Operational amplifiers nonideal behavior

1
Operational amplifiers - non-ideal behavior

• Difference Amp
• Bandwidth
• Voltage Offset
• Input Currents
• Frequency response
• CMRR
• Op-amp parameters

Homework Barnaal 5,6 (pg 230) , 26 (pg 235)
extra credit Barnaal 12 (pg.230) Lab
Operational Amplifiers II Read Chapter A5 and A6
2
Review ideal op - amp

• Ideal op-amp
• characteristics
• Zin ?
• Zout 0
• Av ?
• bandwidth ?

-
Zin
Vout
Vin
AvVin
Zo

Note Real op amps depart from these
characteristics and affect circuit behavior
3
Review golden rules for op - amps
Assuming that there is negative feedback, and
that the output is within the range of voltages
and currents provided by the power supplies we
can analyze op-amp circuits with the following
rules Golden Rule I The output attempts to do
whatever is necessary to make the voltage
difference between the inputs zero. Golden Rule
II The inputs draw no current.
The rules are good enough for almost everything
you will ever do!
4
Review inverting/non-inverting amplifier
Note Can replace Rin, Rf with general
impedances, such as capacitors ? Get frequency
dependent devices (integrator, differentiator)
5
Review Follower

• Ideal as a buffer amplifier.

• G 1
• Zin ?
• Zout 0

In the non-inverting amplifier we can let Rf 0
and R1 ?, then
This is perfect! We will not load any signal
source, because we draw no current when we attach
the follower - it is like it is not even there.
6
Review feedback equation
Vin
Vout
A
B
G closed loop gain A open loop gain AB loop
gain
7
Difference or differential amplifier
(show using golden rules)
(Requires precise resistor matching!)
8
Op-amp frequency behavior
9
Frequency behavior - first non-ideal case
In the lab we will notice discrepancies from
ideal behavior. The most important to note is the
frequency response. In the part of the op-amp
that causes voltage gain there is a low pass
filter on the input that results in the gain
being frequency dependent. It also limits how
quickly the output voltage can change (this is
called slew rate and is 0.5 V/ms), which can
distort the shape of the output. Note that the
open loop gain is still large over a big range (
f lt 10 Hz, AV 100 dB 100,000. It is still 10
at 100 kHz).
741 properties
additional corner
10
Bode plot of open-loop gain
Aol (dB)
Midrange
100
75
3 dB open-loop bandwidth BWol fc(ol)
-20 dB/decade roll-off
50
Unity-gain frequency fT
Corner frequency fc(ol)
25
0
f (Hz)
1
10
100
1k
10k
100k
1M
10M
11
Closed - loop vs. open-loop gain
Av
Open-loop gain
Aol(mid)
Closed-loop gain
Acl(mid)
(in case of non-inverting amplifier)
fc(ol)
fc(cl)
f
closed loop gain Acl drops where Aol reaches 1Rf
/ Rin drops to 1 (unity gain) at higher
frequencies ? bandwidth is limited
12
Op-amp representation
-
R
Aol(mid)
Vout
Vin
Low Pass Filter

C
Op-amp
fc
f
Phase shift
-45o
-90o
q
Rolloff accompanied by phaseshift (output lags
behind input).
13
Stability criterion
If the phaseshift accumulates beyond 180 degrees,
the output signal being fed back is in-phase to
the input and will reinforce the signal already
there at high frequencies. This is when positive
feedback occurs and the op-amp starts to become
unstable ? it produces oscillatory behavior. The
criterion for stability against oscillation for a
feedback amplifier is that its open-loop phase
shift must be less than 180o at the frequency at
which the loop gain (in the feedback
configuration) is unity.
14
Positive feedback stability

• Positive feedback, where the output signal being
  fed back is in-phase to the input, will cause the
  amplifier to oscillate.
• Phase margin, qpm , is used to specify the
  difference between the phaseshift at fT (unity
  gain frequency) and 180o.
• To ensure stability for all midrange frequencies,
  an op-amp must be operated with an Acl such that
  the roll-off rate beginning at fc is ? -20
  dB/decade.

15
Phase compensation
Aol
Uncompensated Aol
With some compensation
-20 dB/dec
-20 dB/dec
With more compensation
0
f
fc1
fc2
fc3
Add external low pass filter and adjust the
corner frequency such that the open loop gain
drops to unity before the next natural RC
filter.
16
Compensating circuit

• Compensation is used to either eliminate
  open-loop roll-off rates greater than -20 dB/dec
  or extend the -20 dB/dec rate to a lower gain.
• Two basic methods of compensation for IC op-amps
  internal and external.
• (the 741 is internally compensated)
• In either case an RC series circuit is added so
  that its critical frequency is less than the
  dominant (i.e. lowest) fc of the internal lag
  circuits of the op-amp.

17
Op - amp compensation

• Some op-amps (e.g. 741) are fully compensated
  internally, i.e., their -20 dB/dec slope is
  extended all the way down to unity gain. Hence,
  they are unconditionally stable.
• A disadvantage of fully compensated op-amps is
  that the bandwidth and slew rate are reduced.
• Many op-amps (e.g. LM101A) have provisions for
  external compensation with a small capacitor.
  This allows for optimum performance.

18
Voltage offset
Due to mismatches in the transistors in the input
branch, there is always a voltage offset. One
way to observe this would be to construct an
inverting amplifier as shown below.
Applying the golden rules we find
19
Input voltage offset

• Input stages not perfectly balanced
  (manufacturing)
• Connect inputs ? output saturates at VCC or VEE
• ? unpredictable

• Input offset voltage and its drift with
  temperature are usually permanently trimmed at
  wafer testing to low level.
• Further adjustment possible by use of a nulling
  potentiometer

20
Voltage offset drift with temperature

• Largest drift during the turn on process, chip
  temperature changes by 300-400C, gets very hot
• Leave the unit running to obtain thermal
  equilibrium
• deal with offsets after warm up

• Shown for LT 1028/1128
• also drift caused by self heating of op amp when
  it drives a low impedance load

21
Input offset voltage compensation
The correction is to add a small current to the
input to balance this difference using the -15 V
supply and a 10k pot.
V
7
2
1
8
-
NC
Offset null
6
Invert
V
741
741
Noninvert
Output
V-

Offset null
3
1
5
8-pin DIP or SMT Package
10 kW
4
-V
With no input, the potentiometer is adjusted
until the output voltage is 0V.
22
Input current
Rf
The small base currents flowing into the
transistors can also cause errors. For BJT
op-amps it is 10 nA ( 30 nA typically for 741)
and 10 pA for FET op-amps. Both non-inverting
and inverting inputs have similar currents so a
common repair is to make the resistance of both
the same (add R). Then the output will be zero
if both inputs are grounded because the voltage
due to the currents are the same.
Rin
Rf
Rin
23
Common mode rejection ratio (CMRR)
An ideal op-amp is a differential amplifier,
meaning that it will not output a voltage if
exactly the same value is on both inputs. As an
example suppose that an inverting op-amp with a
gain of -10 had 5.00 V on the inverting input and
5.05 V on the non-inverting input and for Vout
you get 5.5 V. That is the common part of both
voltages, 5.00 V, had a gain of 1 and the
difference, -0.05 V, had a gain of -10. The
ratio of the difference gain to the common gain
is called the CMRR, which for this amp is only 10
or 20 dB.
A perfect op-amp has a CMRR of infinity. Real
op-amps (like the 741) have CMRR of 90 dB,
meaning the ratio of gains is 30,000.
24
Op - amp parameters

• Input offset voltage, VOS is the difference in
  the voltage between the inputs that is necessary
  to make Vout(error) 0. Vout(error) is caused
  by a slight mismatch of VBE1 and VBE2 of the
  input transistors. Typical values of VOS are 2
  mV.
• Input offset voltage drift specifies how VOS
  changes with temperature. Typically a few mV/oC.
• Input bias current is the dc current required by
  the inputs of the amplifier to properly operate
  the first stage. By definition, it is the
  average of the two input bias currents, IBIAS
  (I1 I2)/2.

25
Op - amp parameters (contd)

• Differential input impedance is the total
  resistance between the inverting and
  non-inverting inputs.
• Common-mode input impedance is the resistance
  between each input and ground.
• Input offset current is the difference of the
  input bias currents IOS I1 - I2. Typically
  in the nA range.
• Output impedance is the resistance viewed from
  the output terminals.
• Open-loop voltage gain, Aol, is the gain of the
  op-amp without any external feedback connections.

26
Op - amp parameters (contd)

• Common-mode rejection ratio for an op-amp is
  defined as CMRR Aol/Acm or 20 log (Aol/Acm) in
  dB.
• Slew rate is the maximum rate of change of the
  output voltage in response to a step input
  voltage. Slew rate DVout/Dt. The unit for
  slew rate is V/ms.
• Frequency response is the change in amplifier
  gain versus frequency and is limited by internal
  junction capacitances.
• Other features include short circuit protection,
  and input offset nulling.