by Mark Blackwood, Fairview Microwave
RF filters are a key component in practically any signal chain, and these devices essentially consist of an electrical network that discriminates the amplitude and phase characteristics of a signal with respect to a certain frequency range. Depending on the application, it could be necessary to filter out noise and unwanted signals, or to limit a transmit signal to a pre-specified frequency band in order to prevent interfering with other signals in the vicinity. There are libraries of knowledge dedicated simply to the topic of filter design, as the foundations were laid in the mid-1930s. It may be beneficial to have a basic understanding of filter design in order to better comprehend the inner workings of these devices. Filters are often a component in a massive array of applications, and due to their many uses, filters can be analog or digital, active or passive, linear or nonlinear, time-invariant or time-variant, causal or non-causal. Additionally, filters can have an infinite impulse response (IIR) or a finite impulse response (FIR). Generally, most filters implemented are causal, time invariant, and linear. This article focuses on RF, analog filters which operate on continuous-time signals, or in real-time. These filters are oftentimes still applied as discrete components as opposed to integrated into a system on chip (SoC) as they tend to offer better selectivity with high frequency signals.
Filters at a Glance
There are essentially four different types of analog filters: a low pass filter (LPF), high pass filter (HPF), bandpass filter (BPF), and a band reject (notch) filter. The ideal filter has an input port, an output port, and allows signals in a predetermined frequency band, also known as the passband, to pass without substantial loss, while attenuating frequency components beyond the passband.
A LPF discriminates all frequencies below a certain frequency point and allows signals to pass beyond that threshold. A HPF could be perceived as a complement to the LPF where signals can pass above a certain frequency point while all lower frequency signals are attenuated. Similarly, a BPF and band reject filter could also been seen as complements. Where a BPF supports transmission in a preselected frequency band and rejects all other signals, a band reject filter suppresses signals in a preselected frequency band and allows signal transmission at all other frequencies.
Filter design essentially arranges inductors, capacitors, resistors, and resonators in various formations and topologies in order to develop a specific filter type and frequency response. The inductance and capacitance of a filter contributes to the overall reactance (imaginary component of impedance) of the circuit. That, in addition to the resistance (real component of the impedance) generates the overall impedance as a function of frequency. These impedance changes generate matches at certain frequency bands, thereby passing certain signals while suppressing others.
Inductance, capacitance, and resistance can be realized in various physical formations. For instance, an inductor can be a coil of copper wrapped around a ferrite, or a metallized spiral printed onto a PCB. Inductive reactance increases with frequency while the capacitive reactance decreases with respect to frequency. Resonators are mechanical structures that present a complex impedance response to varying frequency stimulus. These features allow for a wide array of filter form factors for various applications.
Filter mathematics involves transfer functions, or the ratio of input and output signals, where the numerator roots are the zeroes of a filter and the denominator roots are the poles of a filter. The order of the filter is the highest power variable (e.g.: s^2 is a 2nd order filter) or the number of capacitors and inductors in a circuit. Generally, the higher the order, the more effective a filter is at suppressing signals at different frequencies at the tradeoff of complexity and filter element performance requirements. The filter response can be readily visualized in a Bode Plot, or a logarithmic plot of gain versus frequency and phase versus frequency, where the slope of the gain turns positive at a zero while the slope goes negative at a pole. Therefore, the more poles or zeroes a filter typology generates, the sharper the slope turns to effectively attenuate signals.
The passband is calculated at the point where the gain has dropped 3 dB from its peak, and these -3 dB frequencies are also known as the cutoff frequencies. The peak value of the filter gain can be determined from the measured gain at the center frequency, or the frequency average of the -3 dB frequencies. The filter Q is another parameter that assesses the quality of a filter, and essentially describes the “sharpness” of the filter amplitude response. Or, how sharply unwanted signals are attenuated. Filters with a high Q have more reactance than resistance in their circuits.
The higher the capacitor and inductor count, the higher the reactance, the order, and the Q of a filter become. It may at first glance seem like a simple solution to add more inductive and capacitive components to a circuit to create a steeper roll off. However, additional filter elements increase the complexity, size, and weight of the overall filter. Depending upon the application, the practical implementation of a filter may call for the tradeoff among competing requirements including size, weight, powerhandling, and cost (SWAP-C) and other performance criteria.
There are many methods and techniques for realizing a given filter typology, and some common filter constructions include lumped element, piezoelectric, cavity, waveguide, and microstrip technology.
Lumped element filters are typically leveraged around the VHF-band, but can also be used in RF applications (up to 40 GHz). However, lumped element filters are difficult to implement at millimeter-wave frequencies, in part due to the dimensional limitations of fabrication process technology—the filter elements and lead wires must be much smaller than the wavelength of the transmission line. These filters are realized through discrete resistive, capacitive, and inductive elements, as through hole or surface mount technology (SMT) thin film processes.
In planar, or thin film technology, the filter’s transmission lines can be printed in various configurations, optimized to yield a preferred performance. The planar lumped element filters can be constructed as microwave integrated circuits (MICs), monolithic microwave integrated circuits (MMICs), low temperature co-fired ceramics (LTCC), and even in high temperature superconductors (HTS). Generally, planar lumped element filters are limited by a lower Q and lower power handling over the bulkier lumped element filters.
Not to be confused with thin film lumped element technologies, a distributed element filter inherently relies on evenly distributed transmission lines for partitioning in space and time, as opposed to localized metallization to yield discrete components. Typically used in the UHF-band, the distributed element filter can be designed to tighter tolerances to provide a higher frequency alternative to a lumped element filter. Distributed element filters can be realized through the same construction methods used to fabricate a lumped element filter. Furthermore, microstrip-based lumped element filters and distributed element filters could be found in diplexers for mobile and wireless communications.
Cavity filters are normally designed as notch filters and are tuned to a specific resonance in order to pass specific frequencies. Typically, these filters offer a very high Q and low insertion loss over a narrow bandwidth as compared to the lumped element and distributed element filters. Cavity filters can be realized through several architectures including combline, helical, and interdigital configurations. These filters are assembled in coaxial connector packages constructed of a metal alloy body with “tuning screws” to finetune the frequency response.
Cavity filters are often integrated in duplexers for radio communications, and these duplexers are essentially composed of very high-Q bandpass and band reject filter networks in the transmit and receive paths to and from the radio antenna. The highly tuned circuitry is necessary as these adjacent channels occupy different frequencies that oftentimes are as close together as possible.
The piezoelectric filter leverages physical vibrations in some sort of dielectric material to generate an electrical response. These piezoelectric substrates can be based in ceramic, quartz crystals, lithium niobate, or any other materials that can be mechanically tuned for specific electrical characteristics. Quartz crystal filters tend to be more accurate and temperature stable than ceramic filters, while ceramic filters tend to be less costly and smaller than crystal filters. For this reason, ceramic filters have proliferated in solid state electronics.
While ceramic and quartz filters are typically used in the lower HF-band applications, surface acoustic wave (SAW) resonators and bulk acoustic wave (BAW) resonators are a type of piezoelectric filter that can be leveraged with microwave frequencies. SAW filters convert an RF signal to an “acoustic wave” using interdigital transducers (IDT), or interdigitated metallic fingers, and then back to an electrical output. The SAW filter is commonly used in mobile communications systems. Current SAW filters are compact, present low insertion loss, and are able to operate reliably to S-band frequencies.
BAW filters function similarly to SAW filters, except the resonant wave propagates through the “bulk” of the material. These filters generally operate well into the Ku-band, and are therefore often considered the high-frequency counterpart of the SAW filter.
Contrary to the limited frequency bands of the lumped element filters, distributed element filters, and piezoelectric resonators, the waveguide filter offers selectivity up to millimeter wavelengths and has the ability to handle high powers. While waveguide filters are generally higher in cost and naturally greater in size, the waveguide filter offers options for radar, satellite communications, and microwave links where both high frequency and high power are available. Waveguides inherently operate with low insertion loss, and when combined with a waveguide constructed at resonant length, they can deliver very sharp filters with extremely high Qs. These filters are often leveraged in duplexers for radar applications, as they function at high frequencies, offer the frequency selectivity necessary, and can handle high transmit powers to hundreds and thousands of watts.
The choice of a filter technology varies greatly depending on the application—size, power handling, frequency range, noise addition, and cost are all variables. For instance, microcontrollers employ low frequency quartz crystal oscillators where space and temperature stability are critical, while larger lumped element filters can offer solutions where power handling and cost are valued most. The specific filter necessary for a low frequency application can differ greatly from a filter leveraged at higher RF frequencies.
Baseband Analog Filter Applications
The baseband includes bandwidths that begin near DC and end at a higher cutoff frequency. Typically, baseband signals will come from a digital source or an analog sound source, such as a microphone. Baseband signal processing does come with its restrictions because of the limited dynamic range of active filters and unwanted variations due to nonlinearities.
The active components in a filter network offer linear functionality within certain frequencies and the baseband signals can fall beyond the dynamic range of these components. Tuning circuitry is also often integrated in a baseband filter to compensate for any frequency shifts from temperature and process variations. These devices can also affect the dynamic range of the signal chain, specifically in a receiver typology.
Baseband filters are a core component of baseband receivers, transmitters, and transceivers in wireless communications applications. Hence, baseband filters in wireless communications are required to process high data rate signals where baseband analog filters must have wide bandwidths while maintaining high linearity, low noise, and low power consumption . The quality of the equipment can very heavily depend upon the wideband performance of these filters.
Often employed in analog telecommunication architectures, Frequency Division Multiplexing (FDM) allows for multiple baseband signals from multiple telephones to operate simultaneously through a single transmission channel. This is possible by modulating each signal to an non-overlapping sub-band to transmit and then demodulating the signal through BPFs at the receiver end. Oftentimes, LPFs will be leveraged before modulation in order to limit the bandwidth of the source and avoid interference between parallel transmissions.
Intermediate Frequency (IF) Analog Filter Applications
Using an intermediate frequency (IF), or the frequency that is obtained by down-converting an RF signal through a mixer or the signal prior to upconversion, is often necessary to increase the selectivity of a radio receiver and perform other signal processing functions. Otherwise, the receiver would have to successfully demodulate signals over a massive frequency band. Without using intermediate frequency stages, the entirety of the RF signal chain would require a reliably flat response across too wide a bandwidth.
Carrier frequencies are instead filtered through a fixed series of BPFs and downconverted or upconverted to a specific IF frequency connected to a highly optimized modulation/demodulation circuit. This process is often called heterodyning, and is the core of a superheterodyne receiver. This approach leverages several stages of filters in order to downconvert a carrier signal to IF, while rejecting harmonics, interference, and noise prior to demodulation.
Applied in television, mobile, satellite communications, and radar applications, the filter construction and type of filters employed in a superheterodyne receiver will vary based on the application requirements. Crystal and ceramic-based filters are most often found in these applications, due to their cost effectiveness and small size. These filters are also used to take advantage of the inherent strength of the superheterodyne receiver, that the use of the fixed IF frequency permits extremely precise tuning available with piezoelectric resonators. Active filters in IF applications generally have the added benefit of having a higher gain and greater selectivity, and this naturally leads to less stages in the signal chain.
RF Filter Applications
High frequency (RF) filtering without any downconversion typically eliminates crystal and ceramic filters as an option for many applications based on their frequency limitations. The shaping of signals at the microwave frequency can be complex, as the control over the tolerances of the mechanical structure becomes significant compared to the wavelength of the signals. Ohmic dissipation is greater at microwave and millimeter-wave frequencies because of the large loaded Q factor. Waveguide filters are more often used for filtering in the RF band and beyond, particularly in satellite and radar communications where there are high transmit powers and extremely sensitive receivers are used.
Analog filters come in many form factors, passbands, and frequency responses in order to cater to their respective applications. Solid state electronics may include piezoelectric filters, while hybrid MICs in test instrumentation would employ lumped and distributed element filters. While much greater in size, waveguide and cavity filters are necessary for duplexers where cavity filters can be tuned for extreme selectivity in radio communications and waveguide filters can handle the high power necessary in radar. In order to select the ideal filter, it may be important to understand the construction and electrical characteristics to properly integrate a specific filter into an architecture.
1. Design of Analog Baseband Circuits for Wireless Communication Receivers