designer determines the impedance that must be added to 1/mY to make the image impedance ZiT the same as the image impedance of the original constant k section. From the general formula for image impedance, the additional impedance required can be shown to be To obtain the m-derived shunt half section, an admittance is added to 1/mZ to make the image impedance ZiΠ the same as the image impedance of the original half section. The additional admittance required can be shown to be The general arrangements of these circuits are shown in the diagrams to the right along with a specific example of a low-pass section. A consequence of this design is that the m-derived half section will match a k-type section on one side only. Also, an m-type section of one value of m will not match another m-type section of another value of m except on the sides which offer the Zi of the k-type. Operating frequency For the low-pass half section shown, the cut-off frequency of the m-type is the same as the k-type and is given by The pole of attenuation occurs at; From this it is clear that smaller values of m will produce closer to the cut-off frequency and hence will have a sharper cut-off. Despite this cut-off, it also brings the unwanted stopband response of the m-type closer to the cut-off frequency, making it more difficult for this to be filtered with subsequent sections. The value of m chosen is usually a compromise between these conflicting requirements. There is also a practical limit to how small m can be made due to the inherent resistance of the inductors. This has the effect of causing the pole of attenuation to be less deep (that is, it is no longer a genuinely infinite pole) and the slope of cut-off to be less steep. This effect becomes more marked as is brought closer to , and there ceases to be any improvement in response with an m of about 0.2 or less. Image impedance The following expressions for image impedances are all referenced to the low-pass prototype section. They are scaled to the nominal impedance R0 = 1, and the frequencies in those expressions are all scaled to the cut-off frequency ωc = 1. Series sections The image impedances of the series section are given by and is the same as that of the constant k