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Received July 16, 1912.


THE writers have made a series of measurements of the resistance and inductance of several forms of telephone receivers over a wide range of frequency of current. In the course of the measurements some interesting results have been obtained, which form the subject of this paper.

As the period of the e. m. f. used in the measurements approaches the natural period of the diaphragm, the note emitted by the telephone receiver increases markedly in loudness, and the resistance and inductance of the receiver undergo wide deviations from values obtained when the diaphragm is prevented from vibrating by being damped. That is to say, the motion of the diaphragm has an effect upon the resistance and inductance of the receiver, and this effect grows rapidly as the electrical period approaches the mechanical period.

In the tests to be described, the resistance and the inductance of a given receiver were measured, first with the diaphragm free and sounding, and, second, with the diaphragm damped, or arrested. The values when the diaphragm is free may be called free values; the values when the diaphragm is damped may be called damped values. The difference obtained by subtracting the damped values from the corresponding free values may be called the motional values of resistance, inductance, etc.; since such differences are due to the motion of the diaphragm.

It is found that when the impressed frequency differs widely from the natural frequency of the diaphragm, the motional resistance and inductance are very small. In the neighborhood of resonance, which is often very sharply marked, these motional values become relatively large, and one or both pass through a change of sign, in such a manner that, when the motional impedance for different frequencies is drawn vectorially from a fixed point as origin, all the points given by the observations lie upon a circular graph, which may be called the mo

tional impedance circle, or for brevity, the circular graph of the receiver. Different telephone receivers have very different circular graphs, and the circular graph of any given receiver defines its characteristics in various important practical respects, both mechanical and electrical. Also, from a theoretical standpoint, the reactive influence of the motion of the diaphragm upon the current through the coils of a tele

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FIGURE 1. Diagram of connections of the Rayleigh Bridge and Vreeland Oscillator.

phone is interesting from its analogy to the effects of an optical medium upon transmitted light in the neighborhood of an absorption band.

The experiments also give information regarding the natural period of vibration, and the natural damping factor of the diaphragm, and the power drawn by the instrument when it is sounding and when it is damped.


Measurement of Resistance and Inductance. The measurements of resistance and inductance were all made with a Rayleigh equal-arm bridge, with connections as indicated in Figure 1. The arms AD and DC of the Bridge were 5-ohm non-inductive resistances. The Arm AB contained the telephone receiver T under test. The arm BC contained the adjustable non-inductive resistance R and the adjustable Ayrton-Perry Variometer L. A head telephone H served to determine a balance.


The source of e. m. f. used in the measurement was a Vreeland SineWave Oscillator V, capable of supplying any desired frequency between the limits 430 and 2400 cycles per second. The secondary.coil S of the Vreeland oscillator was connected to the bridge terminals A and C through a resistance of usually 50 or 100 ohms, not indicated. The potential difference of the Vreeland secondary terminals was kept constant throughout a given set of measurements, and was measured by a Paul static voltmeter E. In order to approximate working conditions in the telephone, the voltage at E was kept down to a low value (6 to 12 volts, differing in different experiments). From the known voltage at E, the voltage at the terminals of the telephone was known, and was maintained in different series of tests at values between 0.3 and 1.0 volt.

Measurement of Frequency. The frequency of the oscillator was measured by comparing the pitch of the sound from the telephone T with that of a set of 75 tonometer tuning forks, ranging from 256 to 552 vibrations per second, with successive differences of 4 vibrations per second. Intermediate pitches were estimated by beats. As a check, a stroboscope was in some instances used upon the flickering illumination from the Vreeland bulb, but this was found to be much less convenient than measurement by the tonometer. The pitches were also obtained by calculation from the electrical constants of the Vreeland oscillation circuit, and this method was found to be the most reliable in interpolations for small changes of frequency. In order to obtain the small gradations of frequency that were sometimes necessary, an auxiliary standard condenser was used in connection with the condensers in the Vreeland oscillation circuit. In certain cases it was necessary to vary the capacity in successive measurements by increments as small as 0.001 microfarad.

Procedure. The procedure in making a test was as follows: The frequency of the Vreeland oscillator was first set to the required value by the adjustment of the capacity, and occasionally of the inductance, of its oscillation circuit. The magnitude of the voltage at the Vreeland terminals was then adjusted by adjusting the distance between the primary and secondary Vreeland coils, while an observer watched the indications of the Paul static voltmeter E. A balance on the Rayleigh Bridge was then obtained by successive adjustments of R and L (Figure 1) with the diaphragm of the telephone 7 free and sounding. After recording the values of R and L so obtained, the balance

1 Physical Review, 27, p. 286, 1908.

was repeated with the diaphragm of the telephone 7 at rest and silent. The damping was effected usually by lightly pressing upon the diaphragm with the finger, but in some cases it was affected by inserting a light wedge (a quill) between the diaphragm and pole, when this operation was permitted by an open structure telephone. The balance, when the diaphragm was damped, gave practically complete silence in the head-telephones H, and the settings of resistance and inductance. were consistent within about of 1%. The balance, on the other hand, when the diaphragm was in motion, was not so good. In this case, difficulties were introduced by parasitic notes probably due to currents of higher frequency generated by the motion of the telephone diaphragm. It was usually possible, however, to balance out the fundamental tone, with adjustments consistent within 1 or 2 ohms.


Several telephones were submitted to measurements. Four of the instruments, for which the results are presented in the present account,


1. A Western Electric Bipolar Bell Telephone, Type 122, here designated "Rь",

2. A Western Electric Bipolar Watch-case Telephone receiver, designated "Watch-case,"

3. An experimental specially-constructed monopolar receiver, here designated "Experimental monopolar," and

4. An experimental bipolar telephone receiver, provided with exploring coils, and here designated “Experimental bipolar.”

The following table (Table I) contains some of the mechanical particulars of these instruments.


The data obtained by measurements of the resistance and inductance of the first three of the above receivers are contained in Tables II to VI. The data with the "experimental bipolar" receiver are not tabulated, as they were taken for the specific purpose of determining the angle of lag of magnetization of the iron behind the actuating current and this subject is discussed later.

Explanation of Tables. A brief explanation of Table II, obtained with the bipolar Bell "R" with 0.3 effective volts applied at its terminals, will be given as typical of all the tables. The first column

contains the frequency in cycles per second. The second column gives the corresponding angular velocity in radians per second. The third column gives R' the resistance free, at each frequency, as measured on the Rayleigh bridge; while the fourth column gives R the corresponding resistance obtained with the diaphragm damped. The

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Area of each pole in cm. x cm. 1.4x.225 1.61 ×.16 0.53 0.53 1.17 0.38

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fifth column, headed "motional," gives R' - R; or the difference between the free and damped resistances with a proper sign for the difference. The three remaining columns contain the corresponding reactances, as obtained by multiplying the inductances observed on the Rayleigh bridge by the angular velocity w in each case. The final column, marked "motional," gives the excess of free reactance over damped reactance, with proper sign.

Tables III to VI contain data similar to those in Table II, but with different applied voltages or different receivers.

An examination of these tables shows that there are two independent phenomena of interest; namely,

First, the effect of the frequency on the resistance, reactance and inductance of the receiver when damped; and

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