1. BASIC INSTRUMENTATION ELECTRICITY

2. Voltage and Current 1.5V R I I=V/R Q=P/R R Electrical current Liquid flow

3. Resistance Every substance has resistance Conductor is substance having low resistance Isolator is substance having high resistance 16 AWG wire resistance is ±12 Ω/km 18 AWG wire resistance is ± 20 Ω/km Question: –What is the resistance of 600 m 16 AWG wire?

4. Voltage Drop When current flows across a wire the voltage will drop Example PT I=16 mA V=24 V length= 500 m What is the voltage across the PT

5. Problem The allowed voltage for a Pressure Transmitter is 18V to 30 V. What is the maximum wire length if the power supply voltage in the control room is 24 V?

6. AC VOLTAGE AND CURRENT R V AC Frequency, f = 50 Hz/ 60 Hz T = 1/f = 1/50 = 0.02 s ω = 2πf  is the phase angle v(t) ωtωt VmVm 2π2π 0  v(t) = V m cos(ωt +  )

7. AC VOLTAGE and CURRENT in RESISTOR v(t) = V m cos ωt i(t) = v(t)/R = V m (cos ωt) /R = I m cos ωt I m = V m /R v(t) ωtωt VmVm i(t) ωtωt ImIm V and I in resistor are in phase R V AC

8. v(t) = V m cos ωt i(t) = I m cos ωt v(t) ωtωt 2π2π i(t) p(t) = v(t) i(t) = V m I m cos 2 ωt = V m I m {1+cos(2ωt )}/2 p(t)p(t) AC VOLTAGE, CURRENT and POWER in RESISTOR

9. CAPACITOR -------- ++++++++ + - Unit of C is F (Farad) 1 Farad = 1 Coul/Volt = 1As/V Real capacitor always have intrinsic capacitor and resistor with it

10. VOLTAGE AND CURRENT IN CAPACITOR v(t) = V m cos(ωt +  ) C V AC The current lead the voltage v(t) ωtωt VmVm 2π2π0 i(t) ImIm π/2

11. POWER IN CAPACITOR v(t) = V m cos(ωt +  ) p(t) = v(t) i(t) = V m I m cos (ωt +  )sin(ωt +  ) v(t) 2π2π i(t) + + - - p(t)p(t) C V AC

12. inductor i(t)i(t) Unit of L is H(Henry) 1 H = 1 Vs/A Inductor is made of coil and core. Real inductors always have intrinsic capacitor and resistor with it coil inductor core Equivalent Ckt of inductor

13. VOLTAGE AND CURRENT IN INDUCTOR v(t)v(t) for v(t) ωtωt VmVm 2π2π i(t) ImIm The voltage lead the current We have i(t)i(t)

14. POWER IN INDUCTOR v(t) =  V m sin(ωt +  ) v(t) 2π2π i(t) p(t) = v(t) i(t) = V m I m cos (ωt +  )sin(ωt +  ) + + - - p(t)p(t) v(t)v(t)

15. V and I in RL circuit for ωtωt  v i v(t)v(t) i(t)i(t)

16. Power in RL circuit v(t) ωtωt 0 i(t)  + + - - p(t)p(t) v(t)v(t) i(t)i(t)

17. VOLTAGE AND CURRENT RC CIRCUIT for v(t)v(t) i(t)i(t) C v(t) ωtωt i(t) 

18. Power in RC circuit v(t) ωtωt 0 i(t)  + + - - p(t)p(t) v(t)v(t) i(t)i(t) C

19. v ωtωt i v ωtωt i v ωtωt i p(t)p(t) AC VOLTAGE, CURRENT and POWER in R, L, and C (summery ) RESISTOR CAPACITOR INDUCTOR

20. Power in RC circuit v(t) ωtωt 0 i(t)  + + - - p(t)p(t) v(t) ωtωt 0 i(t)  + + - - p(t)p(t) RC CIRCUIT RL CIRCUIT

21. Phasors A phasor is a complex number that represents the magnitude and phase of a sinusoid:

22. Example for V and I phasor in resistor R V AC v(t) = V m cos(ωt +  ) i(t) = V m /R cos(ωt +  ) v(t) ωtωt i(t) I m /√2 Vm/√2Vm/√2 

23. Example for V and I phasor in capacitor v(t) = V m cos (ωt+  ) v(t) ωtωt VmVm 2π2π0 i( t) ImIm C V AC I m /√2 Vm/√2Vm/√2 

24. Example for V and I phasor in capacitor We can set the angle  arbitrarily. Usually we set the voltage is set to be zero phase abritrary v(t) = V m cos ωt Vm/√2Vm/√2 Im/√2Im/√2 Vm/√2Vm/√2  Im/√2Im/√2

25. Example for V and I phasor in inductor v(t)v(t) i(t)i(t) Here we can set the voltage to be zero phase, then the phase of current will be  Vm/√2Vm/√2 Im/√2Im/√2 Vm/√2Vm/√2 Im/√2Im/√2

26. Impedance By definition impedance (Z) is Z = V/I AC steady-state analysis using phasors allows us to express the relationship between current and voltage using a formula that looks likes Ohm’s law: V = I Z

27. Impedance (cont’d) Impedance depends on the frequency . Impedance is (often) a complex number. Impedance is not a phasor (why?). Impedance allows us to use the same solution techniques for AC steady state as we use for DC steady state. Impedance in series/parallel can be combined as resistors

28. Impedance of resistor R V AC v(t) = V m cos(ωt +  ) i(t) = V m /R cos(ωt +  ) I m /√2 Vm/√2Vm/√2  Z R = R

29. Impedance of capacitor C V AC I m /√2 Vm/√2Vm/√2  v(t) = V m cos (ωt+  )

30. Impedance of capacitor inductor v(t)v(t) i(t)i(t) ωLI m /√2 Im/√2Im/√2 Z L = jωL

31. Impedance Z L = jωL Z R = R

32. Impedance Example: f = 50Hz Find Z C Answer: Z c = 1/j  C  f =2 × 3.14 × 50 = 314 rad/s Z c = 1/j  C=1/(j × 314 × 10  6 ) Z c =  j3184.71 1F1F + -

33. Symbol of Impedance Z Impedance in series Impedance in parallel Z1Z1 Z2Z2 Z1Z1 Z2Z2 Z T = Z 1 + Z 2

34. Impedance in series example C = 15  F  R = 1K2 Z T = ? Answer: Z c = 1/j  C=1/(j × 314 × 15 × 10  6 ) Z c =  j212.31 Z T = 1200 – j212.31

35. Impedance in series example L = 5 m   R = 1K2 Z T = ? Answer: Z L = j  L=j × 314 × 5 × 10  3 Z L = j1.57 Z T = 1200 + j1.57

36. Impedance in series example Answer: Z T = 1200 – j212.31 + j1.57 = 1200 –j210.74 C = 15  F  R = 1K2 Z T = ? L = 5 m   Z L = j1.57 Z c =  j212.31

37. Impedance, Resistance, and Reactance Generally impedance consist of: The real part which is called Resistance, and The imaginary part which is called reactance Z = R + jX Resistanceimpedance reactance

38. Example: Single Loop Circuit 20k  + - 1F1F10V  0  VCVC + -  = 377 Find V C

39. Example (cont’d) How do we find V C ? First compute impedances for resistor and capacitor: Z R = 20k  = 20k  0  Z C = 1/j (377 1  F) = 2.65k  -90 

40. Impedance Example (cont’d) Then use the voltage divider to find VC: 20k  0  + - 2.65k  -90  V i =10V  0  VCVC + -

41. Impedance Example (cont’d) 20k  0  + - 2.65k  -90  V i =10V  0  VCVC + -

42. Complex Power Complex power is defined as S = VI * The unit of complex power is Volt Ampere (VA) S= VI * = I 2 Z = I 2 (R+jX) = I 2 R+jI 2 X = I 2 Z cos  +jI 2 Z sin  S = VI cos  +jVI sin  = P + jQ S is called apparent power and the unit is va P is called active power and the unit is watt and Q is called reactive power and the unit is var

43. SIGNAL CONDITIONER Signals from sensors do not usually have suitable characteristics for display, recording, transmission, or further processing. They may lack the amplitude, power, level, or bandwidth required, or they may carry superimposed interference that masks the desired information.

44. SIGNAL CONDITIONER Signal conditioners, including amplifiers, adapt sensor signals to the requirements of the receiver (circuit or equipment) to which they are to be connected. The functions to be performed by the signal conditioner derive from the nature of both the signal and the receiver. Commonly, the receiver requires a single-ended, low-frequency (dc) voltage with low output impedance and amplitude range close to its power-supply voltage(s).

45. SIGNAL CONDITIONER A typical receiver here is an analog-to-digital converter (ADC). Signals from sensors can be analog or digital. Digital signals come from position encoders, switches, or oscillator-based sensors connected to frequency counters. The amplitude for digital signals must be compatible with logic levels for the digital receiver, and their edges must be fast enough to prevent any false triggering. Large voltages can be attenuated by a voltage divider and slow edges can be accelerated by a Schmitt trigger.

46. Operational Amplifiers The term operational amplifier or "op-amp" refers to a class of high-gain DC coupled amplifiers with two inputs and a single output. The modern integrated circuit version is typified by the famous 741 op-amp. Some of the general characteristics of the IC version are:741 op-amp High input impedance, low output impedance High gain, on the order of a million Used with split supply, usually +/- 15V Used with feedback, with gain determined by the feedback network.

47. Inverting Amplifier

48. Non-inverting Amplifier For an ideal op-amp, the non-inverting amplifier gain is given by

49. Voltage Follower But this turns out to be a very useful service, because the input impedance of the op amp is very high, giving effective isolation of the output from the signal source. You draw very little power from the signal source, avoiding "loading" effects. This circuit is a useful first stage. The voltage follower is often used for the construction of buffer for logic circuits. The voltage follower with an ideal op amp gives simply

50. Current to Voltage Amplifier A circuit for converting small current signals (>0.01 microamps) to a more easily measured proportional voltage. so the output voltage is given by the expression above.

51. Voltage-to-Current Amp The current output through the load resistor is proportional to the input voltage

52. Summing Amplifier

53. Integrator

54. Differentiator

55. Difference Amplifier

56. Differential Amplifier