Definitions

# Virtual ground

In the theory of electrical networks, a virtual ground (or virtual earth) is a node of the circuit that is maintained at a steady reference potential, without being connected directly to the reference potential. In some cases the reference potential is considered to be the surface of the earth, and the reference node is called "ground" or "earth" as a consequence.

The virtual ground concept aids circuit analysis in operational amplifier and other circuits and provides useful practical circuit effects that would be difficult to achieve in other ways.

In circuit theory, a node may have any value of current or voltage but physical implementations of a virtual ground will have limitations of current handling ability and a non-zero impedance which may have practical side effects.

## Creating a simple virtual ground

In electronics, virtual ground is usually created by summing two opposite voltages. Since direct parallel connection of voltage sources will cause excessive current flow (a voltage "conflict") resistors must be included. For example, in the simple virtual ground circuit (Fig. 2), two opposite voltage sources (+V1 and -V2) are connected through respective resistors (R1 and R2) to the virtual ground point A.

You can think of the circuit as two parallel connected current sources: I1 (comprising V1 and R1) and I2 (comprising V2 and R2). The parallel connection of the two sources has given the name of circuits with parallel negative feedback. From another viewpoint, the two resistors constitute an extremely useful resistive circuit of a Circuit Idea/Parallel Voltage Summer, which is frequently used in circuits with parallel feedback (op-amp inverting amplifier, op-amp inverting summer, op-amp non-inverting Schmitt trigger, etc.)

Figuratively speaking, the circuit may be considered as an electrical "tug of war", where two voltage sources "fight" each other - V1 "pulls" the point A up while V2 "pulls" it down. In this "game", the pull-up resistor R1 and the pull-down resistor R2 serve as electrical "ropes". If V1/V2 = -R1/R2, zero voltage appears in the point A; it is a virtual ground. In this arrangement, a current I = V1/R1 = V2/R2 passes continuously through the circuit; as a result, the resistors dissipate power continuously.

The requirements needed for appearance a virtual ground in the common point between two series connected resistors can be seen directly as geometrical relations in the similar triangles constituting the voltage diagram of a linear potentiometer (Fig. 1):

• two voltages have to be applied to the other ends of the resistors,
• the voltages have to have opposite polarities regarding to the ground,
• the voltages have to bear the same proportion as between the respective resistors.

## Obtaining a perfect virtual ground

Once the virtual ground is created, it has to be kept steady since the input sources and the loads connected to this point affect it by "injecting" or "sinking" a current. This is the well-known problem of keeping up a constant voltage (zero voltage is also a voltage).

The most popular way of keeping up a virtual ground is a negative feedback. In this case (Fig. 2), the varying voltage source B2 "observes" continuously the voltage VA of the virtual ground point and changes its voltage V2 so that the voltage VA is always zero.

An op-amp inverting amplifier (Fig. 3a) is a typical circuit where the virtual ground point is kept up by a negative feedback. Since an operational amplifier has very high open loop gain, the amplifier acts automatically to make the potential difference between its inputs tend to zero. The non-inverting (+) input of the operational amplifier is grounded; then its inverting (-) input, although not connected to ground, will assume a similar potential, becoming a virtual ground. The circuit operation is illustrated more attractively on Fig. 3b by means of a voltage diagram; for this purpose, the two resistors are replaced by one linear potentiometer.

It seems strange but, in order to understand how an op-amp sustains the virtual ground, it is useful to think of it as an integrator rather than an amplifier.

According to this viewpoint, if the input voltage source changes its voltage -VIN towards the negative supply voltage -V, a negative voltage VA = -VR2/(VR1 + VR2) tries to appear in the point A. However, the op-amp "observes" that and immediately reacts: it changes its output voltage VOA toward the positive supply voltage +V until it manages to zero again the potential VA (to restore the virtual ground).

On the graphical presentation, the two sources "pull" the virtual ground point A in opposite directions; as a result, the voltage diagram rotates around the point A. The op-amp serves here as the varying voltage source V2 from Fig. 1.

## Applications

### Virtual ground serving as a power ground

Real ground. Voltage is a differential quantity, which appears between two points. In order to deal only with a voltage (an electrical potential) of a single point, the second point has to be connected to a reference point (ground) having usually zero voltage. Usually, the power supply terminals serve as steady grounds; when the internal points of compound power sources are accessible, they can also serve as real grounds (Fig. 4a).

Real ground is a point with a steady voltage belonging to the supply voltage source.

 Fig. 4a. Any point inside a compound voltage source can act as a real ground Fig. 4b. Circuit points having steady potentials can serve as artificial virtual grounds

Virtual ground. If there are not accessible source internal points, external circuit points having steady voltage towards the source terminals can serve as artificial virtual grounds (Fig. 4b). Such a point has to have steady potential, which does not vary when the electrical sources "attack" the virtual ground by "injecting" or "sucking" a current to/from it.

Virtual ground is a circuit point with a steady voltage outside the supply voltage source.

### Virtual ground serving as a circuit point:

#### Circuit input

In all the circuits with parallel negative feedback (e.g., the inverting op-amp circuits), the main duty of the (op-amp) amplifier is to "look after" the virtual ground, in order to keep an almost zero voltage in this point. However, the input sources affect the virtual ground by "injecting" or "sucking" a current to/from this point. In the simplest case, the input current sources do this directly (examples: transimpedance amplifier - Fig. 5, current integrator and charge amplifier).

A virtual ground presents a very low impedance to any signal connected to it and it therefore provides the perfect type of input for current type signal sources (piezoelectric sensors, photodiodes etc.) For example, in the circuit of a charge amplifier, stray capacitance at the input to the amplifier is not detrimental to operation because this capacitance is always at a virtual ground.

#### Internal circuit node

"Conflict point" in differential circuits. If a differential input signal is applied to a transistor differential amplifier, a virtual ground appears in the common "conflict" point between the emitters of the two "fighting" transistors. Similarly, a virtual ground appears in the internal middle point of the common resistor Rgain connecting the outputs of the input op-amp followers of an instrumentation amplifier. Also, two virtual grounds appear simultaneously at the inverting and the non-inverting inputs of a fully differential amplifier.

"Intervention" point in negative feedback circuits. The input voltage sources affect the virtual ground existing in the op-amp circuits with parallel negative feedback through a circuit component acting as a voltage-to-current converter. It can be a resistor (in an inverting amplifier, integrator, logarithmic amplifier), a capacitor (in a differentiator), a diode (in an antilogarithmic amplifier), etc. In some circuits, for example, a summing amplifier (Fig. 6), a few input sources "attack" simultaneously the virtual ground. The op-amp reacts to the input intervention, in order to restore the normal virtual ground state (VA = 0). For this purpose, it changes its output voltage, in order to "suck" or "push" a current through another circuit component (a capacitor, a diode, a resistor, etc.) from/to this point.

In this way, the op-amp's output voltage in circuits with parallel negative feedback actually represents the op-amp's reaction to the input intervention and serves as an output. Actually, the virtual ground point is the "true" output but it is non-used.

Purposely worsened virtual ground. In some single-supplied circuits with positive feedback (for example, an op-amp inverting comparator with hysteresis named also op-amp Smitt trigger), the virtual ground is preliminarily worsened. In this arrangements, this point has significant internal resistance, in order to be easily influenced by the op-amp output. The same trick of a "soft" virtual ground is frequently used in the single supply op-amp circuits with negative feedback.

#### Circuit output

It seems strange but, in some odd circuits, the virtual ground point serves as a circuit signal output.

Clipping indicator. In the circuits with parallel negative feedback, the voltage of the virtual ground point indicates the system's state. When the system works properly, its output quantity (usually voltage) manages to "neutralize" the input influence in the virtual ground; there is approximately a zero voltage in this point. If the system runs out of output voltage, it saturates and a voltage appears in the virtual ground. Actually, this voltage is a part of the input voltage. For example, in the circuit of an inverting amplifier (Fig. 3a), the resistors Rin and Rf act as a voltage divider; therefore, Rf/(Rf + Rin) part of the input voltage begins crossing over to the op-amp's inverting input when the op amp saturates. This voltage may be used (for example, in audio amplifiers) as an output signal indicating the onset of clipping.

Diode limiter. In the clever circuit of an op-amp parallel diode limiter (Fig. 7), the op-amp's output is non-used as a conventional circuit output (as it is in a logarithmic converter); instead, the inverting op-amp's input serves as an output. At a positive input voltage (when the circuit limits), the op-amp adds a compensating voltage VOA = VF in series with the forward voltage drop VF across the diode. As a result, the imperfect diode becomes an almost ideal one having zero forward voltage drop VF ≈ 0. Respectively, the imperfect passive diode limiter (the resistor R and diode D) that clips the input positive voltage at approximately 0.7V becomes an almost ideal limiter that clips the voltage at ≈ 0V.

## Virtual ground problems

Static error. Negative feedback seems to be a perfect technique for keeping up a virtual ground as it compensates various disturbances. However, it can't keep up exactly zero voltage in this point; this voltage is VA = VOA/A (where A is the op-amp gain without a negative feedback applied). Typically, A > 105; therefore, VA is almost zero.

Sensitivity. Virtual ground is a sensitive point, especially if the circuit components are highly resistive. The op-amp reacts to any influence at this point (e.g., due to leakage on the PCB) by changing its output voltage.

Inertness. In response to an input voltage or current step, the op-amp output voltage does not change instantaneously; the finite circuit bandwidth results in a ramp-like initial response as with an integrator. As a result, the virtual ground moves from zero until the op-amp responds. For example, in the circuit of an inverting amplifier - Fig. 3a, Rf/(Rf + Rin) part of the input voltage appears at the virtual ground point.

Instability. In an inverting amplifier adding a capacitor between ground and the virtual ground at the (-) op-amp input can make the amplifier unstable. Stray capacitance from a probe is often sufficient.

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