TLWG Unit1

EC2305 TRANSMISSION LINES AND WAVEGUIDES

Handled By Franklin Vijay S.

AP/ECE

UNIT 1: FILTERS

If filter passes all frequencies upto the cut-off frequency and attenuates all frequencies above it, then it is called low pass filter.

If filter attenuates all frequencies upto the cut-off frequency and passes all frequencies above it, then it is called high pass filter.

FILTER FUNDAMENTALS :

One can design a filter with two cut-off frequencies to get more filter sections.

If filter passes all the frequencies between the two cut-off frequencies and attenuates all other frequencies, then it is called band pass filter.

If filter attenuates all the frequencies between the two cut-off frequencies and passes all other frequencies, then it is called band stop (or) band reject (or) band elimination filter

FILTER FUNDAMENTALS (CONT..)


It is desired that a filter network transmit or pass a desired band of frequencies, without any loss, whereas it should stop or completely attenuate all undesired frequencies.

The ability of any filter network to work as per requirement is decided by the propagation constant is given by, where, is attenuation constant and is phase constant, both are the functions of frequency.

FILTER FUNDAMENTALS (CONT..)PASS BAND AND STOP BAND

When , the output current of the filter is same as the input current, indicating no attenuation but only phase shift in the output current. This is the operation of filter in the pass band.

When , the magnitude of the output current becomes very less than the input current, indicating attenuation in the output current. This is the operation of filter in the stop band.


For a four terminal network, the propagation constant for a symmetrical T -section is given by,

Putting


It will be assumed that the network contains only pure reactances, and thus will be real, and either positive or negative, depending on the type of reactances used for and .

Case (i): Case (ii):


Case (i): If and are the same type of reactance then , or

the ratio is positive and real. It results in is real and the imaginary term must equal to zero.


Case (i): a) b)


From (a) From (b)

where

Case (ii): If and are opposite types of reactance then ,

or the ratio is negative. It results in is imaginary and the real term must equal to zero.


Case (ii):

Two conditions are possible from the above:


Condition I: Condition II:

; ; ; ; 𝐬𝐢𝐧( 𝛃𝟐 )=±𝟏

Condition I: leads to a pass band or region of zero attenuation.

The phase angle in this pass band is given by,


Condition II: leads to a stop band, or attenuation band. The phase angle in this band is given by , and the attenuation is given by,

Thus the condition that implies a pass band operation.


Values of be classified into three regions, with the corresponding values of and , these regions being bounded by values of and , as given below:


to

Reactance type Same Opposite OppositeBand Stop Pass Stop

The frequencies at which the network changes from a pass network to a stop network, or vice versa, are called cut-off frequencies. These frequencies occur when,


or

or

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TLWG Unit1