Transcript chapter 4

Signal Conditioning Elements (SCE)
1. Voltage dividers
Vo 
R2
Vs
R1  R2
Example :Potentiometer circuit
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Deflection bridges
Deflection bridges are used to convert the output of resistive, capacitive and inductive
sensors into a voltage signal
Amplifiers
Amplifiers are necessary in order to amplify low-level signals, e.g. thermocouple
or strain gauge bridge output voltages, to a level which enables them to be further
processed
Oscillators and resonators
Thévenin equivalent circuit for a deflection bridge
Bridge Parameters
a. Range of output


1
1




Z3
Z4
1
1 Z
Z2
I min

Vmin
Vmax


1
1




Z4
Z3
1

1


Z I max
Z2

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

V
 S




V
 S


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b. Sensitivity
S 
ΔVout
 ΔZ 


Z


c.Maximum power dissipation
VS2
Z1
ˆ
w
2
Z1  Z 4 
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d. Non linearity
 Vmax   Vmax 
  I - 
I min
Videal  
 I max  I min   I max  I min 
E th  Videal
 100  N̂
Vmax
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Design of resistive deflection bridges
Output voltage for resistive deflection bridge
R1 = RI, and R2, R3 and R4 are fixed resistors
Relationship between resistances in a balanced Wheatstone bridge
Often we require VMIN = 0, i.e. the bridge to be balanced when I = IMIN;
Output voltage for single-element strain gauge bridge
Four-element strain gauge bridge
strain-gage arrangements in a Wheatstone bridge
Case 1.
-utilizing a single active gage in position R1
- it is often employed for both static and dynamic strain-gage measurement if temperature
compensation is not required.
-The resistance R1 = Rg and the other three resistances are selected to maximize the circuit
sensitivity while maintaining the balance condition R1R3 = R2R4.
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The sensitivity Ss of the strain-gage—Wheatstone bridge system is defined as the
product of the sensitivity of the gage Sg and the sensitivity of the bridge circuit S. Thus,
Rg Rg  Vo

S s  S g  Sc 
 R R

 g g
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 Vo



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-the dummy gage is inserted in arm R4 of the bridge instead of arm R2.
-The active gage remains in arm R1
- fixed-value resistors are used in arms R2 and R3.
- With this positioning of the dummy gage
-the system sensitivity is the same as that given by case 1.
- Temperature compensation is achieved in the same manner that was illustrated
in Case 2, but without loss of circuit efficiency.
- When a dummy gage is to be used to effect temperature compensation, arm R4
of the bridge is the preferred location for the dummy gage.
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Case 4.
- Four active gages are used in this Wheatstone bridge arrangement: - - it is used
to measure transverse and axial strain
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Load Cell : Force measurement
Link-type Load Cell
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Beam-type load cells
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Ring-type load cell.
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Output voltage for single-element Thermoresistor bridge
Output voltage for double -elements Thermoresistor bridge
Output voltage for cantilever and torque elements
Output voltage for Pillar load cell
Design of reactive deflection bridges
Bridge for capacitive level sensor
Output voltage for capacitance level bridge
Thus in order to get :ETh = 0 at minimum level hMIN, we require C0 = ChMIN(R3 /R2),
giving:
if R3 /R2 is made large compared with 1, this approximates to the linear
form:
Output voltage for capacitance push-pull bridge
This gives:
Output voltage for inductive push-pull bridge
This gives:
Amplifiers
Why do we need Amplifiers?
Signal Amplification (I,V,,P)
 Signal processing
Inverting
Buffering
Filtering
Compression
Integration
Differentiation
Converters * (How)
Ideal operational amplifier characteristics
typical operational amplifier characteristics (Ideal vs. OPA27)
Transfer characteristics of Op Amp
Inverting amplifier
The output voltage of inverting Amplifier
Since V+ = V− = 0
Also
giving
Non-inverting amplifier
The output voltage of Non-inverting amplifier
Since i+ = 0, V+ = VIN
Also since V+ = V−
we have
, RF and R1 form a potential divider, we have
Voltage follower.
Differential amplifier
Strain gauge bridge connected to differential amplifier
Instrumentation amplifier
• High input impedance
• High common mode rejection ratio
• Low input offset voltage
• Low temperature coefficient of offset voltage.
Voltage adder.
Parameters influence the d.c. performance of the amplifier
Input offset voltage VOS
The existence of input offset voltage VOS means that VOUT is unequal to zero
when both V− and V+ = 0 volts, i.e.
Where
AOL -D.C. open-loop gain
Some operational amplifiers have facilities for adjusting VOS to zero, i.e. for
obtaining VOUT = 0 when V+ = V− = 0.
The effect of VOS on inverting amplifier
Appropriate temperature coefficient
VOS is dependent on the temperature TE °C of the amplifier environment
Example
If VOS is set to zero at TE = 15 °C; then if TE subsequently increases to 25 °C, the
resulting input offset voltage is γ (25 − 15), i.e. ≈ 6 μV, which causes a change of
approximately 0.6 × 106 μV, i.e. 0.6 V in the output of the open-loop operational
amplifier
Common mode voltage
Common mode voltage affects on Vout
where ACM is the common mode gain
Common Mode Rejection Ratio (CMRR)
The equivalent circuit for an open-loop amplifier
a.c. performance of a practical operational amplifier
Gain–frequency relation for open-loop amplifier
where f B = 1/2πτ is the −3 dB cut-off frequency
Typical gain–frequency characteristics for operational amplifier
Instrumentation amplifiers
• High input impedance
• High common mode rejection ratio
• Low input offset voltage
• Low temperature coefficient of offset voltage.
Oscillators and resonators
Oscillators
Inductive Oscillators
Capacitive Oscillators
resonator
Mathematical model of resonator
Examples of resonators
Vibrating plate element
Vibrating tube element.
Other types of Op. Amps
Example Find vo for the following circuit.
It follows that
and
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Therefore
From KVL, we have
and
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Example. Find vo for the following circuit.
With the noninverting input connected to ground, we have vp = 0 = vn.
From KVL
and it follows that
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Since no current flows into the op amp, iC = iR.With
and
we have
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Logarithmic amplifiers
- When a sensor’s output dynamic is of a high amplitude (10 mV to 10 V, for
example), it can be useful to compress the signal by using a logarithmic amplifier.
- After amplification and digitization, the signal can be easily transmitted across a
transmission line.
At reception, it is enough to carry out the reverse operation to restore the
measurement signal.
This principle allows us to lower noise sensitivity.
- Logarithmic amplifiers also help us “linearize” sensors, carry out multiplications,
divisions, elevations in the square, and extractions of the root squared.
To construct this type of amplifier , we use the feature of a P-N junction with an
equation (Ebres-Moll equation) in the following form:
where
q is the electron charge
k the Boltzmann’s constant
T is the absolute temperature
U is the direct voltage and i0 is the flow of reverse current
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Schemata of logarithmic amplifier principle
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