December 1952 QST
Here's a topic that never goes out of style. Without bothering to worry about source and load impedances, this brief tutorial on the fundamentals of power supply filter design using series inductors adn parallel capacitor combinations. The author offers a rule-of-thumb type formula for guessing at a good inductor value based on peak-to-average expected current. This is by no means a comprehensive primer on power supply filter design and is directed more toward someone new to the concept.
Fundamental Facts for the Beginner
By Gabriel P. Rumble, EX-W5BBB
If the requirement is pure (that is, unvarying) direct current, the rectifier outputs shown in a previous article1 will not fill the bill.
We must use the properties of L and C (or sometimes R and C) to iron out the ripples in the rectified current.
If a condenser is placed in parallel with the load on a half-wave rectifier, as shown in Fig. 1A, the voltage between alternations does not drop to zero, because the condenser charges during the conducting half-cycle and discharges through the load during the nonconducting half of the cycle, as shown in Fig. 1B.
A comparison of the output waveforms shown previously should make it clear why the output of a full-wave rectifier is easier to filter than that of a half-wave rectifier. In either case, the condenser will by-pass some of the ripple around the load. The greater the capacitance, the slower the RC decay and the shallower the ripple.
The action of a condenser in a filter circuit is analogous to that of shock-absorber springs in a wagon traveling over a cobblestone road. We can further smooth out the ride by adding weight to the wagon. This step is comparable to the addition of a choke (inductance) to the filter circuit, as shown in Fig. 2A. The elasticity of the condenser and the inertia of the inductor are being utilized to smooth out the ripples that would otherwise exists across the load. Further filtering and the consequent approach to pure direct current may be accomplished by additional sections of filter, as shown in Fig. 2B. (Suggestion: Consult your favorite textbook on the interesting subjects of resonant filters and swinging chokes.)
If the full rectifier output voltage is applied to the condenser, as shown in Fig. 2A, the filter is said to be of the condenser-input type. If, instead, the ripple voltage first undergoes an IXL drop before being applied to the condenser, as illustrated in Fig. 2B, the filter has choke input. (Suggestion: Look up the subject of critical inductance.)
A comparison of the voltage regulation of supplies having condenser and choke input is shown in Fig. 3 (p. 130). With condenser input, the output voltage varies considerably with varying loads. With choke input, the output is almost constant for a wide range of load variation. The variation occurring in this flat range is caused by the d.c. resistance of the choke and rectifier resistances and the leakage reactance of the transformer. However, in well-designed components these are usually quite low. The load current at which the knee of the curve occurs is dependent on the inductance of the input choke. The greater the inductance, the smaller the value of load current at which the curve starts to flatten out.
In addition to providing a flatter characteristic, the use of choke input has another advantage. It reduces the ratio of peak to average current passed by the rectifier. If it were desired to design a rectifier for a fixed load current of I amperes and E volts, and if it were further desired that the peak rectifier current should exceed the average by only P%, then the inductance, L, in henrys, of the input choke, should be
L = E / (10*P*I), where:
The knee of the characteristic will occur at a current of P*I amperes. If it were desired to have the knee at a lower current, a smaller value of P would be selected and a higher L would be called for. Where good regulation down to low values of load current is not of interest, and the values of full-load current and rectifier current rating permit, the values of P above 5 per cent will usually be more economical.
Filter chokes are usually placed in the ungrounded side of the rectifier output. If the choke is placed in series with the transformer and ground, the capacitance of the secondary winding of the transformer to grounds tends to by-pass the choke.
If the expected current drain on a rectifier is very slight, resistors, which are comparatively inexpensive, may be used in place of the chokes. A 1000-ohm resistor, for example, will do just as much filtering as 1000 ohms of inductive reactance at any given ripple frequency. It should be stressed that this is practical only when the load resistance is much higher than the filtering resistance. Also, the d.c. voltage drop in the filter resistor and its adverse effect on regulation must be taken into account.
1 Rumble, "How Rectifiers Work," QST, October, 1952, p.42.
Posted April 14, 2016