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 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 2. The bridge shown in Figure 2 is actually the DC Wheatstone bridge; however, the general principles of circuit operation for AC remain the same.
 

Figure 1: Basic bridge circuits. Figure 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 1 and 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 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 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 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.
 

Figure 3: Resistance-ratio bridge residual elements. Figure 4: Wagner ground.

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 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 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. 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.

Capacitance, inductance, and resistance bridges.

You can measure capacitance, inductance, and resistance for precise accuracy by using ac bridges. These bridges are composed of capacitors, inductors, and resistors in a wide variety of combinations. These bridges are operated on the principle of a dc bridge called a Wheatstone bridge.
 

Figure 5: Wheatstone bridge.

The Wheatstone bridge is widely used for precision measurements of resistance. The circuit diagram for a Wheatstone bridge is shown in Figure 5. Resistors R1, R2, and R3 are precision, variable resistors. The value of Rx is an unknown value of resistance that must be determined. After the bridge has been properly balanced (galvanometer G reads zero), the unknown resistance may be determined by means of a simple formula. The galvanometer (an instrument that measures small amounts of current) is inserted across terminals b and d to indicate the condition of balance. When the bridge is properly balanced, no difference in potential exists across terminals b and d; when switch S2 is closed, the galvanometer reading is zero.

The operation of the bridge is explained in a few logical steps. When the battery switch S₁ is closed, electrons flow from the negative terminal of the battery to point a. Here the current divides as it would in any parallel circuit. Part of it passes through R₁ and R₂; the remainder passes through R₃ and R_x. The two currents, I₁ and I₂, unite at point c and return to the positive terminal of the battery. The value of I₁ depends on the sum of resistance R₁ and R₂, and the value of I₂ depends on the sum of resistances R₃ and R_x. In each case, according to Ohm's law, the current is inversely proportional to the resistance.

R₁, R₂, and R₃ are adjusted so that when S₁ is closed, no current flows through G. When the galvanometer shows no deflection, there is no difference of potential between points b and d. All of I₁ follows the a b c path and all I₂ follows the a d c path. This means that a voltage drop E₁ (across R₁ between points a and b) is the same as voltage drop E₃ (across R₃ between points a and d). Similarly, the voltage drops across R₂ and R_x (E₂ and E_x) are also equal. Expressed algebraically,

and 

A wide variety of ac bridge circuits (such as the Wheatstone) may be used for the precision measurement of ac resistance, capacitance, and inductance. Let's look at ac bridges in terms of functions they perform.
 

Figure 6: Resistance bridge (ac).

Resistance bridge. An ac signal generator, as shown in Figure 6, is used as the source of voltage. Current from the generator passes through resistors R1 and R2, which are known as the ratio arms, and through Rs and Rx. Again, Rx is known as resistance. Rs has a standard value and replaces R3 in Figure 6. When the voltage drops across R2 and Rs are equal, the voltage drops across R2 and Rx are also equal; no difference of potential exists across the meter and no current flows through it. As we discovered with the Wheatstone bridge, when no voltage appears across the meter, the following ratio is true: For example, if in Figure 6 we know that R1 is 20 ohms, R2 is 40 ohms, and Rs is 60 ohms, we can find the value of Rx using our formula as follows:

With the ac signal applied to the bridge, R₁ and R₂ are varied until a zero reading is seen on the meter. Zero deflection indicates that the bridge is balanced. (NOTE: In actual practice, the variables are adjusted for a minimum reading since the phase difference between the two legs will not allow a zero reading.)
 

Figure 7: Capacitance bridge.

Capacitance bridge. Because current varies inversely with resistance and directly with capacitance, an inverse proportion exists between the four arms of the bridge in Figure 7; the right side of our expression is inverted from the resistance bridge expression as follows: or