OPERATIONAL AMPLIFIERS. BASIC OP-AMP Symbol and Terminals A standard operational amplifier (op-amp)...
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Transcript of OPERATIONAL AMPLIFIERS. BASIC OP-AMP Symbol and Terminals A standard operational amplifier (op-amp)...
OPERATIONAL AMPLIFIERS
BASIC OP-AMP
Symbol and Terminals
• A standard operational amplifier (op-amp) has;• Vout is the output voltage, • V+ is the non-inverting input voltage,• V- is the inverting input voltage.
• Typical op-amp operates with 2 dc supply voltages, • +ve supply.• –ve supply.
Figure 1a: Symbol Figure 1b: Symbol with dc supply connections
An op amp is an active
circuit element designed
to perform mathematical
Operations of addition,
subtraction,
multiplication, division,
differentiation, and
integration.741 general purpose op-amp made by Fairchild Semiconductor
The Ideal Op-Amp
• The ideal op-amp has;• Infinite voltage gain.• Infinite bandwidth.• Infinite input impedance• zero output impedance.
• The input voltage, Vin appears between the two input terminal.
• The output voltage is AvVin as indicated by the internal voltage source symbol.
_
+
AvVin
Zout=0
Zin=∞Vin
Av=∞
Figure 2a: Ideal op-amp representation
The Practical Op-Amp• Characteristic of a practical op-amp are;
• Very high voltage gain.• Very high input impedance.• Very low output impedance.• Wide bandwidth.
_
+
AvVin
Zout
Zin
Vin
Figure 2b: Practical op-amp representation
OP-AMP INPUT MODES AND PARAMETERS
Input Signal Modes
A) Single-Ended Input• Operation mode;
• One input is grounded.• The signal voltage is applied only to the other input.
• When the signal voltage is applied to the inverting input, • an inverted amplified signal voltage appears at the
output. (figure 3a)
.
V out
.V in
_
+
Figure 3a
• When the signal voltage is applied to the noninverting input with the inverting input grounded,
• a noninverted amplified signal voltage appears at the output. (figure 3b)
.
V out
V in
.
_
+
Figure 3b
B) Differential Input• Operation mode;
• Two opposite-polarity (out-of-phase) signals are applied to the inputs
• This type of operation is also referred to as double-ended.• The amplified difference between the two inputs appears
on the output.
.
V out
V in1
V in2
.
_
+
Figure 3c
C) Common-Mode Input• Operation mode
• Two signal voltages of the same phase, frequency and amplitude are applied to the two inputs. (figure 3d)
• When equal input signals are applied to both inputs, they cancel, resulting in a zero output voltage.
• This action is called common-mode rejection.• Means that this unwanted signal will not appear on the
output and distort the desired signal.
.
V out
V in
V in
.
_
+
Figure 3d
Common-Mode Rejection Ratio
• Desired signals can appear on only • one input or • with opposite polarities on both input lines.
• These desired signals are • amplified and appear on the output.
• Unwanted signals (noise) appearing with the same polarity on both input lines are • essentially cancelled by the op-amp and do not appear
on the output.• The measure of an amplifier’s ability to reject common-
mode signal is called • CMRR (common-mode rejection ration).
• Ideally, op-amp provides • a very high gain for desired signal (single-ended or
differential) • zero gain for common-mode signal.
• The higher the open-loop gain with respect to the common-mode gain, • the better the performance of the op-amp in terms of
rejection of common-mode signals.• Therefore;
where Aol = open-loop voltage gain
Acm = common-mode gain• The higher the CMRR, the better.• A very high value of CMRR means that
• the open-loop gain, Aol is high and • the common-mode gain, Acm is low.
• The CMRR expressed in decibels (dB) is
ol
cm
ACMRR
A
20log ol
cm
ACMRR
A
Open-Loop Voltage Gain
• Open-loop voltage gain, Aol of an op-amp • is the internal voltage gain of the device• represents the ration of output voltage to input
voltage when there are no external components.
• The open-loop voltage gain is set entirely by the internal design.
• Open-loop voltage gain can range up to • 200,000 and is not a well-controlled parameter.
• Data sheet often refer to the open-loop voltage gain as • the large-signal voltage gain.
Example 1
A certain op-amp has an open-loop voltage gain of 100,000 and a common-mode gain of 0.2.
Determine the CMRR and express it in decibels.
Answer: a) 500,000 b) 114dB
Common-Mode Input Voltage Range
• All op-amp have limitation on the range of voltages over which they will operate.
• The common-mode input voltage range is
• the range of input voltages which when applied to both inputs will cause clipping or other output distortion.
• Many op-amp have common-mode input ranges of
• ±10V with dc supply voltages of ±15V.
Input Bias Current
• The input bias current is
• the dc current required by the inputs of the amplifier to properly operate the first stage.
• By definition, the input bias current is
• the average of both input currents and is calculated as;
1 2
2BIAS
I II
Figure 4a: Input bias current is the average of the two op-amp input currents.
V2
V1 _
+
I2 Vout
I1
Input Impedance• Two basic ways of specifying the input impedance of an
op-amp are• Differential.• Common-mode.
• Differential input impedance is • the total resistance between the inverting and the
noninverting input. • Measured by determining the change in bias current
for a given change in differential input voltage.
+
.
_
ZIN(d)
Figure 4b: Differential input impedance
• Common-mode input impedance is
• the resistance between each input and ground.
• Measured by determining the change in bias current for a given change in common-mode input voltage.
+
.
_
ZIN(cm)
Figure 4c: Common-mode impedance
Output Impedance
• The output impedance is
• the resistance viewed from the output terminal of the op-amp as indicated in figure 4d
.
+
_
Zout
Figure 4d: Op-amp output impedance
Slew Rate• What is slew rate?
• The maximum rate of change of the output voltage in response to a step input voltage.
• Is dependent upon the high-frequency response of the amplifier stages within the op-amp.
• Is measured with an op-amp connected as shown in figure 4e
R
+
V out
V in
_
Figure 4e: Test circuit
• A pulse is applied to the input, the output voltage is measured as indicated in figure 4f.
• The width of the input pulse must be sufficient • to allow the output to slew
from its lower limit to its upper limit.
• A certain time interval ∆t, is required for the output voltage • to go from its lower limit
–Vmax to its upper limit +Vmax, once the input step is applied.
Figure 4f: Step input voltage and the resulting output voltage
-Vmax
∆t
Vout
+Vmax
Vin
0
• The slew rate is expressed as
Where ∆Vout = +Vmax-(-Vmax).
• The unit is volts per microsecond (V/μs).
outV
t
Example 2The output voltage of a certain op-amp appears as shown in figure below in response to a step input.
Determine the slew rate.
t
2μs
12μs
-9
-10
9
10
0
Vout(V)
Answer: 1.8 V/us
OP-AMPS WITH NEGATIVE FEEDBACK
Closed-Loop Voltage Gain, Acl
• The closed-loop voltage gain is • the voltage gain of an op-amp with external
feedback.• The amplifier configuration consists of
• the op-amp • an external negative feedback circuit that
connects the output to the inverting input.• The closed-loop voltage gain is determined by
• the external component values and can be precisely controlled by them.
Noninverting Amplifier
• Noninverting amplifier is • an op-amp connected in a closed-loop with a controlled
amount of voltage gain is shown in figure 5.• The input signal is applied to
• the noninverting (+) input.• The output is applied back to
• the inverting (-) input through the feedback circuit (closed loop) formed by the input resistor Ri and the feedback resistor Rf.
V in
V f
.
Ri
_Rf
+
V out
Figure 5: Noninverting amplifier
Feedback network
• This creates negative feedback as follows.• Resistor Ri and Rf form a voltage divider circuit, which
reduces Vout and connects the reduced voltage Vf to the inverting input.
• The feedback voltage is expressed as
• The closed-loop gain of the noninverting (NI) amplifier is
• Where
• Therefore;
if out
i f
RV V
R R
( )
1 i foutcl NI
in i
R RVA
V B R
( ) 1 fcl NI
i
RA
R
i
i f
RB
R R
Example 3
Determine the gain of the amplifier in figure below. The open-loop voltage gain of the op-amp is 100,000.
Ri
_
V in
Rf
+
V out
4.7kΩ
100kΩ
Answer: 22.3
Voltage-Follower
• The voltage-follower configuration is a special case of the noninverting amplifier • where all the output voltage is fed back to the inverting
(-) input by a straight connection. (figure 6)• The straight feedback connection has a voltage gain of 1
(no gain).• The closed-loop voltage gain of a noninverting amplifier is
1/B.
Vout
Vin
_
+
Figure 6: Op-amp voltage-follower
• Since B=1, for a voltage-follower, • the closed-loop voltage gain of the voltage follower is
Acl(VF)=1
• The most important features of the voltage-follower configuration are • very high input impedance• very low output impedance.
• These features make it a nearly ideal buffer amplifier for the • interfacing high-impedance sources• low-impedance loads.
Inverting Amplifier
• Inverting amplifier
• An op-amp connected with a controlled amount of voltage gain. (figure 7)
• The input signal is applied through a series input resistor Ri to the inverting (-) input.
• The output is fed back through Rf to the same input.
• The noninverting (+) input is grounded.
AolVin
Ri
Rf
Vout
+
_
Figure 7: Inverting Amplifier
• For inverting amplifier
• The closed-loop voltage gain is the ratio of the feedback resistance (Rf) to the input resistance (Ri).
• This gain is independent of the op-amp’s internal open-loop gain.
• Thus, the negative feedback stabilizes the voltage gain.• The negative sign indicates inversion. Therefore;
fout
in i
RV
V R
( )f
cl Ii
RA
R
( )f
cl Ii
RA
R
Vin
Ri
Rf
Vout
+
_
Example 4Given the op-amp configuration in figure below, determine the value of Rf required to produce a closed-loop voltage gain of -100.
Aol
2.2kΩ
Answer: 220 kΩ