Week 4

INSTRUMENTATION & MEASUREMENTS(EE-302)

WEEK 4

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Anderson bridge

Its in fact a modification of the basic Maxwell’s bridge used to find the self inductance value using the comparison technique.

Used for precise measurement over a large range of values.

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Anderson bridge

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Anderson bridge Phasor diagram

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Anderson bridge under balance:

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Under the balance condition the Anderson bridge’s unknown parameters are:

Advantages:

Accurate measurement of capacitance in terms of inductance is possible.

Requires a fixed capacitor instead of a variable capacitor.

Bridge comparatively easier to balance with respect to the Maxwell’s bridge.

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Disadvantages:

Anderson’s bridge is more complicated than other bridges.

Uses more components.

Balance equations are more complicated to drive.

Bridge cannot be easily shielded due to additional junction points, to avoid effect of stray capacitances.

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Example

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Example

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Example

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Hay’s Bridge

Maxwell’s bridge is not suitable for high Q values.

Hay’s bridge is suitable for coils having high Q values.

In Hay’s bridge, capacitor is connected in series with the variable resistance, a change from the Maxwell’s bridge.

For larger phase angles, R1 is needed to be very low which is duly practical.

The bridge is shown below:

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Hay’s bridge

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Hay’s bridge

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For the balanced condition of the bridge:

Example

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Example

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Advantages and Disadvantages of Hay’s Bridge

Best suitable for inductances having Q factor higher than 10.

Quite simple expression for Q factor in terms of the bridge elements.

Disadvantage is that it is suitable only for the measurement of inductances with high Q factor.

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Schering bridge

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One of the most widely used AC bridge for the measurement of unknown capacitance, dielectric losses and power factor.

The Schering bridge is widely used for testing small capacitors at low voltages with very high precision.

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Schering bridge and its balance equations

Power Factor, loss angle and dissipation factor

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The dissipation factor is the reciprocal of Q factor and is given by:

High Voltage Schering bridge

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A stepped up transformer is used to rectify the errors caused by the Schering bridge low voltage measurements. This bridge is shown here:

Wien Bridge

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Primarily it is used to measure the frequency but it can also be used to measure an unknown capacitance with accuracy.

Wien bridge

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Hence 𝑓 = 1/2𝜋𝑅𝐶

Digital to Analog Conversion

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For the DAC the binary input is of the form:

And its subsequent Vout is given by the formula:

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The basic DAC symbol

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The DAC transfer characteristics

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DAC conversion techniques

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DAC: binary weighted

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DAC: binary weighted

Wide range of resistors are required. For an 8 bit DAC, the largest resistor is 128 times the smallest, hence greater chances of damaging the smallest resistor due to heavy current flow through it.

Integrated Circuit fabrication limitations when it comes to so many varying resistors.

Finite resistances of the switches disturb the resistors values and hence cause errors.

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Binary Weighed DAC Limitations

Inverted R-2R ladder DAC: an improved version

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Why this DAC is better?

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4 Bit R-2R Binary DAC

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Resolution of the R-2R DAC

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Example

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Advantages of R-2R DAC

Only Two resistors used, hence far more practical as compared to binary weighed ladder.

Any number of bits are possible by just adding more R-2R sections.

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Performance Parameters of DACs

Resolution: Could be defined in terms of the total number of the output values that could be provided by the DAC i.e 2n where n is the number of bits.

It could also be defined as the change in the output voltage of the DAC as a result of change in the LSB at the input only. This could be defined as:

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If we are using an 8 bit DAC the resolution of the DAC in terms of the possible output states would be 28 = 256.

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Accuracy: It could be defined as the difference between the actual output voltage of the DAC and the expected

output. It is expressed in percentage. It must be ±1

2of

its LSB. For the full scale output of 10.2, and for an 8 bit DAC, it could be given as:

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Monotonicty: Good monotonicity means the converter is not missing any steps while stepping through its entire range.

Conversion Time: Also called the setting time. It is the time required for the conversion from application of the digital input to the generation of final analog output voltage.

Settling Time: Time required by the DAC to get settled to ±

1

2𝐋𝐒𝐁 of its final value for a given digital input voltage i.e

zero to full scale.

Stability: The performance of the converter changes with temperature, age and power supply variations. Hence the relevant parameters such as offset, gain, linearity, error and monotonicity must be within a certain limit during the entire operating range of temperature and supply fluctuations. This constitute to stability.

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Week 4

Engineering

Transcript of Week 4