Modern Instrumentation PHYS 533CHEM 620

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Modern InstrumentationPHYS 533/CHEM 620

• Lecture 4
• Amplifiers
• Amin Jazaeri
• Fall 2007

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Amplifiers

• Properties of a perfect amplifier
• Infinite gain
• Infinite input impedance
• will not load down source
• Zero output impedance
• will drive anything
• Infinite CMRR
• Zero Common mode voltage gain
• Infinite Bandwidth

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Operational Amplifiers

• An operational amplifier is modeled as a voltage
  controlled voltage source.
• Properties of Op-amps
• Gain 106
• Input impedance 100 M W
• Output impedance 100 W
• Bandwidth 1-20MHz
• Common mode voltage gain 10-5

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Amplifiers

• Problems
• Gain too high
• slightest input noise causes max output
• Other problems to be discussed later
• Solutions
• Use feedback
• Gain depends only on resistance Rf / Rin
• can control precisely

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Applications of Op Amps

• Amplifiers provide gains in voltage or current.
• Op amps can convert current to voltage.
• Op amps can provide a buffer between two
  circuits.
• Op amps can be used to implement integrators and
  differentiators.
• Lowpass and bandpass filters.

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The Op Amp Symbol
High Supply
Non-inverting input
Output
Inverting input
Ground
Low Supply
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The Op Amp Model
v
Non-inverting input

vo
Rin


Inverting input
A(v -v- )
v-
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Operational Amplifier (OP-AMP)

• Basic and most common circuit building device.
  Ideally,
• No current can enter terminals V or V-. Called
  infinite input impedance.
• VoutA(V - V-) with A ?8
• In a circuit V is forced equal to V-. This is
  called the virtual ground property.
• An opamp needs two voltages to power it Vcc and
  -Vee. These are called the rails.

A
Vo (A V -A V ) A (V - V )

-

-
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Characters of Operational Amplifiers

• high open loop gain
• high input impedance
• low output impedance
• low input offset voltage
• low temperature coefficient of input offset
  voltage
• low input bias current
• wide bandwidth
• large common mode rejection ratio (CMRR)

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INPUT IMPEDANCE
Input impedance the impedance seen by the sensor
when connected to the op-amp. Typically this
impedance is high (ideally infinite) It varies
with frequency. Typical impedances for
conventional amplifiers is at least 1 M? but it
can be of the order of hundreds of M? for FET
input amplifiers. This impedance defines the
current needed to drive the amplifier and hence
the load it represents to the sensor.
Input Circuit Output
Impedance between input terminals input
impedance
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OUTPUT IMPEDANCE
Output impedance the impedance seen by the load.
Ideally this should be zero since then the
output voltage of the amplifier does not vary
with the load In practice it is finite and
depends on gain. Usually, output impedance is
given for open loop whereas at lower gains the
impedance is lower. A good amplifier will have
an output resistance lower than 1?.
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Voltage output

• The linear range of an amplifier is finite, and
  limited by the supply voltage and the
  characteristics of the amplifier.
• If an amplifier is driven beyond the linear range
  (overdriven), serious errors can result if the
  gain is treated as a constant.

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Bandwidth

• Bandwidth the range of frequencies that can be
  amplified.
• Usually the amplifier operates down to dc and has
  a flat response up to a maximum frequency at
  which output power is down by 3dB.
• An ideal amplifier will have an infinite
  bandwidth.
• The open gain bandwidth of a practical amplifier
  is fairly low
• A more important quantity is the bandwidth at the
  actual gain

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Bandwidth
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Temperature Noise

• Temperature and noise refer to variations of
  output with temperature and noise characteristics
  of the device respectively.
• These are provided by the data sheet for the
  op-amp and are usually very small.
• For low signals, noise can be important while
  temperature drift, if unacceptable must be
  compensated for through external circuits.

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Signal Conditioning
External Power

Filter
Motor, Speaker, Alarm etc.
Amp
Transducer
-
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Op-Amp (Analysis)

• The key to op amp analysis is simple
• No current can enter op amp input terminals.
• gt Because of infinite input impedance
• The ve and ve (non-inverting and inverting)
  inputs are forced to be at the same potential.
• gt Because of infinite open loop gain
• Use the ideal op amp property in all your
  analysis.

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What is inside an op-amp
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Inverting Amplifier
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Analysis of Inverting Amplifier
Ideal transfer characteristics
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Inverting op-amp

• The output is inverted with respect to the input
  (180? out of phase).
• The feedback resistor, Rf, feeds back some of
  this output to the input, effectively reducing
  the gain.
• The gain of the amplifier is now given as

In the case shown here this is exactly 10
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Inverting op-amp

• The input impedance of the amplifier is given as

Here it is equal to 1 k?. If a higher resistance
is needed, larger resistances might be needed
Or, perhaps, a different amplifier will be
needed (noninverting amplifier)
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Inverting op-amp

• The output impedance of the amplifier is given as

AOL is the open loop gain as listed on the data
sheet Open loop gain is the open loop gain at
the frequency at which the device is operated
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Inverting op-amp

• Example, for the LM741 amplifier, the open loop
  output impedance is 75W and the open loop gain at
  1 kHz is 1000. This gives an output impedance of

The bandwidth is also influenced by the feedback
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Non-Inverting Amplifier
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Non-inverting amplifier

• The non-inverting amplifier gain is

For the circuit shown, this is 11 The gain is
slightly larger than for the noninverting
amplifier for the same values of R. The main
difference however is in input impedance.
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Non-inverting amplifier

• Input impedance is

Rop is the input impedance of the op-amp as given
in the spec sheet Aol is the open loop gain of
the amplifier. Assuming an open loop impedance
of 1 M? (modest value) and an open loop gain of
106, we get an input impedance of 1011 ?.
(almost ideal)
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Non-inverting amplifier

• The output impedance and bandwidth are the same
  as for the inverting amplifier.
• The main reason to use a noninverting amplifier
  is that its input impedance is very large making
  it almost ideal for many sensors.
• There are other properties that need to be
  considered for proper design such as output
  current and load resistance but these will be
  omitted here for the sake of brevity.

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The voltage follower
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Voltage follower

• The input impedance now is very large and equal
  to

The output impedance is very small and equal to
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Voltage follower

• The value of the voltage follower is to serve in
  impedance matching.
• One can use this circuit to connect, say, a
  capacitive sensor or, an electronic microphone.
• If amplification is necessary, the voltage
  follower may be followed by an inverting or
  noninverting amplifier

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Differential Amplifier

• Op amp output actually depends on voltage
  difference at two inputs
• Insensitivity to common voltage at both inputs
  CMRR
• Real op amps have problems with unbalanced input
  impedance

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Differential Amplifier
Redefine the inputs in terms of two other
voltages 1. differential mode input vdm ? vb
va 2. common mode input vcm ? (va vb)/2 so
that va vcm (vdm/2) and vb vcm
(vdm/2) Then it can be shown that
common mode gain
differential mode gain
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Differential Amplifier

• An ideal differential amplifier amplifies only
  the differential mode portion of the input
  voltage, and eliminates the common mode portion.
• provides immunity to noise (common to both
  inputs)
• If the resistors are not perfectly matched, the
  common mode rejection ratio (CMRR) is finite

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SUMMING AMPLIFIER
Recall inverting amplifier and If I1
I2 In
If
VOUT -Rf (V1/R1 V2/R2 Vn/Rn) If
R1R2Rf, then Vout V1 V2 Vn
Summing amplifier is a good example of analog
circuits serving as analog computing amplifiers
(analog computers)! Note analog circuits can
add, subtract, multiply/divide (using logarithmic
components, differentiat and integrate in real
time and continuously.
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Frequency Response
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Circuit building Tips
Vcc15V
Signal
1) Pin numbers on the circuit diagram
R2
R1
Eg.
R2
2
7
-
R1
3
8
7
6
5
6

4
To Oscilloscope
741
Gnd
2) Use color coding
1
2
3
4
3) Use power strips

4) Separate components from chip - use
insulated wire back to chip 5) Scope probes - to
scope (ground) BNC cable - from signal
generator 6) Build and check in sections
-Vcc-15V
GND
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Trouble Shooting Tips
Bread board wiring
Check circuit diagram
Check breadboard wiring
Check supply voltages
Check voltages at nodes of Interest in your
circuit
To oscilloscope
8
7
6
5
2
7
-
741
3
6

4
1
2
3
4
To signal generator
Circuit diagram
Write down pin numbers on the circuit diagram
Use different color wires for supply and signals