Expt No: AIM: To plot frequency response of frequency selective network(Twin T Network) SOFTWARE: MATLAB Version 7.5.0.342 (R2007b) THEORY Two symmetrical T networks connected in parallel are as shown below. If the reactances and the resistances of the arms are properly chosen, then this network may be used to give zero output for a certain input at a particular frequency and this frequency is called NULL frequency

Using Z Parameters to Describe a Two-Port Network. There are numerous methods available for analytically describing linear time invariant electrical networks. These include parameterization by Z, Y, H, G, ABCD (chain matrix). And S parameters. The network to be analysed and constructed will be in the audio frequency range hence the classical Z paprmeters are easy to measure and will be used. Any of the representations can be obtained by appropriate linear transformations, including the S (sctterring) parameters. Fig:A general Two- Port NetworkThe matrix eqution for the Z parameters is

The zs are called the open circuit impedances, since typically the output or input port current is forced to zero (open circuited) to evaluate the parameter as shown in equations

For a passive network like the Twin T, at most 3 of the four parameters are independent. The reciprocity theorem ststes that the transfer function of a passive network with the dimensions of impedances (or admittance) remains unchanged if the points of the excitation and response are interchanged. The theorem therefore demands that the transfer impedances z12 and z21 must be equal. Futhermore, if the network is symmetrical with respect to the input and output ports, as in the Twin T, z22 must equal z11.

Constructing a test circuitThis circuit can be constructed using readiy available components. The above analysis assumes ideal zero tolerance components and clearly the agreement between the analysis and measurements will be determined by the tolerance of the components. For best results, use good quality mylar or polystyrere capacitors. Ceramic capacitors with a high dielectric constant are non linear and should be avoided.

The frequency response (gain vs frequency) of a Twin T network is similar to that of aNotch Filter.

%TITLE:-To plot the frequency response selective network (Twin T or Wein bridge)%ROLL NO:-

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r=1000;% value of the resistancec=47e-9;%value of capacitancef=0:25:10000:%frequencyw=2*pi*f*j;a=[r*r*c*c 4*r*c 1];%quadratic equation in sa1=polyval(a,w);%Function to find the value of polynomial at wb=[r*r*c*c 0 1];b1=polyval(b,w);c=[4*r*c*c 4*c 0];c1=polyval(c,w);Z11=a1./c1;%i/p voltageZ21=b1./c1;%o/p voltageX21=Z21./Z11;%gainV=20*log10(abs(X21));%voltage gainPlot(f,v0;xlabel(frequency(Hz));ylabel(Voltage gain(db))

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