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RF filter design – from resonators to filters

By Gergely Simon 19 October 2020

In this blog post, we answer some of the fundamental why, what, and how questions regarding filter design, mainly centered around the requirement imposed by mobile communications.

Why do we need filters?

With the increase in demand for data transfer and communication between mobile devices, and especially the required bandwidth, more and more frequency bands are utilized for mobile data (2G to 5G), WiFi and even simple phone calls. These need to be properly isolated from each other to avoid crosstalk and unwanted noise signals. To achieve this, filters are employed: these allow only certain frequencies to pass, and depending on the range of these, can be grouped as low-pass, high-pass, band-pass and band-stop.

What do we want to achieve?

For simplicity, in this blog post we will look at band-pass filters: these allow most of the energy content between two frequencies to go through the filter, while stopping anything outside this range (see Fig. 1). The real devices are never perfect: insertion loss signifies the non-perfect passing of signals within band, and rejection quantifies the amount of signal passed out-of-band. These are expressed in decibels (dB), and less than -3 dB for insertion loss, and at least 30 dB for rejection is considered adequate filter behavior.

RF Filter Design

Fig. 1. Typical band-pass filter response. Image from [1]

How do we achieve it?

In filters, often resonators are used with typical impedance response shown in Fig. 2.

Resonator Impedance

Fig. 2. Typical resonator impedance and phase. Image from [2]

These are cascaded in various topologies to ultimately achieve the overall band-pass behavior with as high selectivity as possible. In the simplest case, the so-called ladder topology is employed, as shown in Fig. 3.

resonators

Fig. 3. Typical ladder filter configuration and impedance response of the series (Z1) and shunt (Z2) resonators, with the overall filter operation. From [3]

Let us look at this example in detail. Note that the series resonator (magenta curve in Fig. 3) has a higher frequency response than the shunt resonator (blue curve in Fig. 3), and the parallel resonance frequency of the shunt resonator aligns with the series resonance frequency of the series resonator (magenta curve is shifted to the right with respect to the blue curve).

Now, if we consider a setup with only a single stage (one Zs and one Zp in the top of Fig. 3), the following arguments can be made, imagining this is basically a voltage divider:

  1. Out of band (either left of ~2.1 GHz and right of ~2.25 GHz) the impedance of the two resonators is comparable – the output is roughly half the input
  2. Around the series resonance frequency of the shunt resonator (lower cutoff, ~2.1 GHz), the impedance of the shunt resonator goes to zero, virtually grounding the output, dropping the signal significantly
  3. Around the crossover (~2.2 GHz), the impedance of the shunt resonator tends to increase significantly, while the impedance of the series resonator tends to zero – this creates almost a short between the input and output, while isolating the ground through an almost ideal open circuit. This is the passband behavior
  4. Around the upper cutoff (~2.25 GHz) the reverse of point 2 happens: the series impedance tends to infinity, isolating the output from the input, and again a sharp drop in transmittance

Additionally, the impedance of the shunt resonator is generally lower than that of the series resonator (magenta curve is shifted up with respect to the blue curve). This further increases the out-of-band rejection, as the voltage division has always a smaller value at the output (considering out-of-band).

Finally, note that in general these filters are investigated using transmission line theory and power carried by propagating waves. Nevertheless, the voltage divider analogy provides a good qualitative overview.

Other topologies

The ladder filter does not have great rejection out-of-band, as shown in Fig. 4. Therefore, other topologies, such as a lattice structure, or a combined ladder-lattice topology can be employed (Fig. 5).

Fig. 4. Filter response for various configurations. Image from [4]

RF Filter

Fig. 5. Filter topologies (a) ladder, (b) lattice (c) ladder-lattice. Imgae from [4]

Further information on structure and design considerations can be found in the references and in Ken-ya Hashimoto: RF Bulk Acoustic Wave Filters for Communications. For design of resonators for filter applications, refer to our previous blog posts, such as:

References

[1] https://en.wikipedia.org/wiki/Band-pass_filter

[2] Optimal parameters determination for nanostructure-enhanced surface acoustic waves sensor. 2014 37th ISSE International Spring Seminar in Electronics Technology (ISSE). DOI: 10.1109/ISSE.2014.6887638

[3] A Modified Lattice Configuration Design for Compact Wideband Bulk Acoustic Wave Filter Applications, Micromachines 2016, 7(8), 133; https://doi.org/10.3390/mi7080133

[4] Techniques for Tuning BAW-SMR Resonators for the 4th Generation of Mobile Communications. DOI: 10.5772/55131

Gergely Simon
Gergely Simon

Gergely Simon is an Application Engineer at OnScale. He received his PhD in Smart Systems Integration from Heriot-Watt University. As part of our engineering team Gergely assists with developing applications, improving our existing software and providing technical support to our customers.