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Agilent AN 1287-8
Simplified Filter Tuning Using Time
Domain
Application Note
Table of Contents
3 Introduction
3 Difficulties of filter tuning
4 Ideal tuning method
5 Basic characteristics of bandpass filters
6 Time-domain response of simulated filters
7 Effect of tuning resonators
8 Effect of tuning coupling apertures
10 Practical examples of tuning filters
10 Setting up the network analyzer
11 Example 1: Tuning resonators only
13 Example 2: Tuning to a "golden filter"
16 Example 3: Using simulated results for a template
17 Effects of loss in filters
18 More complex filters
18 Cross-coupled filters
19 Duplexers
20 Conclusion
21 References
22 Summary: Hints for time-domain filter tuning
23 Appendix A: Understanding basic bandpass filter design
25 Appendix B: Using time-domain in the network analyzer for
filter tuning
2
Introduction
The increase in wireless communications services Difficulties of filter tuning
is forcing more and more channels into less fre- The interactive nature of coupled-resonator filters
quency spectrum. To avoid interference, very strin- makes it difficult to determine which resonator or
gent filtering requirements are being placed on all coupling element needs to be tuned. Although some
systems. These systems usually employ coupled tuning methods can achieve an approximately cor-
resonator filters to handle the power levels and rect filter response, final tuning often requires the
provide the needed isolation. The difficulty of tun- seemingly random adjustment of each element
ing these filters quickly and accurately often limits until the final desired filter shape is obtained.
manufacturers from increasing their production Experienced tuners can develop a feel for the
volumes and reducing manufacturing cost. proper adjustments, but months are often required
before a novice can be proficient at tuning complex
In a coupled-resonator cavity-tuned filter, the cen- filters. The time and associated cost of tuning, and
ter frequency of each resonator must be precisely the difficulty and cost in training new personnel
tuned. The couplings between resonators must also can limit a company's growth and responsiveness
be precisely set to achieve the proper passband to changing customer needs.
response, low return loss (reflection), and small
passband ripple. Setting coupling coefficients and Some companies have attempted to automate the
tuning the resonators are as much art as science; tuning process, using robotics to engage and turn
often a trial-and-error adjustment process. Until the tuning screws, and an algorithmic process to
now, there has been no alternative. accomplish the tuning. The tuning algorithms are a
particular problem, especially when a filter is nearly
This application note describes a method of tuning tuned, at which point the interaction between
a filter using the time-domain response of its stages can be so great that final tuning cannot be
return loss, which makes filter tuning vastly easier. achieved. New filter designs may require entirely
It is possible to tune each resonator individually, new algorithms, making it even more difficult for
since time-domain measurements can distinguish test designers to keep up with changing require-
the individual responses of each resonator and ments. Manufacturing changes that affect the filter
coupling aperture. Such clear identification of components, such as tool wear or changing vendors,
responses is extremely difficult in the frequency may also cause algorithms and processes to
domain. Coupling coefficients may be precisely set become less effective.
to provide a desired filter response, and any inter-
action caused by adjustment of the coupling struc- In some cases, tuned filters go through tempera-
tures and resonators can be immediately deter- ture cycling or other environmental stress as part
mined and accounted for. of the manufacturing process, and their character-
istics may change as a result. It can be very diffi-
Perhaps the most important advantage of the time- cult to identify which resonators or coupling aper-
domain tuning method is that it allows inexperi- tures need to be retuned using conventional filter
enced filter tuners to successfully tune multiple- tuning methods.
pole filters after only brief instruction. Such rapid
proficiency is impossible with previous tuning
methods. This technique also lends itself well to
the automated production environment, which has
always been a challenge.
3
Ideal tuning method
The solution to these difficulties would be a tuning
method that is simple, flexible, and deterministic.
That is, one in which the individual adjustment
goals for each tuning element, resonator, and cou-
pling aperture would not depend upon the other
elements in the filter. The response to each tuning
screw would be easily identified, and any interactive
effect would be immediately seen and accounted for.
Ideally, each screw would only need to be adjusted
once. Finally, the tuning method would not depend
on filter type or shape, or number of filter poles.
This application note presents a technique that
clearly identifies the resonator or coupling aperture
that needs to be tuned, and enables the operator to
see and correct for interactions. Filters can be tuned
to match any filter shape within their tuning ranges.
Although this technique does not meet the ideal goal
of requiring only a single adjustment of each screw,
it greatly simplifies and speeds up the filter-tuning
process.
4
Basic characteristics of bandpass filters
First, let's review some basic information and char-
acteristics about bandpass filters.
Bandpass filters are commonly designed by trans-
forming a low-pass filter response to one that is
centered about some new frequency. Coupled res-
onators, which may be lumped LC resonators,
coaxial line resonators, cavity resonators, or
microwave waveguide resonators, are used to cre-
ate the upward shift in frequency. The terms res-
onator, cavity resonator, and cavity will be used
interchangeably in this application note. More
details on bandpass filter design can be found in
Appendix A.
The center frequency of the filter is determined by
setting the resonators. In most designs, all res-
onators are set exactly to the center frequency,
with the effects of adjacent coupling included in
the calculation of the resonant frequency.
The filter shape, bandwidth, ripple, and return loss
are all set by the coupling factors between the res-
onators. When properly tuned, the resonators have
almost no effect on the filter shape. The only
exception is that the input and output resonators
set the nominal impedance of the filter. Usually an
input or output transformer is used to match to a
desired impedance. Of course, when the resonators
are not properly tuned, the return loss and inser-
tion loss will not be at the optimal levels.
Because the resonators are coupled to each other,
tuning one resonator will have the most effect on
the adjacent resonators, but it will also have some
smaller effect on the remaining resonators. The
extent of the effect depends on the coupling factor.
With this information in mind, we are ready to
explore the new time-domain tuning technique.
5
Time-domain response of simulated filters
To introduce this tuning method, we will use simu- Figure 2 shows the frequency response and time
lations to examine what happens to the time- response of the filter. Notice the distinctive dips in
domain response of a bandpass filter when it is the time-domain S11 response of the filter. These
tuned. We will start with a relatively simple filter: are characteristic nulls that occur if the resonators
a five-pole coupled resonator filter with four cou- are exactly tuned. The peaks between the nulls
pling structures, designed for a Chebyshev relate to the coupling factors of the filter, as we will
response with 0.25 dB of passband ripple. In this see later. Markers 1 through 5 have been placed to
example, a filter response will be simulated by show the characteristic dips corresponding to res-
Agilent Technologies' Advanced Design System onators 1 through 5 in the filter. Although there are
(ADS) microwave design software, so that the some dips to the left of marker 1, those are not part
exact values of constituent components are known. of the filter response. Generally the peaks corre-
The frequency sweeps will be performed in the sponding to the filter response will be much higher
simulator, and the results will be downloaded to in magnitude than the ones in the t<0 region, which
the vector network analyzer (VNA), where the are not meaningful, and usually the dip correspon-
instrument's time-domain transform application ding to the first resonator will occur near t=0.
can show the effects of filter tuning. The schematic
for the filter is shown in Figure 1.
To set up the measurement for time-domain tuning,
the frequency sweep MUST be centered at the
desired center frequency of the bandpass filter.
This is critical, since the tuning method will tune
the filter to exactly that center frequency. Next, the
span should be set to approximately two to five
times the expected bandwidth.
Figure 1. Schematic for five-pole coupled resonator bandpass filter
S21
S11
Figure 2. The frequency and time-domain response of a bandpass filter
6
Effect of tuning resonators The lower plots show one response with only the
The example filter starts out with the ideal design third resonator mistuned 2% high and another one
values, which yields the desired response since it with only the fourth resonator mistuned 2% low.
is properly "tuned" by definition. To understand Again, it is easy to identify which resonator is mis-
the time-domain response to tuning the resonators, tuned by looking for the first dip that is no longer
we will monitor the time-domain response while minimized. Additional simulations have shown that
changing (mistuning) the resonator components in the characteristic dips are minimized only when
the simulation. Figure 3 shows the time-domain the corresponding resonators are set to their cor-
traces for three conditions (with the ideal response rect values. Changing the tuning in either direction
in the lighter trace). The upper plots show the fil- causes the dips to rise from the minimum values.
ter with the second resonator mistuned 2% low in
frequency. Note that the first dip has not changed, The key to this tuning technique is to adjust the
but the second dip is no longer minimized, and nei- resonators until each null is as low as possible. The
ther are the following dips. If a resonator is sub- adjustment will be mostly independent, although if
stantially mistuned (more than 1%), it will signifi- all the resonators are far from the final value the
cantly mask the dips of following resonators. first time through, adjusting a succeeding resonator
Therefore, to identify the mistuned resonator, look may cause the null of the previous resonator to rise
for the first dip that is no longer at a minimum. In from its minimum. If this occurs, the null for the
this case, we see that mistuning resonator 2 causes previous resonator should be optimized again. Once
the second null to move away from its minimum the succeeding resonator has been tuned and the
value. previous one optimized, additional smaller adjust-
ment to the second resonator will have very little
effect on the dip corresponding to the first resonator.
Resonator 2 mistuned
Resonator 2 mistuned
Ideal (tuned) response
Ideal response
Resonator 3 mistuned Resonator 4 mistuned
Resonator 4
mistuned
Ideal Resonator 3
mistuned
Ideal
Figure 3. The response of a bandpass filter to tuning the resonators 7
Those who are familiar with the resolution limits In the time-domain, there is no change in the first
of time-domain measurements will know that time- peak, but the second peak is smaller. While it
domain resolution is inversely proportional to the might seem that the first peak would be associated
frequency span being measured, and they may with the first coupling factor, remember that the
wonder how it is possible to resolve individual res- first coupling factor comes after the first resonator
onators in a filter when the frequency span is only in the filter, and we have already seen that the first
two to five times the filter's bandwidth. Appendix B dip after the first peak is related to the first res-
explains how the time-domain transform relates to onator. It turns out that the first peak can be asso-
bandpass filter measurements in more detail. ciated with the input coupling, which has not been
adjusted in this filter.
One more thing to note from Figure 3 is that the
S11 frequency response when resonator 2 is mis- The reduction in height of the second peak when
tuned looks almost identical to S11 response when coupling is increased makes sense, because
resonator 4 is mistuned. This illustrates why it can increasing the coupling means more energy is cou-
be difficult to determine which resonator requires pled to the next resonator. Thus less energy is
tuning when viewing only the frequency-domain reflected, so the peak corresponding to reflected
measurements. energy from that coupling should decrease. Note
that the following peaks are higher than before.
Effect of tuning coupling apertures More energy has been coupled through the first
Although simple filters may only allow adjustments coupling aperture, so there is more energy to
of the resonators, many filters also have adjustable reflect off the remaining coupling apertures.
couplings. To understand the effects of adjusting
the coupling , we will go back to our original It is important to recognize that changing the first
"tuned" simulated filter. First, we will examine coupling factor will affect the responses of all the
what happens when we increase the first coupling following peaks. This suggests that coupling factors
factor by 10%. Figure 4 shows the S11 response in should be tuned starting with the coupling closest
both frequency and time domains, both before and to the input and moving towards those in the cen-
after changing the coupling factor. In the frequency ter of the filter. Otherwise, improperly tuned cou-
domain, we see that the filter bandwidth is slightly pling near the input can mask the real response of
wider and the return loss has changed. This makes the inner coupling factors.
intuitive sense, because increasing the coupling
means more energy should pass through the filter,
resulting in a wider bandwidth.
First coupling factor First coupling factor
increased 10% increased by 10%
Ideal
Ideal
Figure 4. Effect of increasing first coupling factor (darker trace is after adjustment)
8
Now consider what happens if we take the original Thus, we have seen that the coupling factor can be
filter and decrease the second coupling coefficient related to the height of the time-domain reflection
by 10%. Figure 5 shows that in the frequency trace between each of the resonator nulls. The
domain, the bandwidth of the filter has been exact relationship also depends on the ratio of the
reduced slightly and the return loss has changed. filter bandwidth to the frequency sweep used to
Again, this makes sense because decreasing the compute the time-domain transform. The wider the
coupling means less energy will pass through the frequency sweep (relative to the filter's band-
filter, corresponding to a narrower bandwidth. width), the more total energy is reflected, so the
higher the peaks.
Examining the time-domain trace, we see no change
in the first 2 peaks, but the third peak is higher, The magnitudes of the peaks are difficult to com-
consistent with more energy being reflected as a pute because changing the coupling of one stage
result of the decreased coupling. Since the amount changes the height of the succeeding peaks. A
of energy coupled to the following resonators and detailed explanation of relationship between the
apertures is reduced, the following peaks are all time-domain response and coupling coefficients is
lower in value. Note how well the time-domain beyond the scope of this application note. Even
response separates the effects of changing each though it may not be easy to calculate these peaks
coupling, allowing the couplings to be individually simply from the coupling coefficients, once the
adjusted. In contrast, the S11 frequency response desired values of the peaks are determined, the
trace in Figure 4 is very similar to the one in apertures may be tuned directly in the time
Figure 5, so it would be very difficult to know domain. One method for determining the desired
which coupling changed from looking at the magnitudes of the peaks is by using a template as
frequency-domain response. described in the next section.
2nd coupling factor
2nd coupling factor
decreased by 10%
decreased by 10%
Ideal
Ideal
Figure 5. Effect of decreasing second coupling factor (darker trace is after adjustment)
9
Practical examples of tuning filters
Now that we have an understanding of the rela- Setting up the network analyzer
tionship between tuning resonators or coupling It is essential to set the center frequency of the
apertures and the corresponding results in the analyzer's frequency sweep to be equal to the
time-domain response, we are ready to to put the desired center frequency of the filter, since tuning
theory into practice. the filter in the time domain will set the filter's
center to this frequency. Choose a frequency span
For multi-pole cavity filters that have fixed aper- that is 2 to 5 times the bandwidth of the filter. A
tures, it is only necessary to tune for the character- span that is too narrow will not provide sufficient
istic dips in the time domain in order to achieve resolution to discern the individual sections of the
optimal tuning of the filter. To tune a filter with filter, while too wide a span will cause too much
variable coupling coefficients, it is easiest to tune energy to be reflected, reducing the tuning sensi-
the coupling to a target time-domain trace or tem- tivity.
plate. This target time-domain response for any fil-
ter type may be determined in several ways. One The primary parameter to be measured is S11
method is to use a "golden" standard filter that has (input match). However, for time-domain responses
the same structure and is properly tuned for the more than halfway through the filter, the responses
desired filter shape. This filter can be measured often get more difficult to distinguish. Even in low-
and the data placed in the analyzer's memory. loss filters, there can be significant return loss dif-
Each subsequent filter can be tuned to obtain the ferences between the input and output due to loss
same response. in the filter. In addition, there is a masking effect
that tends to make reflections from couplings and
An alternative is to create a filter from a simula- resonators farther from the input or output appear
tion tool, such as Agilent's Advanced Design smaller, since some of the incident energy has been
System. The simulated response can be down- lost due to earlier reflections in the device. For
loaded into the network analyzer and used as a these reasons, the most effective way to tune is to
template. This is a very effective approach, as look at both sides of the filter at once, so a net-
there is great flexibility in choosing filter types. work analyzer with an S-parameter test set is rec-
The only caution is that each real filter has limits ommended. To aid in tuning, the instrument's
on the Q of the resonators and the tuning range of dual-channel mode can be used to measure the
the coupling structures and resonators. It is impor- reverse return loss (S22) on a second channel. With
tant to make the attributes of the simulation con- this setup, you will tune the first half of the res-
sistent with the limitations of the structures used onators and couplings using the S11 response, and
in the real filters. tune the remaining ones using the S22 response.
Keep in mind that you need to count resonators
In this section, we will begin with a discussion of and coupling apertures starting from the port
how to set up the network analyzer to tune band- where the signal is entering the filter for that
pass filters in the time domain, and then we will measurement. Thus for S11, the first dip would cor-
show three examples to illustrate how to tune both respond to the resonator closest to the input port
resonators and coupling apertures in real filters. of the filter. For S22, the first dip would correspond
to the resonator closest to the output port of the
filter.
10
For the network analyzer time-domain setup, the Experience has shown that it is best to begin tun-
bandpass mode must be used. The start and stop ing from the input/output sides and move toward
times need to be set so that the individual res- the middle. Figure 6 shows the time-domain
onators can be seen. For most filters, the start time response after the first and fifth resonators have
should be set slightly before zero time, and the been tuned to obtain the lowest dips. Note that the
stop time should be set somewhat longer than first resonator closest to the input corresponds to
twice the group delay of the filter. If the desired the first dip in S11, while the fifth resonator, which
bandwidth is known, the correct settings can be is the first one when looking in the reverse direc-
approximated by setting the start time at t=-(2/BW) tion, corresponds to the first dip in S22. These
and the stop time at t=(2N+1)/(BW), where BW is responses are good illustrations of masking. Even
the filter's expected bandwidth, and N is the num- though the fifth resonator is correctly tuned, you
ber of filter sections. This should give a little extra cannot see that from looking at the S11 response.
time-domain response before the start of the filter Similarly, you cannot see that the first resonator is
and after the end of the filter time response. If you tuned by looking only at the S22 response.
are tuning using both the S11 and S22 responses of
CH1 S11 LOG 8 dB/ REF 0 dB
the filter, you can set the stop time to a smaller
value, since you will use the S22 response to tune
the resonators that are farther out in time (and
closer to the output port).
PRm
C
The format to use for viewing the time-domain
response is log magnitude (dB). It may be helpful
to set the top of the screen at 0 dB.
CH2 S22 LOG 8 dB/ REF 0 dB
Example 1: Tuning resonators only
The first example is a simple five-pole cavity filter
with fixed apertures, so only the resonators can be
tuned to adjust the center frequency. This filter PRm
C
has a center frequency of 2.414 GHz and a 3 dB
bandwidth of 12 MHz. The network analyzer is set
up for this same center frequency and a span of
50 MHz. Dual channel mode is used to display both START -50 ns STOP 250 ns
S11 and S22. The time-domain response is set up to Figure 6. Time-domain response of 5-pole filter after tun-
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