Download Operational Amplifiers

Operational Amplifiers
Op Amps – a useful building block
K. El-Ayat
1
Op Amp: A DC coupled high Gain differential Amplifier
Many useful applications
-ve
+ve
An Op Amp produces an output voltage that is much larger
than the difference between its two inputs (very high gain)
Figure 2.2 The op amp shown connected to dc power supplies.
2
An Ideal Op Amp
•
•
•
•
Infinite input impedance
Zero Output impedance
Infinite open-loop gain A
Infinite bandwidth
Differential input stage
 amplified
Vout= A(v2-v1)
• Op amps are DC (direct coupled)
• Usually used with external
components R, C, …
Figure 2.3 Equivalent circuit of the ideal op amp.
3
Inverting Op Amp - Analysis
Terminal 2 (+ve input)  ground
RF (or R2) connected to terminal 1 (-ve)
Negative feedback
Since open loop gain A very high
Then v1-v2= vo/ A = 0
v1 = v2 = gnd
VO = - (R2 / R1) * Vi
i1 = i2 & Gain G = - R2 / R1
G (closed loop) gain
Figure 2.6 Analysis of the inverting configuration. The circled numbers indicate
the order of the analysis steps.
4
Op Amp – Class Analysis Example
Find all I, v, gain
v1 =
i1 =
i2 =
vo =
iL =
io =
Figure E2.6
5
An Op Amp Application; Weighted
Summing Circuit
in = ?
i =?
vo = - [(Rf / R1) * v1 + (Rf / R2) * v2 +….+ (Rf / Rn) * vn]
Figure 2.10 A weighted summer.
6
Two Op Amp comnibation
Summing Circuit , with both
signs
Can calculate in 2 steps
vo= v1(Ra/R1)(Rc/Rb) + v2(Ra/R2)(Rc/Rb) –v3(Rc/R3) –v4 (Rc/R4)
Figure 2.11 A weighted summer capable of implementing summing coefficients of
both signs.
7
Non inverting Op Amp
Application
Use +ve Op Amp input
Figure 2.12 The noninverting configuration.
8
Non-inverting Op Amp: Analysis
vo = vi + (vi/R1)*R2
vo = vi(1 + R2/R1)
G = 1 + R2/R1
Figure 2.13 Analysis of the non-inverting circuit. The sequence of the steps in the
analysis is indicated by the circled numbers.
9
Unity Gain Op Amp
Voltage follower - unity gain; high current gain
Buffer stage between processors - switches
G = 1 + 0 /R1; R2 0
Figure 2.14 (a) The unity-gain buffer or voltage follower amplifier. (b) Its equivalent circuit model.
10
Op Amp problem – find vo
I
Assume x is voltage at both Amp inputs
–ve, & +ve
x = 3/5 (v1-v2) + v2 ; resistor divider
I = x / 1 = (vo- x) / 9
vo = 10 x
v o= 10 *[ 3/5 (v1-v2) + v2 ]
= 6 v 1 + 4 v2
ANS.
Figure E2.9
11
Another Op Amp problem –
Should be able to analyze
vo =
Figure E2.13
12
Can use as a difference Op Amp
Figure 2.16 A difference amplifier.
13
Frequency response of Op Amp
Gain = +10
Figure 2.23 Frequency response of an amplifier with a nominal gain of +10 V/V.
14
Open-loop gain of Op Amp
Gain declines rapidly with freq
Figure 2.22 Open-loop gain of a typical general-purpose internally compensated op amp.
15
Two-stage CMOS Op Amp - fyi
Figure 9.1 The basic two-stage CMOS op-amp configuration.
16
Frequency Response of CMOS Op
Amp fyi
Figure 9.4 Typical frequency response of the two-stage op amp.
17
Inverting Op Amp
Application to Impedances
Figure 2.37 The inverting configuration with general impedances in the feedback
and the feed-in paths.
18