ANALOG ELECTRICAL METERS

1. ANALOG ELECTRICAL METERS INSTRUMENTATION ENGINEERING EE531.

2. OBJECTIVE • Design instruments to measure electrical signals ( current, voltage and resistance) by using a PMMC meter and characterize they error.

3. ANALOG ELECTRICAL METERS. Summary: • PMMC meter. • Current Measurement. • AC and DC Volltage Measurement. • Loading effect • Resistor Measurement (Ohmmeter). • Multímeter

4. PMMC Movement or Meter • Permanent Magnet Moving Coil Meter (PMMC). • As the deflection is directly proportional to the current passing through the meter (torques are constant) we get a uniform (linear) scale for the instrument. • The interaction force between Magnet field and current provokes a torque and deflection of the pointer. Finally the pointer is stopped in some point of the scale by the balanceof spring.

6. PMMC Characteristics. • It is only sensible to mean value DC current . • Polarity • Maximum current limited by power dissipation in the coil, tipically 10mA. • Minimum limited for mechanical friction, typically 10uA • Low power consume. • High sensitivity. • Linear. • Accurate. • No influyen campos mágneticos externos. • Typical parameters: internal resistance 1000 ohms and maximum current 100 uA.

7. PMMC Electrical Model resistor Rm is determined by the coil resistance. Típically 1000 Ohms. I ≤Im

8. Ammeter shunts. How can we increase the Range of some PMMC? I ≥ Im ?? Solution: When heavy currents are to be measurement, greater than maximum current values , the major part of the current is bypassed through a low resistance called shunt

9. Shunt calculation Rsh. • Given rm and Im and the new maximum current to measure I. • The shunt resistor and the internal Resistor are in parallel. • We have a node, where the total current I is equal to the sum of Im and Ish. • If Rsh < rm , most of the current flows through the shunt

10. Shunt calculation Rsh. If we impose some relation n between I and Im (new scale value) Notice that linearity of scale remains the same. Why?

11. Example 1. • Calculate the required Shunt resistor to convert a PMMC with range 0-10mA into an ammeter of 1mA FSD. • Given rm= 100 Ohm

12. Solution. Example 1. 1- We calculate the maximum voltage drop in the meter. 2- We calculate the current through the shunt 3- We get Rsh.

13. Multiple range Ammeter Ayrton Shunt

14. Ayrton Shunt Calculation. • Step 1. With the low scale current value Ia we obtain the initial shunt, which is given by the sum of all the Resistors.

15. Ayrton Shunt Calculation.. • Step 2. To get the next scale Ib>Ia we move the swich . Notice that now we have a new shunt with Rb+Rc that is in parallel with Rm plus Ra.

16. Ayrton Shunt Calculation... • Step 3. We repeat step 2 many times as new high current scales we have. To get Ic we move the switch . Now we have a shunt given by Rc in parallel with Rm plus Ra+Rb.

17. Voltage Measurement If we connect some voltage directly into a PMMC, the low internal resistance rm provokes a high current value ( I>>Im) and the meter can be damaged. Only very low voltages can be measured directly V≤ Vm For example if rm=1000  and Im=100 μA  100 mV !!!

18. Voltage Measurement The solution is to put a multiplier resistor in series with the meter. This is equivalent to increase the resistance that we see from the input. The voltage range Vm is given by:

19. DC Sensitivity of PMMC • It is defined by the inverse of Im. • A meter with Im=100 uA has Sdc of: To build a 10 V FSD the series resistor is given by: The input resistance is 100KOhms and we see that Ri depends on the FSD. Is it good?.

20. Multiple scale Voltmeter

21. AC Voltmeter • PMMC is not sensitive to AC signals. It can’t detect AC with zero mean value. • It can’t follow high frequency variations. • Solution 1: to employ other meters , for example thermocouple meters. • Solution 2. by employing a rectifier element which converts AC. to a unidirectional DC with some mean value

22. AC Rectifiers for AC voltmeters • Two options: half wave or full wave rectifier. • The meter only detect the mean value of the rectified signal. • The design parameter is some effective value Vrms. • If the signal is sinusoidal we can obtain the peak value Vpk. But there is a known relationship for mean value and peak value of a sinusoidal signal:

23. AC Rectifiers for AC voltmeters • So we get a relationship between mean value and Vrms (valid only for sinusoidal signals) • The design procedure for AC Voltmeter can be state as the same design of a DC voltmeter with a range igual to the mean value of the rectified Vrms value.

24. AC Rectifiers for AC voltmeters • The design methodologies for AC and DC are the same: calculate the series resistor but for AC we use the VRMS range and the AC Sensitivity

25. Half wave rectifier for AC voltmeter.

26. Practical Half wave rectifier

27. Full wave rectifier for AC voltmeter. Notice that these methods are based in to assume perfect sinusoidal signal. Also we have a high error for low Vrms values . Why ? A better solution can be implemented with electronic instruments.

28. Loading effect in Ammeters We get that the measured current is less than the “true current”. It is a systematic error. It is a general result, the instruments always affect the value of the magnitudes that they process. It can be reduced by lowering Rm

29. Loading effect in Voltmeters The measured voltage is also less than the true voltage. It is a systematic error. It can be reduced by increase the input impedance of the voltmeter. But the input resistance of voltmeters depends on the voltage range. It limits the design of low range voltmeters.

30. Resistor Measurement The current I is a function of RXY We set up RS to get Im when short circuit xy.

31. Resistor Measurement When we connected RX the current decreases. If Rx increases I decreases. We can calibrate the current scale in resistance values. But the result scale is inverted and it is not linear.

32. Resistor Measurement We normalize the measured current with Rx to Im We define a half scale point value design given by Ro. Summarizing, electrical ohmmeter presents a non linear inverted scale. The design procedure is obtain the value of RS capable to indicate half scale value when the resistance has a Ro value.

33. Example 2 A PMMC have rm=100 Ohms and a battery of 3V is used to build a Ohmmeter with a resistor ( RZ ) of2.9Kohms, we obtain the following results

34. Example 2….

35. Series ohmmeter When battery drops we get some error because we can get Im when we short Rxy. In practice we split Rs in two elements a potentiometer and a fixed value resistor. But this method has some inconvenient. What?

36. Multirange Ohmmeter

37. Modified serial Ohmmeter To overcome the problem of battery drop we can use this circuit. Notice that R2 is Shunt resistor. So we have a ammeter with increased range. When the battery drops We adjust R2 and the design point changes a little bit.

38. Parallel Ohmmeter.

39. ANALOG MULTIMETER

40. Ohmmeter Applications. • Continuity check. • Detecting Diode and transistor Junction • Leak test in capacitors.

41. ESTUDIO INDEPENDIENTE • Obtenga el modelo eléctrico equivalente de un mecanismo con resistencia de shunt. • Deduzca el algoritmo del Shunt de Ayrton y analice el ejemplo 2.3 (pag. 25) del texto. • Estudie los ejemplos 2.5 y 2.6 (pag 27)de voltímetros de CD. • Estudie los ejemplos 3.1, 3.2 y 3.3 relativos a voltímetros de CA. • Estudie los ejemplos 2.7 y 2.8 relativos a efecto de carga. • Calcule la escala de ohmetro diseñado en el ejemplo2. Grafique los resultados en Matlab. • Rediseñe el ejemplo 2 teniendo en cuenta el envejecimiento de la batería. • Consulte el libro de texto, sección 2.11 y ejemplo 2.14 sobre ohmetros de campo múltiple.

42. CONCLUSION • With a PMMC we can build instruments to measure DC and AC voltages and currents, and resistors values with multiple range . • We get a systematic error that is termed loading effect when we connect the instruments. • Current and voltages scales are linear. • Ohmmeter scales are nont linear and inverted. Ohmeter instrument needs periodic calibration due to battery aged. • AC measurements are indirect measurements. They don’t show the true value of Vrms and are limited to 100% sinusoidal signals. Also are limited to high voltage values around the order of line voltage.