"Based on this wavelength and this narrow bandwidth, communication across 23 billion kilometers with 60 kW of power, and directional reflectors for both transmitting and receiving of 100 square meters, we should still have a signal power exactly equal to the noise power. If these dots and dashes are slow and are visually observed on the screen of an oscilloscope, they can just be distinguished from the grass of the background noises."
"That's a little dim to me," said McRae, the animal trainer. "According to you, the secret of long ranges is to reduce the bandwidth sufficiently; then you say that a wide bandwidth is necessary for music and voice. Nevertheless, we hear beautiful music and speech every evening… How does that fit together?"
"At present we're nothing like 23 billion kilometers away from the transmitter. It's only about 20 million, and we've enough reserve range capacity to set our bandwidth for music and voice. But it won't be long before you'll notice a distinct deterioration in the quality of the reception, for we shall continually have to cut down on our bandwidth as we recede from Earth, so as to prevent the background noise from overwhelming the decreasing signals.
"But you wanted to know how our system really works, so here's the principle of it.
Not far from Lunetta and in her orbit, there's a radio station much like the two we have with us. But instead of our reflecting antenna's 3.56 meter diameter and 10 square meters, the Lunetta station has one of quadruple that area. It is seven meters in diameter, and would be somewhat cumbersome for our circumstances.
"Power actually radiated from both our transmitter and from that of Lunetta is 10 kilowatts. It is the maximum present day transmitters can put out at our operating wavelength of 10 cm.
"If we base good voice reception upon signal strength of 100 times that of the noise level and if we demand a bandwidth of 5,000 cycles for reasonable clarity in voice reception, this means that our system has a range limit for voice communication of about 100 million kilometers. We shall reach this limit on the 160th day of our journey. Then we'll slowly have to dispense with direct voice and music reception from Lunetta.
"Of course, our actual range of communication will then in no wise be used up. If we limit ourselves to fast code, transmitted automatically, we can reduce our bandwidth from 5,000 to 1,000 cycles. Since a receiver for automatic telegraphy still operates well when the signal strength is about 20 times that of the noise, the limit of our range for automatic telegraphy is more than 500 million kilometers.
"Our greatest distance from Earth will be when we are waiting in the Martian orbit and the Earth passes behind the Sun. Our radio transmissions will have to overcome a distance of about 377 million kilometers. So you'll see that we never get beyond the range of automatic telegraphy. We shall never in this voyage utilize the extreme ranges which we could attain by "brass pounding" our dots and dashes slowly, in which case we could further cut down on both bandwidth and surplus signal strength."
Billingsley spoke up once more. "When Earth is hidden behind the Sun, it would seem that radio transmission to our home planet would be blanked off by the Sun?"
"That's right, but the period will be short, for the Earth will soon reappear."
"Do I understand that the reflecting antenna is used for both transmitting and receiving?" asked Ross.
"Yes indeed, Doctor. It works like the reflector of a searchlight, for the actual transmitting rod-antenna lies in its focus. Radio emission emanates from this short rod and is reflected into space as are the light rays from a searchlight. When the rod is connected to the receiving set, arriving radio emanations are concentrated upon it by the reflector, rather like the way a shaving mirror can concentrate sunrays to burn paper."
"Then the directive qualities of the antenna reflectors must be an effective means of increasing range," mused Ross.
"Very much so," answered Lussigny. "If we were to operate the rod-antenna without the reflector, the emanations would spread about spherically into space, so that only an infinitesimal part of them would strike the distant receiving antenna. With the directive reflector, we concentrate the radio emission preferably in the direction of the receiver.
Then the receiving reflector picks up a goodly part of the impinging energy and concentrates it upon the receiving antenna, providing a further gain. Mathematically, the total effect is given by the product of the transmitting and receiving reflectors' areas."
"You just said that Lunetta's reflector has four times the area of our own," objected Billingsley. "Then Lunetta ought to receive our transmissions better than we can get hers…"
"No, that isn't quite correct. We do not concentrate our transmissions quite so effectively with our smaller reflector, but Lunetta is able, with her larger one, to intercept a larger cross section of our beam. So the effective energy caught by her larger reflector from our less concentrated beam is exactly equal to our lesser amount from her highly concentrated emission. Either way, it's the product of the reflector surfaces that counts."
"How sharp is our beam?" asked Ross.
"It's some Wi degrees. Generally this kind of beam is sharper, the greater the diameter of the reflector is in relation to the wavelength employed."
"Just a moment; why, then, don't we shorten the wavelength? Three or 4 centimeters instead of 10 ought to give better results."
"Theoretically you're right, but in practice, our wavelength is affected by other factors as well. The main problem is that it is still difficult to build transmitters for powers of the order of magnitude of 10 kilowatts and wavelengths of less than 10 cm, although it is thought that it may be done some day. If we reduce power, we sacrifice some of our range, while the narrowing of the beam achieved by shorter wavelengths would lose its value."
"One more question, please," asked McRae. "You said that there was no difficulty in reducing the bandwidth for achieving long range. But that means that the receiver must be tuned very accurately to the transmitter's wavelength. How can you find the frequency at all?
I have trouble on my set at home finding the frequency of a certain short wave station…"
"Now you've hit on a touchy question," said Lussigny. "In our case, tuning to the transmitter is complicated by some special factors.
"First of all, there's no way of building a transmitter which will not fluctuate to some extent in the emitted wavelength. Ours are stabilized by crystals whose natural frequencies are sharply defined and which prevent any broad variation of the design frequency. But even these crystals are subject to temperature and other variations which prevent complete steadiness in the frequency. We have the same difficulty in our receivers, for, if we wish to tune to a definite frequency with such high exactitude, we must use superheterodyne circuits. In the latter, we do not tune the carrier frequency proper, but rather its difference from a frequency standard generated in an oscillator in the receiver. The accuracy of this oscillator, however, depends on a crystal. The sum of the irregularities thus introduced by inevitable variations between receiver tuning and transmitting frequency forces us to stay above a certain minimum bandwidth. Otherwise the transmitter may "wander" out of the reception band for which our receiver is set.
Fortunately, the minimum bandwidth needed for these reasons is only a fraction of what we require for voice transmission or automatic telegraphy.