|Figure 1: Emitter voltage measurement|
in simplified schematic view
Usually, that reference point is the circuit's ground, or what we assume to be ground. Ideally, we'd like that ground to be at zero volts. For example, consider the measurement of the voltage at a transistor's emitter as referenced to ground (Figure 1). Looks pretty simple, doesn't it? However, if we expand the schematic view of this measurement scenario to include the oscilloscope probe and the ground connections between the oscilloscope and the circuit under test, we're looking at a significantly more complex picture (Figure 2).
|Figure 2: Emitter voltage measurement including|
oscilloscope, probes, and grounds.
As one may see, the overall measurement scenario now includes numerous impedances, such as ZCIRCUIT, which is the resistance of the emitter-connected resistor R1 in parallel with the emitter impedance of the transistor. ZSCOPEGND is the impedance of the ground lead in the oscilloscope's power cord. ZCOMMON is the impedance between the circuit ground and the ideal earth-ground point. Also, ICOMMON represents currents flowing through ZCOMMON from other sources, such as other instruments connected to the circuit under test. These currents result in VCOMMON.
All of the above is by way of saying that there is, in fact, no ideal earth-ground point. A single-ended probe that theoretically would suffice in measuring the emitter voltage were the situation as simple as shown in Figure 1. In real life, though, what often happens is that the common ground local to the signal being measured is quite different from what the oscilloscope sees as ground (the same issue arises if the chassis of the circuit under test is floating above ground).
Now, if the values of ICOMMON, ZCOMMON, and ZSCOPEGND were all zero, there would be no need to use the oscilloscope probe's ground lead because then there could be no difference between the circuit's common and the oscilloscope's ground. But because they are not zero, the only solution for using a single-ended probe in these circumstances is to try to shunt their effects by grounding the probe at its tip. And guess what? The probe's ground lead introduces resistance and inductance of its own, which depends on the lead's length. That resistance and inductance will cause some amount of corruption of the signal. The voltage drop represented by VCOMMON is the culprit. And no matter what we do, there is no way to completely eliminate VCOMMON. All of this is, of course, frequency-dependent, with the effects being exacerbated at high frequencies.
One quick and dirty cure for all of this complexity is to disconnect the oscilloscope's safety ground. Kids, don't try this at home (or in the test lab). If the magnitude of VCOMMON is high enough, it can be a highly dangerous situation.
|Figure 3: Emitter voltage measurement using differential|
probe and differential amplifier
An ideal differential amplifier will only amplify the difference it sees between its positive and negative inputs. In this respect, it's not unlike using a simple voltmeter to probe two points and find the voltage difference between them. But because the differential amplifier amplifies the difference between the two points, it rejects any voltage that is common to both. Because VCOMMON appears at both points A and B in our circuit, the differential amplifier rejects it and presents the oscilloscope with only the difference between points A and B, or VA-B. Not only that, but the loop-current effects of VCOMMON are greatly reduced because the probes' high impedance prevent VCOMMON from generating much current into the oscilloscope ground. And with no probe ground lead connected to point B, say goodbye to the effects of ZGNDLEAD.
The foregoing described an ideal differential amplifier, but alas, as with many things in life, ideal is hard to come by, isn't it? Our differential amplifier is seeing two voltage waveforms: the one we want to see (differential mode, or the voltage between points A and B) and the one we don't want to see (common mode, or the voltage common to both points A and B). How well the amplifier is able to reject the common-mode voltage is typically stated as the ratio of the output signal's magnitude divided by the differential input signal's magnitude, which is known as common-mode rejection ratio (CMRR).
Another figure of merit for a differential amplifier is its common-mode range. This is how large the amplitude of VCOMMON can become before the amplifier can no longer tolerate it. The value is typically at least several times larger than the differential input range and is specified as a DC value.
How can one help their cause in terms of CMRR? The main thing is to carefully match all attributes of the paths for the positive and negative signals into and through the differential amplifier. This goes for the probes as well.