While it may not be glamorous, the filter is one of the most widely implemented functions across all communication systems.
By Rob Howald
I was pondering topics for this
month’s column over a couple days in late January, during which I took my 9-year old daughter skiing for the first time. I generally do my best thinking when I’m working out or doing some similar physical activity. I figured I’d have a bit of time in lines and on the lifts to go over in my mind some of the ideas for future columns that had been percolating in my mind. However, I was not prepared for the torrent of stories spilling from my daughter about the Backstreet Boys, what one friend said at
recess to another friend, how the boys on the school bus were saying curse words in the back, and on and on. The only thing capable of silencing her was taking a spill on a sharp turn she was unable to negotiate. Ah, it was all so obvious. My column idea became crystal clear when I realized that what I needed was a kid-band voice filter. So, there you have it. Filters — the well thought out topic for another “Building Blocks” column.
The filter is one of the most widely implemented
functions across all communication systems. In any system diagram, blocks representing filters will be present. Actually, to some degree, the need for the filtering function is so fundamentally understood, and the technology considered pedestrian, a block diagram may ignore the filter altogether. In this way, further confusion can be assured by an author with respect to the necessary functionality of a particular subsystem.
For our purposes, filtering refers to the deliberate implementation of a
functional block whose objective is to modify the frequency domain characteristics. Equivalently, we could describe it as a modification of the time domain characteristics, however, filtering is primarily thought of as a frequency domain operation. With that understanding, we will concentrate on the various uses and applications of different types of filters.
RF & IF Filters
Radio frequency (RF) and intermediate frequency (IF) filters are bandpass filters, meaning a selected portion of spectrum is allowed to pass through the filter, and frequencies outside this desired band are rejected. In the RF and microwave world, filters come in many shapes and sizes because implementations must change as the frequency of operation changes. If you spend anytime in the microwave area, you realize that there is no such thing as stand-alone resistors, capacitors, or inductors. Instead, there are
various physical means by which the frequency-shaping properties of inductors and capacitors in the right combinations can be realized.
Figure 1
shows a common RF chain at the input of a generic receiver. There are two filters shown in this diagram, one before the frequency mixer, and one after. The mixer takes the input RF frequency band, mixes it with the local oscillator (LO), such that the RF band moves down (sometimes up) to a different band on its
way to being brought to baseband for processing information that the RF signal carries. In satellite and other relay-type systems, the output of such a cascade may just be another RF frequency. These filters serve the following purposes. The first type of filter provides some broad preselection, keeping excess junk out of the mixing process, as well as ensuring that the mixer image band is attenuated. The image band is a frequency band that appears at the mixer output in the same band as the desired
response, thus causing possible signal degradation. This filter does not achieve exceptionally high performance from the bandpass response standpoint. It is often desirable to have the filter be at low insertion loss for noise figure purposes, and filters deeper in the cascade set the ultimate spectral performance.
The second filter in the cascade is more important to the spectral properties of the system, and is critically important to providing the rejection of undesired mixer output signals. Mixers
inherently generate every combination of LO frequency and RF frequency. Obviously, this is not an acceptable spectrum to pass on to further processing stages. In terms of spectral properties, this filter would be part of defining the channel bandwidth properties, with specifications such as stopband attenuation for adjacent channel rejection and passband performance requirements which emphasize the filter’s effect on the information content (amplitude ripple, group delay variation). This filter in some
systems would be considered the IF filter, due to its relationship between the RF input and baseband output of the cascade.
IF FIlters
The term “IFfilter” can represent many things. The IF filter plays a special role in radio and TV systems, where the input frequency is variable across the set of channels. The heterodyne receiver greatly simplifies radio receiver
implementation. Rather than carefully tuning a high-performance receiver filter to the desired channel, the heterodyne receiver relies on a single frequency high-performance filter. Being single frequency provides the design with more stability, more reliability, and very high performance, something difficult to accomplish for tunable filters at RF frequencies. Instead, the channel frequency is adjusted to a fixed IF frequency by varying the LO frequency, sweeping a different channel through the IF filter as the
mixer stimulus varies. When this technique is used, a single high-performance filter can be implemented to provide the signal quality filtering.
Example filters that fill this function are crystal filters (extremely narrowband filters at RF frequencies), and surface acoustic wave (SAW) filters. SAW filters are known particularly for their impressive shape factor capabilities. That is, the filter characteristics can closely approximate the ideal “brick wall” filter. This technique allows
many more channels to share the spectrum, since large guard bands to avoid interference from adjacent channels are no longer necessary.
Diplexers
Another variant on a standard RF filter is a diplexer arrangement. The word diplexer refers to two filters of adjacent and nonoverlapping passbands. This arrangement is commonly applied to a set of multiple signals that must be
separated. Part of the signal multiplex is within the passband of one side of the diplexer. The rest of the spectrum is in the rejection band of the first filter, and often in the passband of the second. Sometimes, a second filter is used to terminate a second signal multiplex into a load, rather than to allow it to impinge on the rejection band of the first. When a signal falls in the rejection band of the filter, it is reflected from where it came from due to the impedance mismatch, and this can potentially
create other system problems if not treated with care.
A practical example is the CATV multiplex. In this case, the video channels begin above 50 MHz. This is where the broadcast set of channels to the home begin in frequency. For communications from the home to the CATV headend, the reverse path is used and the allotted spectrum is 5 to 40 MHz in North America. In the plant equipment, signals must travel in both directions through the components. To properly process the signals of interest in the
field equipment, a diplexer is placed at the coaxial port. The diplexer has a split of about 40/50 MHz. It consists of a lowpass filter at 40 MHz and below and a highpass filter above 50 MHz. Thus, one side of the diplexer’s traffic travels towards the home carrying video. Coming back through the opposite side of the diplexer is traffic coming from the home towards the headend.
Active Filters
Not long ago, an active filter would have, by implication, described a low-frequency filtering function. The term “active filter” generally refers to the use of operational amplifiers to implement the functionality. Op amps are basically an arrangement of transistor amplifiers in a particular configuration, typically a differential amplifier at the core, so this is not necessarily a definition of active filters. Today, this low frequency limitation is no longer as constraining,
because op amps have pushed their way into the RF domain.
Active filters are particularly useful in several situations. They combine the key functions of gain and spectral manipulation nicely. These filters can simplify designs because low-frequency filtering functions are often difficult and cumbersome to implement at low frequencies, particularly inductors. This makes them extremely valuable parts for audio circuits. Active filters also easily interface to some of the signal processing equipment
that is often cascaded with the filtering function, and provide some flexibility in terms of impedance control. Finally, active filters can be made programmable. Different frequency responses can be generated from the same circuitry.
Active filters can be any type (such as lowpass, bandpass, or highpass). However, in practice, the lowpass structure has had the greatest impact, and there are significant limitations on the sensitivities of high-performance filters, particularly of the bandpass type.
In other words, without precision resistors and capacitors, some filter structures may have a significantly degraded filter response, more so than if implemented with the bulky low frequency passive elements.
Nyquist filters
The Nyquist filter function is considered a time domain function as much as a frequency domain function. By Nyquist filters, I am referring to the
pulse-shaping operations done in transmitters, and also receivers, to guarantee zero intersymbol interference (ISI) in digital communication systems. Without going into too much detail (a December 1998 “Building Blocks” column, “The Shape of Things,” pp. 12 to 17, was devoted exclusively to the topic), the actual modulation function of mapping bits to symbols is a discrete function, leaving what would be rectangular pulses if no filtering were applied beyond this mapping. There are some
problems to signaling using rectangular pulses. While ideal rectangular pulses cannot interfere with one another, this situation is impossible to create in practice, as real channels will cause pulse dispersion. More importantly, unfiltered digital modulation is extremely bandwidth inefficient.
Within the transmitter, discrete rectangular symbols are filtered into pulse shapes with a Nyquist signature. To meet the Nyquist criteria, filtering is implemented such that processing at the receiver results in
zero ISI by design, despite the dispersion of the pulse shape through the filter. This is exactly the point — controlled pulse dispersion, with the properties under the designer’s control. The gain is bandwidth efficiency, while maintaining the ISI mitigation. On the receive side, an additional, identical filter is used. A composite of the two filters actually completes the Nyquist criteria.
A commonly referred to pulse shaping filter is the raised-cosine and/or root-raised cosine
filter. This is actually a family of filters. An example of a raised-cosine pulse is shown in
Figure 2
. The filter takes a finite pulse period and generates a pulse with infinite time domain sidelobes. This may seem like a curious way to do business. However, if we think about the relationship of time domain and frequency domain properties, we would recognize that this type of time domain result corresponds to a bandwidth savings. Additionally, if we consider that the
digital data will be sampled for detection purposes, we can show that the point at which this occurs, the peak, is free of interference from adjacent symbols — in theory. These adjacent symbols would be at the zero crossings on the x-axis of
Figure 2
.
As usual, I failed to contain my verbiage enough to squeeze this all into one column. In an upcoming column, I will discuss other filter topics such as equalizers, anti-alias filters, loop filters, and
digital filters, which are all extremely valuable concepts in communications.
Rob Howald
is the director of systems engineering in the transmission network systems group at General Instrument in Hatboro, PA. He has a BSEE and an MSEE from Villanova University, and received his PhD from Drexel University. He can be reached at
rhowald@gi.com
.
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