EML 4314C

1
EML 4314C

• Exam 1 Review

2
Topics

• Digital Data Acquisition
• Lab 1 characteristics of A/D and D/A
  converters, aliasing
• AC Circuits and Filtering
• Lab 2 filter response amplitude and phase
  shift of output signal compared to that of input
  signal
• Microcontrollers
• Lab 3 microprocessors
• Modeling of 2nd Order Systems
• Lab 4 modeling and solving equations of motion
• Parameter Identification
• Lab 5 From set of system responses determined m,
  k, c, and Lo

3
Data Acquisition

• description of A/D converter
• number of bits
• range, resolution, quantization error
• how digital value is calculated based on bins

4
Data Acquisition

• discrete sampling

5
Data Acquisition

• incorrect conclusions
• clipping
• aliasing

6
Data Acquisition

• aliasing

7
Data Acquisition

• folding diagram

8
Topics

• Digital Data Acquisition
• Lab 1 characteristics of A/D and D/A
  converters, aliasing
• AC Circuits and Filtering
• Lab 2 filter response amplitude and phase
  shift of output signal compared to that of input
  signal
• Microcontrollers
• Lab 3 microprocessors
• Modeling of 2nd Order Systems
• Lab 4 modeling and solving equations of motion
• Parameter Identification
• Lab 5 From set of system responses determined m,
  k, c, and Lo

9
Filtering

• sinusoidal signals v(t) Vm sin(?tf)
• frequency and phase angle
• period (time to complete one cycle)

10
Filtering

• Eulers formula for representing sinusoidal
  signals ej?t cos (?t) j sin (?t)
• imaginary part represents sine wave (projection
  of rotating vector on imaginary axis)
• often written as v(t) Vm ej?t

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• circuit analysis
• resistor
• v(t) Vm sin(?t)
• i(t) Vm/R sin(?t)
• inductor
• v(t) Vm sin(?t)
• capacitor
• v(t) Vm sin(?t)
• i(t) ?C Vm sin(?t 90º)

current in phase
current lags
current leads
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• now lets use the complex notation to describe
  the relationship between current and voltage
• resistor VR R IR
• inductor VL j ? L IL (current
  lags voltage by 90º)
• capacitor VC 1/(j?C) IC (current leads
  voltage by 90º)

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Filtering

• low-pass
• high-pass
• band-pass
• band-stop

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Filtering

• design of 1st order low-pass filter using
  capacitor and resistor

f arctan(-?RC)
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Filtering

• design of 1st order high pass filter

16
Filtering

• first order band-pass filter

17
Filtering

• 2nd order low-pass filter

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Topics

• Digital Data Acquisition
• Lab 1 characteristics of A/D and D/A
  converters, aliasing
• AC Circuits and Filtering
• Lab 2 filter response amplitude and phase
  shift of output signal compared to that of input
  signal
• Microcontrollers
• Lab 3 microprocessors
• Modeling of 2nd Order Systems
• Lab 4 modeling and solving equations of motion
• Parameter Identification
• Lab 5 From set of system responses determined m,
  k, c, and Lo

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Microprocessors
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our chip
16F627
This powerful (200 nanosecond instruction
execution) yet easy-to-program (only 35 single
word instructions) CMOS Flash-based 8-bit
microcontroller packs Microchip's powerful PIC
architecture into an 18-pin package and is
upwards compatible with the PIC16C62XA, PIC16C5X
and PIC12CXXX devices. The PIC16F627 features
4MHz internal oscillator, 128 bytes of EEPROM
data memory, a capture/compare/PWM, a USART, 2
Comparators and a programmable voltage reference
that make it ideal for advantage analog /
integrated level applications in automotive,
industrial, appliances and consumer applications.
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power circuitry
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our application
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reading and writing to pins

• by default, TRISA and TRISB are set to 1111 1111
  which means that all the pins RA0?RA7 and RB0?RB7
  are set as input pins
• clearing bit n in TRISB will set pint RBn as an
  output pin
• the 8 bits of PORTA correspond to the pins
  RA0?RA7
• the 8 bits of PORTB correspond to the pins
  RB0?RB7
• output pin example
• if bit 3 in TRISA has been cleared (set to 0),
  i.e. 1101 1111, then pin RA3, is set as an output
  pin
• setting bit 3 in PORTA to 1 will cause pin RA3 to
  have a potential of 5V
• clearing bit 3 in PORTA will cause pin RA3 to
  have a potential of 0V
• input pin example
• if bit 2 in TRISA has been set, then pin RA2 is
  set as an input pin
• pin 2 of the register PORTA can be checked at any
  time to determine whether pin RA2 is at 5V or 0V

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our program

• set pin 17 as an input pin
• set pin 6 as an output pin
• loop_label
• read state of pin 17
• set state of pin 6 to state of pin 17
• goto loop_label

25
Topics

• Digital Data Acquisition
• Lab 1 characteristics of A/D and D/A
  converters, aliasing
• AC Circuits and Filtering
• Lab 2 filter response amplitude and phase
  shift of output signal compared to that of input
  signal
• Microcontrollers
• Lab 3 microprocessors
• Modeling of 2nd Order Systems
• Lab 4 modeling and solving equations of motion
• Parameter Identification
• Lab 5 From set of system responses determined m,
  k, c, and Lo

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Spring-Mass-Damper System
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Solution of Diff E Using Laplace Transform

• L(f '(t)) sL (f) - f(0)
• L (f "(t)) s2L (f) - sf(0) - f'(0)

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Analysis of system with no damping

• no driving force no initial velocity

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Analysis of system with no damping
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Analysis of system with damping
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Analysis of system with damping
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Analysis of system with damping
c25
c250
c2.5
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Analysis of system with damping

• solved for time response when there is small
  damping, i.e. c2 lt 4 m1 k1

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Topics

• Digital Data Acquisition
• Lab 1 characteristics of A/D and D/A
  converters, aliasing
• AC Circuits and Filtering
• Lab 2 filter response amplitude and phase
  shift of output signal compared to that of input
  signal
• Microcontrollers
• Lab 3 microprocessors
• Modeling of 2nd Order Systems
• Lab 4 modeling and solving equations of motion
• Parameter Identification
• Lab 5 From set of system responses determined m,
  k, c, and Lo

35
Parameter Identification
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Parameter Identification
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Parameter Identification

• we can measure the frequency that will give us

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Parameter Identification
Use the logarithmic decrement, d, to find ?

• L01 can be obtained from the data as the steady
  state position
• (x1(t1)-L01) and (x1(tn)-L01) can be measured
• solve for ?

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Parameter Identification

• add a known mass ?m to the car and obtain ?2 and
  then ?n2

• use a large ?m so ?n and ?n2 will differ enough
  so that any error in measuring the frequencies
  will not significantly impact the calculations
• Lastly, determine c for
• the two cases from ?

40
Topics

• Digital Data Acquisition
• Lab 1 characteristics of A/D and D/A
  converters, aliasing
• AC Circuits and Filtering
• Lab 2 filter response amplitude and phase
  shift of output signal compared to that of input
  signal
• Microcontrollers
• Lab 3 microprocessors
• Modeling of 2nd Order Systems
• Lab 4 modeling and solving equations of motion
• Parameter Identification
• Lab 5 From set of system responses determined m,
  k, c, and Lo