QUANTITATIVE MEASUREMENTS

LEARNING OBJECTIVES

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

• Explain the purposes and benefits of performing quantitative measurements.
• Identify the various methods of performing impedance measurements.
• Identify the various methods of performing power measurements.
• 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.

Figure 3-1. - Basic bridge circuits.

Figure 3-2. - Typical bridge circuit configuration.

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 C_B and R_B in series connection, provides a striking contrast with the parallel connection of C_B and R_B 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, R_A and R_B, for the range of values selected. The same signal voltage is impressed across the branches S and X of the bridge. The variable control, R_S, 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 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 R_S 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 R_A and R_B are common to both switch positions X and Y.

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

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?