# Bridge Methods For Measurements At Radio Frequencies

under measurement are at first used, and as experience and technique improve, more elaborate but more convenient and flexible methods are developed.

The earliest methods of measuring resistance were the voltmeter-ammeter and later the substitution methods. Bridges, which increased the sensitivity of the substitution method by introducing a differential comparison and extended its range by using ratio arms, naturally developed from the substitution method. Bridges are now universally used for direct-current and audio-frequency measurements.

In the higher frequency ranges, voltmeter-ammeter methods have been extensively used. At radio frequencies (say 100 kc. to 2 Mc.), the tuned-circuit substitution method is generally favored. In this measurement the unknown resistance is replaced in a tuned circuit by a standard wrhich is adjusted to give the same voltage drop at constant current, as the unknown. The object of the tuned circuit is to reduce the effect of reactance on the measurement.

Bridge methods have several advantages over voltmeter-ammeter and tuned-circuit substitution methods. They are not limited to narrow frequency ranges, and they grant more latitude in the choice of standards. They involve, however, the introduction of other circuit elements into the measurement and are, therefore, just I y viewed with some suspicion when used under conditions where the values of the additional circuit elements are not entirely known.

The essential difficulty with measurements at high frequencies lies in the fact that the circuit elements of inductance, capacitance, and resistance cannot be individually isolated but are present together in all circuit units, and between the units themselves, as well as between units and ground. Most of the technique of alternating-current bridge methods involves the develop-

merit of circuit units whose characteristics approach lumped constants and means of eliminating the effect of residuals from the measurement.

Leads, also, which are ignored at lower frequencies, may have impedances approaching in magnitude those under measurement. These problems, it should be observed, are present at 1000 cycles, although too frequently ignored. In any bridge method it is necessary to distinguish between a balance of the bridge and a balance between the unknown and standard elements. The effect of residuals is frequently such as to give a false balance involving unknown and extraneous impedances.

Bridges have been used at frequencies well above the audio-frequency range, and there is no question that with proper care bridge measurements can be used at very high frequencies.

The main difference between measurements at audio and radio frequencies is summed up in the one-thousandfold increase in series inductive reactance and the corresponding decrease in parallel capacitive reactance. This means that distributed inductance and capacitance which were entirely negligible at audio frequencies frequently have controlling influence at frequencies of the order of one megacycle.

The absence of proper standards offers as great an obstacle to high-frequency bridge methods as the difficulties inherent in the bridge circuit itself. Resistance standards usually have some reactance at high frequency, and reactance standards have resistance.

Air condensers have the smallest time constants of any impedance ele ment and their law of variation with capacitance and frequency is known. They may be either fixed or variable. Solid dielectric mica condensers may be made which also have a small time constant varying only with frequency. Fixed straight wire resistors have very small time constants, which can be calculated provided the wire used is non-magnetic. Resistors of the bifilar, Ayrton-Perry, mica-card, and woven -tape forms also have small time constants. Their equivalent series inductances and time constants are independent of frequency over a wide range. They cannot, however, be calculated, but must be compared with the straight wire standards. Variable resistors are inferior to fixed resistors because of the added reactance of the switching mechanism. Inductors make poor radio-frequency standards, since their time constants are large and variable, depending upon skin effect and the characteristics of the iron core if one is used.

Their natural frequencies are low and variable inductors show variation of resistance with setting. They must be compared with standard condensers.

In considering bridge circuits for radio frequencies it is the natural course to select simple circuits and those having similar elements permitting a symmetrical arrange men I. The equal-arm bridge should be used, although this limits the usefulness of the bridge method somewhat. It is nol too difficult to make similar units having practically identical lumped and distributed constants, but to make dissimilar units in which the lumped and distributed constants bear like ratios is far more difficult. Equal resistances are normally used for the ratio arms, although capacity ratio arms can be used.

An elementary bridge circuit suitable for use at radio frequencies is shown in Fig. 1. Tt consists simply of the two fixed ratio arms, the shielded input transformer, and terminals for standard and unknown impedances. This diagram is, of course, exactly what would be used at audio or lower frequencies. The modifications necessary for high-frequency use lie entirely in the arrangement of parts and leads and the shielding which is required.

While this elementary bridge circuit can be reasonably well balanced at 1000 cycles, at higher frequencies a double balance is necessary in order to eliminate all factors of stray capacitance. Two methods of accomplishing this offer themselves. One is the addition of a Wagner ground circuit by means of which the capacitances to ground are first balanced before obtain-ing a balance of the main bridge. A second arrangement is the substitution method which is, of course, extensively used in precision measurements at 1000 cycles, in this method, the unknown and standard are placed in parallel in the same side of the bridge and balanced in the other arm by an un-ca libra ted condenser which must, however, possess reasonably good characteristics. The bridge is balanced once with the unknown disconnected and again with the unknown shunted across the standard. The technique is the same as that used at lowTer frequencies, except that greater care must be taken and it is particularly important that the arrangement of leads be unchanged for the two balance conditions. The resistance balance is obtained by adding resistance in series or parallel with

Figure 1. Basic bridge circuit commonly used at audio frequencies and suitable for radio-frequency work if precautions are taken

the capacitance arms. When the added resistance is changed between measurements, correction must be applied for the change in inductance of the resistance unless it can be established that this is negligible. In calculating results from the bridge measurements at high frequencies it is important to use the original bridge equations before eliminations based on orders of magnitude have been made. These equations may be easily derived or are given in most textbooks on bridges. Many of the order-of-magnitude eliminations do not hold at high frequencies.

In an endeavor to test out the practicability of bridge methods at radio frequencies, the General Radio Company has developed the Type 516-A

Figure 2. The new Type 516-A Radio-Frequency Bridge, an experimental in-Htrument for the determination of reactance and resistance at high frequencies. Its use is recommended for laboratories having a considerable experience with other methods for measuring impedance

Figure 2. The new Type 516-A Radio-Frequency Bridge, an experimental in-Htrument for the determination of reactance and resistance at high frequencies. Its use is recommended for laboratories having a considerable experience with other methods for measuring impedance

Radio-Frequency Bridge. This is illustra led in Figures 2 and 4 and the w iring diagram is shown in Figure 3.

The entire bridge is enclosed in one shield, while separate internal shields enclose the ratio arms, the balance condenser, ihe power-factor balance resistor, and the output transformer. The latter also contains a shield between primary and secondary.

The shielded transformer is placed in the output of the bridge, so that at balance it will have no current in it and no external field. It is an air-core transformer with concentrated windings, whose capacitances to each other and to the shield have been minimized. By a suitable choice of the number of __

turns the band of frequencies between 10 kc. and 5 Me. may he covered. The

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