# Quarter wave resonant cavity

1. Dec 21, 2012

### FrankJ777

I've been self studying microwave engineering for a little while, and also I work in the radio telecommunications field. I try to relate what I've learned in the book to what I encounter in out in the field. Recently I was studying resonant cavities. From what I thought I understood about them, they need to be an integer multiple of the electrical half-wavelength to accommodate the electric field zero at the conductor walls. I notice at work we commonly use duplexes, bandpass and reject filters, that in the literature says they are quarter wave cavities. Can anyone explain how a quarter wave cavity would work, as it don't think there would be a zero electric field at the conducting walls.

Thanks

2. Dec 22, 2012

### the_emi_guy

You are right to notice that, in order to satisfy boundary condition at metal walls, we need half wavelength from wall to wall.

However, the equivalent circuit for such cavity is drawn as back to back quarter wave sections, each starting from the center.

3. Dec 22, 2012

### FrankJ777

Thanks emi guy. I'm trying to understand your description.

I notice these duplexers have two 1/4 wave cavities on each side, the low pass side and high pass side. You don't mean that the two quarter wave cavities make a 1/2 wave resonator do you? If not do you know where I can find the derivation of the equivalent circuit? In my textbook (Pozar), a coaxial quarter wave resonator is derived, but not the 1/4 wave cavity. I assume they work quite differently, eg TEM vs. TE, TM mode.