EE303Sp09 L05 Filters

8/6/2019 EE303Sp09 L05 Filters

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EE303 Lesson 5:

Filters


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90.7

WSDL

Ocean City

90.3

WHID

Salisbury

Frequency

(MHz)

Receiver tuned to 90.9 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 FM radio station.

What allows your radio to isolate one station

from all of the adjacent stations?


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Filters

A filter is a frequency-selective circuit.

Filters are designed to pass some frequencies

and reject others.

Frequency

(MHz)

Receiver tuned to 90.9 MHz

90.9

WETA

Washington


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Basic kinds of filters

There are four basic kinds of filters:

Low-pass filter. Passes frequencies below a criticalfrequency called the cutoff frequency and attenuates

those above. High-pass filter. Passes frequencies above critical

frequency but rejects those below.

Bandpass filter. Passes only frequencies in anarrow range between upper and low cutoff.

Bandstop filter. Rejects or stops frequencies in anarrow range but passes others.


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Basic kinds of filters

Bandpass filter response

f(Hz)fco

passband stopband

f(Hz)fco

passbandstopband

f(Hz)fc

passband

f1

f2

passbandstopband

f(Hz)fc

passband

f1

f2

stopband stopband

Low-pass filter response High-pass filter response

Bandstop filter response


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Filters construction

There are numerous ways to construct filters.

Passive filters a composed of only passive

components (resistors, capacitors, inductors)

and do not provide amplification. Active filters typically employ RC networks and

amplifiers with feedback and offer a number ofadvantages.


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Filter circuits

Filter circuits depend on the fact that theimpedance of capacitors and inductors is afunction of frequency.

Some common bandpass filter circuits


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Calculate the impedance of a resistor, a capacitor and aninductor at the following frequencies.

Example Problem 1

100 Hz

ZC

ZL

R

10,000 Hz1000 Hzf

2C

jZf C

2L Z j f L


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Calculate the impedance of a resistor, a capacitor and aninductor at the following frequencies.

Example Problem 1

-j1000

j10

100

100 Hz

-j10 -j100 ZC

j1000 j100 ZL

100 100 R

10,000 Hz1000 Hzf


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RC low-pass filter

What is the ratio of the output voltage (Vo) to theinput voltage (Vs)?


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RC low-pass filter

What is the ratio of the output voltage (Vo) to theinput voltage (Vs)?

2

1

1

1 1

1

1

Co s

C

o

s

o

s

j C

j RC R

j C

RC

ZV V

R Z

V

V

V

V


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RC low-pass filter

A low-pass filter passes frequencies below acritical frequency called the cutoff frequency andattenuates those above.

f(Hz)fco

RClow-pass filter response

actual filter output

passband stopband

ideal filter output

cutoff frequency

o

s

V

V

0 dB


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Cutoff frequency

The cutoff frequency is frequency at which theoutput amplitude is 70.7% of the input.

f(Hz)fco

RClow-pass filter response


passband stopband

ideal filter output

cutoff frequency

2

co

co

1 1

21

which implies

[rad/sec]

or [Hz]2

o

s RC

RC

fRC

V

V

o

s

V

V

0 dB


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What is the cutoff frequency of a single-section RC low-

pass filter with R = 8.2 k and C = 0.0033 F?

Example Problem 2


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RL low-pass filter

A low-pass filter can also be implemented with aresistor and inductor, the cutoff frequency isgiven

f(Hz)fco

RL low-pass filter response


passband stopband

ideal filter output

cutoff frequency

o

s

V

V

0 dB

co [Hz]2

RfL


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Filters

Notice the placement of the elements in RC andRL low-pass filters.

What would result if the position of the elementswere switched in each circuit?

RL low-pass filterRClow-pass filter


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High-pass filter

Switching elements results in a high-pass filter.

f(Hz)fco

high-pass filter response

actual

passbandstopband

ideal

cutoff frequency

o

s

V

V

0 dB

co co

1or [Hz]

2 2

Rf f

RC L


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What resistor value R will produce a cutoff frequency of

3.4 kHz with a 0.047F capacitor? Is this a high-pass orlow-pass filter?

Example Problem 3


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Improving filter response

One method of creating a more selective filter isto cascade filter stages.

The attenuation of this two-stage filter is 40dB/decade instead of 20 dB/decade.

Two stage RCfilter


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LCFilters

At higher frequencies (> 100-kHz), it is morecommon to find LC filters made with inductorsand capacitors.

The response curves of the major families offilters are shown below.


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Bandpass filter

A bandpass filter passes frequencies below acritical frequency called the cutoff frequency andattenuates those above.

f(Hz)fc

LCbandpass filter response


passband

ideal filter output

center frequency

o

s

V

V

0 dB

f1 f2

upper cutofflower cutoff


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Cascading bandpass filter

Improved selectivity with steeper skirts on thecurve can be obtained by cascading severalbandpass sections.

How cascading filter sections narrow the bandwidth and improve selectivity.


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Active filters

Active filters incorporate RCnetworks andamplifiers with feedback to produce low-pass,high-pass, bandpass and bandstop responses.

Active bandpass and notch filters.

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EE303Sp09 L05 Filters