notes on power Measurement in communication Circuits
By John d. Crawfoid
ANOTHER communication meas-j—urement problem makes its appearance when it is desired to determine experimentally how much power a given power source is capable of delivering to a specified load or sink. So long as the source itself is available for test, it is merely necessary to set up the equipment and make the measurements. If, however, the source is not available, some means must be found of simulating it. At least two methods for doing the job are available, and we propose to describe them. Both are perfectly general: the "source" may be a vacuum-tube oscillator or a microphone or an incoming transmission line; the "load" may be a loud-speaker or an attenuation network or an outgoing transmission line. There are only two restrictions: the "source" must supply a sinusoidal voltage, and the impedance of the "load" must not depend upon the current in it.
A generalized statement about networks called Thevenin's Theorem gives directly one of the methods for setting up a simulating source. We shall defer stating it until later because it will simplify matters to set up a specific hypothetical problem, follow through its solution, and with that as a basis, state the general law. Our discussion must be understood to be an attempt f POWER SOURCE
LOAD
* This is the second part of an article begun in the October issue of the Experimenter. Although complete in itself, this section depends upon the introduction preceding Part I.
Figure 3
to show that Thevenin's Theorem is plausible without trying to prove it.
Consider, for example, the load circuit shown in Figure 3. Its impedance at a given frequency is ZR\ the voltage drop, current, and absorbed power which correspond to ZR are, respectively, ER, IR, and IVR. Inasmuch as ZR is assumed to be independent of
Iwe can make the obvious statement that for any value of ZRy TVR will depend only upon the magnitude of ER (or of IR, since E and I are linked by Ohm's Law).
Now suppose that we want to determine experimentally how much power the load will absorb at different frequencies from a given power source which is not available for the tests. What must we do in order to set up a simulating source? We have just seen that the only way a source can affect WR is to change ER. Therefore, all we need do to simulate the given source is to make sure that, no matter what value ZR may assume (as a result of changing the test frequency, tor example), Er for the simulating source is the same as ER for the source itself. In other words, no power measurements on the load could tell us which of two sources was supplying power if the terminal voltages (ER) of each were the same.
Let us also assume that the source to be simulated is an alternator which delivers a constant voltage at its output terminals no matter what load is thrown upon it.* Because of a high-impedance line between the alternator
- Figure 4
and its load terminals, the voltage at the load terminals depends upon the size of the load. This condition is represented in Figure 4, where E is the voltage of the alternator, G, and Z2 is the
*An oscillator which could do exactly that would be a curiosity, having, as we shall point out later, a negligible "internal impedance."
impedance of the line. ER is therefore always less than E by E2, the voltage drop in Z2. In other words, IVR depends upon Z2.
From what has gone before, Z2 may be considered a part of a new load, Z'Ry having an impedance of Z2-\-ZR. The power delivered to this new load will, as before, be fixed if the voltage drop across it is fixed. The generator, G, delivers constant voltage under all conditions of load, a fact which enables us to build a simulating source. Since the load cannot distinguish between one generator and another if the impressed voltages are the same, we can take any generator, maintain its terminal voltage equal to E by manual adjustment, and the power delivered to Z'R will be the same for both the actual and the simulating sources. Furthermore, the voltage drop in Z2 will be the same under both conditions, and the power delivered to ZR will be the same as though it were connected, to the original source. Therefore, we have shown that any generator connected in series with an impedance equal to Z2 will simulate this particular source, if the voltage at the generator terminals is maintained constant and equal to E.
From the foregoing discussion we may conclude that the presence of -Z2, the internal impedance for the given power source, is the reason why changes in the magnitude of ZR affect the terminal voltage ER. If Z2 is equal to zero, ER would be constant and equal to E, the open-circuit voltage of the source; but if Z2 is not zero, then every decrease in the magnitude of ZR causes ER to be less than E by the voltage drop in Z2=IRZ2. Furthermore, any generator or any source behaves as though it had no internal impedance if its terminal voltage is maintained constant.
Suppose that G were not a constant-voltage generator, or, in other words,
November, 1929
November, 1929
- Figure 5. Two methods for simulating a power source when its open-circuit voltage E=IZ and its internal impedance Z are known. Left: Constant-voltage method. Right: Constant-current method
suppose that its terminal voltage E depended upon the amount of current taken by the load. This would, of course, indicate that somewhere ahead of its output terminals there existed an appreciable impedance. To simulate this new source we would proceed exactly as before: maintain the simulat-ing-generator voltage constant and equal to the open-circuit voltage of the source and connect in series with it an impedance equal to ZG-\-Z2, the sum of the internal impedance of G and the impedance of the intervening connecting wires.
It is now time to discard all of our labored attempts at a simple and orderly development to state the general law about which we spoke at the beginning of this section. It is a corollary of Thevenin's Theorem, a theorem that is capable of a formal proof with which we shall not concern ourselves here. Thevenin's Theorem permits us to state that any power source can be simulated (Figure 5) by a generator with a terminal voltage E connected in series with an impedance Z-, E being equal to the no-load or open-circuit voltage of the source and Z being equal to the impedance of the source as seen from its output terminals. This can be verified experimentally for a simple source like the one we have been discussing by connecting an oscillator to a load of adjustable but known impedance and observing its terminal voltage as a function of delivered power or of load impedance or of current. Errors due to bad waveform and overloading in the oscillator must not be allowed to enter.
The diagram at the right in Figure 5 shows the second simulating method and although it does not follow directly from Thevenin's Theorem, it can be shown to be entirely consistent with it. In the second method, constant current is maintained through the parallel circuit formed by Z, the impedance of the simulating source, and the load impedance; the constant current being such as to make the no-load voltage drop across the simulating impedance equivalent to the no-load voltage of the power source. If we can show that for any value of ZR the voltage ER is the same for both the constant-current and the constant-voltage methods, the two are equivalent.
Imagine that both circuits are terminated in a load ZR:
(a) for constant-voltage method,
(b) for constant-current method, / ZRZ \ E( ZRZ \ = EZr
Ii the voltage of the source is non-sinusoidal or the impedance of the load is non-linear (i.e., a function of current), special care must be used in applying these simulating methods. The same care must be exercised when studying transient effects, since our discussion has been tacitlv limited to the steadv-state condition.
a non-polar relay
4 S their names indicate, the new /-\ Type 507 Non-Polar Relays contain an armature that is not permanently magnetized. They do not, therefore, distinguish between the two directions of current as does the Type 481 Low-Current Relay.* Their principal use is in cases where contacts of low current-carrying capacity must control heavier currents, as in the Type 547-A Temperature-Control Box.
There are two of the new Non-Polar
*C. T. Burke, "A New Relay," General Radio Experimenter, III, February, 1929.
Relays, bearing the type numbers 507-A and 507-B, respectively. Their specifications are as follows, currents given corresponding to positive operation in either vertical or horizontal positions:
Type 507-A Non-Polar Relay. Current to close, 10 mla. Current to open, 6 mla. Resistance (±5%), 250 ohms. Code Word, nitre. Price $12.00.
Type 507-B Non-Polar Relay. Current to close, 2 mla. Current to open, 1 mla. Resistance (=t=5%), 4000 ohms. Code Word, noble. Price $15.00.
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