term "modern" in the title of any book or article never has set
right with me because it is utterly ambiguous about the era to which
"modern" refers. Sure, it sounds good at the time, but when applied
to this 1966 QST article, "modern" should be replaced with "four-decade-old."
However, in this case the content is still relevant even thought
it was written so long ago (or else I would not be reproducing it
here). It may well have been most people's first exposure to elliptical
filters. As you might expect, the rigorous, headache-inducing mathematics
is omitted, but the article does give an example of implementing
an audio frequency bandpass filter by cascading a lowpass filter
and a highpass filter. If you are familiar with filter design, you
know that because of phasing and inband impedance mismatch issues
you cannot simply butt the two together to yield an equivalent bandpass
filter. In fact, the author found it necessary to insert a 13 dB
attenuator between them in order to get acceptable performance.
July 1966 QST
of Contents]These articles are scanned and OCRed from old editions of the
ARRL's QST magazine. Here is a list of the
QST articles I have already posted. All copyrights are hereby acknowledged.
See all available
vintage QST articles.
An Amateur Application of Modern Filter Design
By Edward E. Wetherhold, * W3NQN
Completed speech filter, less cover, showing the component mounting
boards and front panel with bypass switch and microphone connectors.
The low-pass filter components, marked with the 3-kc. cutoff
values, are mounted on the top phenolic component mounting board.
The transistor amplifier is mounted on the bottom phenolic board,
the high-pass filter with the resistor pad on the middle board.
Note the phenolic washers used to hold the 60- and 88-mH. toroids
firmly in place.
method of filter design known as "modern network synthesis" leads
either to simpler circuits for a given performance or improved performance
for a given degree of circuit complexity, as compared with the longer-established
design procedures. Here the author uses the system to come up with
a simplified "Filterfier" plus a design for an accompanying high-pass
Low- and High-Pass Audio Filters for
Over the past several years,
there has been a major revolution in the design of electric wave
filters. The old image-parameter approach developed by Campbell
and Zobel1 in the early 1920s with the now-familiar terminology
of "characteristic impedance," "constant-k section," and "m-derived
section" has finally been superseded by a vastly superior filter-design
method generally known as "modern network synthesis." Although this
method is not new, having been first mentioned in 1929 and later
expanded during 1940-19502, it was not practical to apply
it to practical filter problems until the digital computer became
available as a design tool. The recent publication of two texts3,4
with design tables derived by the computer now makes it possible
for the progressive radio amateur to take advantage of this most
recent development in filter design.
The fact that many
radio amateurs apparently are not yet aware of the advantages of
modern filter design techniques is indicated by recent articles5,6
in which the now-passé image-parameter design approach was
employed. The purpose of this article is to illustrate an application
of modern design to a simple filter problem already "solved" by
the image-parameter filter. By comparing the performance and components
of the filters that result from these two different approaches,
the degree of superiority and advantages of the modern filter over
the image-parameter filter should be evident.
The most recent image-parameter design conveniently accessible to
QST readers is the"Filterfier6,"
a low-pass filter designed to be used with s.s.b, phasing-type exciters
to restrict the speech frequency range to that at which the phasing
network performs best (approximately 300-3000 c.p.s.), to reduce
the possibility of generating unwanted side frequencies in excess
of 3 kc. This was accomplished by choosing a cutoff frequency of
2.40 kc. and designing an m-derived, constant-k image-parameter
filter which produced 37 db. of attenuation at 3.0 kc. At higher
frequencies, the attenuation in the stop band was never less than
39 db. The filter required four readily-available inductors and
seven capacitors and was designed to be terminated in equal resistances
of 1106 ohms.
1 - Dual-section elliptical-function lowpass filter.
Desired performance requirements for the comparative
low-pass modern filter design therefore were as follows:
1) A cutoff frequency of 2.4 kc. to permit ease of performance
comparison with the image-design filter.
2) An attenuation
of at least 37 db. at 3.0 kc.
3) A minimum attenuation in
the stop band of approximately 39 db.
4) Equal source and
load resistances of approximately 1000 ohms.
It was also
desirable to utilize the currently-available 88-mH. toroidal inductors
because of their high Q and very low cost.7
Modern Filter Design Applied to the Filterfier
With these thoughts in mind, a filter type classified
by the filter theorists as a "dual-section elliptic function" was
chosen as being most suitable for this particular application. From
the many possible variations available in the computer-derived tables
of Geffe's book'' for the elliptic-function type, one was chosen
which best approximated the desired performance requirements. The
tabulated computer-derived design parameters, all normalized for
a cutoff frequency of 1 radian/sec. and 1-ohm resistance terminations,
were scaled to the desired levels simply by multiplying all normalized
values by the proper factors. Normalized frequencies were scaled
by multiplying them by the cutoff frequency in kilocycles. Component
values were scaled by multiplying all capacitances by 1/Rω
and inductances by R/ω, where ω is
The source and load resistances, R, were specifically chosen to
assure that the higher inductance required by the filter would be
88 mH. The lower inductance came out to be 60.3 mH. The filter values
associated with cutoff frequencies of 2.40 kc. and 3.0 kc. are presented
in Table I. The second cutoff frequency of 3.0 kc. is presented
as an alternate for those who may prefer a wider passband for their
particular application. Note that the same inductance values are
required, but the source and load values are different as are also
the capacitance values.
The toroidal inductor used has two separate 22-mH. windings on a
toroidal core. When the windings are connected in series aiding,
the total inductance is 88 mH. with a Q of 45 at 1 kc. One of these
inductors is used in its unmodified form for L2.
A second 88-mH. toroid is modified by removing 62 turns from each
22-mH. winding so that when the modified coils are connected in
series aiding, the resulting inductance is 60 mH., which is the
amount of inductance required for L4.
2 - Single-section elliptical-function highpass filter.
Mylar capacitors were used because of their small size,
low loss and excellent capacitance stability relative to change
of temperature and time. The capacitances of a large number of Mylar
capacitors were measured with an impedance bridge and the true value
marked on each capacitor case. Appropriate values were then selected
and paralleled to produce the capacitances of C1
through C5 to within ±2
percent of the value specified in Table I. The two toroids and associated
capacitors were mounted on a phenolic board 2-7/16 by 3-5/8 by 1/16
inch thick and wired according to the low-pass filter schematic
of Table I. This completed the filter construction.
Filter Response Evaluation and Performance
The completed filter was subjected to a transmission-loss response
evaluation, the results of which are shown in Fig. 1. Transmission-loss
response is defined as the ratio of the voltage amplitude V1
of the load signal before filter insertion to the value of load
signal V2 at the filter
output terminals after insertion of the filter. This ratio is generally
expressed in decibels.
Fig. 1 - Transmission loss vs. frequency,
low-pass filter with
2.4·kc. cutoff using the values shown in
Table I. Peak rejection
frequencies are 3.14 kc. (ƒ004)
and 4.51 kc. (ƒ002).
A Heathkit Audio
Generator, Model AG-9 (step-frequency type) was calibrated against
a digital frequency counter to provide known test frequencies to
better than 1-percent accuracy. Input and output voltage amplitudes
were measured with a Heathkit a.c. v.t.v.m., Model AV-2. Resistive
terminations, as specified in Table I, were provided for the filter
input and output.
The response curve shows two" ripples"
in the filter passband of less than 1 db., which is sufficiently
in accord with the expected maximum passband attenuation of 0.5
db. The two passband ripples are typical of the dual-elliptic-type
filter. The measured cutoff frequency occurs at 2.40 kc. where the
response curve continues rising above the level of the maximum passband
attenuation. The remainder of the filter performance is equally
in accord with the design specifications.
Fig. 2 - Transmission loss vs. frequency,
low-pass filter with 3.0.kc.
cutoff using the values shown in
Table I. Peak rejection
frequencies are 3.92 kc. (ƒ004)
and 5.63 kc. (ƒ002).
Comparing the response curve of the modern filter with that of the
image filter (Fig. 3, page 33, November 1965 QST), no outstanding
differences are noted above 1 kc. However, in comparing the two
filter circuits, the modern filter design requires significantly
fewer components only two inductors and five capacitive elements
compared to four inductors and seven capacitive elements. Another
advantage of the modern design not immediately obvious is the fact
that the transmission loss in the modern filter passband is less
than 1 db. whereas the image design used in the Filterfier has a
loss in excess of 6 db. as a result of the 660 (640)-ohm resistor
separating the m-derived section from the constant-k section. If
it is desired to install the modern filter in the Filterfier circuit,
it is only necessary to provide the required filter source and load
resistances of 1305 ohms or 1630 ohms, depending on whether the
2.4-kc. or 3.0-kc. cutoff filter is used.
Another view of the filter, showing the back side of the front
panel. The input transformer is clearly visible in this view.
Speech Filter Using Modern Filter Design
the results of applying modern filter design techniques to the low-pass
filter application were so successful, it was decided also to design
and construct a high-pass filter so that, in combination, the two
filters would provide a bandpass of 300-3000 c.p.s. The bandpass
filter is intended to be used with an active device that will be
inserted between a microphone and speech input amplifier so as to
provide approximately unity gain. The component values and other
associated information for the 3.0-kc. low-pass filter are presented
in Table I. The transmission-loss response curve is shown in Fig.
Considerations for the design of the high-pass filter
were that, for simplicity, only one toroid be required, the minimum
attenuation in the stop band be 20 db., and that maximum pass-band
ripple be 0.5 db. The most suitable compromise appeared to be a
design which required two 0.1-µf. capacitors, one 0.235-µf.
capacitor and one 3.11-henry toroid for source and load impedances
of 4260 ohms. See Table II for filter parameters and schematic.
With these component values, the cutoff frequency was 294 c.p.s.
and the resonant frequency of the series-tuned circuit was 186 c.p.s.
The cutoff frequency and impedance level were deliberately juggled
to make C1 and C3
come out to a nice even 0.10 µf. The 3.11-henry toroid uses
a core of permalloy and has a Q of 50 at 1 kc., or approximately
15 at the ƒco of
294 c.p.s. The filter was assembled, evaluated and found to perform
satisfactorily in every respect. The next step was to cascade the
low-pass and high-pass filters to form the desired bandpass filter.
Fig. 3 - Relative attenuation vs. frequency,
cascaded low-pass and high-pass filters.
Insertion loss due to
matching pad is 13 db. Arrows indicate attenuation
of measurement capability of equipment.
Cascading the Low-Pass and High-Pass Filters
A 13-db. pad was installed between the high-and low-pass
filters to provide impedance matching and also some degree of isolation.
The cascaded filters and pad were then evaluated for relative attenuation
vs. frequency, using the test circuit shown in Fig. 3. The response
curve is also presented in Fig. 3. The high-pass filter was purposely
placed after the low-pass filter so as to attenuate any 60-cycle
hum that might be picked up by the low-pass filter. The output of
the high-pass filter is terminated in its specified load impedance
of 4300 ohms. Since the filter is designed to work into the input
resistor of a microphone preamplifier, which is generally in excess
of 1 megohm, the filter load termination of 4300 ohms will be relatively
unaffected by connection to the speech preamplifier. In fact, if
a volume control is desired a 5000-ohm potentiometer shunted by
30,000 ohms could be used as the high-pass filter load with the
potentiometer arm wired to the output connector.
Cascading the Low-Pass and High-Pass Filters
Transistor Amplifier Design
overcome the losses in the resistive filter matching pad and input
matching transformer, an amplifier voltage gain of approximately
40 db. was required. Also, a low-impedance source was required to
drive the filter input for best results. The required gain was obtained
from a common-emitter transistor stage with a voltage gain of between
100 and 150. Using the input transformer specified in Fig. 4, an
input impedance of about 300,000 ohms is anticipated, which should
be sufficient to assure a flat response down to 300 c.p.s. even
if a crystal microphone is used. The low-impedance signal source
for the filter is provided by a common-collector stage which is
direct-coupled from the common-emitter amplifier stage, thus eliminating
the necessity for a coupling capacitor and bias resistors. The output
impedance of the common-collector stage is approximately 40 ohms.
Placing a 1600-ohm 5 percent resistor between the emitter follower
and low-pass filter very nicely solves the matching problem.
The transistors, manufactured by General Electric and available
from Allied Radio Corp. for about 80 cents each, are n-p-n silicon
planar passivated types specifically designed for low-level audio
applications. The input transistor, a 2N3391A, has a controlled
noise figure and high beta and so is very well suited to its application
in this design. The 2N3392 is similar but has a lower beta and no
specification regarding noise figure.
of parallel resistors were installed for R1 until a Q1
emitter current of 1.3 ma. was obtained. In this particular case,
the required resistance for R1 was 44,000 ohms. Switch
S1, which simultaneously bypasses the entire circuit
and also switches out the battery, was provided as a convenient
means to permit comparison of the modulated transmitter output with
and without the bandpass speech filter. With an operating duty cycle
of 2 hours per day, the useful life of the 15-volt battery may be
expected to be in excess of one month. If it is desired to omit
the resistive pad and the high-pass filter, simply terminate the
low-pass filter with a 1600-ohm resistor, change R4 to
1300 ohms, and if R2 is made 220 ohms unity gain should
Fig.4 - Circuit diagram of the bandpass speech
filter. Resistances are in ohms,
K = 1000; resistors are 1/2·watt,
5 percent tolerance.
The desired filter performance
will be assured if reactors with a ±2 percent tolerance, resistive
terminations with a ±5 percent tolerance, and inductors with as
high a Q as practical are used. There will be relatively little
difficulty and expense in obtaining the 88- and 60-mH. inductors.
However, obtaining the 2 percent capacitors will require some extra
effort. Also, the 3. 1-henry toroid may prove to be more expensive
than anticipated. This toroid is available from the Allen Organ
Co. (3.11 henry, ±2 percent, Q = 50 at 1 kc.) at a cost of $1.43
each with a minimum billing charge of $20. An alternate source is
Newark Electronics Corp. (Stock No. 39F2806, Collins toroid type
MP-930-37B, 3.0 henry, ±1 percent, Q = 58 at 1.5 kc.) at a cost
of $7.23. The author employed the following procedure: Mylar capacitor
and Allen toroid data sheets were requested from the Components
Division of Allen Organ Co., Macungie, Pa., and $20 worth of mylar
capacitors and permalloy toroids was selected and ordered. The capacitor
cost ranged from 13 cents for 0.007 µf. to 17 cents for 0.10 µf.,
and about fifty capacitors of mixed values were obtained for $8.
The remainder of the $20 was invested in toroids, one of which was
the 3.11-henry value. An impedance bridge was borrowed and all the
capacitors were measured to an accuracy of 2 percent or better and
the values marked on the capacitor cases. Appropriate values were
then selected and paralleled to produce the desired filter capacitance
Performance of the Completed Unit
When first tested, the gain of the bandpass speech
filter was found to be greater than unity by 4.5 db. R2
was added to the circuit and adjusted until the desired unity gain
was achieved. The 3.1-henry toroid in the high-pass filter was found
to be sensitive to hum pickup, and therefore the filter should not
be placed in the immediate vicinity of power transformers. The overall
frequency response of the entire unit was found to he essentially
the same as that of Fig. 3 except that the attenuation was greater
than indicated by the response curve at frequencies below 100 c.p.s.,
because of the roll-off effects of C3 and possibly T1.
An operational check of the filter on the air was satisfactory in
The author wishes to thank John Brennan, Jr. for providing the photographs,
Tom Miller, W7QWH/3, for performing the operational checkout, and
Millicent Schaffer for typing the manuscript.
* Dept. 2N, Electro International, Inc., Box 391, Annapolis,
1 Zobel, "Theory & Design
of Electric Wave Filters," The Bell System Technical Journal, January.
2 Zverev, "Introduction to Filters," Electro-Technology,
3 Geffe, Simplified Modern Filter Desiqn,
John F. Rider Publisher, Inc., New York City, 1963.
A Handbook on Electrical Filters, published by White Electromagnetics,
Inc., Rockville, Maryland, 1963.
5 Genaille, "Low-Pass Audio
Filters for Increased Talk Power," Electronics World, September,
and Thompson, Jr., "The Filterfier," QST, November, 1965.
7 For example, 88- and
44-mH. toroids are available 5 for $1.75, postpaid, from Buchanan &
Associates, 1067 Mandana Blvd., Oakland, California 94610.