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Prior to network synthesis, networks, especially filters, were designed using the image impedance method.
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The image impedance technique is used for the design of input/output terminating networks.
The difficulty that he was trying to overcome was that the image impedance techniques being used to design filter sections only gave the mathematically predicted response if they were terminated in their respective image impedances.
A new image impudence matrix is defined to accommodate the extension of the theory from two- to four-port networks, and a practical realization of the image impedance matrix is presented using the available circuit elements in CMOS technology.
These are normally required to be resistive but the image impedance will be complex.
The image impedance of a half-section is \scriptstyle Z_{\mathrm i m} on one side and a different impedance, \scriptstyle Z_{\mathrm i mm'} on the other.
The image impedance of the input and output port of a section will generally not be the same.
Likewise, the image impedance of a mid-shunt section is designated ZiΠ due to the "Π" topology.
See also Image impedance#Derivation The image impedances of the section are given by :{Z_\mathrm{iT}}^2=Z^2 + k^2 and :\frac{1}{{Z_\mathrm{i\Pi}}^2}={Y_\mathrm{i\Pi}}^2=Y^2 + \frac{1}{k^2} Given that the filter does not contain any resistive elements, the image impedance in the pass band of the filter is purely real and in the stop band it is purely imaginary.
Find and use the image.
The most important rule when constructing a composite image filter is that the image impedances must always face an identical impedance; like must always face like.
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