC
V
RR
R
R
R
R
f
T
kHz
ms
RC
1
1
1
12
1
0
12
1
1
i
i
ss
ss
ss
ss
ss
00 0
0
0
0
0
0
2
$
$
$
$
$
$
$
$
$
$$
$
$
!
1
b
b
b
b
b
b
b
b
b
b
b
b
b
x
&
=
=
=
+
=
+
=
+
=
+
=
=
x
x
x
=-
-
+
-
-
-
+
_
d
d
d
i
n
n
n
. When the input
is large negative value output saturates
at
--
V
bV
==
1
1
1
1
1
2
2
1
1
1
1
1,5
4
ln
ln
ln
VA
V
V
A
A
RR
R
A
A
A
V
V
V
V
V
TRC
RC
t
RC
V
RR
R
R
R
R
f
T
kHz
ms
RC
1
1
1
12
1
0
12
1
1
i
i
ss
ss
ss
ss
ss
00 0
0
0
0
0
0
2
$
$
$
$
$
$
$
$
$
$$
$
$
!
1
b
b
b
b
b
b
b
b
b
b
b
b
b
x
&
=
=
=
+
=
+
=
+
=
+
=
=
x
x
x
=-
-
+
-
-
-
+
_
d
d
d
i
n
n
n
as input in increased output
remain at
--
V
bV
==
1
1
1
1
1
2
2
1
1
1
1
1,5
4
ln
ln
ln
VA
V
V
A
A
RR
R
A
A
A
V
V
V
V
V
TRC
RC
t
RC
V
RR
R
R
R
R
f
T
kHz
ms
RC
1
1
1
12
1
0
12
1
1
i
i
ss
ss
ss
ss
ss
00 0
0
0
0
0
0
2
$
$
$
$
$
$
$
$
$
$$
$
$
!
1
b
b
b
b
b
b
b
b
b
b
b
b
b
x
&
=
=
=
+
=
+
=
+
=
+
=
=
x
x
x
=-
-
+
-
-
-
+
_
d
d
d
i
n
n
n
until input reaches
--
V
bV
==
1
1
1
1
1
2
2
1
1
1
1
1,5
4
ln
ln
ln
VA
V
V
A
A
RR
R
A
A
A
V
V
V
V
V
TRC
RC
t
RC
V
RR
R
R
R
R
f
T
kHz
ms
RC
1
1
1
12
1
0
12
1
1
i
i
ss
ss
ss
ss
ss
00 0
0
0
0
0
0
2
$
$
$
$
$
$
$
$
$
$$
$
$
!
1
b
b
b
b
b
b
b
b
b
b
b
b
b
x
&
=
=
=
+
=
+
=
+
=
+
=
=
x
x
x
=-
-
+
-
-
-
+
_
d
d
d
i
n
n
n
at this point it changes to stable state
--
V
bV
==
1
1
1
1
1
2
2
1
1
1
1
1,5
4
ln
ln
ln
VA
V
V
A
A
RR
R
A
A
A
V
V
V
V
V
TRC
RC
t
RC
V
RR
R
R
R
R
f
T
kHz
ms
RC
1
1
1
12
1
0
12
1
1
i
i
ss
ss
ss
ss
ss
00 0
0
0
0
0
0
2
$
$
$
$
$
$
$
$
$
$$
$
$
!
1
b
b
b
b
b
b
b
b
b
b
b
b
b
x
&
=
=
=
+
=
+
=
+
=
+
=
=
x
x
x
=-
-
+
-
-
-
+
_
d
d
d
i
n
n
n
. Now when the input is decreased it
can change state only at
--
V
bV
==
1
1
1
1
1
2
2
1
1
1
1
1,5
4
ln
ln
ln
VA
V
V
A
A
RR
R
A
A
A
V
V
V
V
V
TRC
RC
t
RC
V
RR
R
R
R
R
f
T
kHz
ms
RC
1
1
1
12
1
0
12
1
1
i
i
ss
ss
ss
ss
ss
00 0
0
0
0
0
0
2
$
$
$
$
$
$
$
$
$
$$
$
$
!
1
b
b
b
b
b
b
b
b
b
b
b
b
b
x
&
=
=
=
+
=
+
=
+
=
+
=
=
x
x
x
=-
-
+
-
-
-
+
_
d
d
d
i
n
n
n
. Thus hysteresis of
--
V
bV
==
1
1
1
1
1
2
2
1
1
1
1
1,5
4
ln
ln
ln
VA
V
V
A
A
RR
R
A
A
A
V
V
V
V
V
TRC
RC
t
RC
V
RR
R
R
R
R
f
T
kHz
ms
RC
1
1
1
12
1
0
12
1
1
i
i
ss
ss
ss
ss
ss
00 0
0
0
0
0
0
2
$
$
$
$
$
$
$
$
$
$$
$
$
!
1
b
b
b
b
b
b
b
b
b
b
b
b
b
x
&
=
=
=
+
=
+
=
+
=
+
=
=
x
x
x
=-
-
+
-
-
-
+
_
d
d
d
i
n
n
n
is seen around 0. This kind
of comparator is a must while driving a MOSFET as a switch in ON-OFF controllers
SMPS (Switched Mode Power Supply), pulse width modulators and class-D audio
power ampliers. The symbol for this invertingtype Schmitt trigger is shownin
Figure 2.2. The non-inverting Schmitt trigger is as shown in Figure 2.3.
R1
R2
VI
VO
+VSS
-VSS
Figure 2.2: Symbol for an Inverting
Schmitt Trigger
An astable multivibrator is shown in Figure 2.4. The square and the triangular
waveformsshowninthegurearebothgeneratedusingtheastablemultivibrator.
We refer to
--
V
bV
==
1
1
1
1
1
2
2
1
1
1
1
1,5
4
ln
ln
ln
VA
V
V
A
A
RR
R
A
A
A
V
V
V
V
V
TRC
RC
t
RC
V
RR
R
R
R
R
f
T
kHz
ms
RC
1
1
1
12
1
0
12
1
1
i
i
ss
ss
ss
ss
ss
00 0
0
0
0
0
0
2
$
$
$
$
$
$
$
$
$
$$
$
$
!
1
b
b
b
b
b
b
b
b
b
b
b
b
b
x
&
=
=
=
+
=
+
=
+
=
+
=
=
x
x
x
=-
-
+
-
-
-
+
_
d
d
d
i
n
n
n
as the regenerative feedback. The time period of the multivibrator is
given by