Week 3

INSTRUMENTATION & MEASUREMENTS(EE-302)

WEEK 3

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Measurement of High Resistance

Such resistances may include:

insulation resistance of machines and cables.

Leakage resistance of capacitors

Resistance of high voltage circuit elements like vacuum tubes etc.

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Very small current due to high resistance, hence its measurement difficult.

Leakage currents comparable with the measurement current, hence errors possible.

Stray charges due to electrostatic effects.

Insulation resistance measurement at times involves a certain time delay between application of the test voltage and subsequent measurement of resistance. For accurate measurements, this time delay has to be mentioned accurately.

Requirement of high applied test voltage since resistances are high.

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Measurement of High Resistance: Difficulties

Use of Guard Circuits

Used to eliminate errors due to leakage currents.

Provide a bypass mechanism for the leakage current so that it could not get mixed with the actual measurement current.

A typical guard arrangement is shown below:

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Guard Circuit

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A Guard terminal is added to the resistance terminal block.

Terminal surrounds the resistance entirely, connecting it to the battery side of the ammeter.

The leakage current IL has now a separate path to circulate and bypass the micro ammeter.

Actual guard arrangement is shown below:

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Guard Circuit

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Guard Circuit: practical implementation

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Guard Circuit: used with the bridge

AC Bridges

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Sources & Detectors

At very low frequencies, the power line itself can act as source of supply.

For high frequencies, electronic oscillators are used as supply.

A typical oscillator has a range of 50 Hz to 125kHz with a power output of around 7 W.

Common detectors for AC bridges are Headphones, Vibration galvanometers and Tunable amplifier detectors.

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Headphones: from 250 Hz upto 4kHz.

Vibration Galvanometers: low audio frequencies 5 Hz to 1000 Hz.

Tunable amplifier detectors: 10 Hz to 100 kHz.

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Bridge balance equations

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The summary….

THE PRODUCTS OF THE MAGNITUDES OF THE OPPOSITE ARMS MUST BE EQUAL WHILE SUM OF THE PHASE ANGLES OF THE OPPOSITE ARMS MUST BE EQUAL.

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Example

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Example (contd.)

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Capacitance Comparison bridge

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Capacitance comparison bridge

For this bridge the ratio arms are resistive in nature.

Z3 consists of known standard capacitance.

R3 is the variable resistance used to balance the bridge.

Z4 contains Cx the unknown capacitance and its small leakage resistance Rx.

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Capacitance comparison bridge

For this bridge, under the balanced condition:

Example

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Inductance Comparison bridge

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By this bridge unknown inductance and its internal resistance can be calculated.

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Example

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Maxwell’s Bridge

Maxwell’s bridge can be used to measure inductance by comparison either with a variable standard self inductance or with a standard variable capacitance.

Thus divided into:

Maxwell’s Inductance Bridge

Maxell’s Inductance Capacitance Bridge

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Maxwell’s Inductance bridge

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Inductance can be measured by comparing it with a standard variable self inductance.

Note that two branches 1 and 2 have non inductive resistances R1 and R2.

Standard inductance L3 is accompanied by its resistance ‘r’ serially connected with it.

One arm contains the unknown inductance Lx.

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Maxwell’s Inductance bridge under balance: Phasor Diagram

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Maxwell’s Inductance Capacitance bridge

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Maxwell’s Inductance Capacitance bridge: Phaserdiagram

Since the bridge contains one arm in which the resistance and inductance is in parallel, hence it would be better to write the equations in the admittance form.

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Advantages of using standard known capacitor for measurement

Less expensive as compared to inductors.

Almost lossless.

External fields have lesser effect on the capacitor as compared to inductor.

Comparatively quicker measurement.

Smaller in size.

Greater reliability

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Advantages of Maxwell’s bridge

Balance equation is independent of the losses associated with the inductor.

Balance equation is independent of frequency.

Scale of resistance could be calibrated to read the inductance directly.

Scale of R1 could be calibrated to read the Q value directly.

When the bridge is under balance the only component in series with the coil is R2. If R2 is chosen so that it could carry high current, then heavy current carrying coils can also be tested.

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Limitations of the Maxwell’s bridge

Useful only for the low Q values measurement ( i.e Q varies from 1 to 10). Its proof is thru the phase balance condition. We kn𝑜𝑤 that 𝜃1+ 𝜃4 = 𝜃2+ 𝜃3, but 𝜃2 𝑎𝑛𝑑 𝜃3 are zero because of the pure resistances. For high Q values, 𝜃4 is almost 900. Hence 𝜃1should be -900, for which the value of R1 should be very high as 𝜃1 is governed by the parallel combination of R1 and C1. Practically such high resistances are not possible.

Interaction between the balance of resistance and reactance, thus balancing a bit tricky and difficult.

Not suitable for coils having Q<1 because of the balance convergence problem.

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Though the bridge balance equations are independent of frequency, but practically the properties of coils under test may vary with frequency, which can cause errors.

Commercial Maxwell bridge measures the inductance from 1-1000H with an error of about ± 1%.

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Limitations of the Maxwell’s bridge

Example

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Example

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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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Week 3

Engineering

Transcript of Week 3