Cascaded Op Amp Circuits
 Op amp circuits have the advantage that they can be cascaded without changing
their input-output relationships.
 This is due to the fact that each (ideal) op amp circuit has infinite input
resistance and zero output resistance.
 Although the cascade connection does not affect the op amp input-output
relationships, care must be exercised in the design of an actual op amp circuit to
ensure that the load due to the next stage in the cascade does not saturate the op
amp.
A three-stage cascaded connection.
40
Example 11
Find vo and io in the circuit.
41
Example 12
Determine vo and io .
a
b
V
42
Instrumentation Amplifiers
(a) The instrumentation amplifier with an external resistance to adjust the gain,
(b) schematic diagram.
43
Instrumentation Amplifiers
The IA has three major characteristics:
1.
The voltage gain is adjusted by one external resistor RG.
2.
The input impedance of both inputs is very high and does not vary as the gain
is adjusted.
3.
The output vo depends on the difference between the inputs v1 and v2, not on
the voltage common to them (common-mode voltage).
44
Example 13
Let R = 10 kΩ, v1 = 2.011 V, and v2 = 2.017 V. If RG is adjusted to 500 Ω , determine:
(a) the voltage gain, (b) the output voltage vo.
45
Integrator
is + i f = 0
vs
dvo
is =
, if = Cf
Rs
dt
An op amp integrator
dvo
1
=vs
dt
Rs C f
1
vo = Rs C f
ò
t
to
vs d +vo (to )
An integrator is an op amp circuit whose output is proportional to
the integral of the input signal.
46
Differentiator
An op amp differentiator
An differentiator is an op amp circuit whose output is proportional
to the rate of change of the input signal.
The differentiating amplifier is seldom used in practical applications
because it is a source of noise.
Why ?
47
Cascaded Integrators
Op amp 1:
vg
R1
+ C1
dvo1
=0
dt
dvo1
1
=vg
dt
R1C1
Op amp 2:
vo1
dv
+ C2 o = 0
R2
dt
dvo
1
vo1
=dt
R2C2
d 2 vo
dt 2
d 2 vo
dt 2
1 dvo1
=R2C2 dt
=
1
1
vg
R1C1 R2C2
Cascaded integrators and differentiators can be combined in analogue
computers to solve differential equations.
48
Review 1
49
Review 2
50
Review 3
For this op amp circuit, voltage vo is:
51
Review 4
For
Fig. 5.40,
For the
this circuit
op ampin
circuit,
current ix is:
52
Review 5
If vs = 0, current i0 is:


5.41,


53
Review 6
If vs = 8 mV, voltage v0 is:
5.41,
54
Review 7
5.41. va is:
If vs = 8 mV, voltage
55
Review 8
The power absorbed in the 4-k resistor is:
56