6.002 CIRCUITS ANDELECTRONICS Op Amps Positive Feedback... Representing dynamics of op amp…Consider this circuit and let’s analyze its dynamics to build insight... Consider a small distu
Trang 16.002 CIRCUITS AND
ELECTRONICS
Op Amps Positive Feedback
Trang 2Consider this circuit — negative feedback
+
– +
1
R
vIN
IN
– OUT R vIN
R v
1
2
−
=
2
R
What’s the difference?
Consider what happens when there is a pertubation…
Positive feedback drives op amp into saturation:
S OUT V
v → ±
and this — positive feedback
+ –
+
IN
–
2
R
IN
R
R v
1
2
−
=
see an
aly sis
on next
pa ge
Negative vs Positive Feedback
Trang 3+ –
+
IN
v
2
R
OUT
v
( + − −)
= A v v
v OUT
+
−
2 1
IN
R R
v v
A
IN 2
1
IN 1 OUT
2 1
R R
v AR v
R R
+
− +
=
+
= Av
IN 1
2 IN
1
2 1
1
R
R Av
AR
R R
R 1
−
+
−
=
+
−
=
+
−
2 1
1 IN
2 1
1 OUT
R R
R 1
A
v R
R
AR 1
v
+
IN
v
2
R v OUT
+
v
−
v +– A(v+ − v−)
Static Analysis of Positive Feedback Ckt
Trang 4Representing dynamics of op amp…
+
v
−
v
o
v
*
Av
+ –
+ –
*
v
) ( v+ − v−
R C
+ –
Trang 5Representing dynamics of op amp…
Consider this circuit and let’s analyze its dynamics to build insight.
+ –
1
o v
3
Let’s develop equation representing time
behavior of vo .
Circuit model
1
R
2
R
3
+ –
*
v
) ( v+ − v−
R C
+
+ –o
v
+
v
−
v
A
vo
Trang 6v v
Av
o = * or * =
) γ γ
( A
RC T
where
0 T
v dt
+
−
−
=
= +
or
o
R R
R
v
+
=
2 1
1
o
R R
R
v
+
=
4 3
3
0 )
γ γ
( − − + =
RC
A dt
dv
1 time−
0 )
γ γ
(
RC
A RC
dt
dv
or
neglect
_
*
*
v v
v dt
dv
RC + = + −
o
v
) γ γ
( + − −
=
Dynamics of op amp…
_
v
v A
v dt
dv A
RC o + o = + −
0 )
0 (
Trang 7Consider a small disturbance to vo
(noise).
Now, let’s build some useful circuits with
+
>
− γ γ
if
stable e
K v
positive is
T
T
t o
−
=
−
>
+ γ γ
if
unstable e
K v
negative is
T
T t
o =
−
=
+ γ γ
if
neutral K
v
large very
is T
o =
o
v
t
neutral stable
K
disturbance
unstable
Trang 8One use for instability: Build on the
basic op amp as a comparator
+ –
+
v
o
v
S
V
+
S
V
−
−
v
− + − v
v
o
v
S
V
+
S
V
−
0
t
0
v
Trang 9Now, use positive feedback
+
–
2
R
o v
1
R
i v
2 1
1
R R
R
v
+
= +
5 7
v+ =
5 7
v− = −
15
vo =
15
vo = −
15
e.g. 1 2
=
=
S
V
R R
5 7
v
5 7 ) v
v
( i
>
>
=
−
−
5 7
−
<
<
−
+
−
v
v v
i v
Trang 10Now, use positive feedback
+
–
2
R
o v
1
R
i v
2 1
1
R R
R
v
+
= +
2 1
1
R R
R
V
+
=
+
2 1
1
R R
R
V
+
−
=
−
S
o V
v = + 15
S
o V
v = − − 15
15
e.g. 1 2
=
=
S
V
R R
5 7
v
v ) v v
( i
>
>
=
−
+
−
5 7
−
<
<
−
+
−
v
v v
i v
Trang 11Why is hysteresis useful?
e.g., analog
to digital
o
v
i
v
S
V
S
V
−
0 7 5 5
7
−
15
−
15
hysteresis
Demo
Demo
t
i v
5 7 5 7
−
o v
Trang 12Without hysteresis
analog
to digital
t
i v
5 7 5 7
−
i v
o v
Trang 13Oscillator — can create a clock
Demo
+ –
R C
v
1
R
1
R
o v
2
o v C
0
0
at
=
=
= S
o
v
t V
v
Assume
t
S V
S V
−
2
S V
2
S
V
−
o v
+
v
+
v
−
v
−
v C
v
−
v
−
v C
v
Trang 14 We built an oscillator using an op amp.
t
Why do we use a clock in a digital system?
(See page 735 of A & L)
1 1 0
a 1,1,0?
b When is the signal valid?
Æ Discretization of time
one bit of information associated with
an interval of time (cycle)
Clocks in Digital Systems
can use as a clock
common timebase when to “look” at a signal (e.g whenever the clock is high)
clock