Download Bridge Circuits

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Bridge Circuits
 Bridge circuits are used very commonly as a variable conversion element in
measurement systems and produce an output in the form of a voltage
level that changes as the measured physical quantity changes.
 They provide an accurate method of measuring resistance, inductance and
capacitance values, and enable the detection of very small changes in
these quantities.
 Many transducers measuring physical quantities have an output that is
expressed as a change in resistance, inductance or capacitance.
Lecture 6
Chapter 8: Signal Conditioning
Dr. Eng. Sameh Shaaban
11 May 2014
Slide Nr. 1 of 16 Slides
Null-Type, DC Bridge [Wheatstone Bridge] (1)
Sir Charles Wheatstone
1802 - 1875
Lecture 6
Chapter 8: Signal Conditioning
Dr. Eng. Sameh Shaaban
11 May 2014
Slide Nr. 2 of 16 Slides
Null-Type, DC Bridge [Wheatstone Bridge] (2)
If a high impedance voltage-measuring instrument
is used, the current Im drawn by the measuring
instrument will be very small and can be
approximated to zero.
For Im = 0
I1 = I3 and I2 =I4
Lecture 6
Chapter 8: Signal Conditioning
Dr. Eng. Sameh Shaaban
11 May 2014
Slide Nr. 3 of 16 Slides
Null-Type, DC Bridge [Wheatstone Bridge] (3)
Looking at path ADC, we have a voltage Vi
applied across a resistance Ru + R3 and by
Ohm’s law
I1 
I1 = I3 and I2 = I4
Vi
R u  R 3 
Similarly for path ABC
I2 
Vi
R v  R 2 
Lecture 6
Chapter 8: Signal Conditioning
Dr. Eng. Sameh Shaaban
11 May 2014
Slide Nr. 4 of 16 Slides
Null-Type, DC Bridge [Wheatstone Bridge] (4)
Now we can calculate the voltage drop across
AD and AB
I1 = I3 and I2 = I4
Vi R u
VAD  I1R u 
R u  R 3 
VAB  I 2 R v 
Vi R v
R v  R 2 
By the principle of superposition
Vo = VBD = VBA + VAD = -VAB + VAD
Lecture 6
Chapter 8: Signal Conditioning
Dr. Eng. Sameh Shaaban
11 May 2014
Slide Nr. 5 of 16 Slides
Null-Type, DC Bridge [Wheatstone Bridge] (5)
I1 = I3 and I2 = I4
Vo = VBD = VBA + VAD = -VAB + VAD
Thus
Vi R v
Vi R u
V0  

R v  R 2  R u  R 3 
At the null point Vo = 0, so
Rv
Ru

R v  R 2  R u  R 3 
Lecture 6
Chapter 8: Signal Conditioning
Dr. Eng. Sameh Shaaban
11 May 2014
Slide Nr. 6 of 16 Slides
Null-Type, DC Bridge [Wheatstone Bridge] (6)
I1 = I3 and I2 = I4
Inverting both sides
R v  R 2   R u  R 3 
Rv
Ru
R3 R 2
i.e.

Ru Rv
or R u 
R 3R v
R2
If R2 = R3, then Ru = Rv
Lecture 6
Chapter 8: Signal Conditioning
Dr. Eng. Sameh Shaaban
11 May 2014
Slide Nr. 7 of 16 Slides
Deflection-Type DC Bridge
I1 = I3 and I2 = I4
 Ru

R1
V0  Vi 






R

R
R

R
 u
3
1
2 
If Ru = R1, then Vo = 0
For other values of Ru, V0 has negative and
positive values that vary in a non-linear way
with Ru.
Lecture 6
Chapter 8: Signal Conditioning
Dr. Eng. Sameh Shaaban
11 May 2014
Slide Nr. 8 of 16 Slides
Example (1)
I1 = I3 and I2 = I4
Example:
A certain type of pressure transducer, designed to
measure pressures in the range 0–10 bar, consists
of a diaphragm with a strain gauge cemented to it
to detect diaphragm deflections. The strain gauge
has a nominal resistance of 120Ω and forms one
arm of a Wheatstone bridge circuit, with the other
three arms each having a resistance of 120 Ω. The
bridge output is measured by an instrument whose
input impedance can be assumed infinite. If, in
order to limit heating effects, the maximum
permissible gauge current is 30 mA, calculate the
maximum permissible bridge excitation voltage. If
the sensitivity of the strain gauge is 338 mΩ /bar
and the maximum bridge excitation voltage is
used, calculate the bridge output voltage when
measuring a pressure of 10 bar.
Lecture 6
Chapter 8: Signal Conditioning
Dr. Eng. Sameh Shaaban
11 May 2014
Slide Nr. 9 of 16 Slides
Example (2)
R1 = R2 = R3 = 120Ω
Defining I1 to be the current flowing in path ADC
of the bridge, we can write
Vi = I1 (Ru + R3)
At balance, Ru = 120 Ω and the maximum value
allowable for I1 is 0.03 A. Hence
Vi = 0.03 (120 + 120) = 7.2 V
Thus, the maximum bridge excitation voltage
allowable is 7.2 volts.
Lecture 6
Chapter 8: Signal Conditioning
Dr. Eng. Sameh Shaaban
11 May 2014
Slide Nr. 10 of 16 Slides
Example (3)
For a pressure of 10 bar applied, the resistance
change is 3.38 Ω, i.e. Ru is then equal to 123.38
Ω
 Ru
R1 
V0  Vi 


R

R
R

R




3
1
2 
 u
 123.38 120 
 7.2 

 50 mV

 243.38 240 
Thus, if the maximum permissible bridge
excitation voltage is used, the output voltage is
50 mV when a pressure of 10 bar is measured.
Lecture 6
Chapter 8: Signal Conditioning
Dr. Eng. Sameh Shaaban
11 May 2014
Slide Nr. 11 of 16 Slides
Deflection-Type DC Bridge Non-Linearity (1)
 Ru

R1
V0  Vi 






R

R
R

R
3
1
2 
 u
The non-linear relationship between
output reading and measured quantity
exhibited by the above equation is
inconvenient and does not conform with
the normal requirement for a linear
input–output relationship.
One special case is where the change in
the unknown resistance Ru is typically
small compared with the nominal value of
Ru.
Lecture 6
Chapter 8: Signal Conditioning
Dr. Eng. Sameh Shaaban
11 May 2014
Slide Nr. 12 of 16 Slides
Deflection-Type DC Bridge Non-Linearity (2)
The new voltage V´0 when the resistance Ru changes by an amount dRu, is given by
 R u  dR u

R1
V´0  Vi 


R

d
R

R
R

R




u
3
1
2 
 u
The change of voltage output is therefore
given by
dV0  V´0  V0 
Vi dR u
R u  dR u  R 3 
If dRu << Ru, then the following linear relationship
is obtained
dV0
Vi

dR u R u  R 3 
Bridge sensetivity
Lecture 6
Chapter 8: Signal Conditioning
Dr. Eng. Sameh Shaaban
11 May 2014
Slide Nr. 13 of 16 Slides
Deflection-Type DC Bridge Non-Linearity (3)
Consider a platinum resistance thermometer
with a range of 0°–50°C, whose resistance at
0°C is 500 Ω and whose resistance varies with
temperature at the rate of 4 Ω/°C. Over this
range
of
measurement,
the
output
characteristic of the thermometer itself is
nearly perfectly linear. Taking first the case
where R1 = R2 = R3 = 500 Ω and Vi = 10 V
At 0C; V0  0 V
 600 500 
At 25C; R u  600 and V0  10

  0.455V
1100
1000


 700 500 
At 50C; R u  700 and V0  10

  0.833V
 1200 1000 
Lecture 6
Chapter 8: Signal Conditioning
Dr. Eng. Sameh Shaaban
11 May 2014
Slide Nr. 14 of 16 Slides
Deflection-Type DC Bridge Non-Linearity (4)
Now take the case where R1 = 500Ω but R2 = R3 = 5000 Ω
and let Vi = 26.1 V
At 0C; V0  0 V
500 
 600
At 25C; R u  600 and V0  26.1

  0.424V
 5600 5500 
500 
 700
At 50C; R u  700 and V0  26.1

  0.833V
5700
5500


Lecture 6
Chapter 8: Signal Conditioning
Dr. Eng. Sameh Shaaban
11 May 2014
Slide Nr. 15 of 16 Slides
Deflection-Type DC Bridge Non-Linearity (5)
 Increasing R2 and R4 reduces
non-linearity of the circuit
output.
 However,
Vi
must
be
increased to maintaine the
same output level.
 Circuit heating
avoided.
must
be
Lecture 6
Chapter 8: Signal Conditioning
Dr. Eng. Sameh Shaaban
11 May 2014
Slide Nr. 16 of 16 Slides
Lecture 6
Chapter 8: Signal Conditioning
Dr. Eng. Sameh Shaaban
11 May 2014