2. Outlines of Filters
input output
Filter
Filtering:
Certain desirable features are retained
Other undesirable features are suppressed
Dr. Ashraf Saleem 2
3. Classification of Filters
Signal Filter
Analog Filter
A l Filt Digital Filter
Di it l Filt
Element Type Frequency Band
Active Passive Low-Pass Band-Pass All-Pass
High-Pass Band-Reject
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4. Classification of Filters
Filter classification according to
g
implementation
Active filters include RC networks and op-amps
Suitable for low frequency, small signal
Active filters are preferred since avoid the bulk and non-linearity
of inductors. However, active filters require a power supply
, q p pp y
Passive filters consist of RCL networks
Simple, more suitable for frequencies above audio range, where
active fil
i filters are li i d b the op-amp b d id h
limited by h bandwidth
Digital filters
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5. Classification of Filters
Filter classification according to frequency response
Low-pass filt
L filter
High-pass filter
Band pass
Band-pass filter
Band-stop (Notch) filter
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6. State-
State-variable filters
Also known as a Universal Active Filter
Consists of one amplifier and t
C i t f lifi d two i t
integrators
t
High-pass, low-pass and band-pass in the same IC
Example below: Burr Brown UAF42
p
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7. Low Pass RC Filters
The critical frequency (fc): is the frequency for which
q y( ) q y
the ratio of the to the input voltage is approximately
0.707. in terms of the resistor and capacitor, the
critical frequency is given by:
1
fc =
2πRC
The output-input voltage ratio can be computed by:
Vout 1
=
Vin 1 + ( f / fc )2
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8. Example:
p
A measurement signal has a frequency < 1
kHz, but there is unwanted noise at
about 1 MHz Design a low-pass filter
MHz. low pass
that attenuates the noise to 1%. What is
the effect on the measurement signal at
its maximum of 1 kHz?
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9. High Pass RC Filters
High p
g pass filter p
passes high frequencies and blocks
g q
low frequencies.
1
fc =
2πRC
The output input voltage ratio can be computed by:
output-input
Vout
=
( f / fc )
Vin 1 + ( f / fc )2
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10. Example:
p
Pulses for stepping motor are being
transmitted at 2000 Hz. Design a filter to
reduce 60-Hz noise but reduce the
60 Hz
pulses by no more than 3 dB
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11. Band Pass RC Filters
Band pass filter blocks frequencies below a low limit
p q
and above a high limit while passing frequencies
between the limits.
1 1
fH = fL =
2πRL C L 2πRH C H
The output-input voltage ratio can be computed by:
Vout fH f
=
Vin ( f 2 − f H f L ) 2 + [ f L + (1 + ( RH / RL )) f H ]2 f 2
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12. Example:
p
A signal-conditioning system uses a
signal conditioning
frequency variation from 6 kHz to 60 kHz
to carry measurement information There
information.
is a considerable noise at 120 Hz and 1
MHz.
MHz Design a band pass filter to reduce
the noise by 90%.
Dr. Ashraf Saleem 12
13. Data Acquisition System
Mechatronic systems use digital data acquisition for a
y g q
variety of purposes such as:
process condition monitoring and performance
evaluation,
l ti
fault detection and diagnosis,
product quality assessment
assessment,
dynamic testing,
system identification ( , experimental modeling), and
y (i.e., p g),
feedback control.
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15. A/D Converter: Input Signal
p g
Analog
Signal is continuous
Example: strain gage. Most transducers
gage
produce analog signals
Digital
Signal is either ON or OFF
Si l i ith
Example: light switch.
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18. Example 1
p
What is the output voltage of a 10-bit
Ladder DAC with a 10 V reference
voltage if the input is 00101101012.
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19. Conversion Resolution
The conversion resolution is a function of the
reference voltage and the number of bits in the
word. The more bits, the smaller the change in
analog output for a 1-bit change in binary word.
g p g y
−n
ΔVout = VR 2
Where ∆Vout = smallest output change
VR = reference voltage
n = number of bits in the word
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20. Example 2:
p
Determine how many bits a D/A converter
must have to provide output increments
of 0 04V or less. The reference is 10V
0.04V less
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21. Example 3:
p
A control valve has a linear variation of opening as the
p g
input voltage varies from 0 to 10V. A microcomputer
outputs an 8-bit word to control the valve opening
using an 8-bit DAC to generate the valve voltage.
g g g
a- Find the reference voltage required to obtain a full
open valve (10V)
(10V).
b- Find the percentage of valve opening for a 1-bit
change in the input word.
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22. DAC Error Sources
Code Ambiguity. In many digital codes (e.g., in the straight
binary code), i
bi d ) incrementing a number by an LSB will involve
ti b b ill i l
more than one bit switching. If the speed of switching from 0-1
is different from that for 1-0, and if switching pulses are not
applied to the switching circuit simultaneously, the switching of
li d t th it hi i it i lt l th it hi f
the bits will not take place simultaneously.
Settling Time. The circuit hardware in a DAC unit will have
some dynamics, with associated time constants and perhaps
oscillations (underdamped response). Hence, the output voltage
cannot instantaneously settle to its ideal value upon switching.
The time required for the analog output to settle within a certain
band (say :t2% of the final value or :t resolution), following the
application of the digital data, is termed settling time.
pp g g
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23. DAC Error Sources
Parametric Errors. resistor elements in a DAC might not
be
b very precise, particularly when resistors within a wide
i ti l l h i t ithi id
range of magnitudes are employed, as in the case of
weighted-resistor DAC. These errors appear at the
analog output. Furthermore, aging and environmental
output Furthermore
changes (primarily, change in temperature) will change
the values of circuit parameters, resistance in partic-ular.
This also will result in DAC error.
Reference Voltage Variation: Since the analog output of
a DAC is proportional to the reference voltage vref, any
variations in the voltage supply will directly appear as an
error. Thi problem can b overcome b using stabilized
This bl be by i t bili d
voltage sources with sufficiently low output impedance.
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24. Analog to Digital Converters (ADC)
The formulae of analog to digital conversion is as
following:
−1 −2 −n Vin
b1 2 + b2 2 + ......... + bn 2 =
Vr
Where b1b2b3….bn = n-bit digital output
Vin = analog input voltage
Vr = analog reference voltage
The output uncertainty/resolution can be given by:
∆V=Vr2-n
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25. Example 1:
p
Temperature is measured by a sensor with
an output of 0.02 V/oC. Determine the
required ADC reference and word size to
measure 0o to 100oC with 0.1oC
resolution
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26. Example 2:
p
Find the digital word that results from a
3.127 V input to a 5-bit ADC with a 5V
reference?
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30. Example 4:
p
A dual-slope ADC as shown previously
dual slope
has R=100 kΩ and C=0.01μF. The
reference is 10V and the fixed
10V,
integration time is 10 ms. Find the
conversion time for a 6 8V input
6.8V input.
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