General mntype image filter
Linear analog electronic filters 


Simple filters 
These filters are electrical wave filters designed using the image method. They are an invention of Otto Zobel at AT&T Corp..^{[1]} They are a generalisation of the mtype filter in that a transform is applied that modifies the transfer function while keeping the image impedance unchanged. For filters that have only one stopband there is no distinction with the mtype filter. However, for a filter that has multiple stopbands, there is the possibility that the form of the transfer function in each stopband can be different. For instance, it may be required to filter one band with the sharpest possible cutoff, but in another to minimise phase distortion while still achieving some attenuation. If the form is identical at each transition from passband to stopband the filter will be the same as an mtype filter (ktype filter in the limiting case of m=1). If they are different, then the general case described here pertains.
The ktype filter acts as a prototype for producing the general m_{n} designs. For any given desired bandform there are two classes of m_{n} transformation that can be applied, namely, the midseries and midshunt derived sections; this terminology being more fully explained in the mderived filter article. Another feature of mtype filters that also applies in the general case is that a half section will have the original ktype image impedance on one side only. The other port will present a new image impedance. The two transformations have equivalent transfer functions but different image impedances and circuit topology.
 Parts of this article or section rely on the reader's knowledge of the complex impedance representation of capacitors and inductors and on knowledge of the frequency domain representation of signals.
Midseries multiple stopband
If Z and Y are the series impedance and shunt admittance of a constant k half section and;
 where Z_{1}, Z_{2} etc are a cascade of antiresonators,
the transformed series impedance for a midseries derived filter becomes;
Where the m_{n} are arbitrary positive coefficients. For an invariant image impedance Z_{iT} and invariant bandform (that is, invariant cutoff frequencies ω_{c}) the transformed shunt admittance, expressed in terms of Z_{mn}, is given by;
 where and is a constant by definition. When the m_{n} are all equal this reduces to the expression for an mtype filter and where they are all equal to one it reduces further to the ktype filter.
A result of this relationship is that the N antiresonators in Z_{mn} will transform into 2N resonators in Y_{mn}. The coefficients m_{n} can be adjusted by the designer to set the frequency of one of the two poles of attenuation, ω_{∞}, in each stopband. The second pole of attenuation is dependant and cannot be set separately.
Special cases
In the case of a filter with a stopband extending to zero frequency, one of the antiresonators in Z will reduce to a single inductor. In this case the resonators in Y_{mn} are reduced by one to 2N1. Similarly, for a filter with a stopband extending to infinity, one antiresonator will reduce to a single capacitor and the resonators will again be reduced by one. In a filter where both conditions pertain, the number of resonators will be 2N2. For these end stopbands, there is only one pole of attenuation in each, as would be expected from the reduced number of resonators. These forms are the maximum allowable complexity while maintaining invariance of bandform and one image impedance.
Midshunt multiple stopband
By dual analogy, the shunt derived filter starts from;
For an invariant image admittance Y_{iΠ} and invariant bandform the transformed series impedance is given by;
Simple bandpass section
The bandpass filter can be characterised as a 2bandstop filter with ω_{c} = 0 for the lower critical frequency of the lower band and ω_{c} = ∞ for the upper critical frequency of the upper band. The two resonators reduce to an inductor and a capacitor respectively. The number of antiresonators reduces to two.
If, however, ω_{∞1} is set to zero (that is, there is no pole of attenuation in the lower stopband) and ω_{∞2} is set to correspond to the upper critical frequency ω'_{c1}, then a particularly simple form of the bandpass filter is obtained consisting of just antiresonators coupled by capacitors. This was a popular topology for multisection bandpass filters due its low component count, particularly of inductors.^{[2]}^{[3]} Many other such reduced forms are possible by setting one of the poles of attenuation to correspond to one of the critical frequencies for various classes of basic filter.^{[4]}
See also
Notes
References
 Zobel, O. J.,Theory and Design of Uniform and Composite Electric Wave Filters, Bell System Technical Journal, Vol. 2 (1923), pp. 146.
 Mathaei, Young, Jones Microwave Filters, ImpedanceMatching Networks, and Coupling Structures McGrawHill 1964.
 Bray, J, Innovation and the Communications Revolution, Institution of Electrical Engineers, 2002 ISBN 0852962185