chapter 2: operational amplifiers - m5zn op amp in conjunction with 100-kΩ and 10-mΩ ... output...
TRANSCRIPT
Section 6 Chapter 2: Operational Amplifiers
Reference : Microelectronic circuits ‘Sedra’ sixth edition
2013
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Contents:
1- DC imperfections
A. Offset voltage
B. Solution of offset voltage
C. Input bias current
D. SOLUTION OF BIAS CURRENT
E. Offset current
2- Finite open loop gain and bandwidth
a. Frequency Dependence of the Open-Loop Gain
b. Frequency Response of Closed Loop Amplifiers
3- Large signal operation
a. Output voltage saturation
b. SLEW RATE
c. FULL BANDWIDTH POWER
4- AC Coupled Amplifiers
5- ASSIGNMENT
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1- Dc Imperfection
A. Offset Voltage
If the two input terminals of the op amp are connected to ground, it
will be found that a finite dc voltage exists at the output
Vo=Vos (1+R2/R1)
B. It’s Solution
Capacitive coupling
This circuit will have high pass filter
response.
For dc input bias
Vo =Vos(1+R2/Z1) Z1=
Vo = Vos
So the aim of this solution is that Vos will not be amplified at dc gain
C. Input bias current
IB1=IB2=IB
VO =IB1R2= IBR2
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D. Solution of bias current
To make Vo =0
We put R3=R1//R2
Proof???
E. Offset current
Having selected R3 as above, let us evaluate the effect of a finite offset
current Ios
IB1 = IB + los/2 and IB2 = IB – los/2
The result is
Vo=IosR2 Proof???
We conclude that to minimize the effect of the input bias currents,
one should place in the positive lead a resistance equal to the
equivalent dc resistance seen by the inverting terminal.
Example
Effect of offset voltage:
Vo =Vos+
∫
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Problem 98
A particular inverting amplifier with nominal gain of 100 VN uses an
imperfect op amp in conjunction with 100-kΩ and 10-MΩ resistors. The
output voltage is found to be +9.31 V when measured with the input open
and +9.09 V with the input grounded.
(a) What is the bias current of this amplifier? In what direction does it
flow?
(b) Estimate the value of the input offset voltage.
(c) A 10-MΩ resistor is connected between the positive input terminal
and ground. With the input left floating (disconnected), the output dc
voltage is measured to be 0.8 V. Estimate the input offset current.
Solution
a. If the input is open
Vo - Vos =IB1R2
9.31 = Vos + 10000 IB1 1
If the input is grounded
IB1 = –
–
IB1 =
-
2
From 1&2
IB1=930 nA
b. Vos = -2.2mV
c. As 10-MΩ resistor is connected between the positive input terminal
and ground = R2
Vo =IosR2
0.8=10000 Ios
Ios = -80 nA
2- Finite open loop gain and bandwidth
A. Frequency
Dependence of the
Open-Loop Gain
The differential open-loop gain A of an op amp is not infinite but it is finite and decreases with frequency. Its
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response is similar to the response of low pass filter and its gain can be written as
A(s)
For high frequencies w>>> wo
A(jw)
|A(jw)|
To reach unity gain, let’s define gain bandwidth product or unity gain bandwidth Wt=AoWo
B. Frequency Response of Closed Loop Amplifiers
For inverting configuration
For very small wb(wo)
2
1
2
1
1
1
R
RG
R
R
A s
2
1
2
1 0
11 1 b
R
RG
sR
R A
2
1
2
1
1
1
t
R
RG s
R
R
32
1
1
tdB R
R
03
2
1
1dB b
A
R
R
2
1
3
1dB
R
RG s
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Problem 112
A particular op amp characterized by a gain bandwidth product of 10 MHz
is operated with a nominal closed-loop gain of 100 V/V. What 3-dB
bandwidth results? At what frequency does the closed-loop amplifier
exhibit -6o phase shift? – 84o phase shift?
Solution
Ft = 10 MHz
1+
F3db =
=200 KHz
G(jw)=
Ø=tan-1( ) =-6
f=tan (-6)* f3db =21 KHz
3- Large signal operation
A. Output voltage saturation
Similar to all other amplifiers, op amps operate linearly over a limited range of output voltages. Specifically, the op-amp output saturates in the manner shown with L and L within 1 V or so of the positive and negative power supplies, respectively. Thus, an op amp that IS operating from + 15-V supplies will saturate when the output voltage reaches about + 13 V in the positive direction and 13 V in the negative direction. For this particular op amp the rated output voltage IS said to be ± 13 Y. To avoid saturation the input signal must be kept correspondingly small.
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B. Slew rate
Another phenomenon that can cause nonlinear distortion when large output signals are present is slew-rate Limiting. The name refers to the fact that there IS a specific maximum rate of change possible at the output of a real op amp. This maximum is known as the slew rate (SR) of the op amp and is defined as
C. Full power bandwidth
The op-amp data sheets usually specify a frequency fM, called the
full-power bandwidth, It IS the frequency at which an output sinusoid
with amplitude equal to the rated output voltage of the op amp
begins to show distortion due to slew-rate limiting. If we denote the
rated output voltage Vomax then fM is related to SR as follows
max|Odv
SRdt
ˆ sin
ˆ sin
ˆ cos
ˆ cos
ˆ
I i
O i
O i
Oi
i
i
OMax
M OMax
v V t
v G v
v GV t
dvGV t
dt
SR GV t
SR GV
SR V
SR V
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Problem 124 For operation with 10 V output pulses with the requirement that the sum of the rise and fall times represent only 20% of the plus width (at half amplitude). What is the slew-rate requirement for an op amp to handle pulses 2 µs wide?
(Note: The rise and fall times of the pulse signal usually measured between the 10% and 90% height points). Solution:
4- AC Coupled Amplifiers
The concept of AC coupled is not to pass the dc voltage to the circuit
Also we need to decrease all Dc imperfections as offset voltage, bias
current and offset current, all this can done by
a. selecting R3 = R2
b. selecting R3 = R2
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Biomedical department
2nd year
1st term 2013
Electronics course
Assignment no.6
Student name:
Problem 105
An op amp intended for operation with a closed loop gain of -100 V\ V
uses resistors of 10 kΩ and 1 MΩ with a bias-current-compensation
resistor R, What should the value of R be with input grounded. The
output offset voltage is found to be +0.2 V. Estimate the input offset
current assuming zero input offset voltage. If the input offset voltage can
be as large as 1 mV of unknown polarity, what range of offset current is
possible?
Solution
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Problem 117
This problem illustrates the use of cascaded closed-loop amplifiers to
obtain an overall bandwidth greater than can be achieved using a single-
stage amplifier with the same overall gain.
(a) Show that cascading two identical amplifier stages. Each having a low-
pass STC frequency response with a 3-dB frequency f1 , results in an
overall amplifier with a 3-dB frequency given by
(b) It is required to design a non-inverting amplifier with a dc gain of 40
dB utilizing a single internally compensated op amp with f1 = I M Hz. What
is the 3-dB frequency obtained?
(c) Redesign the amplifier of (b) by cascading two Identical non-inverting
amplifies each with a dc gain of 20 dB. What is the 3-dB frequency of the
overall amplifier? Compare this to the value obtained In (b) above.
Solution
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Problem 118
A designer wanting to achieve a stable gain of 100 V/V at 5 MHz.
considers his choice of amplifier topologies. What unity-gain frequency
would a single operational amplifier require to satisfy his need?
Unfortunately the best available amplifier has an f of 40 MHz. How many
such amplifiers connected in a cascade of identical non-inverting stages
would he need to achieve his goal? What is the 3-dB frequency of each
stage he can use? What is the overall 3-dB frequency?
Solution