Introduction
All Measurements Are Two-Point
Voltage is always measured between two points in a circuit. This is true whether using a voltmeter or an oscilloscope. When an oscilloscope probe touches a point in a circuit, a waveform usually appears on the display, even if the ground lead is not connected. In this situation, the reference for the measurement is conducted through the safety ground of the scope chassis to the electrical ground in the circuit.
By virtue of their two probes, digital voltmeters measure potential between two points. Because they are isolated, these two points can be anywhere in the circuit. This has not always been the case. Before the advent of the digital voltmeter, hand-held meters known as VOMs (Volt-Ohm-Meters) were used to measure "floating" circuits. Because they were passive, they tended to load the circuit-under-test. Less invasive measurements were made with the high-impedance VTVM (Vacuum Tube Volt Meter). The VTVM had one major limitation - the measurement was always referenced to ground. The VTVM housing was grounded and connected to the reference lead. With the introduction of solid-state gain circuits, high performance voltmeters could be isolated from ground, allowing floating measurements to be made.
Most oscilloscopes today, like the venerable VTVM, can only measure voltages that are referenced to earth ground, which is connected to the scope chassis. These are referred to as "single-ended" measurements - the probe ground provides the reference path. Unfortunately, there are times when this limitation lowers the integrity of the measurement, or makes measurement impossible.
If the voltage to be measured is between two circuit nodes, neither of which is grounded, conventional oscilloscope probing cannot be used. A common example is measuring the gate drive in a switching power supply (see Figure 1).
Figure 1. Gate drive signal in a switching power supply is measured between TP1 and TP2. Neither point is grounded.
Signals which are balanced (between two leads without a ground return) such as a common telephone line cannot be measured directly. As we shall see, even some "ground referenced" signals cannot be faithfully measured using single-ended techniques.
When Ground Is Not Ground
We've all heard of "ground loops" and been taught to avoid them. But how do they corrupt a scope measurement? A ground loop results when two or more separate ground paths are tied together at two or more points. The result is a loop of conductor. In the presence of a varying magnetic field, this loop becomes the secondary of a transformer which is essentially a shorted turn. The magnetic field which excites the transformer can be created by any conductor in the vicinity which is carrying a non-DC current. AC line voltage in primary wiring or even the output lead of a digital IC can produce this excitation. The current circulating in the loop develops a voltage across any impedance within the loop. Thus, at any given instant in time, various points within a ground loop will not be at the same potential.
Connecting the ground lead of an oscilloscope probe to the ground in the circuit-under-test results in a ground loop if the circuit is "grounded" to earth ground (see Figure 2). A voltage potential is developed in the probe ground path resulting from the circulating current acting on the impedance within the path.

Figure 2. Ground loop formed by a scope probe. Metal chassis of both scope and device under test are connected to safety ground and internal power supply common. Scope probe ground connects to scope chassis at the input BNC connector.
Thus, the "ground" potential at the oscilloscope's input BNC connector is not the same as the ground in the circuit being measured (i.e., "ground is not ground"). This potential difference can range from microvolts to as high as hundreds of millivolts. Because the oscilloscope references the measurement from the shell of the input BNC connector, the displayed waveform may not represent the real signal at the probe input. The error becomes more pronounced as the amplitude of the signal being measured decreases, as is common in transducer and biomedical measurements.
In these situations, it's often tempting to remove the probe ground lead. This technique is only effective when measuring very low-frequency signals. At higher frequencies, the probe begins to add "ring" to the signal caused by the resonant circuit from the tip capacitance and shield inductance (see Figure 3). (This is why you should always use the shortest ground lead possible.)

Figure 3. Series resonant tank circuit formed by probe-tip capacitance and ground inductance.
We now have a dilemma: create a ground loop and add error to the measurement or remove the probe ground lead and add ring to the waveform!
The next technique often tried to break ground loops is to "float" the scope or "float" the circuit being measured. "Floating" refers to breaking the connection to earth ground by opening the safety-ground conductor - either at the device-under-test or at the scope. Floating either the scope or the device-under-test (DUT) allows the use of a short ground lead to minimize ring without creating a ground loop.
This practice is inherently dangerous, as it defeats the protection from electrical shock in the event of a short in the primary wiring. (Some special battery-operated portable scopes incorporate insulation which allows safe floating operation.) Operator safety can be restored by placing a suitable ground-fault circuit interrupter (GFCI) in the power cord of the oscilloscope (or device-under-test) with the severed ground. However, be aware that without a low-impedance ground connection, radiated and conducted emissions from the scope may now exceed government standards - as well as interfere with the measurement itself. At higher frequencies, severing the ground may not break the ground loop as the "floating" circuit is actually coupled to earth ground through stray capacitance (see Figure 4).

Figure 4. "floating " battery-powered cellular telephone probed with and grounded oscilloscope. Capacitance between the phone circuitry and steel bench frame forms a virtual ground loop at high frequencies.
Even when the measurement system doesn't introduce ground loops, the "ground is not ground" syndrome may exist within the device being measured (see Figure 5). Large static currents and high-frequency currents act on the resistive and inductive components of the device ground path to produce voltage gradients. In this situation, the "ground" potential referenced at one point in the circuit will be different than that referencing another point.

Figure 5. Minute parasitic inductance and resistance in ground distribution system result in VG not equal to VG.
For example, ground at the input of the high-gain amplifier in a system differs from the "ground" potential at the power supply by several millivolts. To accurately measure the input signal seen by the amplifier, the probe must reference the ground at the amplifier input.
These effects have challenged designers of sensitive analog systems for years. The same effect is seen in fast digital systems. The small inductance within the ground distribution system can create a potential across it, resulting in "ground bounce". Troubleshooting systems affected by ground-voltage gradients is difficult because of the inability to really look at the signal "seen" at the individual component. Connecting the oscilloscope probe ground lead to the "ground" point of the device results in the uncertainty of what effects the new path adds to the ground gradient. A sure clue that a change is occurring is seen when the problem in the circuit either gets better (or worse) when the probe ground is connected. What we really need is a method to make a scope measurement of the actual signal at the input of the suspect device.
By using an appropriate differential amplifier, probe, or isolator, accurate two-point oscilloscope measurements can be made without introducing ground loops or otherwise corrupting the measurement, upsetting the device-under-test, or exposing the user to shock hazard.
There are several types of differential amplifiers and isolation systems available for oscilloscopes, each optimized for a particular class of measurements. In order to choose the proper solution, an understanding of terminology is necessary.
