DC & AC METERS (continue)

CHAPTER OUTLINE 5 DC Ohmmeter 6 Introduction to AC meter 7 d’Arsonval meter movement (half-wave rectification) 8 d’Arsonval meter movement (full-wave 9 Loading effects of AC meter

OBJECTIVES Explain the purpose of Ohmmeter At the end of this chapter, students should be able to: Explain the purpose of Ohmmeter Describe the construction and operation of a basic Ohmmeter Describe the operation of half-wave rectifier circuit Trace the current path in a full-wave bridge rectifier circuit Calculate ac sensitivity and the value of multiplier resistors for half-wave and full-wave rectification

5 DC OHMETER The purpose of an Ohmmeter is to measure resistance Resistance reading is indicated trough a mechanical meter movement which operates on electric current. Thus, Ohmmeter must have an internal source of voltage to create current necessary to operate the movement. It also must have an appropriate ranging resistors to allow just the right amount of current. A simple Ohmmeter comprises battery and meter movement as in figure below:

5 DC OHMETER When there is infinite resistance (no continuity between test leads), there is zero current through the meter movement, and the needle points toward the far left of the scale. In this regard, the ohmmeter indication is "backwards" because maximum indication (infinity) is on the left of the scale, while voltage and current meters have zero at the left of their scales.

5 DC OHMETER If the test leads of the Ohmmeter are directly shorted together (measuring zero Ω), the meter movement will have a maximum amount of current through it, limited only by the battery voltage and the movement's internal resistance: With 9 volts of battery and only 500 Ω of internal movement resistance, current will be 18mA, which is far beyond the full-scale rating of the movement  will likely damage the meter.

5 DC OHMETER So, to avoid this, add series resistance to the meter’s circuit so that the movement just registers full-scale when the test leads are shorted together To determine the proper value for R, calculate the Rtotal needed to limit current to only 1mA (full-scale) with 9V of potential from the battery, then subtract the movement's internal resistance:

5 DC OHMETER Ohmmeters only function correctly when measuring resistance that is not being powered by a voltage or current source. In other words, you cannot measure resistance with an ohmmeter on a "live" circuit! The reason for this is simple: the ohmmeter's accurate indication depends on the only source of voltage being its internal battery. The presence of any voltage across the component to be measured will interfere with the ohmmeter's operation. If the voltage is large enough, it may even damage the ohmmeter.

EVALUATION Find the value of R, ¼ scale, ½ scale and ¾ scale of this Ohmmeter?

SUMMARY In this sub-topic, we have learned about: Ohmmeters contain internal sources of voltage to supply power in taking resistance measurements. An analog ohmmeter scale is "backwards" from that of a voltmeter or ammeter, the movement needle reading zero resistance at full-scale and infinite resistance at rest. Ohmmeters should never be connected to an energized circuit (that is, a circuit with its own source of voltage). Any voltage applied to the test leads of an ohmmeter will invalidate its reading.

3.6 INTRODUCTION TO AC METER Review Most meters use a moving coil. A coil of wire to which the pointer is attached is pivoted between the poles of a permanent magnet. When a current is present in the coil, it sets up a magnetic field that interacts with the field of the magnet to cause the coil to turn.

6 INTRODUCTION TO AC METER An ac meter measures ac voltages; a dc meter measures dc voltages. The actual scale calibration of commercially made (ac) voltmeters is almost always in terms of RMS (root mean square) values useful when variates are positive and negative, e.g., sinusoids For sine waves this is satisfactory, and useful since RMS is the standard measure at power-line frequency.

6 INTRODUCTION TO AC METER

6 INTRODUCTION TO AC METER There are two types of ac meters that will be discussed. i) Half-wave rectifier voltmeter ii) Full-wave rectifier voltmeter

6 INTRODUCTION TO AC METER AC Waveforms

6 D’ARSONVAL METER MOVEMENT (HALF-WAVE RECTIFICATION) Still remember our DC Voltmeter, using d’Arsonval MM? To measure ac with d’Arsonval MM, rectify the ac current by using a diode rectifier This process will produce a uni-directional current flow Several types of diode rectifiers are available: - copper oxide, vacuum diode, semiconductor diode etc. The d’Arsonval meter movement used in a DC voltmeter

3.6 D’ARSONVAL METER MOVEMENT (HALF-WAVE RECTIFICATION) If we add a diode to a DC Voltmeter, then we have a meter circuit capable of measuring ac voltage.

6 D’ARSONVAL METER MOVEMENT (HALF-WAVE RECTIFICATION) In half wave rectification, either the positive or negative half of the AC wave is passed, while the other half is blocked Because only one half of the input waveform reaches the output, it is very inefficient if used for power transfer Half-wave rectification can be achieved with a single diode in a one phase supply, or with three diodes in a three-phase supply. http://www.falstad.com/circuit/e-rectify.html

3.6 D’ARSONVAL METER MOVEMENT (HALF-WAVE RECTIFICATION) Now, suppose we replace the 10-Vdc with 10Vrms, what will happen? The voltage across the MM is just the positive ½ cycle of the sine wave because of rectifying action of the diode. The peak value of the ac sine wave is :

6 D’ARSONVAL METER MOVEMENT (HALF-WAVE RECTIFICATION) The MM will respond to the average value of sine wave where the average, or DC value equal to 0.318 times the peak value. The average value of the AC sine wave is :

6 D’ARSONVAL METER MOVEMENT (HALF-WAVE RECTIFICATION) Let say Vin=10Vrms Since the diode conducts only during positive half cycle, the average value over the entire cycle is one half the average value of 9V  4.5V Therefore, the pointer will deflect for a full scale if 10V dc is applied and 4.5V when a 10 Vrms sinusoidal signal is applied Thus, ac voltmeter is not as sensitive as dc voltmeter

6 D’ARSONVAL METER MOVEMENT (HALF-WAVE RECTIFICATION) In order to have a full scale deflection meter when a 10-Vrms is applied, we have to design the meter with Rs having 45% of Rs of DC Voltmeter. Since the equivalent DC voltage is 45% of RMS value, we can write like this:

EXAMPLE 9 Compute the value of Rs for a 10-Vrms AC range on the voltmeter shown in figure below. Given: Ein= 10-Vrms, Ifsd= 1mA, Rm=200Ω.

EXAMPLE 9 (solution)

6 D’ARSONVAL METER MOVEMENT (HALF-WAVE RECTIFICATION) Commercial AC voltmeter Rsh  increase current flow through D1 during the +ve ½ cycle  diode will be operating in linear region  improve linearity of AC meter during measurement of low voltage, but further reduces the ac sensitivity

6 D’ARSONVAL METER MOVEMENT (HALF-WAVE RECTIFICATION) Commercial AC voltmeter D2  +ve ½ cycle = no effect (Reverse-bias) -ve ½ cycle = provides an alternate path for reverse biased leakage current that would normally flow through meter movement and D1.

EXAMPLE 10 (a) Rs value (b) Sac (c) Sdc In the ½ wave rectifier shown below, D1 and D2 have an average forward resistance of 50Ω and are assumed to have an infinite resistance in reverse biased. Calculate the following: (a) Rs value (b) Sac (c) Sdc Given that Ein = 10-Vrms, Rsh = 200Ω, Ifs = Im=100µA, Rm = 200Ω

EXAMPLE 3.10(solution)

SUMMARY d’Arsonval MM can be used to measure both DC and AC current/ voltages. The MM will respond to the average value of sine wave where the average, or DC value equal to 0.318 times the peak value. Sac = 0.45Sdc

8 D’ARSONVAL METER MOVEMENT (FULL-WAVE RECTIFICATION) It is more desirable to use a full-wave rectifier in AC voltmeters because it shows higher sensitivity rating compared to ½ wave rectifier. The most frequently used circuit for full-wave rectification is the bridge-type rectifier, as shown below

8 D’ARSONVAL METER MOVEMENT (FULL-WAVE RECTIFICATION) Figure 2: Full-Wave Bridge Rectifier used in an AC voltmeter Positive ½ cycle Current flows from Vin trough D2, trough the MM from positive to negative, then trough D3. Negative ½ cycle Current flows from Vin trough D4, trough the MM from positive to negative, then trough D1.

8 D’ARSONVAL METER MOVEMENT (FULL-WAVE RECTIFICATION) Even though the polarity of Vin changes in every ½ cycle, the direction of current that flows through MM does not change. Since current flows through MM on both ½ cycles, then the deflection of MM will be greater compared to ½ wave rectification.

EXAMPLE 11 For the circuit below, given Vin = 10Vrms, Rm= 250Ω and Ifs = 1mA. Calculate: a) Vp b) Vave c) Sdc d) Sac e) Rs

EXAMPLE 11 (solution) Vp = 1.414 x Vrms = 1.414 x 10V = 14.14V Vave = 0.9 x Vrms = 0.9 x 10V = 9V Sdc = 1 / Ifsd = 1 / 1mA = 1kΩ/V Sac = 0.9 x Sdc = 0.9 x 1kΩ/V 0.9kΩ/V Rs = Sac x range – Rm = 0.9kΩ/V x 10V -250Ω = 8.75Ω

EXAMPLE 12 For the circuit below, given that Vin = 10Vrms, Rm=500Ω, Ifs = 1mA, Rsh=500Ω, average forward resistance of 50Ω and infinite reverse resistance of each diode, calculate the following: a) the multiplier, Rs b) the ac sensitivity, Sac c) the dc sensitivity Sdc.

9 LOADING EFFECTS OF AC METER As already being discussed, the sensitivity of AC Voltmeters, using either ½ wave or Full wave rectification, is always less than the sensitivity of the DC Voltmeters. Therefore, the loading effect of an AC Voltmeter is always greater than that of a DC Voltmeter.

9 LOADING EFFECTS OF AC METER Determine the reading obtained with DC voltmeter at RB when the switch is set at point A. Determine the reading at the same RB using ½ wave and Full wave rectifier AC meter respectively when the switch is set at point B. Given that Ifs = 100-mA and set at 10-V dc or rms range.

EXAMPLE 13 (solution)

ANY QUESTIONS?