## Filters

Filters of either the choke-input or the condenser-input type may be employed to minimize rectifier ripple voltage. With either type of filter, the maximum ratings shown under CHARACTERISTICS for each rectifier tube should not be exceeded.

A choke-input filter has the advantages of providing good voltage regulation, of limiting current surges during switching, and of limiting peak plate current during rectifier operation. This type of filter is preferable from the standpoint of obtaining the maximum continuous d-c output from a rectifier tube under the most favorable conditions. It is especially recommended for use with mercury-vapor rectifier tubes and with high-vacuum rectifier tubes having closely-spaced electrodes. The performance of a good choke-input filter can be calculated accurately.

A condenser-input filter has the advantage of increasing the voltage output from a rectifier. It has the disadvantages of causing poor voltage regulation, of causing high switching surges, and of reducing the d-c load current over that permissible when choke input is used. A large input capacitance causes a high surge current when the power switch is closed; a small input capacitance reduces the surge current but decreases the filtering action and the voltage output. When a condenser-input type of filter is used, a current-limiting resistor should be connected between the rectifier tubes and filter to reduce the tube current to a safe amount at the time of switching on the rectifier. The value of this resistance, which also includes the power transformer resistance, can be determined as follows:

Current-limiting resistance in ohms=-:-;-;-;——-:-

rated peak plate tube current in amperes where k is equal to 1.41 for circuits of Figs. 20 through 23, and 2.45 for Fig. 24. After the rectifier-filter system has been switched on, the resistor can be short-circuited to avoid reducing the d-c output voltage. The resistor is employed at each switching operation. Because of the many variable factors involved in the functioning of a condenser-input filter, its performance is more difficult to determine than that of a choke-input system.

The general filter-design curves in Figs. 25A and 25B are useful in the selection of suitable combinations of chokes and condensers for choke-input filters. Values can be chosen from these curves to limit the peak plate current and the average plate current to the maximum rating of any rectifier tube for a given percentage of ripple voltage in single-phase, full-wave circuits operating from a 60-cycle supply. When the power supply is operated from a 50-cycle source, multiply the values of selected inductance and capacity by 60/50, or 1.2. When the power supply is operated from a 25-cycle source, multiply the selected filter values by 60/25, or 2.4.

The load resistance curves, identified by Ri,, give the minimum or critical value of inductance that should be used with the indicated load resistance. Lower than the minimum inductance values may result in overloading of the rectifier tubes under steady operating conditions, and in poor regulation. The value of Rl for any specific design is obtained by dividing the required rectifier d-c output voltage by the desired load current (in amperes). The d-c output voltage used for this calculation is taken as 90% of the RMS voltage per rectifier tube plate. It does not take into consideration the regulation of the power transformer, filter choke (s), or rectifier tube(s). The percentage ripple curves, identified by Eri, represent the percentage ripple for any single-section filter combination. An Esus line is given for each rectifier tube type. It shows the various combinations of minimum filter inductance and maximum filter capacitance (Ci) that will limit the surge current to the maximum peak plate current rating of the particular tube it represents, at the maximum peak inverse voltage rating of the tube. Always select filter constants to the left of Ehms. When lower than the rated maximum peak inverse voltage is used for a tube type, lower inductance and higher capacitance values may be used without exceeding the peak current rating of the tube. In this case, the filter combination is selected to the left of a new Ekhs line, the points of which are determined from the equation.

where Ci = First filter condenser capacitance in microfarads Lj = First filter choke inductance in henries I Mix. ■= Peak plate current rating of tube in amperes Edis = RMS transformer voltage per tube

When more filtering is required than can be obtained economically by means of a single filter section, a second filter section may be added to the first. The size of L2 and C2 for the second section may be easily determined from Fig. 25B. Since Ehi is known for the first section, the values of L2 and C2, as a product, may be read from the appropriate Ebi curve for any desired value of percentage ripple Eb2- Practically any values of L2 and C2 forming the product read from the curve can be used for the second section. However, in order to avoid serious circuit instability and impairment of filtering due to 120-cycle resonance, L2 (in henries) must always be greater than 3 (Ci + C2) -r- 2Ci C2, where Ct and ¿2 are in microfarads.

When designing a single-section filter, use Fig. 25A and observe the following rules. Always select inductance values, (1) above the proper Rl curve, (2) to the left of the proper Ermb curve, and (3) along the desired E«j curve. Use the corresponding value of filter capacitance for each selected value of inductance. When designing the second section of a double-section filter, use Fig. 25B and observe the following rules. (1) Select desired percentage of output ripple voltage Ex2 on appropriate curve of Exi- (2) Read corresponding L2C2 product. (3) To satisfy this product, choose convenient values of L2 and C2. (4) Check the chosen value of to insure that it is greater than 3 (Ci + C2) -i- 2Ci ¿2.

When the load resistance varies over a wide range, good regulation may be obtained by (1) connecting a bleeder resistance across the filter output to restrict the range over which the effective load varies, (2) using an input choke with sufficient inductance to meet all values of load resistance up to the highest attained, or (3) using a swinging input choke. The last method is the more economical.

The inductance of a well-designed swinging choke rises from its normal value at rated load current to a high value at low load current. The required minimum and maximum values of swinging choke inductance can be determined from Fig. 25A at the intersection of the proper Eems curve with the minimum and maximum Rl curves, respectively. It is generally more economical to select low values of swinging choke inductance and to depend on additional filter sections to provide the required smoothing.

### EXAMPLE No. 1

Problem: Given a d-c output voltage of 3180 volts (corresponds to a peak inverse voltage of 10,000 volts) from a 60-cycle full-wave rectifier employing two 872-A's, design a single-section filter of the choke-input type which will limit the ripple voltage to 5% at a load current equal to the combined maximum d-c load-current rating of the tubes (2.5 amperes), and prevent the peak plate current of either tube from rising higher than the maximum peak plate-current rating of the 872-A.

Procedure: Ekuk is equal to 3180x1.11, or 3535 volts. Rl is equal to 3180/2.5 amperes, or 1272 ohms. From Fig. 25A, Rl=1272 lies below curve Ems = 3535 (as shown for the 872-A) and, therefore, is not required for the selection of filter constants. Any combination of inductance and capacitance along the curve E»i = 5% and to the left of the curve E*ms= 3535 will satisfy the requirements. A suitable combination is a filter section employing a 25-henry choke and a 1-microfarad condenser.

### EXAMPLE No. 2

Problem: Given a d-c output voltage of 2385 volts (corresponds to a peak inverse voltage of 7500 volts) from a 60-cycle full-wave rectifier employing two type 866's, design a double-section filter which will limit the output ripple voltage to 0.5% at a load current equal to the combined maximum d-c load-current rating of the tubes (500 milliamperes) and prevent the peak plate current of either tube from rising higher than the maximum peak plate-current rating of the 866. The input choke is to be of the swinging type and the voltage regulation is to be good from no-load to full load.

Procedure: E*ms is equal to 2385 x 1.11, or 2650 volts. At maximum load, Ri.= 2385/0.5 ampere, or 4770 ohms. Since curve Rl = 4770 lies below curve Ehms = 2650 volts (as shown for the 866), it is not needed in the selection of constants for the first filter section. A value of 10% ripple at the output of the first filter section will be assumed to be satisfactory. The minimum value of swinging-choke inductance and corresponding value of capacitance for the first-section filter condenser may, therefore, be selected along curve Eri = 10% and to the left of curve Eems = 2650 volts (for 866). Suitable values are 13.5 henries and 1 microfarad. The maximum value of swinging choke inductance to be used with a condenser having a capacity of 1 microfarad should be as high as practical. Assume that this value is 40 henries. Then, with a capacitance value of 1 microfarad, the maximum value of Rl is 44,000 ohms. Therefore, a bleeder resistance of 44,000 ohms is required to keep the d-c output from "soaring" at no-load conditions With a load resistance of 44,000 ohms, the bleeder current is 2385/44000 = 0.054 ampere, or 54 milliamperes. The total useful d-c output current is then 500—54, or 446 milliamperes.

The design of the second filter section should now be considered. It must be capable of reducing the ripple voltage from 10% in the first section to 0.5% in its own output. From Fig. 25B, the value of the product L2C2 is 37 as read on the curve E11 = 10% when E»2==0.5%. If C2 is chosen to be 2 microfarads, L2 = 37/2, or 18.5 henries. This value of L2 is greater than 3 (Ci 4- C2) -i- 2 Cj C2 = 3 (1 + 2) -=- 2 (1 X 2). or 2.25, and therefore it of ample size to avoid resonance effect«

FILTER DESIGN CURVES FOR FULL-WAVE SINGLE-PHASE CIRCUITS ONLY 60-CYCLE SINE-WAVE SUPPLY*

Fig. 25A—Curves for choice of filter values for (1) the first section of a double-

section filter, or (2) a single-section filter. Fig. 25B—Curves for choice of filter values for second section of a double-section filter.

CAPACITANCE (C|) - MICROFARADS 0.3 0.4 0.6 0.8__4 6 10

Fig. 25A—Curves for choice of filter values for (1) the first section of a double-

section filter, or (2) a single-section filter. Fig. 25B—Curves for choice of filter values for second section of a double-section filter. 10 20 30 40 60 80 100