## Signal Conditioning Circuits for RTD

Hello friends, today we will see Signal Conditioning Circuits for RTD. We know that sensitivity of RTD depends on the temperature resistance coefficient of the metal used for RTD. The value of this coefficient is very small and thus RTD requires the amplifying circuit which is the first signal conditioning circuit for RTD which we are going to see in next post.

#### Linearization of RTD:

Another signal conditioning circuit required for RTD is linearization circuit. We know that temperature vs resistance curve of RTD is non linear and therefore for wide range of measurements we need to use Linearization circuit for RTD.

We know that RTD is a low resistance device that means it has a very small range of resistance and therefore there should not be any lead resistance effect on the output of RTD i.e. Lead wire resistances should not be added with the RTD resistance. Therefore another signal condition circuit for RTD includes lead resistance elimination.

Sensor fault detection is also one of the important signal conditioning circuits for RTD. Sometime due to corrosion of connecting leads RTD may get opened. In such cases signal conditioners may indicate some finite voltages. So to avoid these wrong readings we have to design a signal conditioning circuit for RTD.

In short There are four main signal conditioning circuits for RTD as follows:

• Bridge amplifier
• Linearization circuit for RTD output
• Sensor fault detection circuit

## Carey Foster Bridge: Construction & Working Principle

Hi friends, this post provides an information about Carey Foster bridge. We will also learn how this bridge can be used to determine the resistance in detail with deriving an expression for determining resistance.

## Carey-Foster bridge Experiment

We have already seen some basic methods for measuring medium resistances. Carey foster bridge is the method used for measurement of medium resistances. Carey foster bridge is specially used for the comparison of two equal resistances. The circuit for Carey-Foster Bridge is shown in figure below. A slide wire having length L is included between R and S. resistance P and Q are adjusted so that the ratio P/Q is approximately equal to R/S. this can be achieved by sliding contact on slide wire.

Carey foster bridge circuit

### Carey Foster Bridge: Working Principle

The working principle of Carey Foster bridge is similar to the Wheatstone bridge. The potential fall is directly proportional to the length of wire.This potential fall is nearly equal to the potential fall across the resistance connected in parallel to the battery.

### Description:

Let l1 be the distance of the sliding contact from the left hand end of the slide-wire of Carey foster bridge. The resistance R and S are interchanged and balance is again obtained. Let the distance is now l2.

Let r= resistance/unit length of slide wire

For first balance,

For second balance,

Comparing,

Where l1 and l2 are balanced points when slide wire is calibrated by shunting S with a known resistance and S’ is value of S when it is shunted by a known resistance. Thus Carey foster bridge can be used to measure the medium resistance.

## Effects of temperature changes in Ammeters:

This post provides an information about effects of temperature changes in ammeters.

Errors due to temperature changes in can be eliminated by using the same material for both shunt and moving coil and kept at the same temperature. But in practice this method is not suitable because temperature of both parts (shunt and moving coil) does not changes at the same rate. If we use same material like copper, there is one more disadvantaging of copper that they are likely to be bulky as the resistivity of the copper is small.

So to avoid these difficulties, there is one another method in which we use swamping

The arrangement of this method is as shown in the figure. In this method we use a resistance of material having negligible temperature coefficient like mangnin and this resistance is called as ‘swamping resistance’. Its resistance is equal to 20 to 30 times the resistance of the coil used in ammeter. The swamping resistance is connected in series with the coil and shunt of mangnin is connected across this combination as shown in figure. Since copper forms a small fraction of the series combination, the proportion in which the currents would divide between the meter and the shunt would not change appreciably with the change in the temperature.

In this manner the effects of change in temperature on ammeters can be minimized.

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Anderson’s Bridge is the modification of the Maxwell’s inductance-capacitance bridge. In Anderson’s bridge a standard capacitor is used for the measurement of self inductance. A main advantage of this method is that it can be used for the vide range of self inductance measurement.

Following figure shows the Anderson’s bridge for the balance conditions.

Let,

• L1 = Self inductance to be measured,
• R1 = resistance of self-inductor,
• r1 = resistance connected in series with self-inductor,
• r, R2, R3, Ra = known non-inductive resistances,
• C = fixed standard capacitor.

At balance,

1)      In Anderson’s bridge it is very easy to obtain the balance point as compared to Maxwell’s bridge.

2)      In this bridge a fixed standard capacitor is used therefore there is no need of costly variable capacitor.

3)      This method is very accurate for measurement of capacitance in terms of inductance.

1) It is more complex as compared with Maxwell’s inductance bridge. It has more parts and hence complex in set up and manipulate. The balance equations of Anderson’s bridge are quite complex and much more tedious.

2) An additional junction point increases the difficulty of shielding the bridge.

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## Schering Bridge (Measurement of Capacitance)

Hi friends, this post provides an information about Schering bridge which is used for measurement of capacitance. We will also see its phasor diagram, advantages and disadvantages.

The connections and phasor diagram of the Schering bridge under balance conditions are shown in figure below.

Schering Bridge Circuit
Schering Bridge Phasor Diagram

Let

• C1= capacitor whose capacitance is to be determined,
• r1 = a series resistance representing the loss in the capacitor C1
• C2 = a standard capacitor
• R3 = a non – inductive resistance
• C4 = a variable capacitor
• R4 = a variable non-inductive resistance in parallel with variable capacitor C4

Now when the Schering Bridge is balanced, then

By equating real and imaginary part of the equation we get,

Two independent balance equations are obtained if C4 and R4 are chosen as the variable elements.

The dissipation factor is given by:

Therefore values of capacitance C1 and its dissipation factor are obtained from the values of bridge elements at balance.

Permanently set up Schering bridges are sometimes arranged so that balancing is done by adjustment of R3 and C4 remaining fixed. Since R3 appears in both the balance equations and therefore there is some difficulty in obtaining balance but it has certain advantages which are explained as follows:

We know that the equation for unknown capacitance is,

In the above equation value of R4 and C2 are fixed therefore the dial resistor R3 may be calibrated to read the capacitance directly.

• 1)    The balance equation is independent of frequency.
• 2)    It is used for measuring the insulating properties of electrical cables and equipments.

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## CRO and its Working

Hi friends, in this post we are going to learn about Basics of Cathode Ray Tube (CRO) and its function. We will also see the working of CRO.

### Block Diagram of CRO:

CRO block diagram

### Cathode Ray Tube (CRT):

CRT Produces a sharply focused beam of electrons, accelerated to a very high velocity. This electron beam travels from electron gun to the screen. The electron gun consists of filament, cathode, control grid, accelerating anodes and focusing anode. While travelling to the screen, electron beams passes between a set of vertical deflecting plates and a set of horizontal deflection plates. Voltages applied to these plates can move the beam in vertical and horizontal plane respectively. The electron beam then strikes the fluorescent material (phosphor) deposited on the screen with sufficient energy to cause the screen to light up in a small spot.

### Vertical Amplifier:

The input signal is applied to vertical amplifier. The gain of this amplifier can be controlled by VOLT/DIV knob. Output of this amplifier is applied to the delay line.

### Delay Line:

The delay Line retards the arrival of the input waveform at the vertical deflection plates until the trigger and time base circuits start the sweep of the beam. The delay line produces a delay of 0.25 microsecond so that the leading edge of the input waveform can be viewed even though it was used to trigger the sweep.

### Trigger (Sync.) Circuit:

A sample of the input waveform is fed to a trigger circuit which produces a trigger pulse at some selected point on the input waveform. This trigger pulse is used to start the time base generator which then starts the horizontal sweep of CRT spot from left hand side of the screen.

### Time base (Sweep) Generator:

This produces a saw – tooth waveform that is used as horizontal deflection voltage of CRT. The rate of rise of positive going part of sawtooth waveform is controlled by TIME/DIV knob. The sawtooth voltage is fed to the horizontal amplifier if the switch is in INTERNAL position. If the switch is in EXT. position, an external horizontal input can be applied to the horizontal amplifier.

### Horizontal Amplifier:

This amplifies the saw – tooth voltage. As it includes a phase inverter two outputs are produced. Positive going sawtooth and negative going sawtooth are applied to right – hand and left – hand horizontal deflection plates of CRT.

### Blanking Circuit:

The blanking circuit is necessary to eliminate the retrace that would occur when the spot on CRT screen moves from right side to left side” This retrace can cause confusion if it is not eliminate. The blanking voltage is produced by sweep generator. Hence a high negative voltage is applied to the control grid during retrace period or a high positive voltage is applied to cathode in CRT.

When a sawtooth voltage is applied to horizontal plates and an input signal is applied to vertical plates, display of vertical input signal is obtained on the screen as a function of time.

### Power Supply:

A high voltage section is used to operate CRT and a low voltage section is used to supply electronic circuit of the oscilloscope.

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## Three ammeter method for measurement of power:

Following figures shows the circuit diagram and phasor diagram of three ammeter method for measurement of power. The current measured by the ammeter A1, is the vector sum of the load current and that taken by the non-inductive resistor R, this latter being in phase with V.

From phasor diagram, we have:

• The advantage of this method is that the value of determined is independent of supply frequency and waveforms.
• The disadvantages of measurement of power by three voltmeter method are overcome in this method.

Let us solve one numerical based example on three ammeter method for clear understanding.

### Example 1:

The following readings were obtained from three ammeters used for a single phase power measurement: An inductive load takes a current of 2.5 A; a non-inductive resistor connected in parallel takes 2.4 A, when connected across 250 V supply. The total current taken from the supply is 4.5 A. Calculate:

a)    Power absorbed by the load.

c)     Power factor of the load.

### Solution:

Given: I3 = 2.5 A; I2 = 2.4 A; I1 = 4.5 A; V = 250 V.

Non-inductive resistance, R = (V/I2) = 250/2.4 = 104.17 Ω.

i)                  Power absorbed by the load, P:

P = (R/2)*(I1^2 – I2^2 – I3^2)

= (104.17/2)((4.5^2)-(2.4^2)-(2.5^2)) = 429.2 W     (Ans.)

Z = (V/I3) = (250/2.5) = 100 Ω   (Ans.)

iii)             Power factor of the load, cos ф = (I1^2 – I2^2 – I3^2) /2I2I3

= [(4.5^2)-(2.4^2)-(2.5^2)]/(2*2.4*2.5) = 0.687    (Ans.)

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Three voltmeter method for measurement of power.

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## Three voltmeter method for measurement of power:

As we know, wattmeters are used for measurement of power in inductance AC circuits, but in some cases it is not possible to use wattmeters because of their incorrect readings or sometime wattmaters may not available. So in such cases three voltmeters or three ammeter method is used for measurement of power.

### Three voltmeter method:

Following figure shows the circuit diagram for three voltmeter method.

V1, V2 and V3 are the three voltmeters and R is a non-inductive resistance connected in series with the load as shown in figure.

From the phasor diagram, we have:

The assumptions are made that the current in the resistor R is same as the load current.

• Supply voltage higher than normal voltage is required because an additional resistance R is connected in series with the load Z (inductive circuit).
• Even small errors in measurement of voltages may cause serious errors in the value of power determined by this method.

Let us solve one simple numerical example based on three voltmeter method for clear understanding.

### Example 1:

The following readings were obtained from three voltmeters used for a single phase power measurement:

V2 = 180 voltas across a non-inductive resistaor; V3 = 200 volts across an inductive load; V1 = 300 volts across the two in series.

Calculate the power factor of the inductive load.

### Solution:

Given: V2 = 180 V; V3 = 200 V; V1 = 300 V

Power factor, cos ф = (V1^2 – V2^2 – V3^3)/2V2V3

Or cos ф = [(300^2) – (180^2) – (200^2)]/(2*180*200) = 0.244   (Ans.)

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## Thermal wattmeter:

Following figure shows the arrangement of thermal wattmeter for measurement of power:

This wattmeter uses two similar thermocouples (1 and 2) whose outputs are connected in opposition with a galvanometer in between. Rh is the resistance of each thermocouple heating element. R is high series resistance, and between C and D is a low resistance R2 capable of carrying the load current i. the resistance R2 develops a potential difference which depends upon the load current, together with the current of one heater, and the series resistance R carries the current of both heaters.

If v be the instantaneous voltage at the load, then assuming identical thermocouples, we have:

From above two equations, we get:

e.m.f. of thermocouple 1,

If  Rh+R  is not very different from Rh, the C2*i^2 may be neglected and T(inst.) is directly proportional to v*i or instantaneous power.

Thus, galvanometer may be calibrated to read the power.

• The commercial thermal wattmeters employ a number of thermocouples connected in the form of a chain in order to increase the output. C.T.s and P.T.s are also used with these instruments.
• For high frequency measurements careful shielding is required.

The thermal wattmeters can be used for measurement of power is several circuits and the sum of their outputs can be applied to a recording potentiometer which records the total power.

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Electrostatic type Wattmeter

Dynamometer type wattmeter

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## Electrostatic Wattmeter:

These wattmeters are used for measurement of small amount of power, practically when the voltage is high and power factor is low. This type of wattmeter is also used for measurement of dielectric loss of cables on alternating voltage and for calibration of wattmeters and energy meters.

Electrostatic wattmeter consists of a quadrant electrometer used with a non-inductive resistor R as shown in figure below.

Instantaneous torque,

Instantaneous torque,

i.e. instantaneous torque is proportional to the instantaneous power in the load plus half of the power lost in noninductive resistance.