Transcript Analysis of a Non-Inverting Amplifier

Operational Amplifiers
What is an amplifier?
A device that takes an input (current, voltage,
etc.) and produces a correlated output
Input
Signal
Output
Signal
Usually the output is a multiple of the input
The output signal may be of the same form as the
input signal, i.e. Vin produces Vout
However, the input and output may be of
different forms, i.e. Iin produces Vout
For any form of amplifier, the amplifier gain is
defined generically as
gain = signal in/signal out
There are many forms of amplifiers possible, and
the design of specific forms for discrete
component amplifiers is an involved process.
• We will not discuss the general design of
transistor/tube/etc. amplifiers, but only the use
and properties of the much simpler integrated
circuit amplifier.
Spending a few dollars on an integrated circuit
device allows one to buy the results of hundreds of
thousands of developer dollars and man-years of
development time.
The simplest form of such amplifiers to use is the
Operational Amplifier!
Operational Amplifiers
What is an operational amplifier?
A very high gain DC amplifier that uses
external feedback networks to control its
response
Notice particularly that the external network
connected to the IC device determine the
characteristics of the amplifier constructed!
• An Perfect Operational Amplifier is a device with
certain special characteristics…
–
–
–
–
–
1. infinite open-loop gain Aol
2. infinite input resistance Rin
3. zero output resistance Rout
4. infinite bandwidth
5. zero offset (output is exactly 0 when the
input is 0)
Clearly no real operational amplifier can meet all
these characteristics. However, under certain
conditions, most of these conditions can be
approximately met - though not all at once.
• A diagram representing a generalized
operational amplifier is given below
Rin is the input resistance
of the op amp,
vi
Rin
Vin
R0
Aolvi
V+
Rout is the output
resistance, and
Rout
Aolvin represents the
active amplification effect
of the amplifier in terms
of the input voltage vin.
AolVin
Vout
V-
Vout
The output voltage Vout is determined by the
combination of open loop gain (Aol) and output
resistance (Rout).
Typical values of these quantities for a standard
741 operational amplifier would be:
Rin = 2 M
Rout = 75 
Aol = 200,000
•In using an operational amplifier, one needs to be aware
of certain information about the device that can usually be
obtained from the DATA SHEET for the particular amplifier.
• Maximum Ratings (exceeding these can destroy the
device)
– 1. Supply Voltage ( Vs ) : maximum bipolar () voltage
that can be used to power the amp
– 2. Internal Power Dissipation (PD) : maximum power that
can be dissipated internally by the op amp without
exceeding a specified max temperature.
e.g. 500 mW @ < 75 C
– 3. Differential Input Voltage (Vid) : maximum voltage that
can exist across + and - inputs
– 4. Operating Temperature (Ta) : maximum safe
temperature of operation
– 5. Outout Short-Circuit Duration : maximum length of time
that the output could be shorted to either ground or to
Vs.. For many op amps this is infinite.
• There are many other specifications for op amps
that are important for their use, but which do
run the risk of destruction if exceeded.
One other characteristic of “perfect” op amps is
the fact of infinite bandwidth (amp operates from
DC to  frequencies).
Real op amps have a finite bandwidth that “rolls
off” with frequency, i.e. the gain at DC is usually >
the gain at 40 kHz.
• A typical gain-bandwidth curve for a 741 op amp
is shown below:
1.E+06
1.E+05
1.E+04
G
a
i
n
1.E+03
1.E+02
1.E+01
1.E+00
1.E+00
1.E+01
1.E+02
1.E+03
frequency
1.E+04
1.E+05
1.E+06
Real op amps have a frequency
response that is very large at DC
(~200,000 for a 741) but begins to "roll
off" at higher frequencies. The 741
begins to roll off beginning about 6 to
10 Hz at about -6 db per octave (-20 db
per decade), reaching a value of unity
gain at about 1.0 MHz.
• Different op amps will have different
frequency response curves, but all will
have the same general form. For any
op amp the Gain-Bandwidth product is
approximately constant.
• As the gain goes up, the bandwidth---goes down.
• There is always a trade-off between --available gain and the maximum ------frequencies the amplifier can ----------amplify without significant distortion.
• In practice operational amplifiers are always
operated with some type of feedback, either
positive in the case of some oscillators, or
negative feedback which greatly stabilizes the
amplifier output.
• In negative feedback, a portion of the output
signal is fed back out of phase with the input
effectively reducing the total gain but keeping
the output stable.
fV
out
Vin
Vout
• With negative feedback the gain always
decreases, so that the closed-loop gain Acl is
always < Aol. The loop gain is defined as:
•
loop gain AL = Aol / Acl
• As mentioned before, the gain bandwidth
product is approximately constant
– GBW = ( AL)( BW)
– Thus reducing the gain usually increases the
bandwidth of the amplifier.
• Since op amps have such a high open-loop
gain, the reduction in gain still allows
sufficient gain for most practical purposes
Operational amplifiers are usually operated as
inverting (meaning the output has the opposite
phase as the input) or non-inverting (where input
and output have the same polarity) amplifiers.
Physically this is governed by whether the input
signal is applied to the inverting (-), or the non
inverting (+) input terminals.
• A diagram for an inverting amplifier
• The relationship between input voltage
and output voltage involves only the
external input and feedback resistors…
– Vout = Aol Vin = Vin [Rf / Ri ]
Let us now consider some simplified ways
of analyzing this operational amplifier
configuration…
Simplifying assumptions for analyzing simple op
amp circuits
1. Vout is ALWAYS < supply voltage. If V+ = 15 V
and V- = -15 V, then the maximum possible
voltage output from the amplifier is < 15
volts
As a consequence of this, consider an op
amp with Aol = 200,000 (typical 741),
then we see
Vout = Vin Aol
and the input voltage producing max output is
Vin = Vout / 200,000 =
15 Volts / 200,000 =
75 x 10-6 V or 75 V
This means that unless one is trying to
amplify V signals, the input voltage is
required to drive the amplifier to maximum
output is ~ 0
When properly operating, the voltage
difference between the(+) and (-) terminals
is ~ 0
2. Since the input resistance of op amps is very
high (typ. Megohms), a negligible amount of
current flows into the op amp from the input
voltage source.
• For a 741 op amp, the input current draw is
typically 200 - 500 nA. Other op amps such
as a CA3140 FET op amp may have input
current draws of about 10 pA! (10 x 10-12
amps)
Based on these two simplifying assumptions, one
can make a practical representation of an
inverting op amp circuit as shown on next slide.
Analysis of an Inverting Amplifier
iin= Vin/Rin
since S is
effectively a
ground
iin
S
Vin
P
Since no current flows into the op amp terminal
at S, the current flow through the feedback
resistor is also iin
• Since no current flows into the op amp terminal
---at S, the current flow through the feedback ------- resistor is also iin….
• Thus the voltage across the feedback resistor is
given by
VRf = iinRf = Rf[Vin/Rin]
• Since the voltage from terminal P to ground is
the same as the voltage from P to S, the output
voltage which is measured from P to ground is
the same as the voltage across the feedback
resistor VRf.
Using this, one can write the output voltage as
Vout = -Rf [Vin/Rin] or equivalently as
Vout = -Vin [Rf/Rin]
effectively set by the ratio of the feedback resistor
to the input resistor. The minus sign is required
since the P side of Rf is negative compared to
the S side.
Notice that the external components connected to
the op amp ( Rf and Rin ) determine its
characteristics when used as an amplifier
The input impedance of an inverting amplifier
is given by Rin
• The output impedance is approximately
[ ACL / Aol ] Rout
where Rout is the output resistance of the
operational amplifier chip.
• Since Aol is much larger than ACL , this makes
the output impedance very low.
•Analysis of a Non-Inverting Amplifier
• Since the circuit analysis for a non-inverting amplifier is
more complicated (see any IC textbook) only the results
for this amplifier will be given
Vin
Since the voltage
between the (+) and (-)
inputs to the op amp are
essentially zero, the
voltage applied to the
(+) input and gnd. which
is Vin is also the voltage
between the (-) terminal
and gnd and
consequently also the
voltage across the input
resistor Rin
• There is a voltage divider circuit formed by the
feedback resistor Rf and the input resistor Rin .
This voltage divider sets the equation for the
gain.
– Vin = (Vout Rin )/( Rin + Rf ) or
– Vout = Vin ( Rin + Rf )/ Rin
The voltage gain for the non-inverting amplifier is
Vout = [1 + Rf /Rin ]
• The input impedance is determined by the input
resistance of the op amp itself and by the gain
ratios.
•
Rinput = [ Aol / ACL ] Rin
• For a common 741 amplifier, the open-loop gain
is ~200,000 while the closed-loop is ~100 and
the amplifier input resistance is 75. This would
give
•
Rinput = [200,000/100] 75
•
= 1.5 x 106  or 1.5 M
•
If we let Rf go to zero, and drop R, if we desire,
then in the non-inverting circuit, we get
•
Vout = (1) Vin
gain = 1
• In this circuit the output voltage exactly follows
the input.
• The input resistance of such a circuit is 150 M
Such an amplifier serves as a buffer (or isolation)
amplifier. With ~ infinite input resistance and ~ 0
output resistance, it does not alter the input signal
at all..
Non-Inverting Buffer or Unit-Gain Amp
Any changes in the output circuit (short circuit, etc.) has no
effect on the input circuit. However, such a circuit CAN
multiply the POWER by increasing the current which can be
drawn (from Op Amp).
Summing Amplifier
Op Amps can also be used to perform electronic equivalents
of mathematical operations such as integration,
differentiation, addition, etc. (see the attached sample
circuits). A summing amplifier does a weighted summation
of several input voltages
• The output voltage is given by the weighted sum
of the input voltages
– Vout = - [V1(Rf/R1) + V2 (Rf/R2) + V3 (Rf/R3)]
The negative sign occurs since this is an inverting
circuit.
•Difference Amplifier
• Recall that fundamentally, every operational
amplifier is a difference amplifier, amplifying the
difference between the signals at the inverting (-)
and non-inverting (+) inputs.
• Small variations in the input transistors in the op
amp are reflected in the fact that there are small
differences in quiescent voltages from the two
inputs.
• One can reduce these differences and increase the
op amps CMRR (common-mode rejection ratio) by
connecting a variable resistor to one input and
adjusting the value of that resistor to null out the
output when the same signal is applied to both
inputs.
The next shows shows the circuit with CMRR
adjustment potebtiometer
R1 will usually be a value close to R2
• Instrumentation Amplifier
A high-gain, low-drift, high input impedance,
differential input operational amplifier is usually
known as an instrumentation amplifier. These are
high performance, higher cost amplifiers, are often
used for critical amplification needs in research
projects. These amplifiers are basically high quality
op amps with voltage follower buffers on each input
to produce the desired high input resistance.
Vout = (Vin+ - Vin-)Rf/Rin
• Corrections for REAL Op Amps
• Input Offset Voltage – voltage that must be
applied to one of the input terminals to give zero
output.
• Vinoffset = Voutoffset/Acl
• Input Bias Current – current flowing into Op
Amp input terminals. Ideally these currents are
identical, but actually are not for real devices.
However, they are quite small ~ 200 nA
Both of these can be partially corrected by using
the offset terminals of the op amp, if available.
Offset
Adj.
• Voltage slew rate – time it takes the
output of the op amp to switch from
max output to minimum output. For the
741 amp, this is about 0.5 V/μsec.
• This can only be changed by using a
different op amp with a different slew
rate. For example the LM318 op amp
has a slew rate of 70 V/ μsec