Radio Broadcast (May 1928-Apr 1929)

No. 16 Radio Broadcast's HomeStudy Sheets February, 1929 Experiments With a Wavemeter METHODS of calibrating a wavemeter were discussed in Home-Study Sheet No. 13. If the experimenter provides himself with a heterodyne wavemeter, that is an oscillating vacuum tube with a grid-current meter and a series of coils and a tuning condenser, he has, in his own laboratory, the most important item of equipment for a whole series of interesting, instructive, and useful experiments. The heterodyne wavemeter can be avoided if an oscillating detector is used with a pair of telephones in its plate circuit according to Fig. 1. The circuit will have to be calibrated, but this can be accomplished as indicated in Home-Study Sheet No. 13. With this system, instead of using a gridcurrent meter to indicate resonance with another circuit, a click in the telephones serves the same purpose. Properties of Coils and Condensers A. Wind up on a form approximately 2.0 inches in diameter about 60 turns of rather large insulated wire, say about No. 20, so that the distributed capacity will be large. Connect the ends of the coil across a variable condenser whose capacity at several settings is known — a calibrated condenser, in other words. A 500-mmfd. condenser will have about the maximum capacity needed. Starting at the maximum condenser capacity, "click," the coilcondenser combination into the oscillating detector, or into the heterodyne wavemeter. Note down the wavelength or frequency, and then change the setting of tire variable condenser and get a new wavelength or frequency setting. Continue until three or four points have been secured, for example, if a 500-mmfd. condenser is used, get the wavelength at 500, 400, 300, 200, and 100 mmfd. Make a table, as in Table 1, showing the condenser capacity, the wavelength, and the wavelength squared. Plot, as in Fig. 2, the wavelength squared against, capacity. A straight line should result, because of the equation, (wavelength)2 = 3.54 x L x C where L = microhenries C = mmfd. This equation states that the wavelength squared is proportional to the capacity. The "proportionality factor," that is. the factor which connects the wavelength squared and the capacity is L, the inductance. The slope of the line divided by 3.54 then, is the value of L, that is. L = 1 3.51 (wavelength)2 capacity It will be noted that the line crosses the vertical axis (the wavelength-squared axis) at some distance above the zero point. In other words, if there were no additional capacity present, except what the coil inherently possesses, the wavelength squared would be given by this value. This point on the curve gives us the natural wavelength of the coil, determined by its inductance and its dis 140,000 S 60,000 100 200 300 400 CO MMFD tributed capacity. To check this value, remove the condenser end click the coil alone into the wavemeter. The point where the line crosses the capacity axis gives us a value for the distributed capacity of the coil. This value when multiplied by the proper value of L gives us the LC product which, when fitted into the formula above, gives us the natural wavelength of the coil. Thus one experiment not only gives us the inductance of a coil, but its distributed capacity and its natural wavelength as well. The greater the distributed capacity of the coil, the more accurately it can be measured by this method. As a check on this method of determining the inductance of a coil, calculate the inductance from the following formula, L = d2 N2 9 d + 10 b where d is the diameter in inches N is the number of turns b is the length of winding in inches Measuring Capacity B. The product of L and C in a circuit determines the wavelength or the frequency to which that circuit will tune. When the circuit is near by a source of energy of this frequency, the circuit begins to absorb energy and a large current will flow in the coil and the condenser. This phenomenon is the basis of all tuning in radio circuits, and has been described in Home-Study Sheets 11 and 12. It can be used for measuring purposes as well as for receiving radio signals as the following experiment will prove. Connect a condenser whose capacity is known across a coil so that the combination will "click" into the range of frequencies over which the wavemeter or oscillating detector will cover. Adjust the circuit to resonance. Connect across the condenser a capacity whose value is unknown but which is desired. Adjust the variable standard capacity until resonance is again obtained. What has happened? We have increased the total capacity in the circuit by adding the unknown condenser to the standard. We must, therefore, reduce the setting of the standard until the total capacity in the circuit is as it was before. For example, if the condenser were set at 400 mmfd. when resonance occurred without the unknown capacity, and at 320 mmfd. with the capacity, the difference, 400 — 320, or 80 mmfd., gives the capacity of the unknown. Such a method enables the experimenter to disregard the capacity of the coil and of the leads since they are in the circuit, at all times and do not affect the difference of capacity produced by adding another condenser to the circuit. If a large condenser is to be measured, it may be necessary to put it in series with the standard condenser to obtain resonance. The experimenter must remember that when two condensers are put in parallel the resultant capacity is the sum of the individual capacities — this is the basis of the experiment just described; but that when two condensers are put in series, the resultant capacity is the product of the individual capacities divided by the sum, or the resultant capacity, Co, of adding Ci in series with C2 is Co = Ci X Ci or ± = 2 , 1 Ci -} C Co Ci C2 Fig. 2 If the capacities of small paper or mica condensers are measured by these methods, i.e., determining their capacity at high frequencies, some strange results will occur. The capacities will differ rather widely from the rated values. Air condensers will give true readings, however. The variation in capacity at different frequencies seems to be a kind of electronic disturbance in the dielectric at high frequencies so that the dielectric constant is not what it is at low frequencies. Such discrepancies are not important where the units are used as bypass condensers but when they are to be used for tuning circuits, one cannot rely on their markings. The experimenter should make a list of the rated capacities, the measured capacities, and the percentage accurate of a series of small fixed condensers. Measuring Antenna Capacity C. Connect a coil in series with the antenna and ground and "click" into the wavemeter or the detector. Then remove the antenna and ground wires and connect across the coil a variable condenser whose capacity is known, or can be obtained. Tune the condenser until resonance is obtained. Then the capacity of the condenser is the same as the capacity of the antenna. Measuring Antenna Inductance D. Connect a known inductance in series with the antenna and ground and measure the wavelength of the system. Then connect another inductance, different in value from the first, and get a new value of wavelength. Then the two wavelengths are related as below: (wavelength) 1 = 1.884 Y(L + La) C, = Xi (wavelength) 2 = 1.884 V(U + La) Ca = X2 where La = antenna inductance Ca = antenna capacity Eliminating Ca from these two equations, gives La = L, X? U X? Xf — \l Problems 1. Two condensers whose capacities are 400 mmfd. and 500 mmfd., respectively, are across two inductances. Both combinations tune to the same frequency. What is the ratio of inductances? If the inductance across the 400-mmfd condenser is 300 microhenries, what is the inductance across the other? 2. What is the inductance of the coil used in the experiment which produced Fig. 2?. What is its distributed capacity? What is its natural wavelength? 3. If the wavelength of a circuit varies as the square root of the capacity, what must be done to the capacity in a circuit to double the wavelength? If the wavelength varies as the square root of the inductance, and if the inductance varies as the square of the number of turns, how is the wavelength related to the number of turns on a coil? That, is, if a coil has 30 turns and tunes to 300 meters, how many turns are necessary to tune to 600 meters? 4. A coil to tune over the broadcast band has 75 turns. It is used with a 0.00035-mfd. condenser. How many turns, approximately, will be needed if the condenser is 0.0005 mfd.? 5. A coil-condenser combination tunes to 450 kc. when the capacity is600 mmfd. When an unknown condenser is placed in series with the condenser, the circuit tunes to 600 kc. What is the value of the unknown capacity? 6. An antenna tunes to 300 meters when 200 microhenries are in series with it, and to 400 meters when the inductance is increased to 300 microhenries. What is the inductance of the antenna? Bemembering that the antenna inductance is in series with the "loading" inductance, and that the total inductance in the circuit can be calculated by adding the individual inductances, what is the capacity of the antenna? What is its natural wavelength? 7. An antenna has a natural wavelength of 400 meters and a capacity of 0.0003 mfd. How would you reduce the natural wavelength to 200 meters? 8. The LC product of a coil and condenser to tune to 220 meters is 0.01362 mfd. If the distributed capacity of the coil to be used plus the minimum capacity of the variable condenser amounts to 50 mmfd. what is the necessary inductance? What will be the tuning range if the maximum capacity of the condenser is 0.00035 mfd? Co MMFD 100 200 300 350 Table I Wavelength 212 283 340 364 (Wavelength) 2 45000 80000 115000 132000 • february, 1929 . . . Page 254 •