CSE 323a: Measurements &Testing (1)a

1. CSE 323a: Measurements &Testing (1)a 2013-2014

2. Grading Scheme Course webpage http://www.staff.zu.edu.eg/amabd/page.asp?id=59

3. References: • William Dunn, Introduction to Instrumentation, Sensors, and Process Control, Artech House, 2006. • William Bolton, Instrumentation and Control Systems, Elsevier, 2004. • Curtis Johnson, Process control instrumentation technology, Prentice-Hall, 6th edition, 2000.

4. Topics to be covered:

5. Lecture 1

6. Resistors, capacitors, and inductors The three basic passive elements used in electrical circuits.

7. Let us have a look at some useful slides from the course 6.091 offered at the Department of Electrical and Computer Science, MIT, available at: http://ocw.mit.edu/courses/electricalengineering-and-computer-science/

8. Resistors

9. Resistors • Used as loads in electrical circuits. • Resistor parameter: resistance, tolerance, and power rating. • Standard values: 10 12 15 18 20 22 27 33 39 47 56 68 82. • Common tolerances: ±5%, ±1%. • Resistor are color coded.

10. Resistor Color Codes

11. 2%, 1% Resistor Codes

12. Capacitors

13. Capacitors Used as dc blocking devices, in level shifting, integrating, differentiating, filters, and delay circuits.

14. Capacitors • Capacitors range from 1 pF (10-12) to 100,000 µF (10-1). • Typically, capacitors larger than 1 µF are polarized. • All capacitors have maximum voltage ratings.

15. Capacitors

16. How to read puff capacitor codes • Source: http://drakedev.com/pic/capacitors.php

17. Inductors

18. Inductors • Used as current limiting devices. • Found in relays, audio to electrical conversions, electromagnetic devices, light dimmers, and tuned circuits. • They are also the basis for transformers and motors.

19. Inductors

20. 3.2 Circuits with R, L, and C 3.2.1 Voltage Step Input

21. When the current in the resistor is maximum, the voltage across it is maximum, given by E = IR. i.e. the voltage is said to be in phase with the current. • For the capacitor, the voltage is zero when the current is maximum, and the voltage is a maximum when the current is zero. In this case, the voltage lags the current, or there is a phase shift between the voltage and the current of 90°. • The voltage across the capacitor builds up exponentially, at a rate determined by the values of R and C.

22. Step input to RL circuit

23. Similarly, the voltage and current in the resistor are in phase, but in the inductor are out of phase. The voltage leads the current by of 90°. • The voltage across the resistor increases exponentially, at a rate determined by the value of L and R.

24. Time constant • In RC circuit, the voltage across the capacitor, while charging, is given by: where E is the source voltage. • and while discharging, is given by:

25. Time constant • It is the time taken by the response to reach 63.2% of its full change. • The time constant of RC circuit is given by RC, while for RL circuit, it is L/R. • Practically, the response will complete its full change in 4 to 5 time constants.

26. Time constant • Applies not only to electrical circuits, but also to sensor outputs when there is a change in the measured variable. • The output signal from the sensor changes exponentially, so that there is a delay before the sensor output reaches its final value.

27. 3.2.3 Sine-wave inputs • Assuming that the circuit is capacitive.

28. In series RLC circuit, the same current will flow through all three devices. • When an ac sine wave is applied to RLC circuits, the same phase shift between voltage and current occurs as when a step voltage is applied: • IR and VRare in phase; • ICleads VCby 90°; • ILlags VLby 90°; • That is, • VCand VLare 180° out of phase; and • VCand VLare 90° out of phase with VR

29. Vector addition • Since the voltages and currents in capacitors and inductors are not in phase, they have impedance and not resistance. • Impedance and resistance cannot be directly added. • However, they can be combined using vectors.

30. E: supply voltage • VR, VL , VC are voltage across resistor, inductor, capacitor

31. Example • What is the current flowing in the series RLC if R = 27 kΩ, C = 2.2 nF, L = 33 mH, E = 20V and the input frequency = 35 kHz?

32. Resonance • XLand XCare frequency dependent. • As the frequency increases, XL and XC. • A frequency can be reached where XL= XC, and the voltage across these components are equal, opposite, and cancel. • At this frequency, Z=R, E=IR, and the current is maximum. • This frequency is called the resonant frequency of the circuit. • At resonance:

33. When the input frequency is below the resonant frequency XC> XL, the circuit is capacitive. • Above the resonant frequency XC< XL, the circuit is inductive. • Plotting the input current against the input frequency shows a peak at the resonant frequency as shown:

34. Example What is the resonant frequency of the series RLC if R = 27 kΩ, C = 2.2 nF, and L = 33 mH? What is the current at this frequency? The current can be obtained as (at resonance Z = R) I = E/R = 20/(27 x 103) = 0.740 mA