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Electronic Instruments and Instrumentation Technology Dr. Shaikshavali Chitraganti EEE Department BITS Pilani Hyderabad Campus Lecture 04, Semester: Aug-Dec, 2017 Lecture-04: Study of Basic Analog meters Source: (T) Electronic Instruments & Instrumentation Technology by M.M.S. Anand, PHI, 2005. ...

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Electronic Instruments and Instrumentation Technology Dr. Shaikshavali Chitraganti EEE Department BITS Pilani Hyderabad Campus

Lecture 04, Semester: Aug-Dec, 2017

Lecture-04: Study of Basic Analog meters

Source: (T) Electronic Instruments & Instrumentation Technology by M.M.S. Anand, PHI, 2005. Chapter-1.

INSTR F311 - Lecture 03

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Contents

Ohm meter: series type, shunt type AC analog meters

INSTR F311 - Lecture 03

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Ohmmeter: Series type Objective: To compute the unknown resistance using Series type Ohmmeter

INSTR F311 - Lecture 03

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Ohmmeter: Series type Objective: To compute the unknown resistance using Series type Ohmmeter When Rx = ∞, Im = 0 =⇒ 0 current reading ≡ ∞ ohms

R1 : Current limiting resistor R2 : Zero adjust resistor Rx : Unknown resistor E: Internal batter voltage Rm : Internal resistance of PMMC INSTR F311 - Lecture 03

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Ohmmeter: Series type Objective: To compute the unknown resistance using Series type Ohmmeter When Rx = ∞, Im = 0 =⇒ 0 current reading ≡ ∞ ohms When Rx = 0, R2 is adjusted to get Im = If sd =⇒ Full scale current reading ≡ 0 Ω. It is used to design R1 and R2 ! R1 : Current limiting resistor R2 : Zero adjust resistor Rx : Unknown resistor E: Internal batter voltage Rm : Internal resistance of PMMC INSTR F311 - Lecture 03

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Ohmmeter: Series type Objective: To compute the unknown resistance using Series type Ohmmeter When Rx = ∞, Im = 0 =⇒ 0 current reading ≡ ∞ ohms

R1 : Current limiting resistor R2 : Zero adjust resistor Rx : Unknown resistor E: Internal batter voltage Rm : Internal resistance of PMMC INSTR F311 - Lecture 03

When Rx = 0, R2 is adjusted to get Im = If sd =⇒ Full scale current reading ≡ 0 Ω. It is used to design R1 and R2 ! How to verify R1 and R2 ? (i.e., Calibration)

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Ohmmeter: Series type Objective: To compute the unknown resistance using Series type Ohmmeter When Rx = ∞, Im = 0 =⇒ 0 current reading ≡ ∞ ohms

R1 : Current limiting resistor R2 : Zero adjust resistor Rx : Unknown resistor E: Internal batter voltage Rm : Internal resistance of PMMC INSTR F311 - Lecture 03

When Rx = 0, R2 is adjusted to get Im = If sd =⇒ Full scale current reading ≡ 0 Ω. It is used to design R1 and R2 ! How to verify R1 and R2 ? (i.e., Calibration) Rh : Internal resistance from terminals A and B

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Ohmmeter: Series type Objective: To compute the unknown resistance using Series type Ohmmeter When Rx = ∞, Im = 0 =⇒ 0 current reading ≡ ∞ ohms

R1 : Current limiting resistor R2 : Zero adjust resistor Rx : Unknown resistor E: Internal batter voltage Rm : Internal resistance of PMMC INSTR F311 - Lecture 03

When Rx = 0, R2 is adjusted to get Im = If sd =⇒ Full scale current reading ≡ 0 Ω. It is used to design R1 and R2 ! How to verify R1 and R2 ? (i.e., Calibration) Rh : Internal resistance from terminals A and B When Rx = Rh , it leads to for half scale deflection, i.e., I Im = f2sd (Why?) 4

Ohmmeter: Series type cont’d Step-1: Design R1 and R2 When Rx = 0, R2 is adjusted to get Im = If sd =⇒ Full scale current reading ≡ 0 Ω.

R1 : Current limiting resistor R2 : Zero adjust resistor Rx : Unknown resistor E: Internal battery voltage Rm : Internal resistance of PMMC

INSTR F311 - Lecture 03

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Ohmmeter: Series type cont’d Step-1: Design R1 and R2 When Rx = 0, R2 is adjusted to get Im = If sd =⇒ Full scale current reading ≡ 0 Ω. Rh = R1 +

R2 Rm R2 + Rm

R1 : Current limiting resistor R2 : Zero adjust resistor Rx : Unknown resistor E: Internal battery voltage Rm : Internal resistance of PMMC

INSTR F311 - Lecture 03

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Ohmmeter: Series type cont’d Step-1: Design R1 and R2 When Rx = 0, R2 is adjusted to get Im = If sd =⇒ Full scale current reading ≡ 0 Ω. Rh = R1 +

R1 : Current limiting resistor R2 : Zero adjust resistor Rx : Unknown resistor E: Internal battery voltage Rm : Internal resistance of PMMC

INSTR F311 - Lecture 03

It =

R2 Rm R2 + Rm

E , I2 = It −If sd , I2 R2 = If sd Rm Rh

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Ohmmeter: Series type cont’d Step-1: Design R1 and R2 When Rx = 0, R2 is adjusted to get Im = If sd =⇒ Full scale current reading ≡ 0 Ω. Rh = R1 +

R1 : Current limiting resistor R2 : Zero adjust resistor Rx : Unknown resistor E: Internal battery voltage Rm : Internal resistance of PMMC

INSTR F311 - Lecture 03

It =

R2 Rm R2 + Rm

E , I2 = It −If sd , I2 R2 = If sd Rm Rh

Solving the equations above: R2 =

If sd Rm Rh E−If sd Rh ,

R 1 = Rh −

If sd Rm Rh E

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Ohmmeter: Series type cont’d Step-1: Design R1 and R2 When Rx = 0, R2 is adjusted to get Im = If sd =⇒ Full scale current reading ≡ 0 Ω. Rh = R1 +

R1 : Current limiting resistor R2 : Zero adjust resistor Rx : Unknown resistor E: Internal battery voltage Rm : Internal resistance of PMMC

It =

R2 Rm R2 + Rm

E , I2 = It −If sd , I2 R2 = If sd Rm Rh

Solving the equations above: R2 =

If sd Rm Rh E−If sd Rh ,

R 1 = Rh −

If sd Rm Rh E

Step-2: Verify R1 and R2 When Rx = Rh , it must lead to I half scale deflection, i.e., Im = f2sd

INSTR F311 - Lecture 03

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Ohmmeter: Series type cont’d Exercise-1: In the circuit below, a 1mA meter movement with an internal of 50Ω is to be used. The battery voltage is 3V. Half-scale deflection should be for 2500Ω 1. Calculate the values of R1 and R2 2. Find the change in the value of R2 if the battery voltage reduces by 10% 3. What is the half-scale deflection if battery voltage reduces by 10%?

Try! INSTR F311 - Lecture 03

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Ohmmeter: Shunt type

Used for low values of resistance

INSTR F311 - Lecture 03

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Ohmmeter: Shunt type

Used for low values of resistance When Rx = 0 & switch is closed, then Im = 0 =⇒ 0 current reading ≡ 0 ohms

INSTR F311 - Lecture 03

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Ohmmeter: Shunt type

Used for low values of resistance When Rx = 0 & switch is closed, then Im = 0 =⇒ 0 current reading ≡ 0 ohms When Rx = ∞, then R1 is adjusted to get Im = If sd =⇒ Full scale current reading ≡ ∞ ohms.

INSTR F311 - Lecture 03

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Ohmmeter: Shunt type

Used for low values of resistance When Rx = 0 & switch is closed, then Im = 0 =⇒ 0 current reading ≡ 0 ohms When Rx = ∞, then R1 is adjusted to get Im = If sd =⇒ Full scale current reading ≡ ∞ ohms. In this case If sd =

INSTR F311 - Lecture 03

V V =⇒ R1 = −Rm R1 + Rm If s

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Ohmmeter: Shunt type cont’d For calibration, what is the value of Rx that will give half scale delflection? With such Rx ,   If sd V Rx Im = = . Rx 2 Rx + Rm R1 + RRmm+R x (1) From previous slide If sd =

V . R1 + Rm

(2)

Using (1) and (2), Rx = INSTR F311 - Lecture 03

R1 Rm . R1 + Rm 8

Ohmmeter: Shunt type cont’d

Exercise-2: In the circuit below, a 1 mA meter movement with an internal resistance if 50Ω is to be used. The battery voltage is 3V. Half-scale deflection should be for 0.5Ω. Calculate the values of R1 and Rsh .

Try!

INSTR F311 - Lecture 03

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Decibel (dBm scale)

Measurements in audio frequency are often expressed in dBm scale to accommodate wide range of frequencies, which is not possible on linear scale; dBm is expressed in terms of logarithm scale In terms of power (P Watts ≡ 10 log P ) or voltages (V Volts ≡ 20 log V )

INSTR F311 - Lecture 03

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AC Analog meters

PMMC meter movements do not work correctly if directly connected to alternating current, because direction of the needle movement changes with each half-cycle of the ac ac must be rectified to dc before applying to PMMC

INSTR F311 - Lecture 03

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Half-wave Rectifier-based Meter

Ip =

Vp Rs + Rm

Ip (Vp ): Peak value of the current (voltage)

INSTR F311 - Lecture 03

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Half-wave Rectifier-based Meter

Ip =

Vp Rs + Rm

Ip (Vp ): Peak value of the current (voltage) For low frequency, deflection follows current variations

INSTR F311 - Lecture 03

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Half-wave Rectifier-based Meter

Ip =

Vp Rs + Rm

Ip (Vp ): Peak value of the current (voltage) For low frequency, deflection follows current variations For high frequency, the deflection converges upon the average value of the current

INSTR F311 - Lecture 03

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Half-wave Rectifier-based Meter

Ip =

Vp Rs + Rm

Ip (Vp ): Peak value of the current (voltage) For low frequency, deflection follows current variations For high frequency, the deflection converges upon the average value of the current Z π  Z 2π 1 Ip Iav = IP sinθdθ + 0dθ = 2π 0 π π INSTR F311 - Lecture 03

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Half-wave Rectifier-based Meter cont’d

For ac voltmeters, the scale is calibrated in rms value, s Z 2π 1 Vp Vrms = Vp2 sin2 θdθ = √ 2π 0 2

Vrms

INSTR F311 - Lecture 03

= 0.707Vp = 0.707Ip (Rs + Rm ) 0.707 = Iav (Rs + Rm ) 0.318

(∵ Ip = πIav )

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Half-wave Rectifier-based Meter cont’d

For ac voltmeters, the scale is calibrated in rms value, s Z 2π 1 Vp Vrms = Vp2 sin2 θdθ = √ 2π 0 2

Vrms

= 0.707Vp = 0.707Ip (Rs + Rm ) 0.707 = Iav (Rs + Rm ) 0.318

This leads to Rs = 0.45

INSTR F311 - Lecture 03

Vrms − Rm Iav

(∵ Ip = πIav )

(1)

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Half-wave Rectifier-based Meter cont’d

For ac voltmeters, the scale is calibrated in rms value, s Z 2π 1 Vp Vrms = Vp2 sin2 θdθ = √ 2π 0 2

Vrms

= 0.707Vp = 0.707Ip (Rs + Rm ) 0.707 = Iav (Rs + Rm ) 0.318

This leads to Rs = 0.45

Vrms − Rm Iav

(∵ Ip = πIav )

(1)

What does Rs denote?

INSTR F311 - Lecture 03

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Half-wave Rectifier-based Meter cont’d

Figure:

INSTR F311 - Lecture 03

Practical half-wave rectifier voltmeter

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Half-wave Rectifier-based Meter cont’d

Figure:

Practical half-wave rectifier voltmeter

In the negative half cycle D2 conducts, thus shunting all the current to safeguard the Ammeter.

INSTR F311 - Lecture 03

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Half-wave Rectifier-based Meter cont’d

Figure:

Practical half-wave rectifier voltmeter

In the negative half cycle D2 conducts, thus shunting all the current to safeguard the Ammeter. ( Rs + Rm in the positive-half cycle Input resistance = Rs in the negative-half cycle

INSTR F311 - Lecture 03

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Half-wave Rectifier-based Meter cont’d

Figure:

Practical half-wave rectifier voltmeter

In the negative half cycle D2 conducts, thus shunting all the current to safeguard the Ammeter. ( Rs + Rm in the positive-half cycle Input resistance = Rs in the negative-half cycle Since Rs  Rm , input resistance= Rs through out the cycle INSTR F311 - Lecture 03

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Half-wave Rectifier-based Meter cont’d

From (1), Rs = 0.45

INSTR F311 - Lecture 03

Vrms − Rm Iav

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Half-wave Rectifier-based Meter cont’d

From (1), Rs = 0.45

Vrms − Rm Iav

Let

Figure:

Practical half-wave

rectifier voltmeter

INSTR F311 - Lecture 03

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Half-wave Rectifier-based Meter cont’d

From (1), Rs = 0.45

Vrms − Rm Iav

Let If sd : Full scale average current Vf sd : Full scale deflection rms votlage

Figure:

Practical half-wave

rectifier voltmeter

INSTR F311 - Lecture 03

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Half-wave Rectifier-based Meter cont’d

From (1), Rs = 0.45

Vrms − Rm Iav

Let If sd : Full scale average current Vf sd : Full scale deflection rms votlage & since Rs  Rm Input resistance Rs ≈ 0.45 Figure:

Practical half-wave

rectifier voltmeter

INSTR F311 - Lecture 03

where Sac = voltmeter

0.45 If sd

Vf sd = Sac Vf sd If sd

is the ac sensitivity of the

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Reducing the effect of nonlinearity Nonlinearity is maximum at low values of current. To reduce nonlinearity, operate diode in linear range via operating at relatively high values of current

INSTR F311 - Lecture 03

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Reducing the effect of nonlinearity Nonlinearity is maximum at low values of current. To reduce nonlinearity, operate diode in linear range via operating at relatively high values of current

Reduce Rs and connect Rsh in parallel, which increase the current through the diodes INSTR F311 - Lecture 03

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Reducing the effect of nonlinearity Nonlinearity is maximum at low values of current. To reduce nonlinearity, operate diode in linear range via operating at relatively high values of current

Reduce Rs and connect Rsh in parallel, which increase the current through the diodes What is the trade-off? INSTR F311 - Lecture 03

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Reducing the effect of nonlinearity cont’d

If Rsh = Rm , then the current though diode D1 doubles to 2Iav in order for the ammeter to draw Iav . In general case Rs = 0.45

Vrms − (RD + (Rsh kRm )) (Try!) 2Iav

where RD : the diode forward resistance

INSTR F311 - Lecture 03

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Reducing the effect of nonlinearity cont’d

If Rsh = Rm , then the current though diode D1 doubles to 2Iav in order for the ammeter to draw Iav . In general case Rs = 0.45

Vrms − (RD + (Rsh kRm )) (Try!) 2Iav

where RD : the diode forward resistance ac sensitivity: Sac =

INSTR F311 - Lecture 03

0.45 2If sd

(sensitivity is reduced!)

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Reducing the effect of nonlinearity cont’d

If Rsh = Rm , then the current though diode D1 doubles to 2Iav in order for the ammeter to draw Iav . In general case Rs = 0.45

Vrms − (RD + (Rsh kRm )) (Try!) 2Iav

where RD : the diode forward resistance ac sensitivity: Sac =

0.45 2If sd

(sensitivity is reduced!)

How to improve sensitivity? INSTR F311 - Lecture 03

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Full-wave Rectifier-based meter

Average current Iav =

2Ip π

− Rm (Try!) Multiplier resistance Rs = 0.9 VIrms av Sensitivity Sac = rectifier) INSTR F311 - Lecture 03

0.9 If sd

(Sensitivity is double that of the half-wave 18

Voltmeters for nonsinusoidal waveform input Average value need not be rms value Form factor= VV¯rms av

i hR t +T V¯av = T1 t00 |V (t)|dt (different from expression in text book) q R t +T Vrms = T1 t00 V 2 (t)dt

0.707Vp (2/pi)Vp = 1.11 1V Rectangular wave form: Form factor = 1Vpp = 1 Triangular wave form: Form factor = 0.577V 0.5V = 1.154

Sinusoidal wave form: Form factor =

INSTR F311 - Lecture 03

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Thank You!!

INSTR F311 - Lecture 03

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