Download Lecture 5

Analog Electronics
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–
Lecture 5
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Electronic Devices, 9th edition
Thomas L. Floyd
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© 2012 Pearson Education. Upper Saddle River, NJ, 07458.
All rights reserved.
Operational Amplifers
Op-amp is an electronic device that amplify the difference of voltage
at its two inputs.
Most op-amps operate from plus
and minus supply voltages, which
may or may not be shown on the
schematic symbol.
+V
–
+
–V
Very high gain dc coupled amplifiers with differential inputs.
One of the inputs is called the inverting input (-); the other is called the
non-inverting input. Usually there is a single output.
Electronic Devices, 9th edition
Thomas L. Floyd
© 2012 Pearson Education. Upper Saddle River, NJ, 07458.
All rights reserved.
The Ideal Op-Amp
Ideally, op-amps have characteristics (used in circuit analysis):
o
Infinite voltage gain
o
Infinite input impedance (does not load the driving sources)
o
Zero output impedance (drive any load)
o
Infinite bandwidth (flat magnitude response, zero phase shift)
o
Zero input offset voltage.
The ideal op-amp has characteristics that
simplify analysis of op-amp circuits.
The concept of infinite input impedance is
particularly a valuable analysis tool for
several op-amp configurations.
Electronic Devices, 9th edition
Thomas L. Floyd
–
Zin = ‘
Vin
AvVin
Zout = 0
Vout
Av = ‘
+
© 2012 Pearson Education. Upper Saddle River, NJ, 07458.
All rights reserved.
The Practical Op-Amp
Real op-amps differ from the ideal model in various respects.
In addition to finite gain, bandwidth, and input impedance,
they have other limitations.
o Finite open loop gain.
o Finite input impedence.
o Non-zero output impedence.
o Input current.
o Input offset voltage.
oTemperature effects.
Electronic Devices, 9th edition
Thomas L. Floyd
–
Vin
Zin
Vout
AvVin
Zout
+
© 2012 Pearson Education. Upper Saddle River, NJ, 07458.
All rights reserved.
Input and Output Impedances
Electronic Devices, 9th edition
Thomas L. Floyd
© 2012 Pearson Education. Upper Saddle River, NJ, 07458.
All rights reserved.
Input Signal modes
The input signal can be applied to an op-amp in differentialmode or in common-mode.
Vin
–
Vout
+
Differential-mode signals are
applied either as single-ended
(one side on ground) or
double-ended (opposite phases
on the inputs).
–
Vin
Vout
+
Electronic Devices, 9th edition
Thomas L. Floyd
© 2012 Pearson Education. Upper Saddle River, NJ, 07458.
All rights reserved.
Signal modes
Common-mode signals are
applied to both sides with the
same phase on both.
Vin
–
Vout
+
Vin
Usually, common-mode
signals are from unwanted
sources, and affect both inputs
in the same way. The result is
that they are essentially
cancelled at the output.
Electronic Devices, 9th edition
Thomas L. Floyd
–
Vout
+
Vin
Common-mode
signals
© 2012 Pearson Education. Upper Saddle River, NJ, 07458.
All rights reserved.
Common-Mode Rejection Ratio
The ability of an amplifier to amplify differential signals and
reject common-mode signals is called the common-mode
rejection ratio (CMRR).
CMRR is defined as CMRR 
Aol
Acm
where Aol is the open-loop
differential-gain and Acm is the
common-mode gain.
Acm is zero in ideal op-amp and much less than 1
is practical op-amps.
Aol ranges up to 200,000 (106dB)
CMRR = 100,000 means that desired signal is amplified 100,000 times
more than un wanted noise signal.
 Aol 
CMRR can also be expressed in decibels as CMRR  20log 

A
 cm 
Electronic Devices, 9th edition
Thomas L. Floyd
© 2012 Pearson Education. Upper Saddle River, NJ, 07458.
All rights reserved.
Example
Common-Mode Rejection Ratio
What is CMRR in decibels for a typical 741C op-amp?
The typical open-loop differential gain for the 741C is 200,000 and the
typical common-mode gain is 6.3.
 Aol 
CMRR  20log 

A
 cm 
200, 000
 20 log
 90 dB
6.3
(The minimum specified CMRR is 70 dB.)
Electronic Devices, 9th edition
Thomas L. Floyd
© 2012 Pearson Education. Upper Saddle River, NJ, 07458.
All rights reserved.
Current Offsets
I BIAS 
IBIAS: The input bias current is the
average of the two dc currents required to
bias the differential amplifier
IOS: The input offset current is the
difference between the two dc bias
currents
Electronic Devices, 9th edition
Thomas L. Floyd
I1  I 2
2
VOUT(ERR) = AvIos.Rin
IOS  I1 - I 2
Vos = Ios.Rin
© 2012 Pearson Education. Upper Saddle River, NJ, 07458.
All rights reserved.
Schematic
Electronic Devices, 9th edition
Thomas L. Floyd
© 2012 Pearson Education. Upper Saddle River, NJ, 07458.
All rights reserved.
Voltage and Current Parameters
VO(p-p): The maximum output voltage swing is determined by
the op-amp and the power supply voltages
VOS: The input offset voltage is the differential dc voltage
required between the inputs to force the output to zero volts
IBIAS: The input bias current is the
average of the two dc currents required to
bias the differential amplifier
I BIAS
IOS: The input offset current is the
difference between the two dc bias
currents
IOS  I1 - I 2
Electronic Devices, 9th edition
Thomas L. Floyd
I1  I 2

2
© 2012 Pearson Education. Upper Saddle River, NJ, 07458.
All rights reserved.
Impedance Parameters
–
ZIN(d) : The differential input impedance is
the total resistance between the inputs
ZIN(d)
+
–
ZIN(cm) : The common-mode input
impedance is the resistance between each
input and ground
ZIN(cm)
+
Zout: The output impedance is the resistance
viewed from the output of the circuit.
–
Zout
+
Electronic Devices, 9th edition
Thomas L. Floyd
© 2012 Pearson Education. Upper Saddle River, NJ, 07458.
All rights reserved.
Slew Rate
Slew rate: The slew rate is the maximum rate of change of
the output voltage in response to a step input voltage
Vout
Slew Rate 
t
Determine the slew rate for the output
response to a step input.
Vout  12 V  -  -12 V 
Slew Rate 

t
4.0 μs
= 6 V/ms
Electronic Devices, 9th edition
Thomas L. Floyd
Vout (V)
13
12
t
0
–12
–13
4.0 ms
© 2012 Pearson Education. Upper Saddle River, NJ, 07458.
All rights reserved.
Extremely High Gain
Open loop gain of an op-amp is in order of 100,000.
Even an extremely small input such as input offset voltage can saturate
the out put.
Vin * Aol= (1mv * 100,1000) = 100V
It limits the use to comparator.
It is not well-controlled parameter.
Electronic Devices, 9th edition
Thomas L. Floyd
© 2012 Pearson Education. Upper Saddle River, NJ, 07458.
All rights reserved.
Negative Feedback
One of the most useful concepts in electronics
Negative feedback is the process of returning a portion of the
output signal to the input with a phase angle that opposes the
input signal.
Vin
+
Vf
–
Vout
Internal inversion makes Vf
180° out of phase with Vin.
Negative
feedback
circuit
The advantage of negative feedback is that precise values of amplifier
gain can be set. In addition, bandwidth and input and output impedances
can be controlled.
The gain with external feedback is called closed loop gain, Acl
Electronic Devices, 9th edition
Thomas L. Floyd
© 2012 Pearson Education. Upper Saddle River, NJ, 07458.
All rights reserved.
Noninverting Amplifier
A noninverting amplifier is a configuration in which the
signal is given on the noninverting input and a portion of the
output is returned to the inverting input.
The difference of input voltage, Vin and the feedback voltage Vf is the
differential input to op-amp .
Difference is amplified with Aol
+
Vout
–
Vin
The closed-loop gain of the
noninverting amplifier is
Acl (NI)  1 
Electronic Devices, 9th edition
Thomas L. Floyd
Rf
Vf
Feedback
circuit
Ri
Rf
Ri
© 2012 Pearson Education. Upper Saddle River, NJ, 07458.
All rights reserved.
Example
Noninverting Amplifier
Determine the gain of the noninverting amplifier shown.
Vin
Acl (NI)  1 
+
Rf
Ri
82 kW
 1
3.3 kW
Vout
–
Rf
82 kW
Ri
3.3 kW
= 25.8
Electronic Devices, 9th edition
Thomas L. Floyd
© 2012 Pearson Education. Upper Saddle River, NJ, 07458.
All rights reserved.
Voltage Follower
A special case of the inverting amplifier is when Rf =0 and
Ri = ∞. This forms a voltage follower or unity gain buffer
with a gain of 1.
This configuration offers very high input impedance and its very low
output impedance.
These features make it a nearly ideal buffer amplifier for interfacing
high-impedance sources and low-impedance loads.
VVinin
It produces an excellent
circuit for isolating one
circuit stage from another,
which avoids "loading"
effects.
Electronic Devices, 9th edition
Thomas L. Floyd
++
VVout
out
––
Rf
82 kW
Ri
3.3 kW
© 2012 Pearson Education. Upper Saddle River, NJ, 07458.
All rights reserved.
Inverting Amplifier
An inverting amplifier is a configuration in which the
noninverting input is grounded and the signal is applied through a
resistor to the inverting input.
Concepts of infinite open loop gain and infinite input resistance
extends to ’virtual ground’ at inverting input.
Current through Ri and through
Rf is equal as no current to the
inverting input.
Rf
Iin
The closed-loop gain of the
inverting amplifier is
Acl (I)  -
Rf
If
Ri
I1=0
Vin
–
Vout
+
Ri
0 V (virtual ground)
Electronic Devices, 9th edition
Thomas L. Floyd
© 2012 Pearson Education. Upper Saddle River, NJ, 07458.
All rights reserved.
Example
Inverting Amplifier
Determine the gain of the inverting amplifier shown.
Rf
Acl (I)  -
Rf
Ri
82 kW
3.3 kW
82 kW
Ri
–
3.3 kW
Vin
Vout
+
= -24.8
The minus sign indicates phase inversion.
Electronic Devices, 9th edition
Thomas L. Floyd
© 2012 Pearson Education. Upper Saddle River, NJ, 07458.
All rights reserved.
Impedances
Noninverting amplifier:
Zin(NI)  1  Aol B  Zin
Zout (NI) 
Electronic Devices, 9th edition
Thomas L. Floyd
Zout
1  Aol B 
© 2012 Pearson Education. Upper Saddle River, NJ, 07458.
All rights reserved.
Impedances
Inverting amplifier:
Z in (I)  Ri
Z out (I)
Z out

1  Aol B 
Note that the output impedance has the same form for both amplifiers.
Electronic Devices, 9th edition
Thomas L. Floyd
© 2012 Pearson Education. Upper Saddle River, NJ, 07458.
All rights reserved.
Impedances
Noninverting amplifier:
Zin(NI)  1  Aol B  Zin
Zout
Zout (NI) 
1  Aol B 
Generally, assumed to be ∞
Generally, assumed to be 0
Inverting amplifier:
Z in (I)  Ri
Z out (I)
Z out

1  Aol B 
Generally, assumed to be Ri
Generally, assumed to be 0
Note that the output impedance has the same form for both amplifiers.
Electronic Devices, 9th edition
Thomas L. Floyd
© 2012 Pearson Education. Upper Saddle River, NJ, 07458.
All rights reserved.
Bias Current and Offset voltage with compensation techniques
 Transistors within op-amp need bias current.
 Practical op-amp has small input bias currents.
 Small imbalances in transistors produce a small offset
voltage between the inputs.
Electronic Devices, 9th edition
Thomas L. Floyd
© 2012 Pearson Education. Upper Saddle River, NJ, 07458.
All rights reserved.
Bias Current and Offset voltage with compensation techniques
Electronic Devices, 9th edition
Thomas L. Floyd
© 2012 Pearson Education. Upper Saddle River, NJ, 07458.
All rights reserved.
Bias Current Compensation
To compensate for input offset current, a resistor equal to
Ri||Rf is added to one of the inputs.
Rf
Rf
Ri
–
–
Vout
Ri
+
Vin
Rc = Ri || Rf
Vin
Electronic Devices, 9th edition
Thomas L. Floyd
Vout
Noninverting
amplifier
+
Rc = Ri || Rf
Inverting
amplifier
© 2012 Pearson Education. Upper Saddle River, NJ, 07458.
All rights reserved.
Input Offset Voltage Compensation
Most ICs provide a mean of compensation.
An external potentiometer to the offset null pins of IC package
Electronic Devices, 9th edition
Thomas L. Floyd
© 2012 Pearson Education. Upper Saddle River, NJ, 07458.
All rights reserved.
Bandwidth Limitations
Many op-amps have a roll off rate determined by a single
low-pass RC circuit, giving a constant -20 dB/decade down
to unity gain.
The blue line
represents the openloop frequency
characteristic (Bode
plot) for the op-amp.
Aol (dB)
Midrange
106
100
75
–20 dB/decade roll-off
50
25
Unity-gain frequency (fT)
Critical frequency
f (Hz)
0
1
Electronic Devices, 9th edition
Thomas L. Floyd
10
100
1k
10k
100k
1M
© 2012 Pearson Education. Upper Saddle River, NJ, 07458.
All rights reserved.
Bandwidth Limitations
For op-amps with a -20 dB/decade open-loop gain, the closed-loop
critical frequency is given by fc(cl) = fc(ol)(1 + BAol(mid))
The closed-loop critical
frequency is higher than
the open-loop critical
frequency by the factor
(1 + BAol(mid)). This
means that you can
achieve a higher BW by
accepting less gain. For
a compensated op-amp,
Acl f(cl) = Aol fc(ol).
Av
Open-loop gain
Aol(mid )
Closed-loop gain
Acl(mid )
0
fc( ol)
fc (cl )
f
.
Electronic Devices, 9th edition
Thomas L. Floyd
© 2012 Pearson Education. Upper Saddle River, NJ, 07458.
All rights reserved.
Example
Bandwidth Limitations
The equation, Acl f(cl) = Aol fc(ol) shows that the product of the gain
and bandwidth are constant. The gain-bandwidth product is also
equal to the unity gain frequency. That is fT = Acl fc(cl), where fT is
the unity-gain bandwidth.
The fT for a 741C op amp is 1 MHz.
What is the BWcl for the amplifier?
82 kW
 25.8
Ri
3.3 kW
f
1 MHz
BWcl  T 
 38.8 kHz
Acl
25.8
Acl (NI)  1 
Electronic Devices, 9th edition
Thomas L. Floyd
Rf
 1
Vin
+
741C
–
Vout
Rf
82 kW
Ri
3.3 kW
© 2012 Pearson Education. Upper Saddle River, NJ, 07458.
All rights reserved.
Selected Key Terms
Operational A type of amplifier that has very high voltage
amplifier gain, very high input impedance, very low
output impedance and good rejection of
common-mode signals.
Differential A mode of op-amp operation in which two
mode opposite-polarity signals voltages are applied to
the two inputs (double-ended) or in which a
signal is applied to one input and ground to the
other input (single-ended).
Common mode A condition characterized by the presence of
the same signal on both inputs
Electronic Devices, 9th edition
Thomas L. Floyd
© 2012 Pearson Education. Upper Saddle River, NJ, 07458.
All rights reserved.
Selected Key Terms
Open-loop The voltage gain of an op-amp without external
voltage gain feedback.
Negative The process of returning a portion of the output
feedback signal to the input of an amplifier such that it is
out of phase with the input.
Closed-loop The voltage gain of an op-amp with external
voltage gain feedback.
Gain- A constant parameter which is always equal to
bandwidth the frequency at which the op-amp’s open-loop
product gain is unity (1).
Electronic Devices, 9th edition
Thomas L. Floyd
© 2012 Pearson Education. Upper Saddle River, NJ, 07458.
All rights reserved.