Radio Broadcast (May 1928-Apr 1929)

DECEMBER, 1928 RADIO BROADCAST 107 O No. 11 Radio Broadcast's Home Study S Resonance in Radio Circuits Part I December, 1928 o TTTHENEVER one tunes his radio receiver or transmitter he performs V' one of the most interesting and most fundamental experiments in all electrical science; he demonstrates a phenomenon that underlies practically all radio work. This is the phenomenon of resonance which occurs in an a.c. circuit under certain conditions of inductance, capacity, and frequency. To study, experimentally, this phenomenon of resonance, we will need the following: LIST OF APPARATUS 1. A simple radio-frequency generator consisting of a vacuum tube connected to a coil and 100,000 u condenser as in Fig. 1. The plate potential of 150-180 volts may be supplied by a standard B-power unit. 2. A meter which will read radio-frequency current. The Weston Model 425 thermogalvanometer is a good „ example. It will measure 3 115 milliamperes at > radio frequencies, has a § resistance of 4.5 ohms, £ and costs $18.50. This 12 is rather expensive, but, in view of the number of uses to which it can be put, it is found in every well-equipped laboratory. Other meter manufacturers make similar meters. FIG. I 3. A coil. The one used in taking data for this experiment was part of a Browning-Drake Kit and had the following dimensions: number of turns, 46; length of winding 1-11/16"; diameter, 2-11/16". The wire was about No. 24 and was spaced about the diameter of the wire. 4. A calibrated variable condenser — a good one is a General Radio Type 247-E in which the capacities are engraved on the dial. PROCEDURE Start up the generator, and if possible, measure its frequency or wave length. This is not essential, however. Connect the coil, the condenser, and the current meter in series. Couple the coil loosely to the generator inductance, and slowly tune either the generator or the tuning condenser until some current is read on the meter. Tune through "resonance," indicated when the current is a maximum, making sure that the meter does not go off scale. Now use as loose coupling as possible to the generator, and plot the current (or deflections of the meter) against condenser degrees and condenser capacities, as the tuning condenser is varied through resonance with the generator. A specimen "resonance" is shown in Fig. 2. Add a 10 to 30-ohm resistance in series with the circuit and repeat. Calculate the inductance of the coil from the formula given in Home Study Sheet No 2 (August Radio Broadcast) and from the formula connecting wavelength, inductance and capacity, (wavelength)==3.54 X L X C where C is in mmfd. L is in microhenries wavelength is in meters. DISCUSSION What is happening that the current in such a combination of apparatus, known as a series-resonant circuit, increases at first slowly, then more rapidly, then decreases sharply, and finally falls off to a very low figure? The answer may be found in Home Study Sheets 7, 8 and 10. In these sheets the effect of a capacity, and an inductance upon the a.c. current in a circuit was discussed. Thus, in an inductive circuit 1 = Xl 6.28 L. J and in a capacitive circuit, Xc = EX6.28xCXf and when L, C, and R all exist in a series circuit, the current I is I = E= E z l/R2+ (Xl — Xc)2 = E VR2+(Lw-c^y where Z is called the impedance of the circuit to is equal to 6.28 X f f is the frequency in cycles X is the reactance of L or C Now an inspection of this formula for current shows that the capacity reactance is to be subtracted from the inductive reactance to get the total reactance in the circuit which, combined with the resistance, forms the impedance which controls the flow of current. If, therefore, we add sufficient capacity reactance to the circuit, so that it is equal to the inductive reactance, the two, when combined by subtracting their values, add up to zero, and the impedance then is composed of the resistance only. In other words, tuning the condenser changes the capacity reactance, thereby decreasing the total reactance, decreasing the impedance, and increasing the current. This is exactly what was done in the above experiment. We balanced out the inductive reactance, which is determined by the coil and the frequency, by changing the capacity reactance, which is determined by the condenser and the frequency. When the two reactances are equal in value but of opposite effect, the total impedance offered to the flow of current is very low, consisting of R only at this value of L, C, f, and the current is a maximum. In a series resonant circuit the current may become very high although the driving voltage, which is across the entire circuit, may be fairly small, and although the individual reactances of the coil and condenser are large. VOLTAGE IN CIRCUIT As in all circuits the voltage across any part is the product of the current through it and its impedance. Thus the voltages across a resistance, inductance, or condenser in such a circuit are: Er = IXR El=I X Xl=ILw Ec=IXXc= and since the current at resonance may become very high — it is governed by the voltage and resistance only — the voltage across the coil and condenser may become very high. For example, if 100 milliamperes flow in a circuit at a resonant frequency of 1000 kc. when the inductance is 200 microhenries, the voltage across the coil is El = I x Lto=(100 X 10-3) x (200 X 10-«) X (6.28 X 1000 X 103) =125.6 volts although, if the resistance in the circuit is 10 ohms, the impressed voltage necessary to drive 100 milliamperes through it is only one volt. A series circuit may be tuned to resonance by varying either the capacity as is usually done — or the inductance, or the frequency. Below the resonant frequency the principle reactance is capacitive. The inductance offers little reactance at low frequencies. At frequencies higher than resonance, the major reactance is the inductance, because the condenser reactance steadily decreases with frequency. At the resonant frequency the two reactances are equal, and hence the voltages across them are equal. This occurs when Xl = Xc, or when f= 159200 ) L x c when L=y.h, C=mmfd. f =kc. Thus a series-resonant circuit is a kind of voltage multiplier. A small driving voltage across a low-resistance ("Low-loss") circuit will cause a high current flow at resonance and a large voltage to appear across the inductance and coil. z o PROBLEMS 5 1. Assume L = 200 iij microhenries, C = 500 Q mmfd, R=10 ohms. Calculate the reactances, impedance, current, resistive, and inductive and capacitive voltages in the circuit when E=10 volts. Plot all these against frequency from 400 to 600 kc. If the experiment outlined under Procedure has been carried out , use the values of L and C obtained there and assume R=10 ohms. Since the current is known, calculate the voltage across the circuit at resonance. 2. How do the two calculated inductance values check? 3. Does the current lag or lead the voltage below the resonant frequency? At the resonant frequency what happens to the phase angle? What above the resonant frequency? 4. In an amateur transmitter tuned to 40 meters, the antenna current is one ampere. This flows through a series tuning condenser of 100 mmfd. capacity at resonance. What voltage must the condenser stand? 5. In Problem 1, what is the ratio between the current at resonance and at 20 kc. below resonance? What would be this ratio if R were doubled, or halved? Do you see the importance of low -resistance circuits? 500 510 FIG. 2