Post on 21-May-2021
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19ELC201
Sensors and Sensor Circuit Design
Capacitor Measurements
Input Impedance
Measurement should not alter the value of the measured signal
If alters the value – loading error
Can be minimized by impedance matching of the source with the
measuring instrument
The measuring instrument input impedance controls the energy that is
drawn from the source, or measured system
The power loss through the measuring instrument is
Z2 is the input impedance of the measuring instrument,
E is the source voltage potential being measured
To minimize the power loss, the input impedance should be large.
P = 𝐸2
𝑍2
Input Impedance
For more than one instruments in a signal chain, the subsequent
instrument draws energy from the previous instrument in the chain
Output signal from one instrument provides the input signal to a
subsequent device in a signal chain
Difference between the actual potential E1 at the output terminals of
device 1 and the measured potential E2 is a loading error.
Input Impedance
A high input impedance Z2 relative to Z1 minimizes loading error
General rule - the input impedance to be at least 100 times the source
impedance to reduce the loading error to 1%.
Null instruments and null methods will minimize loading errors – provide
very high input impedance to the measurement
Deflection instruments and deflection measuring techniques will derive
energy from the process being measured and therefore require attention
to proper selection of input impedance
Bridge Circuits
Bridge circuits are used to convert impedance variations into voltage variations
Application of bridge circuits is in the precise static measurement of an
impedance
DC Bridges
AC Bridges
Wheatstone Bridge
Used in signal-conditioning applications where a sensor changes resistance with
process variable changes
Assume the detector impedance is infinite—an open circuit
Potential difference, ΔV, between points a and b is
ΔV = Va - Vb
The voltage difference or voltage offset is
Wheatstone Bridge
The voltage difference or voltage offset is
This can be reduced to
Combination of resistors will result in zero difference
and zero voltage across the detector— that is, a null
When designed properly, the resistor values satisfy the indicated equality - does
not matter if the supply voltage drifts or changes; the null is maintained.
Problem #1If a Wheatstone bridge, nulls with R1 = 1000 Ω, R2 = 842 Ω and R3 = 500 Ω, Find
the value of R4.
Problem #2The resistors in a bridge are given by R1 = R2 = R3 =120 Ω and R4 = 121 Ω. If
the supply is 10V, find the voltage offset.
Null detector - Galvanometer The use of a galvanometer as a null detector in the bridge circuit introduces
some differences - because the detector resistance may be low
offset current is
Thévenin equivalent circuit for the bridge determine the current
through any galvanometer with internal resistance, RG
Problem #3
Current Balance Bridge
Current Balance Bridge
One disadvantage of the Wheatstone bridge is the need to obtain a null by
variation of resistors in bridge arms
A technique that provides for an electronic nulling of the bridge and that uses
only fixed resistors - using current to null the bridge
The standard Wheatstone bridge is modified by
splitting one arm resistor into two, R4 and R5.
A current, I, is fed into the bridge through the
junction of R4 and R5
The size of the bridge resistors is such that the
current flows predominantly through R5
If a high-impedance null detector is used
Current Balance Bridge
The voltage at point b is the sum of the
divided supply voltage plus the voltage
dropped across R5 from the current, I.
The bridge offset voltage is given by
Potential Measurements using Bridges
Bridge circuit is useful to measure small potentials at a very high impedance,
using either a Wheatstone bridge or a current balance bridge.
Measurement is performed by placing the potential to be measured in series
with the detector
The null detector responds to the potential between points c and b
Using current balance bridge, null condition is,
AC Bridges
The bridge concept can be applied to the matching of impedances in general,
as well as to resistances.
AC bridges employs an ac excitation, usually a sine wave voltage signal.
The bridge offset voltage is
A null condition is defined by a
zero offset voltage ΔE = 0.
Measurement of Capacitance
AC Bridges are used for precise measurements of unknown capacitances
and associated losses in terms of some known external capacitances and
resistances
Most commonly used bridges are:
Series-resistance-capacitance bridge,
Parallel-resistance-capacitance bridge,
Wien bridge, and
Schering bridge
Series-Resistance-Capacitance Bridge
Used for the comparison of a known capacitance with an unknown capacitance
The unknown capacitance is represented by Cx and Rx.
A standard adjustable resistance R1 is connected in series with a standard
capacitor C1.
The voltage drop across R1 balances the resistive voltage drop when the
bridge is balanced.
Additional resistor in series with Cx increases
the total resistive component
Bridge balance is most easily achieved
when capacitive branches have substantial
resistive components
Most suitable for capacitors with a
high-resistance dielectric and hence
very low leakage currents
Series-Resistance-Capacitance Bridge
At balance,
Substituting impedance values gives
The real and imaginary parts must be independently equal.
Equating the real terms gives,
Equating imaginary terms gives,
Problem #4The four impedances of an ac bridge as shown below are Z1 = 50040º Ω,
Z2 = 100 90º Ω, Z3 = 45 -20º Ω, Z4 = 30 30º Ω. Find out whether the bridge is
balanced or not.
Problem #5An ac bridge employs impedances as shown in Figure. Find the value of Rx and Cx
when the bridge is nulled.
Parallel-Resistance-Capacitance Bridge
Unknown capacitance is represented by its parallel equivalent circuit Cx in
parallel with Rx.
Z2 and Z3 impedances are pure resistors with either or both being adjustable.
Z1 is balanced by a standard capacitor C1 in parallel with an adjustable
resistor R1.
Bridge balance is achieved by adjustment
of R1 and either R2 or R3
Most suitable for capacitors with a
low-resistance dielectric and hence
very high leakage currents
Parallel-Resistance-Capacitance Bridge
At balance,
Substituting impedance values gives
Equating the real terms gives,
Equating imaginary terms gives,
Wien Bridge
Special resistance-ratio bridge that permits two capacitances to be compared
once all the resistances of the bridge are known.
Used to compare two capacitors directly.
Finds applications particularly in determining the frequency in RC oscillators
At balance, the unknown resistance and the capacitance are:
Schering Bridge
Used for measuring the capacitance, the dissipation factors, and the loss angles.
Unknown capacitance is directly proportional to the known capacitance C3.
At balance, bridge equations are:
Frequently used in high voltage applications
with high-voltage capacitor C3
Used as high-frequency bridges.
Problem #6