MAE 170 Experimental Techniques Lecture 4 OpAmps and Wheatstone Bridge Prof' McKittrick

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MAE 170Experimental TechniquesLecture 4Op-Amps
and Wheatstone BridgeProf. McKittrick

• Oct. 16, 2006

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Announcements

• Mid-term exam next week, Oct. 23 at 5 pm
• Consists of 20-25 multiple choice and/or T/F
  questions (includes today's lecture)
• No LabView questions
• 8 of your grade
• Lecture will follow immediately after the exam
• Lab 5, Thermocouples and heat transfer

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Topics

• Operational amplifiers
• OPerational AMPlifiers (op-amps)
• Basically a differential amplifier having a large
  voltage gain, high input impedance and low output
  impendence
• Used for many applications e.g. filters,
  voltage and current regulators, A/D converters,
  waveform generators.
• Wheatstone bridge
• How to measure an unknown resistance
• Based on Ohms Law (VIR) and on Kirchoffs Law
  (current in current out)

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Objectives of this weeks lab experiments

• Construct Op-Amp amplifier circuit
• Inverting mode
• Measure frequency response
• Construct another op-amp circuit
• e.g. non-inverting op-amp
• Construct a Wheatstone bridge circuit
• Measure an unknown resistance

Implement above using LabView VIs
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General characteristics of signal amplification

• Many transducers produce signals with low
  voltage (mV)
• Difficult to transmit low signals
• Many processing systems require voltages in the
  range 1-10 V
• Amplitude can be increased with an amplifier

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Signal amplification

• Simple amplifier
• Vi is input differential voltage
• Vo is output voltage, usually higher
• Degree of amplification is the gain, G
• G Vo/Vi

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Gain

• Gain can be lt1 (attenuation) or gt1
• Commonly expressed in a log scale in decibels
• GdB 20 log G 20 log (Vout/Vin)
• Amplifier can distort signal
• E.g. frequency distortion
• V(t) GVmisin(2 pft f)
• Ami in the amplitude of the input sine wave
• And f is the phase angle (either 0 or 180)

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Op-Amps

• Practical signal amplifiers are constructed with
  op-amps. An op-amp is a large integrated
  circuit, which consists of gt 50 transistors
• An op-amp has
• non-inverting input ()
• an inverting input (-)
• one output

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Op-Amps
V
Gain g Vout/Vin
Vout
V-
Vin V - V-
Op-amps are written as a triangle
Bode Plot
g
Voltage gain of up to 106 (1 mV ? 1 Volt)
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Types of op-amps
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Op-Ampsideal open loop

• Two input terminals (,-)
• Two power supply voltages (Vs ,-)
• One output voltage

Vout g(V - V-)
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Ideal op-amp

• Infinite voltage gain
• Infinite input impedance
• Zero output impedance
• Infinite bandwidth
• Zero input offset voltage (i.e., exactly zero
  out if zero in).

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741 op-amp

• Input resistance rd 2 MW
• Ouput resistance ro 75 W
• Gain g 200,000
• CMRR 70 dB

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Real and ideal Op-Amps
Parameter Ideal Typical
Op-Amp Op-Amp Differential
voltage gain, g ? 105-109 Common mode voltage
gain 0 10-5 Gain bandwidth product, GBP ? 1-20
MHz Input resistance ? 106-1012 Output
resistance 0 100-1000 ?
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Frequency responseopen loop

• Low frequencies gain constant
• Above 6 Hz, frequency drops at - 6 dB/octave
  or - 20 dB/decade
• An octave is a doubling, a decade is a 10 fold
  increase in frequency
• The cutoff frequency is fc 6Hz

fc
Slope -6 dB/octave
Bode Plot
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Characteristics of op-amps

• Gain bandwidth product, GBP
• Product of openloop gain and frequency is a
  constant
• GBP gopenloopfc
• For the 741, GBP is 1 MHz
• Common-mode rejection ratio, CMRR

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Common mode gain

• The op-amp amplifies the difference between two
  input signals V and V- Vout G(V-V-)
• If both signals are the same, Vout 0
• For real op-amps, any signal common to both
  inputs will be amplified by a common mode gain
• Vo GcmVcm

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Common mode rejection ratio CMRR

• Ideal op-amps reject voltages present to both
  inputs
• However in real op-amps small output voltage
  results from a change to input common-mode
  voltage
• Due to mismatching of (transistors, heating of IC
  circuits, noise etc.) at the input common-mode
  voltage
• produces a differential error voltage at the
  input error gets amplified along with any other
  signal present at the input

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CMRR

• CMRR Gdiff/Gcm 20 log (Vdiff/Vcm) dB
• Gdiff Vo/(V-V-)
• Gcm Vo/Vcm, Vcm V V-
• Then V-V- Vcm/CMRR
• CMRR
• Gives how much differential error voltage is
  produced at the input given Vcm and CMRR
• Thus want a large CMRR

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Review principals of feedback
Xo A Xi Input is amplified Xf b
Xo Output is fed-back to the input Now, Xi
(Xs Xf), positive feedback, -
negative feedback
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Why feedback?

• Coupling the output back to reinforce/cancel
  some of the input
• Better control
• Reduce the effect of noise
• Reduces output distortion
• Gain is independent of signal level

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Examples of positive and negative feedback

• Positive feedback
• oscillators
• Negative feedback
• op-amps

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An op-amp schematic of the 747 op-amp
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Golden rules for op-amps

• Voltage rule
• The output attempts to do whatever is necessary
  to make the voltage difference between the inputs
  zero.
• DV 0 around any loop
• Current rule
• The inputs draw no current.
• Si 0 at any junction

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Inverting and non-inverting op-amps

• Inverting op-amps
• Output voltage is the opposite sign as input
  voltage
• Non-inverting op-amps
• Output voltage is the same sign as input voltage

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Non-inverting op-amp
Iin
A
Vin
-
Vout
B
R2
R1
Current flow from B?op-amp negligible (high input
impedance from op-amp) Current flowing through R1
IR1 Vout/(R1R2) Vn VB IR1R1
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Non-inverting op-amp
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Non-inverting op-amp

• The circuit shows a feedback loop
• Output connected to one of the input terminals
• Signal input to the terminal
• Results in a closed loop configuration

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Inverting op-amp
For an inverting amplifier, the current rule
tries to drive the current to zero at point A.
This requires This gives the voltage
amplification
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Wheatstone bridge

• Used to determine an unknown resistance in a
  circuit

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Original Wheatstone bridge
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Wheatstone bridge
Due to their outstanding sensitivity, Wheatstone
bridge circuits are very advantageous for the
measurement of resistance, inductance, and
capacitance.
Wheatstone bridges are widely used for strain
measurements. (This will be done for Lab 7)
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Kirchoffs laws

• Kirchoffs laws
• The sum of the potential drops around any circuit
  loop must equal the sum of the potential
  increases
• DV 0 around any loop
• At a junction point in a circuit where the
  current can divide, the sum of the currents into
  the junction must equal the sum of the currents
  out of the junction.
• Si 0 at any junction

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Wheatstone bridge
The potential drop is zero if I1R3I3R3 and
I2R2I4R4 and as the potential drop 0 I1I2
and I3I4 Unknown resistance is
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What does some of this look like in the lab?

• Protoboard already configured to make inverting
  op-amp measurements

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In more detail

• Op-amp is 8-pin black DIP (Dual In-line Package)
• Red 15 V supply
• Green -15 V supply
• Red Vin 5V
• Black ground
• White output