Applet Notes:

The applet models a typical microwave transmission line lowpass filter design for examining the band shape dependence on manufacturing tolerances and substrate loss.
The filter voltage response is shown in the upper display and the corresponding phase response in the lower.
All line section lengths are fixed at 0.05m, or one-eighth of a wavelength at 0.75GHz, but these are simply scaled for other bands.
The line impedances Z1 to Z5 are adjustable by means of the scrollbars and refer to the schematic at the top right.
The filter base type drop-down menu contains several band shape types and automatically adjusts the correct line impedance values for the selected filter.
The filter design dependency on line impedance, load match, and component line resistive loss can be reviewed.
For a lowpass filter of this type, the stubs should be open-circuit, although the stubs can be short-circuited by means of the lower drop-down menu.

User Notes:
The filter structure was derived from a lowpass lumped component LC prototype and demonstrates the repeated passbands due to the transmission line periodicity. The filter basic shape type is preserved and so could be used for bandpass applications. The repeated bands occur at centre frequencies 4nfc and bandwidth 2fc.
Note how component loss quickly damps resonances to degrade the passband cutoff shape.
Short-circuiting stubs does not produce the highpass complement. However, another class of bandpass filters does use stubs that are shorted, with lengths that are odd multiples of one quarter wavelength. These stubs are separated by quarter wavelength lines of the system characteristic impedance (i.e. Z2 = Z4 = Z0). In this class, open-circuiting the stubs does produce the complementary bandstop design.
Note that the analysis takes into account the transmission line approximation of the discrete component prototype, but, does not include media dispersion, cross-coupling, or corner effects.
Practical designs invariably require tuning, and some required line impedances may not be realisable in a chosen line medium.

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