The voltage of interest, or difference signal, is referred to as the differential voltage or differential mode signal and is expressed as VDM (VDM is the V+in - V-in term in the transfer equation above).

 

Figure 6. Differential amplifier.

The voltage which is common to both inputs is referred to as the Common-Mode Voltage expressed as VCM. The characteristic of a differential amplifier to ignore the VCM is referred to as Common-Mode Rejection or CMR. The ideal differential amplifier rejects all of the common-mode component, regardless of its amplitude and frequency.

In Figure 7, a differential amplifier is used to measure the gate drive of the upper MOSFET in an inverter circuit. As the MOSFET switches on and off, the source voltage swings from the positive supply rail to the negative rail. A transformer allows the gate signal to be referenced to the source. The differential amplifier allows the scope to measure the true VGS signal (a few volt swing) at sufficient resolution such as 2 V/division while rejecting the several hundred volt transition of the source to ground.

 

 

Figure 7. Differential amplifier used to measure gate to source voltage of upper transistor in an inverter bridge. Note that the source potential changes 350 volts during the measurement.

Common-Mode Rejection Ratio (CMRR)

Real implementations of differential amplifiers cannot reject all of the common mode signal. A small amount of common mode appears as an error signal in the output, making it indistinguishable from the desired differential signal. The measure of a differential amplifier's ability to eliminate the undesirable common-mode signal is referred to as Common-Mode Rejection Ratio or CMRR for short. The true definition of CMRR is "differential-mode gain divided by common-mode gain referred to the input":

 

For evaluation purposes, we can assess CMRR performance with no input signal. The CMRR then becomes the apparent VDM seen at the output resulting from common mode input. It's expressed either as a ratio - 10,000:1 - or in dB:

 

A CMRR of 10,000:1 would be equivalent to 80 dB.

For example, suppose we need to measure the voltage in the output damping resistor of an audio power amplifier as shown in Figure 8. At full load, the voltage across the damper (VDM) should reach 35 mV, with an output swing (VCM) of 80 V p-p. The differential amplifier we use has a CMRR specification of 10,000:1 at 1 kHz. With the amplifier driven to full power with a 1 kHz sine wave, one ten thousandth of the common-mode signal will erroneously appear as VDM at the output of the differential amplifier, which would be 80 V/10,000 or 8 mV. The 8 mV represents up to a 22% error in the true 35 mV signal!

 

 

Figure 8. Common-mode error from a differential amplifier with 10,000:1 CMRR.

The CMRR specification is an absolute value, and does not specify polarity (or degrees of phase shift) of the error. Therefore, the user can not simply subtract the error from the displayed waveform. CMRR generally is highest (best) at DC and degrades with increasing frequency of VCM. Some differential amplifiers plot the CMRR specification as a function of frequency.

Let's look at the inverter circuit again. The transistors switch 350 V and we expect about a 14 V swing on the gate. The inverter operates at 30 kHz. In trying to assess the CMRR error, we quickly run into a problem. The common-mode signal in the inverter is a square wave, and the CMRR specification assumes a sinusoidal common-mode component. Because the square wave contains energy at frequencies considerably higher than 30 kHz, the CMRR will probably be worse than specified at the 30 kHz point.

Whenever the common-mode component is not sinusoidal, an empirical test is the quickest way to determine the extent of the CMRR error (see Figure 9). Temporarily connect both input leads to the MOSFET source. The scope is now displaying only the common-mode error. You can now determine if the magnitude of the error signal is significant. Remember, the phase difference between VCM and VDM is not specified. Therefore subtracting the displayed common-mode error from the differential measurement will not accurately cancel the error term.

 

Figure 9. Empirical test for adequate common-mode rejection. Both inputs are driven from the same point. Residual common mode appears at the output. This test will not catch the effect of different source impedances.

This is a handy test for determining the extent of common-mode rejection error in the actual measurement environment. However there's one effect this test will not catch. With both inputs connected to the same point, there's no difference in driving impedance as seen by the amplifier. This situation produces the best CMRR performance. When the two inputs of a differential amplifier are driven from significantly different source impedances, the CMRR will be degraded. The specifics of the effect are discussed later - seeInput Impedance Effects on CMRR.

Other Specification Parameters

Differential-mode range is equivalent to the input range specification of an amplifier or single-ended oscilloscope input. Input voltages which exceed this range will overdrive the amplifier, resulting in output clipping or non-linearity.

Common-mode range refers to the voltage window over which the amplifier can reject the common-mode signal. The common-mode range is usually larger than or equal to the differential range. Depending on the amplifier topology, the common-mode range may or may not change with different amplifier gain settings. Exceeding an amplifier's common-mode range may have various results in the output. In some situations, the output will not clip and may produce a close approximation of the true input, with some additional offset. In this situation, the display may be close enough to what is expected that it's not questioned by the user. It's always a good practice to verify that the common-mode signal is within the acceptable common-mode range before making any differential measurements.

Maximum common-mode slew rate is specified for some differential amplifiers and most isolators. This specification is often confusing but very important. Part of the confusion results from a lack of standard definition between instrument manufacturers. Also, differential amplifiers and isolators behave differently when their maximum common-mode slew rate is exceeded. Essentially, maximum CM slew rate is a supplemental specification to CMRR. The specification is usually given in units of kV/ms.

Some types of differential amplifiers, like other amplifiers, reach a large-signal slew rate limitation before the small-signal bandwidth specification is exceeded. When one or both sides of a differential amplifier are driven to slew-rate limiting, the common-mode rejection is degraded very rapidly. Unlike CMRR, maximum slew rate does not imply an increasing amount of common-mode feed-through in the output. Once the maximum common-mode slew rate is exceeded, all bets are off - the output is likely to clamp at one of the power supply rails.

In isolators, however, the effect is more gradual - like CMR in a differential amplifier. As the common-mode slew rate increases (as opposed to the frequency), more of the common-mode component "feeds through" to the output. Intuitively, the specification would imply a maximum slew rate at which a known amount of feed-through appears in the output. It's important to note that with some isolators, the CM slew rate specification is actually a maximum non-destructive limit. The ability to make meaningful measurements is lost at slew rates much lower than the maximum specification. When using an isolator, it's best to test the common-mode feed-through before making critical measurements. This is easily done by driving both the probe tip and the reference lead with the same common-mode signal and observing the output.

Types of Differential Amplifiers and Probes

Built-in differential amplifiers. Many scopes have the ability to make the simplest differential measurements built right in to them. This mode is referred to as "channel A - channel B" or "quasi-differential". While limited in performance, this technique may be adequate for some measurements. To make a differential measurement, two vertical channels are used - one for the positive input and one for the negative input. The channel used for negative input is set to invert mode and the display mode is set to "ADD Channel A + Channel B". For proper operation, both inputs must be set to the same scale factor, and both input probes must be identical models. The display now shows the difference voltage between the two inputs.

To maximize CMRR, the gain in both channels should be matched. This can be easily done by connecting both probes to a square wave source with an amplitude within the dynamic range of the volts/division setting (about +6 divisions). Set one of the channels to "uncalibrated - variable" gain and adjust the variable-gain control until the displayed waveform becomes a flat trace.

The primary limitation of this technique is the rather small common-mode range, which results from the scopes vertical channel dynamic range. Generally, this is less than ten times the volts/division setting from ground. Whenever VCM > VDM, this mode of obtaining a differential result can be thought of as extracting the small difference from two large voltages.

Most digital storage oscilloscopes perform waveform math in the digital domain, after the analog signal has been digitized. The limited resolution of the analog-to-digital converter is often not adequate to view the resulting differential signal after the common-mode signal is subtracted out. Because the AC gain in the two channels is not precisely matched, CMRR at higher frequencies is rather poor.

This technique is suitable for applications where the common-mode signal is the same or lower amplitude than the differential signal, and the common-mode component is DC or low frequency, such as 50 or 60 Hz power line. It effectively eliminates ground loops when measuring signals of moderate amplitude.

High-voltage differential probes. Recently, high-voltage active differential probes have appeared on the market. A new topology using fixed attenuation with switchable differential gain allows these probes to keep their full common-mode range in all gain settings. The single attenuator greatly reduces complexity resulting in lower cost to the user.

These probes provide an affordable, safe method of measuring line-connected circuits commonly found in switching power supplies, power inverters, motor drives, electronic-lamp ballasts, etc. With common-mode ranges up to 1,000 V, these probes eliminate the need for the extremely dangerous practice of "floating the scope". Recently, workplace hazard monitoring organizations such as the U.S. OSHA (Occupational and Safety and Health Act) have intensified their verification of equipment grounding, issuing costly fines to violators.

In addition to the safety benefits, the use of these probes can improve measurement quality. An obvious benefit is the full use of the scopes multiple channels with the simultaneous viewing of multiple signals referenced to different voltages. Because the probes are true differential, both of the inputs are high impedance - high resistance and low capacitance. Floating scopes and isolators do not have balanced inputs. The reference side (the "ground" clip on the probe) has a significant capacitance to ground. Any source impedance the reference is connected to will be loaded during fast common-mode transitions, attenuating the signal.

 

 

Figure 10. Even when the scope is "floating", parasitic capacitance forms an AC voltage divider which adds error to the measurement. Note that reversing the probe leads will load the gate with >100 pF, possibly destroying the circuit-under-test.

Worse yet, the high capacitance can damage some circuits (see Figure 10). Connecting the scope common to the upper gate in an inverter may slow the gate-drive signal, preventing the device from turning off and destroying the input bridge. This failure is usually accompanied with a miniature fireworks display right on your bench - something many power electronics designers can attest to.

With the balanced low input capacitance of high-voltage differential probes, any point in the circuit can be safely probed with either lead.

High-gain differential amplifiers. A high-gain differential amplifier, often an external accessory, allows scopes to measure very small amplitude signals - down to a few microvolts. To avoid corruption from ground-loop and ground-gradient effects, these signals are always measured differentially - even when they are ground referenced. When the source is not ground referenced, the common-mode can be several orders of magnitude greater than the differential mode signal of interest. To cope with this, these amplifiers have extremely high CMRR, often 1,000,000:1 or greater.

Some high-gain differential amplifiers include additional functionality to improve the integrity of low-amplitude measurements. Selectable low-pass filtering allows the user to remove out-of-band noise from lower-frequency signals. Differential offset can be used to remove galvanic potentials introduced in the input wiring or transducer-bridge bias voltage. To allow use with signal sources which have high driving impedance, some models allow the user to set the input to virtually infinite impedance.

As with any differential amplifier, the slightest mismatch in channel gain greatly reduces the amplifier's high CMRR. When the application requires use of a scope probe, only identical non-attenuating (1X) models should be used, as attenuating probes can not be matched well enough to preserve the CMRR.

High-performance differential amplifiers. With the advent of oscilloscopes with plug-in amplifiers, high-performance differential amplifiers became available. These amplifiers combined many features to allow their use in diverse applications. Calibrated slideback allowed the amplifiers to be used in single-ended mode, with the trace referenced thousands of divisions away from ground.

This makes it possible to precisely measure ripple valley in power supplies and power amplifier headroom. Sophisticated high-speed clamp circuits enable the amplifier to quickly recover from input overloads hundreds of times over-range. This provides the ability to directly measure settling time of amplifiers and DAC circuits.

These amplifiers feature bandwidth specifications of 100 MHz or more, with good CMRR as well. However, the CMRR is specified with both inputs tied directly together and driven from a low-impedance source. In an actual application, the CMRR at higher frequencies will be considerably degraded by differences in source impedance and channel gain.

Differential passive probes. To minimize this degradation, only specially matched differential passive probes should be used with these amplifiers. Be sure to calibrate the individual probe to the amplifier using the procedure provided by the probe manufacturer.

High-bandwidth active differential probes. These probes maintain high-frequency CMRR by buffering the signal right at the probe tip, thereby eliminating the degradation caused by passive probe cables. These probes have high bandwidth (100 MHz or more), high-sensitivity, and excellent high-frequency CMRR performance. They are commonly used to perform measurements in disk-drive read electronics, where the signals are inherently differential. Their use is becoming more common in probing high-speed digital circuits as they do not alter the ground gradient when searching for ground-bounce problems.

Voltage isolators. While voltage isolators are not really differential amplifiers, they provide a means of safely measuring floating voltages. Compared with differential amplifiers, isolators have advantages as well as tradeoffs, and the selection of one over the other depends on the application. As the name implies, isolators have no direct electrical connection between the floating inputs and their ground-referenced output. The signal is coupled via optical or split-path optical/transformer means. Two physical configurations are available: integrated one-piece systems and split transmitter/receiver systems.

The models with separate transmitters and receivers are interconnected with fiber-optic cable. The transmitter, which is powered by rechargeable batteries, can be remotely located from the receiver. This is useful in situations where the signal originates in environments not hospitable to humans or oscilloscopes. They can also be used with very high common-mode voltages. The floating voltage specification is usually limited by the insulation voltage of the hand-held probe. If the probe connections can be made with the DUT powered off, the floating voltage is limited only by the physical separation between the transmitter and ground.

 

Figure 11. Unequal input capacitance caused by the isolated shield. This forms an AC voltage divider, resulting in the Vref' not equal to Vref at the probe clip.

Because isolators have no resistive path to ground, they are a good choice for applications which are extremely sensitive to leakage currents. Circuits equipped with sensitive GFCI (Ground Fault Circuit Interrupters), such as medical electronics, may experience GFCI tripping when connected to a differential amplifier. The lack of ground terminated attenuators also gives isolators infinite CMRR with static (DC) common-mode voltages.

The disadvantage of isolators is the fact that they are not true differential amplifiers, meaning that the input is not balanced (see Figure 11). The capacitance to earth ground is considerably different in the measurement (+) input and the reference (-) input. This results in the same problems as already described when floating scopes. Source impedance in the reference lead forms an attenuator at high frequencies with the ground capacitance.

These problems can be minimized by connecting the reference to the point in the circuit with the lowest driving impedance (invert the scope channel to regain correct polarity if necessary). If the isolator has separate transmitter and receiver units, physically isolate the transmitter from grounded surfaces as much as possible to minimize capacitive coupling to ground. Placing the transmitter on a cardboard box or wooden crate can make a marked improvement in performance!