Post on 16-Jul-2015
Passive Filters
90.7
WSDL
Ocean City
90.3
WHID
Salisbury
Frequency
(MHz)
90.5
WKHS
Worton
91.3
WMLU
Farmville
90.9
WETA
Washington
91.1
WHFC
Bel Air
91.5
WBJC
Baltimore
Tuning a Radio
• Consider tuning in an FM radio station.
• What allows your radio to isolate one station from all of
the adjacent stations?
Filters
• A filter is a frequency-selective circuit.
• Filters are designed to pass some frequencies and reject
others.
Frequency
(MHz)90.9
WETA
Washington
Active and Passive Filters
• Filter circuits depend on the fact that the impedance of
capacitors and inductors is a function of frequency
• There are numerous ways to construct filters, but there
are two broad categories of filters:
– Passive filters are composed of only passive
components (resistors, capacitors, inductors) and do
not provide amplification.
– Active filters typically employ RC networks and
amplifiers (opamps) with feedback and offer a number
of advantages.
Passive Filters
• There are four basic kinds of filters:
– Low-pass filter - Passes frequencies below a critical
frequency, called the cutoff frequency, and attenuates
those above.
Passive Filters
• There are four basic kinds of filters:
– High-pass filter - Passes frequencies above the
critical frequency but rejects those below.
Passive Filters
• There are four basic kinds of filters:
– Bandpass filter - Passes only frequencies in a narrow
range between upper and lower cutoff frequencies.
Passive Filters
• There are four basic kinds of filters:
– Band-reject filter - Rejects or stops frequencies in a
narrow range but passes others.
Low Pass Filters
RL low-pass filterRC low-pass filter
• RC low pass filter works based on the principle of
capacitive reactance, while RL low pass filter works on
the principle of inductive reactance
http://www.learningaboutelectronics.com/Articles/Low-pass-filter.php
Capacitive Reactance
• Capacitive Reactance (Xc) varies with the applied
frequency.
– As the frequency applied to the capacitor increases, its effect is
to decrease its reactance (measured in ohms).
– Likewise as the frequency across the capacitor decreases its
reactance value increases.
(Xc = 1 2𝜋𝑓𝑐) ohms
http://www.electronics-tutorials.ws/filter/filter_1.html
Inductive Reactance
• Inductive Reactance (XL) varies with the applied
frequency.
– To high frequency signals, inductors offer high resistance thus
blocks high frequencies
– As frequencies decrease, the inductor offers low resistance so
low frequencies pass
XL = 2𝜋𝑓𝐿 ohmshttp://faculty.kfupm.edu.sa/ee/malek/EE205/pdfslides-205/Lecture%2028_ee205.pdf
RL low-pass filter RL low-pass filter
at low frequencies
𝜔 = 0
RL low-pass filter at
high frequencies
𝜔 =∞
RC Low-Pass Filter – Frequency Response
• The cutoff frequency is the frequency at which capacitive reactance and
resistance are equal (R = Xc), therefore fc = 1 2𝜋𝑅𝑐
• At cutoff, the output voltage amplitude is 70.7% of the input value or –3 dB
(20 log (Vout/Vin))
RC Low-Pass Filter – Phase
• The phase angle ( Φ ) of the output signal LAGS behind that of the
input and at fc, is -45o out of phase. This is due to time taken to
charge the capacitor as input voltage changes.
• The higher the input frequency, the more the capacitor lags and
circuit becomes more out of phase
fc
Application: RC Integrator Circuit
• The integrator converts square wave input signal into a triangular
output as the capacitor charges and discharges.
• The higher the input frequency, the lower will be the amplitude
compared to that of the input
Filters
Notice the placement of the elements in RC and
RL low-pass filters.
What would result if the position of the elements
were switched in each circuit?
RL low-pass filterRC low-pass filter
RC and RL High-Pass Filter Circuits
Switching elements results in a High-Pass Filter.
co co
1 or [Hz]
2 2
Rf f
RC L
f (Hz)fco
actual
passbandreject-band
“ideal”
cutoff frequency
o
s
V
V
0 dB
–3 dB
Impedance vs. Frequency
Calculate the impedance of a resistor, a capacitor
and an inductor at the following frequencies.
1 L CZ j L Z j
C
f 100 Hz 1000 Hz 10,000 Hz
R 100 W 100 W 100 W
ZL j10 W j100 W j1000 W
ZC -j1000 W -j100 W -j10 W
RC Low-Pass Filter
For this circuit, we want to compare the output (Vo)
to the input (Vs):
v
v2
1
1( )
1 1
1( )
1
Co s
C
o
s
o
s
j CH
j RCR
j C
H
RC
ZV V
R Z
V
V
V
V
Example
What is the cutoff frequency for this filter?Given:
8.2
0.0033
R k
C F
W
co
co
or [Hz]2
RC
fRC
co 5.88 kHzf
RL Low-Pass Filter
Comparing the output (Vo) to the input (Vs):
2
1
1
1
1
o s
L
o
s
o
s
R
R
LR j Lj
R
L
R
V VR Z
V
V
V
V
EXAMPLE – RL Low Pass Filter
Design a series RL low-pass filter to filter out any noise above 10 Hz.
R and L cannot be specified independently to generate a value for fco = 10 Hz
or co = 2fco. Therefore, let us choose L=100 mH. Then,
3(2 )(10)(100 10 ) 6.28coR L W
2 2 22
20( )
400
RL
o s sRL
V V V
f(Hz) |Vs| |Vo|
1 1.0 0.995
10 1.0 0.707
60 1.0 0.164
co co2
1 which implies: or [Hz]
21
o
s
R Rf
L LL
R
V
V
Example: Microphone circuit
Example
What resistor value R will produce a cutoff frequency of 3.4 kHz
with a 0.047 mF capacitor? Is this a high-pass or low-pass filter?
co
co
1 [Hz]
2
1R=
2
fRC
C f
1004R W
This is a High-Pass Filter