Radio Broadcast (May 1928-Apr 1929)

Explaining the Whole "Business931 IMPORTANCE OF IMPEDANCE RELATION By C. T. BURKE Engineering Department, General Radio Company T T IS recorded that a lecturer on sanitation, I speaking in a portion of the country which JL shall from motives of policy, be nameless, upon reaching the inevitable question period was somewhat taken aback by the query "What's sanitation?" Lest the writer find himself in a similar predicament he hastens to define impedance, which he is going to endeavor to explain briefly in this article. The first part of this article is devoted to the general subject of impedance and the latter part of the article to its application to audio transformers. Impedance is that quality in an electrical circuit which impedes or limits the flow of current, and determines the value of the current that flows when a given pressure (voltage) is applied against the obstruction. It should not be necessary to point out that, if we are connecting an electrically operated device in a circuit, the impedance of the device is of the utmost importance, since it regulates the amount of current which is delivered to it from the source. A device of very great impedance approaches an open circuit in effect, that is, little current flows from the generator to the load. On the other hand, if a short circuit (very low impedance) is placed across the generator, all the available voltage will be used up in forcing the large current through the internal impedance of the generator. The power supplied to the load depends neither on current nor voltage alone; it is proportional to the product of current and voltage, that is, power equals volts times amperes. Fig. 3 shows the variation of current, voltage, and power for a source of 5000 ohms impedance (for example, a tube with a plate impedance of 5000 ohms, such as a 210 or 112a) and generating 100 volts, as the load impedance is varied. The current is at maximum when the output or load resistance is zero under which conditions the current is equal to the voltage, 100, divided by 5000 ohms which gives 20 milliamperes. The voltage available across the load is equal to Resistance , , ™ . of load Voltage across the load = 100 volts times =; — r Resistance of load plus internal resistance of generator (5000 ohms) The voltage across the load, therefore, rises as the load impedance is increased and will be at maximum when the load impedance is infinitely high. The power in the load, however, rises to a maximum where the load is 5000 ohms, or equal to the source impedance. This relation is always true; that is, the maximum transfer of energy occurs when the source <RL+ JXL = ZL) (generator) impedance and the load impedance are equal. This is a universal ride applying to batteries, rotary generators, and converters, as well as to vacuum tubes. We are pleased to present this article by Mr. Burke in which he endeavors to clear up some misconceptions regarding impedance, especially as it affects the operation of audio transformers. Impedance is a characteristic possessed by every unit used in a receiver and few things in radio are more important than a clear understanding of what impedance is and how it affects the operation of various devices. — The Editor. Fig. 1 — Diagram of a transformer with load. Conditions in Tube Circuits TN COMMUNICATION circuits, the imA pedance of the circuit elements is often necessarily high, so that the current flow even under short circuit will not cause damage. Under these circumstances, with vacuum tubes it is possible to realize the theoretical maximum output of the device, obtained when the load impedance equals the generator impedance, and the so-called "matching" of impedances becomes important. That is, in connecting two circuits or devices together, it becomes important to have the impedance of the circuit in which the power originates (the source) equal to the impedance of the load (or "sink"). For a concrete example, a power tube of 5000 ohms impedance will deliver maximum power to a load of 5000 ohms impedance, The importance of exact matching of impedance has undoubtedly been over-emphasized. In the power curve of Fig. 3 it will be noted that, while the maximum power to the load occurs with a load resistance of 5000 ohms, the load resistance can vary from 2600 to 10,900 ohms, a range of about 4 to 1, with only ten per cent, reduction in load power. Owing to a peculiarity in the behavior of vacuum tubes, the maximum undislorfed output will be delivered to a load of twice the impedance of the tube, i. e., 10,000 ohms for a 5000-ohm tube, and in designing a circuit this relation is usually aimed at. The impedance of a device is determined generally by certain considerations in its design which cannot be altered conveniently to obtain the optimum impedance relation when the device is worked out of a source of a certain impedance. The remedy for this situation is fortunately quite simple, involving only the use of the so-called impedance adjusting transformer. The remainder of this article is devoted to a discussion of this important device. Impedance Adjustment IT WILL be remembered that impedance was defined as the opposition which a circuit offered to the flow of current, in other words the factor which determines the flow of current from a source of definite voltage and • march, 1929 . . . page 322 • internal impedance. If, then, a load impedance may be so affected as to cause the same current to flow in from the source as would another impedance, it is, so far as the source is concerned, equivalent to the latter impedance. If the load impedance is less than the source impedance there are two methods of increasing it, by means of a series impedance, and by means of a transformer. The series impedance method does not generally accomplish the desired result. Under the conditions in which we are principally interested, i. e., a vacuum tube feeding a loud speaker, the series impedance is not effective. While the ''matching" thus accomplished does increase the power output of the tube, it does not increase the input to the load, since the added power is dissipated in the extra series resistance. Similar reasoning will dispose of the suggestion of the use of a parallel impedance to reduce the load impedance. There is left as a possible means of impedance adjustment, the transformer. The action of a transformer is to step-up or -down an alternating current or voltage. Since the transformer is not a source of power, the power must be the same on both sides except for the losses in the instrument. Power being proportional to the product of current and voltage, this product must be the same on both sides of the transformer, i. e. the current is stepped-up in the same ratio as the voltage is stepped-down. and vice versa. This ratio of transformation is the ratio of turns in the two windings (approximately) . Consider the loaded transformer of Fig. L The definition of impedance may be stated j£ algebraically as : Z = y , i. e., I impedance voltage Then if Zi,e. is the equivalent impedance of the transformer and load (the impedance which would permit the same current to flow as flows with the loaded transformer) : E, NEi _ NEiZl Ii h E2 = N2Zl where Zi.e. — equivalent impedance of load from primary of transformer . N — turns ratio=Ei/E2 Ei — voltage across primary 11 — primary current 12 — secondary current E2 — secondary voltage Zl — load impedance That is, the equivalent impedance of a transformer of a turns ratio of N, loaded with RP RT H2 R, N2Xt Fig. 2 — Equivalent circuit of the loaded transformer. The circuit of Fig. 1 may be replaced by this series-parallel network