# WHY DIFFERENTIAL? instruments connected to the circuit under test and results in V COMMON.

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2 important to know that it is present. Again referring to Figure 2, as i COMMON flows through Z COMMON, it develops a voltage we have chosen to call V COMMON. If the scope probe is not connected, v COMMON will appear through Z GND LEAD since Z SCOPE GND is in parallel with a complex impedance formed by the scope's power transformer inter-winding capacitance in series with the impedance of the power system, Z POWER TO GND. Figure 2 Circuit under test with oscilloscope connections as a voltage that is "common" to both points A and B. The voltage waveform at either of these points with respect to the IDEAL EARTH GROUND will include V COMMON. Point B will equal v COMMON and point A will be v A-B + V COMMON. By applying the scope probe ground lead to point B we can reduce, but not eliminate, v COMMON from the measurement. The reason we cannot eliminate v COMMON is because of the finite value of Z GNDLEAD. Z GNDLEAD, Z COMMON and Z SCOPEGND form a loop through which i COMMON flows. The voltages caused by i COMMON flowing in this loop will further corrupt the waveform v C-G. "Non-Ground" Referenced Measurements The effect of i COMMON can usually be reduced by opening the safety ground on the scope. Depending on the magnitude of v COMMON this technique can be very hazardous and under NO circumstances is it recommended. Opening the safety ground lead of the scope does not fully eliminate the flow of i COMMON The model of v COMMON we have used can also explain measurement constraints that we usually think of when we are making "floating" measurements. Let's assume that v COMMON is the output of a low impedance voltage source, of'i COMMON to flow. This is the case when trying to measure voltages in a "floating" power supply control circuit where v COMMON is the power line voltage. Even if the practice of floating the scope by opening the safety ground lead weren't hazardous, the measurement is still corrupted by the effects of the flow of i COMMON through the scope's power transformer inter-winding capacitance and the power line impedance. Also, the flow of signal current through Z GNDLEAD will contribute the same signal corruption as it did in our earlier ground referenced measurement example. Another, somewhat unrelated point: the practice of floating the chassis of a scope to line level voltages may place more voltage between the scope's power transformer primary and secondary windings than it was designed to handle and could possibly damage the scope.

3 points to find the voltage difference between them. As the differential amplifier amplifies the difference between the two points, it rejects any voltage that is common to both. Since V COMMON appears at both points A points and B in our circuit, the differential amplifier rejects it and presents the scope with the difference between points A and B, which is v A-B. (v A-B + v COMMON ) - (v COMMON ) = v A-B Figure 3 Probe ground lead effects The loop current effects of v COMMON are also greatly reduced because the high impedance of the probes prevents v COMMON from generating an appreciable amount of current into the scope ground. Since the probe ground clip is not connected to Point B, the effects of Z GND LEAD are eliminated. For all of these reasons, v C-G, is much more representative of V A-B than was possible when the scope probe ground lead was used to provide the minus reference. Since a differential amplifier equipped with properly designed probes can reject common voltages of relatively high magnitude, there is no need to float the Figure 4 Circuit under test with a differential amplifier Differential Voltage Measurements One can greatly reduce these corruptive measurement effects by using a scope or a preamplifier that has differential measurement capability. Figure 4 shows our equivalent circuit with the same ground referenced scope and a differential preamplifier. An ideal differential amplifier will only amplify the difference it sees at its + and - inputs. In this respect, it is very similar to the voltmeter where we probe two scope to an unsafe level in order to make good quality measurements.

4 Common Mode Rejection Ratio or CMRR We have been discussing the benefits of using an ideal differential amplifier to make voltage waveform measurements. Unfortunately, the ideal differential amplifier does not exist so we need to understand some of its characteristics and limitations. By again referring to figure 4, we can see that the differential amplifier deals with two voltage waveforms; one we want to see and one we don't. We can call these differential mode (the difference between point A and point B) and common mode (that which is common to both point A and B) waveforms. The waveform we want to see is the differential mode signal, v A-B. All of the characteristics of a single-ended amplifier such as gain and bandwidth apply to the differential mode of the differential amplifier. So if you need a scope with a bandwidth of 50MHz and enough gain to adequately measure a ground referenced signal such as v A-B, then you would need a differential amplifier with the same capability in its differential mode. As we have seen earlier, dealing with the common mode signal, v COMMON, with a single-ended scope input is either done by applying a low impedance shunt (Z GNDLEAD ) or by placing a higher impedance in series with the common mode signal (floating the scope). The differential amplifier deals with the common mode signal by algebraically subtracting it from the measured differential signal. The measure of how well the differential amplifier can remove or reject the common mode signal is specified similarly to the differential bandwidth and gain, except now we want attenuation instead of gain. Common mode bandwidth is measured by simultaneously applying exactly the same signal (frequency, amplitude and phase) to both inputs of the differential amplifier. With these input signals, an ideal differential amplifier would have no signal at its output. Since real world limitations apply to real amplifiers, there will be an output that is a function of amplitude and frequency of the input signal. If we put a 1 volt, 1O MHz signal into both inputs (same phase) and we measure a 1 mv signal at the output, the differential amplifier can reject 1MHz signals by a factor of 1,000. How well the differential amplifier can reject a common mode signal is usually stated as a ratio of the output signal's magnitude divided by the differential input signal's magnitude, or Common Mode Rejection Ratio (CMRR). In this case the CMRR is 1,000 to 1 at 1OMHz. It is also commonly given in db's of attenuation, but it is always the ratio of the output magnitude over input magnitude. It should be specified as a function of attenuation ratio versus frequency since it is a function of frequency. CMRR is highest at DC and declines as the frequency increases. Common Mode Range The next most important characteristic of the differential amplifier that we need to know about is its common mode range. This lets us know how large the amplitude of v COMMON can become before the amplifier can no longer tolerate it. This value is usually at least several times larger than the differential input range and is specified as a DC value, but it applies to the peak magnitude of an AC signal as well. How much common mode range a differential amplifier should have depends on the measurement requirements. If the common mode voltage is a small signal caused by ground loop currents then a volt or two of range will be sufficient. However, if the differential signal we are trying to measure is riding on top of a large common mode voltage, the range will have to be large. As an example, let's assume v A-B is the voltage waveform across a current monitoring resistor in the primary of a switching power supply. In this example, v COMMON is 400 volts (DC+peak AC) and the v A-B waveform is a voltage ramp with a 1 volt peak. By using probes and attenuators that have a combined divide by 100 attenuation factor, v COMMON will be attenuated to 4 volts and v A-B will be attenuated to a 10mV signal. The differential amplifier must have at least 4 volts of common mode range. If the amplifier's CMRR is 10,000 to 1, then the differential amplifier will attenuate the 4 volt v COMMON down to a 400 µv level at its output. In this case, when the CMRR of the amplifier is combined with the attenuation of the probes and the amplifier's internal attenuator, the common mode signal is attenuated by a factor of 1,000,000 to 1 while the differential signal is attenuated by a factor of 100. This output can be easily and safely displayed on a standard ground referenced scope.

5 Obtaining Good CMRR Good common mode rejection performance is obtained by carefully matching all attributes of the paths for the + and - signals into and through the differential amplifier. This matching is as important for the probes as it is for the amplifier. Some scopes provide methods of algebraically subtracting one input from another (commonly referred to as A-B). In analog scopes, this is accomplished by inverting one channel and adding it to another in the scope's input section. Digital scopes (DSO's) provide math functions that allow one acquired waveform to be subtracted from another. CMRR is not normally specified for this type of operation, but a figure for DC can be derived by taking into account the accuracy specifications of each channel. If the DC gain accuracy of each channel is ± 1% then the CMRR could be as low as 50 to 1 and is seldom better than 100 to 1. When AC signals are taken into account, the CMRR deteriorates even further. In our earlier example of the 1 volt signal riding on a 400 volt common mode signal, the output would be 10mV of differential signal and 40mV of common mode signal. It is also unlikely that the inputs could tolerate the 4 volt offset level. To obtain optimum CMRR, the probes used with the differential amplifier should be designed to maximize CMRR. The user needs to make sure the probes are optimally compensated.

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