So, What Exactly Is a Virtual Ground?

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Figure 1

   

摘要

This article presents a discussion of what constitutes a virtual ground and where it can be applied. Moreover, this article will go over virtual potentials and virtual shorts.

Introduction

While op amp circuits are routinely analyzed with the aid of a virtual ground, other circuit configurations exist that use virtual grounds as well. One example of this is performing differential filter analysis. This article will demonstrate this and show that virtual grounds are not just for op amps.

The common-mode/differential-mode (CM-DM) electromagnetic interference (EMI) filter circuit shown in Figure 1 displays the use of a virtual ground model. This model was used to simplify the differential bandwidth analysis in the article “‘Gettin’ In Tune’ with the EMI Filter.” The circuit is implemented with a single differential-mode capacitor but is split into two series capacitors with a virtual ground point placed between them. This allows one to analyze a simpler single-ended circuit.

The Misinterpretation of a Virtual Ground

The concept of a virtual ground is typically taught with the introduction of op amp circuits. In fact, this is implemented and discussed so frequently that the true concept of a virtual ground can be lost.

Without seeing further application of virtual potential models, including virtual ground, an engineer may believe that the virtual potential point exists in only one place: one of the input nodes of an op amp circuit implementing negative feedback. This is, however, not true and will be shown by the application of a half-circuit analysis on the CM-DM EMI filter later in this article.

The circuit shown in Figure 2 is an example of how the concept of a virtual ground is commonly introduced. Unfortunately, the inverting node of an ideal negative feedback op amp circuit is interpretated as being labeled virtual ground. The truth is the inverting node of the ideal negative feedback op amp circuit has a virtual fixed voltage level: ground in this case. This point is not a virtual ground; it is a node that has a virtual ground potential.

Due to the negative feedback implemented and infinite open-loop gain, the ideal op amp model states that V+ = V– at the input of the op amp. With the positive input tied to ground, the potential at the negative input of the op amp is equal to zero volts (ground) via a virtual short.

Figure 3 illustrates an example of an ideal level-shifted op amp circuit. In this case, the inverting node of an ideal negative feedback op amp circuit has a virtual potential of VDC. Analogous to the previous example, we now have a virtual potential at the inverting node. This design technique is commonly used for single-supply systems requiring bipolar signal ranges (for example, ±2.5V) or as buffered voltage sources.

Virtual Potential and Virtual Short Models

Figure 4 proposes a model for a virtual potential. With near-infinite impedance, very little current can flow through the model resistance (R1). Therefore, there is essentially no voltage drop across R1. Thus, a virtual short exists across R1 and the virtual potential output is equal to V_VP.

An Infinite Bridge Too Far?

Engineers and designers typically deal with practicalities where an infinite impedance is essentially an open circuit. While this may seem to clash with the virtual potential model proposed, a very large resistor can be implemented for explanation purposes.

In fact, circuit theorists and teachers slipped a fast one over our eyes. As students, we were probably too naïve to realize the implications of having an infinite impedance at the front of an ideal op amp: “there’s an open circuit at the front end of the amplifier?” We accepted it and were satisfied that a virtual short at the op amp inputs existed in negative feedback configurations. Maybe a better, alternate, view is that one of the op amp inputs mirrors the other input (with some offsets in the real world) in negative feedback circuits.

While the ideal virtual potential model presented serves as an aid to help gain insight as to what virtual shorts and potentials are, this model can be modified for circuit simulations. A large value resistance can be used to implement an approximate virtual potential. Typically, the limiting factor is the simulator convergence, which can be addressed via the resistance value choice and/or simulation node tolerance adjustments (for example, RELTOL, etc.). Figure 5 shows an example of an LTspice^® DC simulation of a circuit that has a virtual potential.

Note: Every time a designer uses high-megaohm resistors to ground (or some other potential) to help circumvent floating node convergence issues in circuit simulators, they are implementing virtual potential models.

Figure 6 highlights an interesting artifact that the virtual potential model is nestled within the op amp model, be it ideal or not. While this may not be commonly presented in this way, a voltage potential is applied at the (+) node of the op amp, which is then connected to the infinite input impedance of the ideal op amp. The infinite input impedance and negative feedback configuration establishes a virtual short, which, in turn, holds the (–) node at the virtual potential of V_DC.

For the nonideal op amp model, open circuit input impedances are typically very large. Through the implementation of negative feedback, these impedances are further increased by an amount approximately equal to the op amp open-loop gain (R_in ≈ A_OL × R12). While not infinite, the large input impedance aligns with the analogous virtual potential model.

Half-Circuit Analysis, Virtual Ground, and the CM-DM EMI Filter

In the introduction of this article, Figure 1 shows an intermediate step of half-circuit analysis for the EMI filter shown in Figure 7. It was done to highlight where the virtual ground gets applied when conducting such an analysis. This section will illustrate the complete half-circuit analysis and how it simplifies the math, allowing one to determine the AC behavior of the circuit much quicker.

Fundamentally, half-circuit analysis splits the circuit into two mirror-image circuits. The mirror-image circuits represent two identical single-ended circuits that have an equivalent transfer function for the differential signals. After analyzing the half circuits, discard one of them and analyze the remaining (simpler) single-ended circuit. Components that are parallel to both differential lines are modified and referenced to virtual ground.

Half-circuit analysis takes advantage of a symmetrical balanced circuit structure, antisymmetric input signals, and superposition. The simpler half circuit can then be analyzed for either common-mode or differential-mode operation.

Note that this input signal configuration is commonly used in the analyses of instrumentation and differential amplifiers to determine the separate common-mode and differential-mode signal transfer functions. More detailed information on this can be found in ADI’s MT-076 tutorial.¹

Figure 8 shows the filter redrawn to identify the line of symmetry. Next, the differential capacitor is shown split into two mirror image devices. Note that these two series caps are equivalent to the original capacitance of C_Diff.

Next, Figure 9 reveals the equivalent common-mode and differential-mode half circuits. Note that the common-mode half circuits are derived by disconnecting (open-circuit) all half-circuit interconnections. The differential-mode half circuits are derived by tying all half-circuit interconnections to virtual ground.

The final step involves replacing the virtual ground with signal ground. While the virtual ground has infinite impedance, the other half of the differential circuit effectively sinks or sources current, as illustrated in Figure 10a. This is equivalent to signal ground: a ground-potential node that can source or sink current.

For circuit transfer function derivations or simulations, the virtual ground is replaced with signal ground. Consequently, there are two capacitors in parallel that can be simply added resulting in the simple RC circuit shown in Figure 10b.

These simpler common-mode and differential-mode half circuits can be used to derive the CM and DM transfer functions with their associated bandwidth expressions. For reference, Figure 11 highlights the equivalent CM and DM circuits and their balanced bandwidths.

Note: More detailed information on the derivation with component tolerances can be found in the ADI MT-070 Tutorial.²

Rail-Splitter Circuits and Virtual Ground

Rail-splitter circuits are commonly used to create bipolar power supplies from a single source such as a battery. Typical circuits employ a rail divider circuit, like a resistor voltage divider, producing a reference level voltage midway between the power rails. In Figure 12, the current output is supplied by the circuit while the output level is held at the virtual ground level of BATT/2 via a negative feedback buffer.

Note: V+ has a potential of BATT/2 and V– has a potential of –BATT/2 relative to VGND.

Unfortunately, there are occurrences where rail-splitter circuits are referred to as virtual ground circuits. As rail-splitter circuits are designed to source and sink current, the output ground node is not virtual, but rather a real ground point where return current has a path. This misnomer can lead to confusion about virtual potentials (including virtual grounds). For further explanation, the article “Difference Between Real Ground and Virtual Ground”³ is a great source.

Excerpt from the article:

“… virtual ground is a conceptual point in a circuit that is maintained at ground potential without a direct connection.”

The concept of a virtual potential applies to this circuit via noting the virtual short of the buffer amplifier that carries the split-rail potential from the battery. However, the overall circuit does not supply a virtual ground.

Conclusion

The application of virtual-potential and virtual-short concepts lend themselves to circuit analysis simplifications beyond those found in negative feedback op amp circuits. In fact, there are numerous scenarios where the identification of these models can be applied, typically leading to a better understanding of the circuit operation while substantially simplifying the math.

Acknowledgements

The author would like to extend a special thank you to Daniel Burton, Tim Green, and Blaise Parker for their review and constructive critique of this article.

References

¹ “MT-076 Tutorial: Differential Driver Analysis.” Analog Devices, Inc., 2009.

² “Analog Devices MT-070: In-Amp Input RFI Protection.” Analog Devices, Inc., 2009.

3 “Difference Between Real Ground and Virtual Ground.” Electrical Technology, October 2019.

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