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Home Amplifier Circuits Wave Filter Principles  
See also: Limitations of Wave Filters  
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Wave Filter Principles
To avoid introducing losses and attenuation in the transmission bands, reactances as nearly pure as practicable are used in the elements of a wave filter.
For example, in the "lowpass" filter Tsection of Fig. 135, the inductance arms shown as L/2 and the capacitance C are made with losses as low as possible. Capacitors ordinarily used in filters have low losses, but it is a problem to make inductors which have low losses. Values of inductor Q ranging from 10 to 200 are common, depending upon the value of inductance and the frequency of transmission. Therefore in wave filters the loss is mostly in the inductors. It can be shown^{(1)} that for pure reactance arms the values of reactance are such that in the transmission band
where Z_{1} is the reactance of the series arm and Z_{2} is the reactance of the shunt arm. In the Tsection of Fig. 135, Z_{1} is 2πf[ (L/2) + (L/2) ] = 2πfL and Z_{2} is the reactance of C. The attenuation for sections of filter like Fig. 135 is shown in Fig. 136, for a pure reactance network starting at the cutoff frequency.
The attenuation is shown in decibels, and the abscissas are onefourth of the ratio of series to shunt reactance in a full section. It is important, in the transmission band, to terminate the sections of filter in the proper impedance. Like a transmission line, a wave filter will deliver its full energy only into an impedance which is equal to its characteristic impedance. Many wave filters are composed of several sections which simulate transmission lines. A properly constructed filter exhibits the same impedance at either end when terminated at the opposite end with an impedance equal to its characteristic impedance. The impedance seen at any one point in the filter is called its image impedance; it will be the same in either direction provided that the source and terminating impedances are equal. In general, however, the image impedance will not be the same for all points in the filter. For example, the impedance looking into the left or Tsection of Fig. 135 (if it is assumed to be terminated properly) will not be the same as that seen across the capacitor C. For that reason, another halfseries arm is added between C and the termination to keep equal input and output impedances. The terminating sections at both the sending and receiving ends of a filter network are halfsections, whereas the intermediate sections are full sections. A full Tsection of the type shown in Fig. 135 includes an inductance L equal to L/2 + L/2. The image impedance seen at the input terminals of the Tsection of Fig. 135 is known as the midseries impedance, and that seen across capacitor C is known as the midshunt impedance. Likewise, in the pisection shown at the right in Fig. 135, the midshunt image impedance is seen at the input or output terminals. The midseries impedance is seen at a point in the middle of coil L. This section terminates properly in its characteristic impedance at either end. Note that adjacent sections have C/2 for the shunt arm, so that a full section would again be composed of a capacitor C and an inductance L. The choice of T or pisections is determined by convenience in termination, or by the kind of image impedance variation with frequency that is desired. If these precautions are not observed, wave reflections are likely to cause a loss of power transfer in the transmission band.


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