July 18, 1944.
,E. s. PURINGTON
'
2,354,141
UNIVERSAL RESISTANCE CAPACITANCE FILTER
Filed Aug. 26, 1942
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INVENTOR
ELLISON s. PURINGTON
BY
719$ 4A/m/W
ATTORNEY
'
Patented July 18, 1944
UNITED
2,354,141
STATES
PATENT ‘ OFFICE
UNIVERSAL RESISTANCE‘ CAPACITANCE
FILTER
Ellison‘ S. Purington. Gloucester, Mass, assignor, '"
by mesne assignments. to Radio Corporation of
America, New York. N. Y., a corporation of
Delaware
Application August 26, 1942, Serial No. 456,286
7 Claims.
This invention relates to a network of resistors
and capacitors which may be used for frequency
discrimination purposes.
It is especially useful
(Cl. 178-44)
where M and N are functions of frequency and
the relative proportionsof the various elements.
From M and N, the performance 'as to effect of
in frequency ranges where inductance elements
the ?lter network upon the magnitude and upon
are not highly practicable, as, for example, in low 5 the phase of the output current is given by
audio or sub-audio ranges. _By properly chosen‘
insertion loss (db) = 10 log") (1112+ N2)
design constants, the network may have the prop
erties of a low-pass,,a high-pass, a band-pass or
a band elimination ?lter, as may be desired.
In the drawing, Figure 1 shows the general
The insertion loss effect is of primary importance
nature of the ?lter network according to the in
in describing the properties of the ?lter network,
vention, and Figures 2 and 3 illustrate curves
but the phase shifting effect is sometimes re
which will serve to explain the performance of
quired.
_
.
the ?lter network of Figure 1 under certain con
In
some
cases,
it
may
be
desirable
to
know
the
15
transmission ratio T instead of the insertion
The circuit of Figure 1 comprises a frequency
ditions.
.
.
discriminating network with structural symme
try which is set up between two equal terminat
ing resistors R, one of which, the sending termi
' ratio, that is, the ratio of the voltage 6r across
energy E. The current i1 in the other termina
tion, the receiving termination, is a function of
the magnitude and the frequency of the source.
T“_E—2(A'1+jN)_
i,_ 1 __< 2(llIZ+N2)
M )_ J.( 2t1’ll2-l-N1)
N )
the receiving termination to the driving voltage
E.
This is deducible from M and N by the rela
nation, contains a source of alternating current 20 tions
Because the performance is on a relative basis,
the performance is independent of the magnitude
the condensers C3, C1, C1 andCa connectedin series 25 of E, but depends only upon the frequency. Fur~~ ,
between the terminating resistors R audit, the
ther the insertion ratio is not modi?ed if the
shunt condensers C2 and C2, the series con
value of each resistor in ohms is multiplied by a
nected resistors R1, R1 which shunt the condens
given factor, and the value of each capacitor in
ers C1, C1, the shunt condenser 2C1 having one
farads
divided by the same factor, since this does
terminal connected to the common terminal of 30
not modify the ratios of the impedances of the
resistors R1, R1 and the shunt resistor
‘
elements. That is, although there are ?ve inde
The frequency discriminating network comprises _
pendently choo'sable elements, there are only a
fourfold in?nitude of performance relations pos
having one terminal connected to the common 35 sible between the insertion ratio and the fre
terminal of the condensers C1, C1. The restric
tion of symmetry is for the purpose of making the
performance a matter of exact computation
quency of the source.
.
The number of in?nitude of performance
curves is further reduced by putting frequency as
well as transmission on a relative basis. That is,
‘
without excessive difficulty, and it will be under
stood that the performance will not change 40 we can set up as a reference frequency F0, the
frequency for which a resistor element of the
abruptly if the conditions o‘f'exact symmetry are
There are ?ve independently choos~
system has the same numerical impedance as a
able elements, R, R1, C1, C2. C3, and the general
possible
capacitor element. Preferably F0 should repre
sent some physically describable phenomenon.
The ?ltering performance is most conveniently
expressed by the insertion ratio, that is, the ratio
of the current, E/2R, which would flow in the
45 For the present purposes, F0 is chosen as the fre
quency for which the capacitor C1 has the same
numerical impedance as resistor R1., That is, for
a given choice of C1 and R1, the reference fre
not met.
performance ‘information
combinations of choices.
covers
all
quency is determinable by‘ Fo=159200/C1R1,
and E, R and R directly in series, to the actual 60 where C1 is in microfarads, R1 in ohms, and F0
in cycles per second. For simplicity, the per
current 'ir ?owing with the ?ltering network
formance can be expressed not in terms of fre
present. Using vector notation
output arm if the ?ltering network were absent
quency, but in terms of the reduced or relative
insertion ratio =
= (.11 +jN)
I
frequency, which is the ratio of any frequency f
to the reference frequency F0. This for simplic
1
2
2,354,141
ity may be termed 0:, the main independent vari
in?nite. The parameter h is assigned three dil
able in expressing the performance.
ferent values.
By thus placing the transmission on a ‘relative
basis, and also the frequency on a relative basis,
For
.
' the insertion loss function is the simplest possible,
the performance of insertion effect as a function
of the relative frequency is expressible by a three
fold in?nitude of curves. That is, the insertion
being the same for a: as for l/m. This arrange
ment is suitable for band elimination purposes.
Theoretically the loss is in?nite at :r-—-l. It will
be understood that the loss in the vicinity of 1:1
the ratios of impedances. These parameters 10' can be made ?nite if desired by causing the vari
ous elements of the ?lter to be inexactly chosen.
will be as follows: ;
The dotted line in the curve is for the purpose of
Parameter h (height) is the ratio of R1 to R,
effect is__a function of a: and of three secondary
independent variablesL or parameters, expressing
tying the two portions of the curve together. But
that is h=R1/R;
with parameter )1 chosen large, say h: 10 as illus
Parameter s (series) is the ratio of C1 to C3,
that is s=C1/Cs;
15
_
Parameter 1) (parallel) is the ratio of C2 to C1,
trated, the system has the properties of a high
pass filter, with high-loss for low values of :r, and
especially high loss near :c=1. Or with h chosen
small, say h=.2 as illustrated, the system has the
The parameter h is an impedance level param
properties of a low-pass ?lter, with high loss for
eter. As it is changed, the impedances of all
elements of the ?ltering network are changed 20 high values of x, and especially high loss near
x=l. That is, the properties of the ?lter can be
with respect to the terminations, without chang
greatly modified by choice of the impedance level
ing the ratios of the impedances of the elements
parameter. While the use of this central network
without the ?lter itself. Parameter s expresses
with p=s==0 is known for purposes of making the
the series condenser effect in blocking the passage
loss in?nite at x=1, it is believed new to choose
of low frequency currents, and this ‘effect is zero
the impedance level as here de?ned either abnor
for s=0, making Ca in?nite. Similarly 1; ex
mally high or abnormally low to produce the low
presses the parallel condenser e?ect in preventing
pass or high pass effect. For ‘example, in the
the passage of high frequency currents, and the
design of resistance-capacitance ?lters for ripple
effect is made zero for p=0, making C2 zero. For
elimination
in power supplies for radio, it would
both s and p zero, the network comprises solely 30
be new to use a ?lter of this type with's=o so that
the central elements R1, C1, R1/2 and 2C1. With
the filter will pass direct current, and also with h
It, s and p all positive quantities, the insertion
abnormally small to permit effective passage.oi
ratio function M and N depend solely upon the
direct current, and F0 chosen at 120 cycles to
main independent variable x, and the secondary _
attenuate especially the double frequency ripple in
independent variables h, s and 1). Without going 35 a full wave recti?er operated from 60 cycle supply.
into the details of the method of solution, it will
Application of the ?lter with s not zero is for
be found that M and N are computable from the
band-pass purposes, illustrated in Figure - 3.
equation below:
Sharpness of cut-off is greatly enhanced by the
fact that the insertion loss must go to in?nity at
40
3::1. The constants are here chosen to make the
insertion loss lowest at a value of: less than unity‘,
and to make the insertion loss for values of a:
greater than ‘unity always greater than for z
‘
45 yielding minimum loss.
With C3 ?nite corresponding to a positive value ,
of s, it is physically apparent that the loss will be
in?nite both at a:=0 and 1:1, therefore with a
minimum ?nite loss at a point between :c=0 and
The quantities P, Q, U, V, W assume numerical 50 :r=1. Also with C: ?nite, corresponding to a
positive value of p, it is apparentthat the loss will
values when parameters h, s and p are ‘specified.
These numerical values are then inserted in the 2
be‘ in?nite also at x: <1 and therefore a minimum
equation involving 0:, h, s and 12.
x=o=, and also to determine the losses at these
?nite loss also at a point between :c=1 and x=¢.
equations for M and N to make the insertion ratio
While of course it is possible to set up the condi
a function of a: vcorresponding to the particular
values of h, s, p chosen. This is simpler than 55 tion to determine the points of minimum loss be
tween rr=0 and x=1, and also between 1:1 and
having M and N expressed in terms of one long
~
In using these equations for design purposes, it.
points of minimum, the equations are so complex
that it is quite impracticable. If the design for
is contemplated that performance curves will be
computed say of insertion loss as a function of a: 60 band-pass purposes is to be by computation, it is
for various combinations of h, s and p.
By a
much simpler to proceed by the method of trial
and error. The two combinations of‘ Figure 3
illustrate designs that have been made for spe
cific purposes. The curve for h=.2, p=0, s=.4
produces a band-pass 'e?'ect without requiring
condenser C2. The ?lter so organized, with Fe
established from the chosen curve as to what
chosen 1000 cycles, is suitable for transmitting
value should be assigned to F0, the various ele- '
well at 120 cycles, and badly at higher frequencies,
merits can be computed by the following for
especially in the range of maximum audibility.
mulae:
70 The curve h=1, p=.2, s=.2 gives band-pass effect
in the vicinity of 2:.2, with p chosen so that for
h=1, s=.2, the ?lter also transmits equally well
For purpose of illustration, in Figure 2 are
a band of frequencies in the vicinity of 2:4. Or
shown curves of insertion loss in decibels under
this arrangement may be considered as a band
the special condition of p=s=0, so that C2 and C:
are not required, one being zero and the other 75 elimination arrangement for which the loss be
method of trial and adjustment, a combination
of h, s and p will be found that best approximates
the desired performance curve shape. The ter
minal resistances R being known, and it being 65
3
2,354,141
comes a minimum at points other than 1:0 or
a:=in?nity.
input terminals, and a. terminating resistor is
connected between the output terminals.
'
These examples will serve to illustrate some of
the three-fold in?nitude of curve shapes which
may be used as a basis of design with this struc
tural arrangement.
Various modi?cations may be made in the in
vention without departing from the spirit and
scope thereof, and it is desired therefore, that
only such limitations shall be placed thereon as
are necessitated by the prior art and set forth
in the appended claims.
4. A resistor-capacitor ?lter network as de
?ned in claim 2 wherein the three-terminal net
work comprises a pair of parallel T-networks, one
T-network comprising series condensers and a
shunt resistor, the other T-network comprising
series resistors and a shunt condenser.
5. A resistor-capacitor ?lter network compris
ing input and output terminating-resistors, a plu
rality of condensers of values Ca, C1, C1 and C3
series-connected between said resistors, a pair of
resistors of equal value R1 connected in shunt
to the condensers of equal value C1, a condenser
of value 201 having one terminal connected to
the common terminal between the resistors of
equal value R1, a condenser of value C2 connected
to each of the other terminals of the resistors of
er ual value R1, and a resistor of value
What I claim is:
1. A resistor-capacitor ?lter circuit compris- I
ing a T-network of series condensers and a shunt
resistance, a second T-network connected in par
allel to. the ?rst having series resistances and
shunt condenser, series and shunt condensers
connected to the input of said networks, and sim
ilar series and shunt condensers connected to
the output of said networks.
2. A resistor-capacitor ?lter network compris
53
20
2
having one terminal connected to the common
ing a pair of input and a pair of output terminals,
terminal of the condensers of equal value C1.
a pair of condensers serially connected across
6. A resistor-capacitor network as de?ned in
the input terminals, a similar pair of condensers
claim
5 wherein the values of the several con~
25
connected across the output terminals, corre
densers and resistors are so chosen that there is
sponding condensers, one from each pair, having
produced a very high insertion loss for one fre
a common terminal which is connected to one of
quency and a minimum of insertion loss at an
the input terminals and also to one of the output
other ?nite frequency other than zero.
terminals, and a three-terminal network com
7. A resistor-capacitor network .as de?ned in
prising resistors and capacitors having one termi 30
claim 5 wherein the values of the several con
nal connected to said common terminal and its
densers and resistors are so chosen that the net—
other two terminals connected respectively to the
work serves as a low pass or as a high pass ?lter
common terminals of the serially connected con
denser pairs.
3. A resistor-capacitor ?lter network as 1de
?ned in claim 2 wherein a frequency source and a
terminating resistor are connected between the
in accordance with the choice of the impedance
level of the ?lter elements with respect to the
terminating resistors.
'
ELLISON S. PURINGTON.