To obtain the m-derived shunt half section, an admittance is added to 1 / mZ to make the image impedance Z i? the same as the image impedance of the original half section.
42.
To obtain the m-derived shunt half section, an admittance is added to 1 / mZ to make the image impedance Z i? the same as the image impedance of the original half section.
43.
The image impedance can be expressed in terms of the open-circuit and short-circuit impedances of the filter as \ scriptstyle Z _ i = \ sqrt { Z _ oZ _ s }.
44.
It is also the image impedance of the section at resonance, in the case of band-pass filters, or at " ? " = 0 in the case of low-pass filters.
45.
As with the k-type section, the image impedance of the " m "-type low-pass section is purely real below the cut-off frequency and purely imaginary above it.
46.
Where the section in question has an image impedance different from the general case a further suffix is added identifying the section type, for instance \ scriptstyle Z _ { \ mathrm { iT } m }.
47.
As mentioned above, the weakness of the image filter approach was that the frequency response of a network was often not as predicted when the network was terminated resistively, instead of by the required image impedances.
48.
The designer now multiplies " Z " and " Y " by an arbitrary constant " m " ( 0 iT the same as the image impedance of the original constant k section.
49.
In fact, in the limiting case of a chain of cascaded networks where the size of each single network is approaching an infinitesimally small element, the mathematical limit of the image impedance expression is the characteristic impedance of the chain.
50.
For an attenuator, " Z " and " Y " are simple resistors and " ? " becomes the image parameter attenuation ( that is, the attenuation when terminated with the image impedances ) in nepers.
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