COMM 704:COMM 704: Communication Systemseee.guc.edu.eg/Courses/Communications/COMM704...Passive FiltersPassive Filters No amppy g ( , plifying elements (transistors, op-ampp, )s,..etc)

COMM 704:COMM 704:Communication Systemsy

Lecture 3: Analog FiltersLecture 3: Analog Filters

Dr Mohamed Abd El GhanyDr. Mohamed Abd El Ghany, Department of Electronics and Electrical Engineering

[email protected]

IntroductionIntroduction A filter is a frequency-selective circuit that passes a specified band of frequencies and blocks or attenuates signals of frequencies outside this band.

FiltersFilters

Employ only passive Make use of properties

Active filters Passive filters

p y y pelements such as capacitors inductors and resistors.

p pof op-amp in addition to resistors and capacitors.

2Dr. Mohamed Abd el Ghany Department of Electronics and Electrical Engineering

COMM 704:Communication Systems Winter 2011

Passive FiltersPassive Filters

No amplifying elements (transistors, op-amps,..etc)p y g ( , p p , )No signal gainRequire no power suppliesNot restricted by the bandwidth limitations of op-ampsCan be used at high frequencyC h dl l l l l h iCan handle large current or voltage level than active devicesBuffer amplifiers might be requiredBuffer amplifiers might be required



Active FiltersActive FiltersFlexibility of gain and frequency adjustment: since op-amps can provide a voltage gain the input signal in active filters is notprovide a voltage gain, the input signal in active filters is not attenuated as it is in passive filters. It is easy to adjust or tune active filters.No loading effect: because of high input resistance and low outputNo loading effect: because of high input resistance and low output resistance of op-amps, active filters do not cause loading of the input source or the load.Cost and size: active filters are less expensive than passive filtersCost and size: active filters are less expensive than passive filters because of the availability of low-cost op-amps and the absence of inductorsFiltering functions: active filter can realize a wider range of filteringFiltering functions: active filter can realize a wider range of filtering functions than passive filtersGain: an active filter can provide gain, whereas a passive filter often exhibits a significant loss



exhibits a significant loss

Disadvantage of Active FiltersDisadvantage of Active Filters

Bandwidth: active component have a finite bandwidth, which limits the applications of active filters to the audio-frequency range.Power supplies: active filters require power supplies, whereas passive filters do not.Di t ti ti filt h dl l li it d f i l it dDistortion: active filters can handle only a limited range of signal magnitudes; beyond this range they introduce unacceptable distortion.Noise: active filters use resistors and active elements, which produce electrical noiseelectrical noise.

In general, the advantages of active filters outweigh their disadvantages in voice and data communication applications. A ti filt d i l t ll hi ti t d l t iActive filters are used in almost all sophisticated electronic systems for communication and signal processing, such as television, telephone, radar, space satellite, and biomedical equipment. However, passive filters are still widely used.



q p , p y

Categories of FiltersCategories of FiltersLow-pass filter (LPF) High-pass filter (HPF)

wo

LPF Passes frequencies fromwo

HPF Is the complement ofLPF Passes frequencies from dc to a desired frequency fo

HPF Is the complement of low-pass filter

|H| Ideal Low-pass filter |H| Ideal High-pass filter

pass stop stop pass



wo w wo w

Categories of Filtersband-pass filter (BPF) Band-reject-pass filter

BPF Passes frequencies from f1 to f2 and stops all other frequencies.

It eliminate all signals within the stop band while passing all frequencies outsides this band

Ideal band-pass filter Ideal band-reject filter|H|

pass stop

Ideal band-pass filter |H|

stop pass

Ideal band-reject filter

stop Pass

w2 w

p p

w

p

w1 w2w1

All-pass filter: passes all frequencies from 0 to infinity, but it provides a phase delay



a phase delay.

Filter Response CharacteristicsFilter Response CharacteristicsAv

ButterworthBesselCh b hChebyshev

f8Dr. Mohamed Abd el Ghany

Department of Electronics and Electrical EngineeringCOMM 704:Communication Systems Winter 2011

f

Bessel CharacteristicBessel CharacteristicAvFlat response in theFlat response in the

passband.Phase response isPhase response is linear.Used for filtering pulse

f

Used for filtering pulse waveforms without distorting the shape of the waveform.



Butterworth CharacteristicButterworth Characteristic

Very flat amplitude, Avy p ,response in the passband.Phase response is not lilinear.Used when all frequencies in the passband must have pthe same gain.Often referred to as a

i ll fl t

f

maximally flat response



Chebyshev CharacteristicChebyshev Characteristic

AvO h t i l iOvershoot or ripples in the passband.Phase response is notPhase response is not linear - worse than Butterworth

f

Butterworth.Used when a rapid roll-off is required. o s equ ed



Passive Filter: Low-Pass FilterPassive Filter: Low Pass FilterTransfer function of LPF:

1

RCs

RCsH 1

1

)(+

=

1Using s=jw

22 )1()(

RCwRCjwH+

=

At the cutoff frequency wc, |H(jwc)| is equal 1/√2 Hmax

11

For low-pass filter:

Hmax = H(j0) = 1

RCwC

1=

22 )1()1(

21)(

RCwRCjwH

c

c+

==

Solving this equation for wc, we get



RC

Passive Filter: High-Pass FilterPassive Filter: High Pass FilterTransfer function of HPF:

s

RCs

ssH 1)(+

=

wUsing s=jw

22 )1()(

RCw

wjwH+

=

At the cutoff frequency wc, |H(jwc)| is equal 1/√2 Hmax

1 w

For High-pass filter:

1)()(max =∞==∞=

jHjwHHw

RCwC

1=

22 )1()1(

21)(

RCw

wjwHc

cc

+==

Solving for wc, we get



RC

Passive Filter: Band-Pass FilterPassive Filter: Band Pass FilterTransfer function of BPF:

sR )(

LCs

LRs

sLsH 1)(

)()(

2 ++=

Using s=jwjwR ))((

)(LRw

LCjw

LRjw

jwLjwH 1)()(

))(()(

2 ++=

222 )()1(

)()(

LRww

LC

LjwH+−

=

At the cutoff frequencies w1 and w2 , H(jwc)| is equal 1/√2 Hmax

)1()2

(2

21 LCL

RL

Rwc ++−= )1()2

(2

22 LCL

RL

Rwc ++=

Assignment : Find W bandwidth and quality factor of BPF



Assignment : Find Wo , bandwidth and quality factor of BPF

Passive Filter: Band-reject FilterPassive Filter: Band reject FilterTransfer function of Band-reject filter:

LCRCSS

LCS

SCLSR

SCSL

sH 1

1

1

1

)(2

2

++

+=

++

+=

Using s=jw

222

2

)()1(

1

)(

RCww

LC

wLCjwH

+−

−=

)()( RCLC

At the cutoff frequencies w1 and w2 , H(jwc)| is equal 1/√2 Hmax

)1()2

(2

21 LCL

RL

Rwc ++−= )1()2

(2

22 LCL

RL

Rwc ++=



Active Filter: Low-Pass FilterActive Filter: Low Pass Filter

1. First order LPF (using Inverting op-amp configuration) ( g g p p g )

2

1//)( SC

RH

1

)(R

SCsH −=

c

c

wSwKsH+

−=)(

1

2

RRK =

CRwc

2

1=




1. First order LPF (using Non-Inverting amplifier) ( g g p )

1 3+RR

1)(

11

2

++=

CSRRsH

c

c

wSwKsH+

=)(

2

31RRK +=

11

1CR

wc =




1. Sallen Key LPFy

a

b

RRK +=1

CCRRK

V

2121221112

2

2121

1)111()(

CCRRS

CRK

CRCRS

CCRRVVsH

i

o

+−+++==




1. Sallen Key LPFy

G

Using the standard notation:

22 )()(

oo

LPF

wSQwS

GsH++

=

11

CCRR

2121

1CCRR

wo =

221112

2121

111CRk

CRCR

CCRRQ

−++=




1. Sallen Key LPFy

If no restriction is imposed on the gain K, we have five element values to design LPF circuit. Hence, we are free to make some arbitrary choices as follows:

Design 1: equal element values In this design, we letC1=C2=1F and R1=R2=R

Design 2: equal capacitance and equal feedback resistancesIn this design we chooseC1 C2 1F and R1 R2 R In this design, we chooseC1=C2=1F and Ra=Rb=R

Design 3: moderate-sensitivity Design 4: minimum sensitivityes g 3 ode ate se s t tydesignIn this design, we chooseC1=√3 Q and C2=1F and K=4/3

Design 4: minimum sensitivityIn this design, we chooseK=1 and R1=R2=1Ω




Definition of sensitivityy

The sensitivity of some performance measure y with respect to a network element value x is defined by:

dxdy

yxS y

x =

If y is a function of several variable [y=f(x1,x2,….,xn)], then the sensitivity of y with respect to xi is

d

i

iyx dx

dyyxS

i= Notes:

2121 yx

yx

yyx SSS +=

2121 / yx

yx

yyx SSS −=



xxx


Example:

Design a fourth-order butterworth low-pass filter using the cascade of two Sallen-key biquads using Design 1 and 2 respectively. Then let wo =2Пx1000 rad/sec and use 0.1 µF capacitors.Th li d t k f ti f th t l filt

1765367.0)( 2

11 ++

=SS

GsH

The normalized network function of the two low-pass filters are:

1765367.0 ++ SS

1847759.1)( 2

22 ++

=SS

GsH



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COMM 704:COMM 704: Communication Systemseee.guc.edu.eg/Courses/Communications/COMM704...Passive FiltersPassive Filters No amppy g ( , plifying elements (transistors, op-ampp, )s,..etc)