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60 The PCB Design Magazine • December 2014 At microwave frequencies, a resonator can be made by using a conductor with a physi- cal length that is exactly ½ wavelength of the wave on the circuit. This ½ wavelength conduc- tor will resonate, which is accomplished by a wave that bounces back and forth and sets up a standing wave. The standing wave generates a lot of energy and resonates at the frequency associated with that ½ wavelength. The big question is this: How do you get the energy on the conductor that is acting like a ½ wavelength resonator? If you have a conductor that connects to the ½ wavelength resonator, that combination creates a much longer con- ductor, and it no longer works as a ½ wave- length resonator. This means that you cannot directly connect to the resonator conductor and you will need to "couple" energy to the resona- tor. This is done by using feed line conductors on both sides of the ½ wavelength conductor, which are physically very close to the resonator conductor; as a result, the energy on the feed lines will have electric fields that radiate onto the resonator. The radiated fields will couple electric en- ergy onto the resonator, and now the conduc- tor that is ½ wavelength long will resonate. An example of a ½ wavelength resonator, with feed lines on both sides of it, is shown in Figure 1a. Filtering Frequencies Let's take this idea and expand it to make a filter. This filter example will only let energy pass from a band (range) of frequencies, and is known as a bandpass filter. Due to the nature of the resonator, it is very frequency-dependent; in other words, the resonator will have a lot of energy only at a narrow range of frequencies. The tight range of frequencies for resonance is based on the physical length of the conductor being a ½ wavelength. To illustrate, if higher frequencies are con- sidered, the wavelength of that energy is shorter and the physical length of the resonator con- ductor is not correct for those frequencies that will not allow resonance. However, if you put together (couple) several resonators that are slightly different, they will resonate within a band of frequencies and let energy through within that range of frequencies. The resonators will not resonate outside of the frequencies of which they are the correct size, so the energy from those frequencies will be shut off. The res- onators in our filter example will be put side-by- side so they can couple energy better from one resonator to the other, as shown in Figure 1b. The best way to view the electrical perfor- mance of the bandpass filter is to show how much energy is passed through the filter and how much is rejected by the filter, when consid- ering a wide range of frequencies. One method of doing this is by using a network analyzer and showing the S21 curve over a range of frequen- cies. The S21 parameter is a scattering (S) param- eter, which basically shows how much of the energy that arrives at port 2 came out of port 1. . It can be thought of as input and output for port 1 and 2 respectively, as shown in Figures 1a and MAkING A CONNECTION WITH CONDUCTOR DISCONTINUITIES continues lightning speed laminates Figure 1: shown is the signal layer of a microstrip (a) gap coupled resonator and (b) edge coupled bandpass filter.