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