US2354141A - Universal resistance capacitance filter - Google Patents

Description

July 18, 1944. ,E. s. PURINGTON 2,354,141

UNIVERSAL RESISTANCE CAPACITANCE FILTER Filed Aug. 26, 1942 c c c Tn l II II I RI RI R C E c 5 2 2 2c D"RI E 2 t l INSERTION LOSS, DECIBELS LIJ LIJ

X 4- INVENTOR ELLISON s. PURINGTON BY 4 719$ A/m/ ATTORNEY Patented July 18, 1944 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 in frequency ranges where inductance elements are not highly practicable, as, for example, in low audio or sub-audio ranges. By properly chosen design constants, the network may have the properties of a low-pass,,a high-pass, a band-pass or a band elimination filter, as may be desired.

In the drawing, Figure 1 shows the general nature of the filter network according to the invention, and Figures 2 and 3 illustrate curves which will serve to explain the performance of the filter network of Figure 1 under certain conditions.

The circuit of Figure 1 comprises a frequency discriminating network with structural symmetry which is set up between two equal terminating resistors R, one of which, the sending termination, contains a source of alternating current energy E. The current i1 in the other termination, the receiving termination, is a function of the magnitude and the frequency of the source.

The frequency discriminating network comprises the condensers C3, C1, C1 andCa connectedin series between the terminating resistors R audit, the shunt condensers C2 and C2, the series connected resistors R1, R1 which shunt the condensers C1, C1, the shunt condenser 2C1 having one terminal connected to the common terminal of resistors R1, R1 and the shunt resistor having one terminal connected to the common terminal of the condensers C1, C1. The restriction of symmetry is for the purpose of making the performance a matter of exact computation without excessive difficulty, and it will be understood that the performance will not change abruptly if the conditions o f exact symmetry are not met. There are five independently choosable elements, R, R1, C1, C2. C3, and the general performance information covers all possible combinations of choices.

The filtering performance is most conveniently expressed by the insertion ratio, that is, the ratio of the current, E/2R, which would flow in the output arm if the filtering network were absent and E, R and R directly in series, to the actual current 'ir flowing with the filtering network present. Using vector notation insertion ratio (.11 +jN) 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 the filter network upon the magnitude and upon the phase of the output current is given by insertion loss (db) 10 log (111 N The insertion loss effect is of primary importance in describing the properties of the filter network, but the phase shifting effect is sometimes required.

In some cases, it may be desirable to know the transmission ratio T instead of the insertion ratio, that is, the ratio of the voltage 6r across well as transmission on a relative basis.

of E, but depends only upon the frequency. Fur-- ther the insertion ratio is not modified if the value of each resistor in ohms is multiplied by a given factor, and the value of each capacitor in farads divided by the same factor, since this does not modify the ratios of the impedances of the elements. That is, although there are five independently choo'sable elements, there are only a fourfold infinitude of performance relations possible between the insertion ratio and the frequency of the source.

The number of infinitude of performance curves is further reduced by putting frequency as That is, we can set up as a reference frequency F0, the frequency for which a resistor element of the system has the same numerical impedance as a capacitor element. Preferably F0 should represent some physically describable phenomenon. For the present purposes, F0 is chosen as the frequency for which the capacitor C1 has the same numerical impedance as resistor R1., a given choice of C1 and R1, the reference frequency is determinable by Fo=159200/C1R1,

This for simplic- That is, for 1 ity may be termed the main independent variable in expressing the performance.

By thus placing the transmission on a relative basis, and also the frequency on a relative basis, the performance of insertion effect as a function of the relative frequency is expressible by a three fold infinitude of curves. That is, the insertion effect is a function of a: and of three secondary independent variables or parameters, expressing the ratios of impedances. These parameters will be as follows:

Parameter h (height) is the ratio of R1 to R, that is h=R1/R;

Parameter s (series) is the ratio of C1 to C3, that is s=C1/Cs;

Parameter 1) (parallel) is the ratio of C2 to C1,

The parameter h is an impedance level parameter. As it is changed, the impedances of all elements of the filtering network are changed with respect to the terminations, without changing the ratios of the impedances of the elements without the filter itself. Parameter s expresses the series condenser effect in blocking the passage of low frequency currents, and this effect is zero for s=0, making Ca infinite. Similarly expresses the parallel condenser efiect in preventing the passage of high frequency currents, and the effect is made zero for p=0, making C2 zero. For both s and p zero, the network comprises solely the central elements R1, C1, R1/2 and 2C1. With It, s and p all positive quantities, the insertion ratio function M and N depend solely upon the main independent variable x, and the secondary independent variables h, s and Without going into the details of the method of solution, it will be found that M and N are computable from the equation below:

The quantities P, Q, U, V, W assume numerical values when parameters h, s and p are specified.

These numerical values are then inserted in the 2 equations for M and N to make the insertion ratio a function of a: corresponding to the particular values of h, s, p chosen. This is simpler than having M and N expressed in terms of one long equation involving 0:, h, s and 12.

In using these equations for design purposes, it.

value should be assigned to F0, the various elemerits can be computed by the following formulae:

For purpose of illustration, in Figure 2 are shown curves of insertion loss in decibels under the special condition of p=s=0, so that C2 and C: are not required, one being zero and the other infinite. ferent values.

' the insertion loss function is the simplest possible,

being the same for a: as for l/m. This arrangement is suitable for band elimination purposes. Theoretically the loss is infinite at :r--l. It will be understood that the loss in the vicinity of 1:1 can be made finite if desired by causing the various elements of the filter to be inexactly chosen. The dotted line in the curve is for the purpose of tying the two portions of the curve together. But with parameter )1 chosen large, say h: 10 as illustrated, the system has the properties of a highpass 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 properties of a low-pass filter, with high loss for high values of x, and especially high loss near x=l. That is, the properties of the filter can be greatly modified by choice of the impedance level parameter. While the use of this central network with p=s==0 is known for purposes of making the loss infinite at x=1, it is believed new to choose the impedance level as here defined either abnormally high or abnormally low to produce the low pass or high pass effect. For example, in the design of resistance-capacitance filters for ripple elimination in power supplies for radio, it would be new to use a filter of this type with's=o so that the filter will pass direct current, and also with h abnormally small to permit effective passage.oi direct current, and F0 chosen at cycles to attenuate especially the double frequency ripple in a full wave rectifier operated from 60 cycle supply.

Application of the filter with s not zero is for band-pass purposes, illustrated in Figure 3. Sharpness of cut-off is greatly enhanced by the fact that the insertion loss must go to infinity at 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:

With C3 finite corresponding to a positive value of s, it is physically apparent that the loss will be infinite both at a:=0 and 1:1, therefore with a minimum finite loss at a point between :c=0 and :r=1. Also with C: finite, corresponding to a positive value of p, it is apparentthat the loss will be infinite also at x: and therefore a minimum finite loss also at a point between :c=1 and x=. While of course it is possible to set up the condition to determine the points of minimum loss between rr=0 and x=1, and also between 1:1 and x= and also to determine the losses at these points of minimum, the equations are so complex that it is quite impracticable. If the design for band-pass purposes is to be by computation, it is much simpler to proceed by the method of trial and error. The two combinations of Figure 3 illustrate designs that have been made for specific purposes. The curve for h=.2, p=0, s=.4 produces a band-pass 'efi'ect without requiring condenser C2. The filter so organized, with Fe chosen 1000 cycles, is suitable for transmitting well at 120 cycles, and badly at higher frequencies, especially in the range of maximum audibility. 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 filter also transmits equally well a band of frequencies in the vicinity of 2:4. Or this arrangement may be considered as a band elimination arrangement for which the loss be- 1. A resistor-capacitor filter circuit compris- I ing a T-network of series condensers and a shunt resistance, a second T-network connected in parallel to the first having series resistances and shunt condenser, series and shunt condensers connected to the input of said networks, and similar series and shunt condensers connected to the output of said networks.

2. A resistor-capacitor filter network comprising a pair of input and a pair of output terminals, a pair of condensers serially connected across the input terminals, a similar pair of condensers connected across the output terminals, corresponding condensers, one from each pair, having a common terminal which is connected to one of the input terminals and also to one of the output terminals, and a three-terminal network comprising resistors and capacitors having one terminal connected to said common terminal and its other two terminals connected respectively to the common terminals of the serially connected condenser pairs.

3. A resistor-capacitor filter network as defined in claim 2 wherein a frequency source and a terminating resistor are connected between the input terminals, and a. terminating resistor is connected between the output terminals.

4. A resistor-capacitor filter network as defined in claim 2 wherein the three-terminal network 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 filter network comprising input and output terminating-resistors, a plurality 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 having one terminal connected to the common terminal of the condensers of equal value C1.

6. A resistor-capacitor network as defined in claim 5 wherein the values of the several condensers and resistors are so chosen that there is produced a very high insertion loss for one frequency and a minimum of insertion loss at another finite frequency other than zero.

7. A resistor-capacitor network .as defined in claim 5 wherein the values of the several condensers and resistors are so chosen that the net work serves as a low pass or as a high pass filter in accordance with the choice of the impedance level of the filter elements with respect to the terminating resistors.

ELLISON S. PURINGTON.

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