Ground and Other Reference Points

Anytime a voltage is measured, the voltmeter is actually indicating the voltage that is present at one point in the circuit with reference to another point. We briefly discussed this idea in Chapter 3 with regard to relative polarities.

The Concept of Ground

In most electronic circuits, there is a point to which all circuit voltages are measured. This common point is called the circuit ground. Most often, but certainly not always, ground is considered to be one side of the circuit’s power source. In all cases, ground is considered

Exercise Problems 4.4 Exercise Problems 4.4

100 V

3.2 W

5.6 W

I = 150 mA

1.0 W

Figure 4-47. What is the total power in this circuit?

1.0 kΩ I₁ = 10 mA

R₁ R₂ R₃

20 V 50 V

V_A

_ +

Figure 4-48. Compute all unknown circuit values.

All voltages must be mea-sured or expressed with reference to some other point.

KEY POINTS

Voltages are often mea-sured with respect to a common point called ground.

KEY POINTS

to be 0 V. This is sensible, since ground is the reference point for all measurements, and since any voltage is zero with reference to itself (i.e., there is no difference in potential).

Figure 4-49(a) shows a series circuit where the negative side of the voltage source is consid-ered to be the circuit ground. Note the symbol ( ) used to represent ground. Figure 4-49(b) shows exactly the same circuit as Figure 4-49(a), but two ground symbols are used. Both ground symbols represent the same electrical point in the circuit. The intercon-necting wire is assumed but not shown. The omission of the interconintercon-necting ground wires on schematic diagrams is the normal practice since it removes unnecessary clutter from otherwise complex diagrams.

When a circuit is physically constructed, ground can take a number of different forms. If the circuit has a metal chassis or frame associated with it, then the frame is usually connected to circuit ground. This is especially true for frequency devices or high-speed digital circuits. Most circuits are constructed on printed circuit boards (PCBs). The conductors on a PCB are traces of copper bonded to an insulating material. The copper traces connect the various components together just as wire might do in a laboratory circuit. Ground on a PCB is often a very wide trace that wanders throughout the board. If the PCB has more than one layer of traces, then one or more of the layers is frequently dedicated as a ground plane. This means that the entire PCB layer (sheet of copper) is connected to ground.

Voltages with Reference to Ground

Figure 4-50 shows a series circuit with one point labeled as the ground connection. The remaining points in the circuit are labeled A through E. When we measure the voltages at points A through E, we connect one lead of the voltmeter to ground and the other lead to the point being measured. For example, suppose we wanted to measure the voltage at point C in Figure 4-50 with reference to ground. We would connect one side of the volt-meter to ground and the other to point C. You can see from inspection of Figure 4-50, that the meter is essentially connected across R₃, so it will indicate 6 V. We label the voltage at point C as V_C. So in the present example, V_C = 6 V.

V_A

R₁

R₂

R₃

V_A

R₁

R₂

R₃

Ground Ground

(a) (b)

Figure 4-49. Ground is a reference point from which other voltages are measured.

The resulting measurement is less obvious if we were to measure the voltage at point E.

There is a simple procedure, however, that will allow you to determine the correct theoret-ical voltage at any point in a circuit.

1. Start at the reference point and write the voltage drops as you move toward the measured point. Use the polarity of the voltage drop that is on the end where you exit a component.

2. When you reach the measured point, the algebraic sum of the accumulated volt-age drops will be the measured value.

The polarities of the voltage drops are determined in exactly the same manner as if we were writing the Kirchhoff ’s Voltage Law equation for the loop. The only differences are that we do not complete the loop, and we do not set the voltages equal to zero. (If you prefer to use the polarity where you enter a component, then you should start at the measured point and move to the reference point.)

EXAMPLE SOLUTION

Determine the voltage at point E in Figure 4-50.

EXAMPLE SOLUTION

We begin at the reference point (ground) and move toward the measured point (point E). As we pass through R₄, we will write its voltage drop as –2 V. Continuing through R₅, we find a drop of –5 V. Since we have reached our destination, the measured value will be equal to the algebraic sum of our accumulated voltage drops. In this particular case, the measured voltage will be

It is important to realize that you may move in either direction as you progress from the reference point toward the measured point. Although the individual voltage drops may be different, the algebraic sums of the two directions will be identical. If, in the present example, we had moved in

R₁

R₂

R₃

R₄

R₅ 5 V

3 V 4 V

6 V

2 V

A B

C

D E

+ V_A

20 V

–

+ +

– + – + – –

Figure 4-50. Voltages can be measured with respect to ground.

V_E = –2 V+–5 V = –7 V

the opposite direction, we would have accumulated the following sequence of voltages: +6 V, +3 V, +4 V, and –20 V (the voltage source). The algebraic sum of these voltages is still –7 V.

EXAMPLE SOLUTION

Determine the voltage that would be measured between ground and point A in Figure 4-50.

EXAMPLE SOLUTION

As we start at ground and move toward point A, we generate the following sequence of volt-ages: +6 V, +3 V, and +4 V. This yields an algebraic total of V_A = +13 V.

Practice Problems Practice Problems

1. Refer to Figure 4-51, and determine the fol-lowing voltages: V_A, V_B, V_C, and V_D.

Answers to Practice Problems

Nonground References

In some cases, a technician must measure a voltage that is referenced to some point other than ground. Suppose, for example, we want to determine the voltage that would be measured at point B with reference to point D in Figure 4-52. We apply the exact same procedure that we used for ground references. In this case, we begin at the reference point (point D) and move toward point B. As we go, we will generate the following sequence of voltages: +10 V and +4 V. The algebraic sum of these voltages is +14 V.

We must be careful to specify the reference point when writing the voltage at a certain point in a circuit. Figure 4-53 shows the accepted method for indicating voltage refer-ences. In the case of a ground reference, the second subscript is omitted and ground is assumed to be the reference point. Exceptions to this labeling method are usually obvious by inspection. In our preceding example, we would label the voltage at point B that was measured with respect to point D as V_BD = +14 V.

Figure 4-51. Determine the voltages at points A, B, C, and D with reference to ground.

Voltages that are mea-sured with reference to some point other than ground are generally identified with a double subscript (e.g., V_AD). The first subscripted letter indicates the measured point in the circuit; the second subscript indi-cates the reference point.

KEY POINTS

EXAMPLE SOLUTION

Refer to Figure 4-54. What is the voltage at point E with reference to point C?

EXAMPLE SOLUTION

We begin at point C and move toward point E as we generate the following sequence of volt-ages: +1 V, +4 V, and +10 V. The algebraic sum is V_EC = +15 V.

EXAMPLE SOLUTION

Refer to Figure 4-54. What is the value of V_AB? EXAMPLE SOLUTION

When moving from point B to point A, we obtain a voltage drop of –2 V. Thus, V_AB = –2 V.

Answers to Practice Problems

R₂

Figure 4-52. Nonground references are also used by technicians.

Measured quantity

Figure 4-53. Method for labeling nonground references.

1. +11 V 2. –15 V 3. –25 V

Figure 4-54. Determine the value of V_EC and V_AB

Other Types of Ground References

There are several alternate symbols that are used to represent ground (i.e., 0 V) reference points on schematic diagrams. Some of these are illustrated in Figure 4-55. Although the

“correct” use of a particular symbol has been documented by standards committees, the actual use of the symbols by manufacturers seems to be somewhat arbitrary. The symbol shown in Figure 4-55(a) is generally used to represent earth ground. That is, a point in the circuit that is connected to the safety ground of the 120 Vac power line and ultimately connects to a metal stake driven into the soil. This is a particularly important reference point for several reasons. If properly implemented, it provides some degree of increased safety with respect to shock from the 120 Vac power line. In particular, if the metal equipment chassis and other metal parts that are accessible to the equipment user are connected to ground, then no shock hazard will exist if an internal wire comes loose or inadvertently touches the chassis.

The symbol shown in Figure 4-55(b) is used to represent circuit ground by some manufac-turers. In some cases, a given circuit may be designed to have multiple grounds that are essentially isolated from each other. In these cases, the ground symbol shown in Figure 4-55(c) can be labeled to identify the various ground connections. Figure 4-55(c) shows the symbol labeled with the letter “A.”

1. Refer to Figure 4-56. Determine each of the following voltages:

2. Refer to Figure 4-56. Determine each of the following voltages: