Module 21 - Test Methods and Practices
Navy Electricity and Electronics Training Series (NEETS)
Chapter 3:  Pages 3-1 through 3-10

Chapter 3

QUANTITATIVE MEASUREMENTS

Learning Objectives

Upon completion of this chapter, you will be able to do the following:

1. Explain the purposes and benefits of performing quantitative measurements.

2. Identify the various methods of performing impedance measurements.

3. Identify the various methods of performing power measurements.

4. Identify the various methods of performing frequency measurements.

Introduction to QUANTITATIVE MEASUREMENTS

You have already studied the basics of performing electronics measurements and how to determine if a component is or is not functioning properly. This chapter will cover techniques used in measurements of specific impedance, frequency, and power. These measurements are extremely important to you in

evaluating the performance of a piece of electronic equipment.

Impedance MEASUREMENTS

Impedance measurements are often used during routine test procedures. Impedance-measuring equipment, such as impedance bridges, are mainly used in determining the capacitance and inductance of component parts. However, the values of combined circuit constants also may be obtained and used in direct calculations of impedance. An impedance measurement effectively totals the inductive and capacitive reactance together with the resistance in a circuit. In addition, impedance measurements are useful in testing and analyzing antenna and transmission line performance and for determining the figure of merit (Q) of electrical parts and resonant circuits. Q meters are impedance-measuring instruments that determine the ratio of reactance to resistance of capacitors or inductors and resistors. Details of Q meters and impedance bridges as well as a number of other methods of measuring circuit impedance are described in the following paragraphs. Also discussed are methods of measuring the impedance of antennas and transmission lines.

BRIDGE Methods

Bridges are among the most accurate types of measuring devices used in the measurement of

impedance. In addition, bridges are also used to measure dc resistance, capacitance, and inductance. Certain types of bridges are more suitable for measuring a specific characteristic, such as capacitance or inductance. Basic schematics for the various bridge circuits are shown in figure 3-1. The bridge circuits shown are similar in that they usually contain two branches in the measuring circuit, two branches in the comparing circuit, a detector circuit, and a power circuit, as shown in figure 3-2. The bridge shown in figure 3-2 is actually the dc Wheatstone bridge; however, the general principles of circuit operation for ac remain the same.

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Figure 3-1. - Basic bridge circuits.

Figure 3-2. - Typical bridge circuit configuration.

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The comparing circuit contains branches a and B and has provisions for changing the ratios of the branches with respect to each other, which enables various measuring ranges to be obtained. Comparison of figures 3-1 and 3-2 shows that either or both branches of the comparing circuit do not necessarily contain resistors alone. Branch B of the Hay bridge, containing CB and RB in series connection, provides a striking contrast with the parallel connection of CB and RB of the Maxwell bridge.

The measuring circuit in figure 3-2 also contains two branches. The resistance, capacitance, or inductance to be measured is connected to branch X of the bridge-measuring circuit. The subscript X is also used in figure 3-1 to designate the circuit parameters involved in computing the values of various electronic parts. Branch S contains the variable control used to bring the bridge into a balanced condition. a potentiometer is used for this purpose in most bridge equipment, because it offers a wide range of smoothly variable current changes within the measuring circuit.

The third arm of the bridge is the detector circuit. The detector circuit may use a galvanometer for sensitive measurements that require high accuracy. In the case of bridges using ac as the power source, the galvanometer must be adapted for use in an ac circuit. In many practical bridge circuits using ac to operate the bridge, an electron-ray indicating tube is used to indicate the balanced condition by opening and closing the shadow area of the tube. Headsets are also used for audible balance detection, but this method reduces the accuracy obtainable with the bridge.

Switches are used in bridge circuits to control the application of operating power to the bridge and to complete the detector circuit. Frequently, the two switching functions are combined into a single key, called a bridge key, so that the operating power is applied to the bridge prior to the detector circuit. This sequence reduces the effects of inductance and capacitance during the process of measurement.

The most unfavorable condition for making a measurement occurs when the resistance, capacitance, or inductance to be measured is completely unknown. In these cases, the galvanometer cannot be protected by setting the bridge arms for approximate balance. To reduce the possibility of damage to the galvanometer, you should use an adjustable shunt circuit across the meter terminals. As the bridge is brought closer to the balanced condition, the resistance of the shunt can be increased; when the bridge is in balance, the meter shunt can be removed to obtain maximum detector sensitivity.

Bridges designed specifically for capacitance measurements provide a dc source of potential for electrolytic capacitors. The electrolytic capacitors often require the application of dc polarizing voltages in order for them to exhibit the same capacitance values and dissipation factors that would be obtained in actual circuit operation. The dc power supply and meter circuits used for this purpose are connected so that there is no interference with the normal operation of the capacitance-measuring bridge circuit. The dissipation factor of the capacitor may be obtained while the capacitor is polarized. In figure 3-2, the signal voltage in the a and B branches of the bridge will be divided in proportion to the resistance ratios of its component members, RA and RB, for the range of values selected. The same signal voltage is impressed across the branches S and X of the bridge. The variable control, RS, is rotated to change the current flowing through the S and X branches of the bridge. When the voltage drop across branch S is equal to the voltage drop across branch A, the voltage drop across branch X is equal to the voltage drop across branch B. At this time the potentials across the detector circuit are the same, resulting in no current flow through the detector circuit and an indication of zero-current flow. The bridge is balanced at these settings of its operating controls, and they cannot be placed at any other setting and still maintain this balanced condition.

The ability of the bridge circuit to detect a balanced condition is not impaired by the length or the leads connecting the bridge to the electronic part to be measured. However, the accuracy of the measurement is not always acceptable, because the connecting leads exhibit capacitive and inductive

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characteristics, which must be subtracted from the total measurement. Hence, the most serious errors affecting accuracy of a measurement are because of the connecting leads.

Stray wiring capacitance and inductance, called residuals, that exist between the branches of the bridge also cause errors. The resistance-ratio bridge, for example, is redrawn in figure 3-3 to show the interfering residuals that must be eliminated or taken into consideration. Fortunately, these residuals can be reduced to negligible proportions by shielding and grounding. a method of shielding and grounding a bridge circuit to reduce the effects of interfering residuals is through the use of a Wagner ground, as shown in figure 3-4. Observe that with switch S in position Y, the balanced condition can be obtained by adjusting Z1 and Z2. With switch S in position X, the normal method of balancing the bridge applies. You should be able to reach a point where there is no deflection of the meter movement for either switch position (X or Y) by alternately adjusting Z1 and Z2 when the switch is at position Y and by adjusting RS when the switch is at position X. Under these conditions, point 1 is at ground potential; and the residuals at points 2, 3, and 4 are effectively eliminated from the bridge. The main disadvantage of the Wagner ground is that two balances must be made for each measurement. One is to balance the bridge, and the other is to balance the Wagner ground. Both adjustments are interacting because RA and RB are common to both switch positions X and Y.

Figure 3-3. - Resistance-ratio bridge residual elements.

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Figure 3-4. - Wagner ground.

Many bridge instruments provide terminals for external excitation potentials; however, do not use a voltage in excess of that needed to obtain reliable indicator deflection because the resistivity of electronic parts varies with heat, which is a function of the power applied.

Q-1. What conditions must be met in order to balance a bridge circuit?

Q-2. When you are measuring a component using a bridge, what is the most common cause of inaccurate measurements?

Wheatstone Bridge

The Wheatstone bridge, shown in figure 3-1, is often used to measure resistance. These instruments are usually portable because they require only a small, dc source to power the bridge, which is easily obtained from flashlight batteries. In those cases where an external supply voltage is desirable for the operation of the bridge, use the minimum voltage that will give a reliable indication by the galvanometer. Increasing the supply voltage any further results in uncompensated thermal variations and decreased bridge accuracy. If greater bridge sensitivity is needed, use a galvanometer with greater sensitivity.

A number of other considerations are involved in the choice of a galvanometer. For example, the galvanometer should not be subjected to false or erratic indications because of external magnetic fields. This requirement dictates the choice of a shielded meter mechanism. It is also desirable to use a critically dampened meter movement to ensure decisive movement of the meter pointer during conditions of bridge unbalance. Thermal agitation sometimes produces voltages that interfere with the balancing of the bridge. For this reason, the Wheatstone bridge usually includes a polarity-reversing switch in the detector circuit. When a measurement is required, note the reading for both positive and negative indications, and figure the average of both readings. With the exception of inaccuracies introduced by thermal variations (caused by excessive supply voltages), the accuracy of the Wheatstone bridge is, otherwise, independent of the value of supply voltages. The units used in calibrating the galvanometer are unimportant to the accuracy of the bridge, since a 0 indication is desired at the balanced condition.

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Resistance values ranging from 1 ohm to 1 megohm can be measured with an accuracy of approximately 0.1%. However, difficulties are encountered when very high and very low resistances are measured. Resistances less than 1 ohm are difficult to measure accurately because of uncertainty arising from the contact resistance present between the resistor to be measured and the binding posts of the bridge. Measurement of resistances greater than 1 megohm becomes difficult because of two factors: (1) The ratio of standard resistances R_A and R_B involve a ratio on the order of 1,000 to 1, and (2) the voltage applied to the bridge must be substantially increased to obtain definite galvanometer action. The result is that an increase in the supply voltage increases the power dissipation (heat) of the bridge resistors. The change in resistance RB, because of the heat, is sufficient to produce an appreciable error. a Kelvin bridge is recommended for measuring resistances lower than 1 ohm. An electronic multimeter is recommended for the indicating device in bridges used for the measurement of very high resistances.

One of the most elementary precautions concerning the use of a bridge, when measuring low resistance, is to tighten the binding posts securely so that the contact resistance between the binding posts and the resistance to be measured is minimum. Leakage paths between the resistor leads along the outside surface of the resistor body must be avoided when resistances greater than 0.1 megohm are measured. Search for defective solder joints or broken strands in stranded wire leads; these defects can cause erratic galvanometer indications. In those cases where wire leads must be used to reach from the resistance under test to the bridge terminals, measure the ohmic value of those leads prior to further measurements.

Q-3. How does the supply voltage affect the accuracy of Wheatstone bridge measurements?

Kelvin Bridge

It is often necessary to make rapid measurements of low resistances, such as samples of wire or low values of meter shunt resistors. a frequently used instrument that is capable of good precision is the Kelvin bridge, shown in figure 3-1. Note the similarity between this and the Wheatstone bridge. Two additional resistances, R1 and R2, are connected in series and shunted across resistance R, which is the circuit resistance existing between the standard and unknown resistances, R_S and R_X, respectively. In performing the adjustment for balance, you must make the ratio of R1 to R2 equal to the ratio of R_A to R_B. When this is done, the unknown resistance can be computed in the same manner as that for the Wheatstone bridge, because resistance R is effectively eliminated.

In using a Kelvin bridge, you must follow precautions similar to those given for the Wheatstone bridge. a rheostat is usually placed in series with the battery so that bridge current can be conveniently limited to the maximum current allowable. This value of current, which affects the sensitivity of the bridge, is determined by the largest amount of heat that can be sustained by the bridge resistances without causing a change in their values. All connections must be firm and electrically perfect so that contact resistances are held to a minimum. The use of point and knife-edge clamps is recommended. Commercially manufactured Kelvin bridges have accuracies of approximately 2% for resistance ranges from 0.001 ohm to 25 ohms.

Q-4. Kelvin bridges are well suited for what type of measurements?

Resistance-Ratio Bridge

The resistance-ratio bridge, shown in figure 3-1, may be used to measure capacitance, inductance, or resistance so long as the electronic part to be measured is compared with a similar standard. The measurement of the value of a capacitor must be made in terms of another capacitor of known characteristics, termed the STANDARD Capacitor. The same requirement is necessary for an inductance measurement. The standard of comparison is designated as X_X, and the losses of the standard are represented as R_X. If you experience difficulty in obtaining a balanced bridge condition, insert

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additional resistance in series with branch S of the bridge. This adjustment becomes necessary because the Q of the unknown capacitor or inductor in branch X is higher than the comparable Q of the standard in branch S.

Schering Bridge

The Schering bridge, shown in figure 3-1, is a commonly used type of bridge for the measurement of capacitors and dielectric losses. The Q of a capacitor is defined as the reciprocal of the dissipation factor, which is the ratio of the capacitor's dielectric constant to its conductivity at a given frequency. Accordingly, capacitor Q is determined by the frequency used to conduct the measurement and the value of the capacitor, CB, required to obtain bridge balance. The accuracy of this type of bridge is excellent, about 2% for dissipation factors ranging from 0.00002 to 0.6. Typical accuracies for capacitive reactances in the range of 100 picofarads to 1 microfarad are 0.2%.

Hay Bridge

The Hay bridge, shown in figure 3-1, is used for the measurement of inductance and the Q of the inductor. It is interesting to note that this type of bridge measures inductance by comparing it with a standard capacitor of known characteristics. This arrangement provides the advantage of a wide measurement range with the minimum use of electronic parts as comparison standards. a typical range of values that can be measured with the Hay bridge is from 1 microhenry to 100 henries. The accuracy of the measurements made with this bridge is about 2%. The frequency used in conducting the inductance measurement must be taken into account because of the series reactance of capacitor CB. The loss factor of the inductor under test is balanced in terms of the Q of the inductor. The Hay bridge, then, is used for measurement of inductances having a Q greater than 10. For instance, a Q of 10 gives a calibration error of 1%, whereas a Q of 30 gives a calibration error of 0.1%.

Q-5. When you are testing an inductor with a Hay bridge, the characteristics of the inductor are compared with what type of device?

 Maxwell Bridge

The Maxwell bridge, shown in figure 3-1, is used for the measurement of inductance and inductive Q. This bridge is similar to the Hay bridge because it also measures inductance by comparison with a standard capacitor of known characteristics. Notice, in particular, that capacitor C_B is connected in parallel with resistor R_B. In connection with this difference, the requirement of an accurately known frequency is removed. This bridge circuit is employed for measuring the inductance of inductors having large losses; i.e., low Q. The range of this type of instrument is much greater than that of the Hay bridge; values ranging from 1 microhenry to 1,000 henries are measurable, with an error of only 2%.

VECTOR BRIDGES

The basic bridges described up to now determined the resistive and reactive components of the unknown impedance; however, the vector bridge indicates the magnitude and phase angle. Typically, vector bridges require two null readings. Consider the basic bridge circuit of figure 3-5. The magnitude of the unknown impedance (Z_X) is determined by the voltages applied across R and ZX and to the bases of emitter followers Q1 and Q2, which bias the balanced rectifiers, CR1 and CR2. Resistors a and B are equal in value. When R is adjusted to equal ZX, the voltages between points 1 and 2 and between points 1 and 4 are equal in magnitude, and the VTVM will indicate 0 volts.

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Figure 3-5. - Typical vector-bridge configuration (amplitude).

The absolute value of Z_X is determined from the dial calibration of R. Without altering the amplitude balance, you reconnect the external circuits as shown in figure 3-6. Note that the voltage between points 1 and 3 is being compared to the voltage between points 1 and 2. Potentiometer R, calibrated in degrees, is adjusted for a null indication on the VTVM; and the phase angle is read directly. If Z_X is purely resistive, the voltage between points 1 and 3 will be zero and the setting of R will be 0 volts. If Z_X is purely reactive (capacitive or inductive), the setting of R will be at maximum voltage. For phase angles between 0º and 90º, the scale of R may be calibrated directly in degrees. The sign of the phase angle can be determined by changing the signal frequency slightly and observing the change in impedance. The presence of harmonics in the signal input will severely hamper the measurements. If a pure frequency source is not available, suitable low-pass filters will have to be employed in the output leads from the bridge.

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Figure 3-6. - Typical vector-bridge configuration (phase).

CONSTANT-CURRENT, Impedance-MEASURING TECHNIQUE

This technique employs an oscillator circuit and a VTVM, as shown in figure 3-7.

Figure 3-7. - Constant-current, impedance-measuring method.

A large value of resistance, R, is selected so that IC is virtually independent of the range of Z_X to be measured. Thus, ICZ X represents the value of voltage measured by the VTVM. If R is chosen so that the voltage drop across ZX corresponds to a full-scale reading on the VTVM, a direct reading impedance meter is realized. For example, assume that the audio oscillator open-circuit voltage is 10 volts (rms) and that the full-scale reading of the VTVM is 0.05 volt. If you want to measure Z_X values ranging up to a maximum of 5,000 ohms, you should use a 1-megohm resistor for R. This will result in a full-scale, 0.05-volt deflection. An oscillator that does not produce harmonics should be used.

Impedance-ANGLE METER

Like vector bridges, impedance-angle meters determine an unknown impedance in terms of magnitude and phase angle. However, a non-bridge technique is used. The simplified circuit of a commercial instrument is shown in figure 3-8. With switches S1 and S2 at the BAL position, the variable

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standard resistor, R, is adjusted until the balanced rectifier outputs of Q1 and Q2 are equal (indicated by a null in the deflection of the voltmeter connected between the emitters of Q3 and Q4). The dial setting of R gives the value of Z_X. For phase angle determination, the circuit is switched to CAL and the input voltage is adjusted for full-scale voltmeter deflection. The circuit is then switched to Phase; thus, the paralleled outputs of Q1 and Q2 are applied to rectifier CR1 only. With S2 in the phase position, there is no input to the base of Q4. If Z is purely resistive, the outputs of Q1 and Q2 cancel, and the voltmeter indicates zero deflection. For a complex impedance, the base of Q3 will be unbalanced with respect to the base of Q4; and the voltmeter deflection, calibrated in degrees, determines the phase angle of the unknown impedance. Typical commercial impedance angle meters, operating at 2 MHz, are accurate to within 4% for impedances of from 10 to 500 ohms.

Figure 3-8. - Impedance-angle meter.

Q-6. What do impedance-angle meters and vector bridges have in common?

Impedance TESTING of Antennas and Transmission Lines

The amount of current that flows in an antenna is one of the most important factors affecting the performance of transmitter equipment. As much of the RF energy generated as possible must be efficiently transferred to the antennas to secure the maximum radiated power from a transmitter. Also, for best reception, maximum transfer of energy from the antenna to the receiver must occur. Efficient transmission and reception conditions prevail whenever the transmitter (or receiver) is properly matched to the transmission line and the transmission line is properly matched to the antenna. Normally, performance tests concerning impedance match consist primarily of taking standing-wave measurements. In certain instances, it may be found that a change in antenna impedance has resulted in an undesirably high standing-wave ratio. This could be the result of a new antenna installation or an interfering structure near the antenna that influences antenna characteristics.

In practice, the antenna-matching network is varied to match the new antenna characteristics, since the transmission line is designed to match equipment impedance. This can best be done by making a series of standing-wave-ratio checks and antenna-matching adjustments until an acceptable standing-wave

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