Transcript Op-Amp Applications

EE 174
Fall 2016
Operational Amplifiers
Contents
• Introduction
• Brief of History
• Fundamentals of Op-Amps
• Basic operation
• Gain
• Offset
• Applications
Introduction
• Operational Amplifier (Op-Amp) name comes from the fact that it was originally used to perform
mathematical operations.
• Op-Amp is an active circuit element which is basic component used to build analog circuits.
• Op-Amp is a low cost integrating circuit consisting of transistors, resistors, diodes and capacitors.
• Op-Amp amplify an input signal produces an output voltage equal to the difference between the two
input terminals multiplied by the gain A.
• Op-Amps are two-port networks in which the output voltage or current is directly proportional to
either input voltage or current. Four different kind of amplifiers exits:
•
•
•
•
Voltage amplifier: Av = Vo / Vi
Current amplifier: Ai = Io / Ii
Transconductance amplifier: Gm = Io / Vi
Transresistance amplifier: Rm = Vo / Ii
•
The op-amp always “wants” both inputs (inverting and non-inverting) to be the same value. If they
are not, the same value, the op amp output will go positive or negative saturation, depending on
which input is higher than the other.
•
Op-Amps are commonly used for both linear and nonlinear applications: Inverting/Non-inverting
Amplifiers, Variable Gains Amplifiers, Summers, Integrators/Differentiators, Filters (High, Low, Band
Pass and Notch Filters), Schmitt trigger, Comparators, A/D converters.
Brief History of Op-Amp
Monolithic IC Op-Amp
Vacuum Tube Op-Amps (1930’s-1940’s) Solid State Discrete Op-Amps
Dual-supply voltage of +300/-300 V
(1960’s)
Output swing +/- 50 volts
Open-loop voltage gain of 15,000 to 20,000,
Slew rate of +/- 12 volts/µsecond
Maximum output current of 1 mA
George Philbrick
Dual-supply voltage of +15/-15 V
Output swing +/- 11 volts
Open-loop voltage gain of 40,000,
Slew rate of +/- 1.5 volts/µsecond
Maximum output current of 2.2 mA
• First created in 1963 μA702
by Fairchild Semiconductor
• μA741 created in 1968,
became widely used due to
its ease of use 8 pin, dual
in-line package (DIP)
• Further advancements
include use of field effects
transistors (FET), greater
precision, faster response,
and smaller packaging
Internal Op-Amp Circuits
Op-Amp Ideal, Equivalent Circuit, Characteristics and Features
Ideal Op-Amp
Op-Amp Equivalent
Circuit
Op-Amp Characteristics
Op-Amp Symbol
741 Op-Amp Features
+V2: Non-inverting input
-V1: Inverting input
+Vs: Positive source PS
-Vs: Negative source PS
Vout: Output voltage
ON: Offset Null
NC: Not Connected
The Ideal Op-Amp Assumptions
vd = v+ - vvo = Avd = A(v+ – v-)
Note: v+ = v2, v- = v1
1) The input impedance Ri is infinite - i.e. no current flows into either input.
2) The output impedance Ro is zero - i.e. the op-amp can drive any load impedance to
any voltage.
3) The open-loop gain (A) is infinite.
4) The bandwidth is infinite.
5) The output voltage is zero when the input voltage difference is zero.
6) The slew rate is infinite
Op-Amp two basic operations
The Inverting Op Amp
The Non-inverting Op Amp
The op-amp always “wants” both inputs (inverting and non-inverting) to
be the same value.
Op-Amp Gain
Open loop gain: This form of gain is measured when
no feedback is applied to the op amp.
Closed loop gain: This form of gain is measured when
the feedback loop is closed and the overall gain of the
circuit is much reduced. It has two forms, signal gain
and noise gain.
The expression for the gain of a closed-loop amplifier
involves the open-loop gain. If G is the actual gain, NG
is the noise gain, and AVOL is the open-loop gain of the
amplifier, then:
 G = NG
0
Since the open-loop gain is very high, the
closed-loop gain of the circuit is simply the
noise gain, G = NG.
Loop gain: The difference between the open-loop gain and the closed-loop gain is known as the loop gain.
This is useful information because it gives you the amount of negative feedback that can apply to the
amplifier system.
Signal Gain and Noise Gain
Signal gain: This is the gain applied to the input signal, with the feedback loop connected. It can be
inverting or non-inverting. It can even be less than unity for the inverting case. Signal gain is the gain that
we are primarily interested in when designing circuits.
Noise gain: Noise gain is the reciprocal of the attenuation from the output of an op amp (or any feedback
loop) to the input. This is the gain applied to a noise source in series with an op amp input. It is also the gain
applied to an offset voltage. It is the same for either an inverting or non-inverting stage. It is the noise gain that
is used to determine stability.
Summary of Signal Gain and Noise Gain
Op-Amp Gain and Bandwidth
The Voltage Gain (A) of the operational amplifier
can be found using the following formula:
and in Decibels or (dB) is given as:
Gain versus Bandwidth
Applying feedback will
reduce the gain but increase
the bandwidth.
Gain Bandwidth Product (GBP)
Gain-bandwidth (GBW) product is defined as the
op-amp gain multiplied by the bandwidth. The
GBW product can be used to calculate the closedloop gain bandwidth.
GBW = A x BW
where A is in ratio (not in dB)
GBW/closed-loop gain = closed-loop BW
Closed-loop BW = GBW / A
Examples: The GBW @ unity gain (from graph)
 GBW = 1 x 10 MHz = 10 MHz
The GBW @ closed-loop gain A = 100
 GBW = 100 x 100 KHz = 10 MHz
BW = 1 MHz, closed-loop gain?
 A = GBW / BW = 10 MHz / 1MHz = 10
Closed loop gain 70 dB. Closed-loop BW?
Gain: 20 log A = 70 dB  log A = 70/20 = 3.5 or
A = 103.5 = 3162
Closed-loop BW = 10 MHz / 3162 = 3163 Hz
Bode Plot Example
Given a transfer function:
H(s) =
=
100
100
=
𝑠
𝑠+30
30 (30 +1)
100
1
1
= 3.3 𝑠
𝑠
30 ( +1)
( +1)
30
30
Constant gain = 3.3
Gain in dB = 20 log (3.3) ≈ 10 dB
Pole at 30 rad/sec
Phase = 45o at 30 rad/sec
Op-Amp Saturation
The op amp has three distinct regions of operation:
• Linear region (−Vsat < Vo < Vsat)
• Positive saturation (Vo > Vsat)
• Negative saturation Vo < −Vsat .
The output voltage of a practical amplifier cannot exceed certain
threshold value is called saturation. A voltage amplifier behaves
linearly, i.e., Vo/Vi = Av = constant as long as the output voltage remains
below the “saturation” voltage,
−Vsat < Vo < Vsat
Note that the saturation voltage, in general, is not symmetric.
For an amplifier with a given gain, Av, the above range of Vo translate
into a certain range for Vi
− Vsat < Vo < Vsat
− Vsat < Av Vi < Vsat
− Vsat / Av < Vi < Vsat / Av
Any amplifier will enter its saturation region if Vi is raised above certain
limit. The figure shows how the amplifier output clips when amplifier is
not in the linear region.
Example: For Av = 105, Vsat,1 = L- = -12V, Vsat,2 = L+ = +15V, find range of input Vi to prevent saturation.
Solution: -12V / 105 < Vi < 15V / 105 or -0.12mV < Vi < 0.15mV
Op-Amp slew rate basics
Square Wave: The slew rate (SR)of an op amp is the rate of
change in the output voltage caused by a step change on the input.
It is measured as a voltage change in a given time - typically V / µs.
The slew rate may be very important in many applications.
For the given graph, it takes 2 µs to swing 10 V so SR = 5V/ µs.
Sine Waves: The maximum rate of change for a sine wave occurs at the
zero crossing and may derived as follows:
Given vo = VP sin(2π f t)
Slew Rate (SR) =
V/µs = 2π f VP cos(2π f t) =
max
= 2π f VP
t=0
SR = 2π fmax VP
Example: Slew rate S0 = 1 V/μs; input voltage vin (t) = sin(2π × 105t);
closed loop gain AV =10.
1) Sketch the theoretically correct output and the actual output of the amplifier in the same graph.
2) What is the maximum frequency that will not violating the given slew rate?
Solutions:
1) With the closed-loop voltage gain of 10  vo(t) = 10 sin(2π × 105t) 
= Aω = A x 2π x f = 10 × 2π × 105 = 6.28 V/μs
max
2) fmax = SR / (A x 2π) = 1 x 106 / (10 x 2π) = 15.9 kHz
Op-Amp Offset Parameters
Another practical concern for op-amp performance is voltage offset.
A perfect op-amp would output exactly zero volts with both its inputs
shorted together and grounded. However, most op-amps off the
shelf will drive their outputs to a saturated level, either negative or
positive even if the op-amp in question has zero common-mode gain
(infinite CMRR). This deviation from zero is called offset.
In the example shown above, the output voltage is saturated at a
value of positive 14.7 volts, just a bit less than +V (+15 volts) due to
the positive saturation limit of this particular op-amp.
Unlike common-mode gain, there are usually provisions made by the
manufacturer to trim the offset of a packaged op-amp. Usually, two
extra terminals on the op-amp package are reserved for connecting
an external “trim” potentiometer. These connection points are
labeled offset null and are used in this general way:
741 OPAMP have offset voltage null capability by connecting 10 K ohm pot between pin 1 and pin 5.
By varying the potentiometer, output offset voltage (with inputs grounded) can be reduced to zero volts. For the 741C
the offset voltage adjustment range is ± 15 mV.
Op-Amp Offset Example
Example: Determine the output voltage in each of the following cases for the open
loop differential amplifier shown below.
(a) vin 1 = 5 µVdc, vin 2 = -7 µVdc
(b) vin 1 = 10 mV rms, vin 2= 20 mV rms
Specifications of the OPAMP are given below:
A = 200,000, Ri = 2 MΩ , RO = 75Ω, + VCC = + 15 V, - VEE = - 15 V, and output voltage
swing = ± 14V.
Solution:
(a). The output voltage of an OPAMP is given by
Remember that vo = 2.4 V dc with the assumption that the dc output voltage is zero
when the input signals are zero.
(b). The output voltage equation is valid for both ac and dc input signals. The output
voltage is given by
Thus the theoretical value of output voltage vo = -2000 V rms. However, the OPAMP
saturates at ± 14 V. Therefore, the actual output waveform will be clipped as shown
fig. 5. This non-sinusoidal waveform is unacceptable in amplifier applications.
Op-Amp Applications
Differential Amplifier
If R1 = R2 and R3 = R4
Op-Amp Applications
Find i, if and vo.
i=0A
For the ideal op amp shown below, what should be the
value of resistor Rf to obtain a gain of 5?
Op-Amp Applications
1) Calculate all voltage drops and currents in this circuit, complete with arrows for current direction and polarity
markings for voltage polarity. Then, calculate the overall voltage gain of this amplifier circuit (AV), both as a ratio and
as a figure in units of decibels (dB):
Solutions: Gain = AV = 1.468 = 3.335 dB
2) Given gain RF/RS = 100, GBW product = A0 ω0 = K = 4π × 106 .
Determine the overall 3-dB bandwidth of the cascade amplifier Solutions: The 3-dB bandwidth for each amplifier is:
below:
Thus, the bandwidth of the cascade amplifier is 4π × 104,
the cascade amplifier gain is A1A1= 100 × 100 = 104.
To achieve the same gain with a single-stage amplifier
having the same K, the bandwidth would be
Op-Amp Applications
Problem: Suppose that we need an amplifier with input resistance of 500 kΩ or greater and a voltage gain of -10. The
feedback resistors are to be implemented in integrated form and have values of 10 kΩ or less to conserve chip area.
Choose a suitable circuit configuration and specify the resistance values.
Solution:
Gain of -10  Use inverting Op-Amp where gain
A = - R2/R1 = -10
To attain desired input resistance R1 = 500 kΩ  R2 = 5MΩ.
These values exceed the maximum values allowed.
To attain large input resistance with moderate resistances
for an inverting amplifier, we cascade a voltage follower
with an inverter.
To achieve the desired gain = - 10.
Choose R1 = 1 kΩ  R2 = 10 kΩ.
R2
Op-Amp Applications
For Rs = 10 kΩ, RL = 1 kΩ  VL = 0.1 Vin
 Huge attenuation of the signal source.
If voltage follower (buffer amplifier) is used.
 VL = Vout = Vin
Active Filters, Integrators & Differentiators
Consider the circuit shown. Various circuits can be made with
different choices for Z1 and Z2. Following the inverting amplifier
solution, we find:
Active Filters, Integrators & Differentiators
Active Filters, Integrators & Differentiators
Integrator
The Op-Amp Comparators
The comparator is an electronic decision making circuit that makes use of an operational amplifiers very high gain
in its open-loop state, that is, there is no feedback resistor. The Op-amp comparator compares one analogue
voltage level with another analogue voltage level, or some preset reference voltage, VREF and produces an output
signal based on this voltage comparison. In other words, the op-amp voltage comparator compares the magnitudes
of two voltage inputs and determines which is the largest of the two.
Then an op-amp comparator can be configured to operate in what is called an inverting or a non-inverting
configuration.
The Op-Amp Comparators
The Schmitt Trigger
Schmitt trigger is a comparator circuit with hysteresis implemented by applying positive feedback to the noninverting
input of a comparator. It is an active circuit which converts an analog input signal to a digital output signal. In the noninverting configuration, when the input is higher than a chosen threshold, the output is high. When the input is below a
different (lower) chosen threshold the output is low, and when the input is between the two levels the output retains its
value. This dual threshold action is called hysteresis.
i
The Schmitt Trigger
Non-symmetrical Inverted Schmitt trigger
The calculation of the two threshold points are followed:
Let Vref = Vout = 5V, R1 = R2 = R3 = 10 kΩ.
 R1//R2 = R1//R3 = 10 kΩ // 10 kΩ = 5 kΩ
References:
• http://www.ume.gatech.edu/mechatronics_course/OpAmp_F08.ppt
• http://www.allaboutcircuits.com/textbook/semiconductors/chpt-8/operational-amplifier-models/
• http://www.ti.com/lit/an/slaa068a/slaa068a.pdf
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• Fundamentals of Electrical Engineering, Giorgio Rizzoni, McGraw-Hill Higher Education
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