Virtual ground

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Fig. 1. A virtual ground point on the voltage diagram of a linear potentiometer

Virtual ground (sometimes called virtual earth) is an important concept found in electronic circuit designs. It identifies a point in a circuit as being held close to the circuit's ground or reference level electric potential. Creation of a virtual ground is due to the actions or effects of the parts in the circuit. It is called virtual since this point does not have any real electrical connection to ground. The reference may or may not be the same as the local utility ground or earth. An ideal virtual ground would be able to source/sink an infinite amount of current. In practice, the sourcing/sinking capability is determined by the other circuit impedances and the amplifier used.

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.

[edit] The basic idea behind a virtual ground phenomenon

[edit] Non-electrical domain: The "neutralizing" idea

Virtual ground phenomenon manifests itself in many situations in human routine when people - especially being lazy and, at the same time, rich enough - solve the problems by continuous wasting of additional energy. Here are some examples.

1. Thermal. The temperature in the room begins dropping since a window has broken in winter. In order to keep the desired temperature (thermal virtual ground), they turn on a heater instead just to repair the broken window. And v.v., in summer, the temperature in the room begins rising when a window has broken. Now, in order to keep the thermal virtual ground, they turn on an air-conditioner instead to repair the broken window. Another "thermal" example: if they warm up a metal bar on the one side and cool it on the other side, a thermal virtual ground appears somewhere along the bar.
2. Hydraulic. Water begins pouring through a hole into the ship's hold because of wreck. In order to keep the desired water level (height virtual ground) the sailors begin continuously pumping out the water instead to plug up the opening. An opposite "hydraulic" example: water begins outflowing from a reservoir because of punching. In order to keep the water level they begin continuously filling the reservoir with water instead to plug up the opening.
3. Pneumatic. Air flows out the tire since it is punctured. In order to keep the desired air pressure (pressure virtual ground) the driver begins pumping up the tire instead to repair it (in motorized forces, they do that in motion). Another "pneumatic" example: if they pump up a pipe on the one side and pump out it on the other side, a pressure virtual ground appears somewhere along the pipe (an old-fashioned air cleaner, which sucks and blows air through a closed loop made from a corrugated hose might be used for this experiment).
4. Money. A husband has given another credit card of his account to his wife (or, v.v.) Then, his wife begins intensely spending money. Trying to keep the desired money virtual ground, the husband begins working hard to earn money instead to scold his wife. It is interesting the fact that in life whether they work and spend hard or they work and spend little, the result (money virtual ground) is the same.
5. Game. In the popular games of arm wrestling and tug of war, a "position" virtual ground appears in the middle when fighting people have equal power.
6. Wiki. A Wikipedian begins improving a Wiki page. At the same time, another Wikipedian begins removing the written, in order to keep the page unchanged. Both the editors are working hard wasting continuously editorial energy; only, the result is zero (an editorial virtual ground). Generally, when someone creates something in this world and someone else destroys continuously the creation, the result is zero and energy is continuously wasted.

All these and many other examples from human routine and nature can be generalized in a conclusion:

If two opposite power sources are connected each other by a conductive medium so that their opposite output quantities are superposed (summed), zero or reference level result referred to as virtual ground appears somewhere along the medium. In this "conflict" point, the efforts of the "fighting" sources are "neutralized". The process is associated with continuous energy wasting from both the sources as a result of a continuous energy flow through the medium.

Shortly, virtual ground phenomenon is summing of opposite equal quantities associated with continuous energy wasting; virtual ground represents the result of summing two opposite equal quantities.

[edit] Electrical domain: Parallel summing of opposite electrical quantities

Fig. 2. Parallel voltage summer is one of the simplest virtual ground circuits

In electricity, virtual ground is usually created by parallel summing two (or more) opposite voltages. Precisely speaking, it is incorrect to connect directly voltage sources in parallel because a conflict will appear (in spite of all, this technique is used in common base amplifier [1], differential amplifiers [2] etc.) That is why, in the simplest virtual ground circuit (Fig. 2), the two opposite voltage sources (+V₁ and -V₂) are connected through the respective resistors (R₁ and R₂) to the virtual ground output (the voltage V_A between the real and the virtual ground). The two resistors soften the conflict between the two "fighting" voltage sources.

Actually, in this circuit there are two parallel connected current sources - I₁ (built by V₁ and R₁) and I₂ (built by V₂ and R₂). From another viewpoint, the two resistors constitute an extremely useful resistive circuit of a parallel voltage summer, which is frequently used in the circuits with parallel feedback (op-amp inverting amplifier, op-amp inverting summer, op-amp non-inverting Schmitt trigger, etc.)

Fig. 3. The electrical "tug of war" creates a virtual ground (a geometrical interpretation of Fig. 2)

This circuit may be considered as an electrical "tug of war" (Fig. 3), where two voltage sources "fight" - V₁ "pulls" the point A up while V₂ "pulls" it down; the pull-up resistor R₁ and the pull-down resistor R₂ serve as electrical "ropes". If V₁/V₂ = -R₂/R₁, 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 continuously power.

Virtual ground appears in the common point between two series connected resistors, if

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

[edit] Keeping up a steady virtual ground...

Once the virtual ground created it has to be kept up steady since the input sources and the loads connected to this point affect it by "injecting" or "sucking" a current. Actually, this is the well-known problem of keeping up a constant voltage (zero voltage is also a voltage); it may be solved by applying a dynamic resistance or negative feedback.

[edit] ...by using a dynamic resistance

Fig. 4. Keeping up a virtual ground by varying the resistance

In order to resist the influences, in this case, the virtual ground is "dynamized" by applying two techniques as follows.

Varying resistance [3]. In order to keep up a virtual ground by varying the resistance, the resistor R₂ has to be implemented as a voltage-stable dynamic resistor (diode, zener diode, LED, etc.) If the voltage V₁ rises, the current I increases and the zero voltage V_A of the point A (the virtual ground) tries to rise. However, the dynamic resistor R₂ decreases its present resistance thus restoring the zero voltage V_A.
On the graphical presentation (Fig. 4), when the IV curve of the voltage source B₁ moves horizontally from left to right the R₂ IV curve rotates contraclockwise. As a result, the working point A slides from bottom to top over a new vertical IV curve, which represents the zero dynamic resistance R_d of the virtual ground.

Fig. 5. Keeping up a virtual ground by varying the voltage

Varying voltage [4]. In order to keep up a virtual ground by varying the voltage, the voltage source B₂ has to be implemented as a varying voltage source (Fig. 1 at the top). Now, if the voltage source B₁ tries to "pull" the virtual ground A up by raising its voltage V₁ towards its positive voltage, the "dynamic" voltage source B₂ "pulls" it down by increasing its voltage V₂ towards its negative voltage and v.v. As a result, the point A retains its zero voltage.
On the graphical presentation (Fig. 5), when the IV curve of the voltage source B₁ moves horizontally from left to right, the IV curve of the voltage source B₂ moves horizontally from right to left and v.v. As a result, the working point A slides from bottom to top over a new vertical IV curve, which represents the zero dynamic resistance R_d of the virtual ground.

This idea is implemented on Fig. 6 by replacing the steady voltage source B₂ with a negative impedance converter (NIC) acting as a negative resistor with resistance -R. In this circuit, the op-amp OA produces a voltage V_OA = -2V_R2.

Fig. 6. By compensating the voltage drop across the resistor R2 an NIC creates a virtual ground between the resistors R₁ and R₂

Half the voltage compensates the voltage drop V_R = V_R2 across the internal NIC's resistor; the rest half compensates the voltage drop V_R2 across the resistor R₂. As a result, a virtual ground appears in the point A between the resistors R₁ and R₂. It is interesting fact that if the negative resistance -R increases (for example, by increasing the resistance R), the virtual ground point A moves somewhere inside the resistor R₁.

Keeping up a virtual ground by the techniques above may be observed in electrical distribution networks, where three-phase electrical "Y" (or star) circuits are said to have a virtual ground node when their sources and loads are balanced respectively. The virtual ground in this case exists at the star point.

[edit] ...by applying a negative feedback

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

Fig. 7a. Op-amp inverting amplifier (a classical view)

An op-amp inverting amplifier (Fig. 7a) 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. 7b by means of a voltage diagram; for this purpose, the two resistors are replaced by one linear potentiometer.

If the input voltage source changes its voltage -V_IN towards the negative supply voltage -V, a negative voltage V_A = -V_R2/(V_R1 + V_R2) tries to appear in the point A. However, the op-amp "observes" that and immediately reacts: it changes its output voltage V_OA toward the positive supply voltage +V until it manages to zero again the potential V_A (to restore the virtual ground).

Fig. 7b. Op-amp inverting amplifier visualized

On the graphical presentation, the two sources "pull" the virtual ground point A in different directions; as a result, the voltage diagram rotates around the point A. Actually the op-amp serves here as the varying voltage source B₂ from Fig. 1.

[edit] Comparison between the two techniques

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 V_A = V_OA/A (where A is the op-amp gain without a negative feedback applied). Typically, A > 10⁵; therefore, V_A is almost zero.

It looks strange, but a perfect virtual ground (having exactly V_A = 0) may be created (Fig. 1) and kept up (Fig. 6) without using negative feedback. However, it will not be as stable as the virtual ground kept by applying a negative feedback.

[edit] Another viewpoint at the virtual ground phenomenon

Actually, there is nothing special about the virtual ground phenomenon; it is nothing else than to create and keep up a steady voltage (usually zero volts). According to this viewpoint, a circuit with virtual ground point acts as a constant voltage source, where the virtual ground point serves as a source output.

[edit] Applications

[edit] Virtual ground serving as a power ground

[edit] Comparison between real and virtual 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. This point has to have steady potential, which does not vary when the electrical sources "attack" the ground by "injecting" or "sucking" a current to/from it. Usually, the power supply terminals serve as grounds; when the internal points of compound power sources are accessible, they can also serve as real grounds (Fig. 8a).

Fig. 8a. Any point inside a compound voltage source can act as a real ground	Fig. 8b. 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. 8b).

Fig. 9. Comparing different kinds of grounds regarding consumption

[edit] Energetical considerations

Real and virtual grounds are compared on Fig. 9 regarding the consumption.

Real ground (the right part of Fig. 9). In this most economical case, only a useful power is dissipated in the load: P₁ = I₁.V.

Static virtual ground (the left part of Fig. 9). This is the worst case as an additional useless power is dissipated in the Element 1 and Element 2 (the current I₂ passes through the lower element of this voltage divider because the load is connected to the positive rail):

P_2,3 = P_L + P^'_E2 + P^"_E2 + P_E1 = 2I₂.V + 2I₃.V = 2(P_L + P_E)

The lower resistive the voltage divider is, the more steady the virtual ground is; however, the consumption increases. In addition, this simple configuration is prone to become unbalanced [5].

Dynamic virtual ground. In this worse case, only a relatively small additional power is dissipated in the dynamic Element 2 (usually, the Element 1 does not exist in this arrangement):

[edit] Virtual ground serving as a circuit point:

[edit] ... an input

Fig. 10. Op-amp current-to-voltage converter (transimpedance amplifier)

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. 10, 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.

[edit] ...an internal point

Fig. 11. Summing amplifier is based on the virtual ground concept. It may, for example, be used as an audio mixing circuit to sum input signals from a few voltage sources (with the input resistors acting as voltage-to-current converters) or from current sources (if no input resistor is used). In the latter case, the op amp realises an ideal current-to-voltage converter. By creating a virtual ground, it provides isolation of the input signals.

A conflict point. A virtual ground appears in the common point between the emitters of the two transistors of a transistor differential amplifier at differential input signal [6]. 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 working at differential input signal.

An intervention point. 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 - a resistor (inverting amplifier - Fig. 7, integrator, logarithmic amplifier), a capacitor (differentiator), a diode (antilogarithmic amplifier), etc. In some circuits (for example, summing amplifier - Fig. 11), 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 (V_A = 0). For this purpose, it changes its output voltage, in order to "suck" or to "push" a current through another circuit component (a capacitor, a diode, a resistor, etc.) from/to this point. Actually, the op-amp's output voltage in the circuits with parallel negative feedback represents the op-amp's reaction to the input intervention.

Although the virtual ground point is the actual output of the circuits with parallel negative feedback, in this case it is non-used. Instead, the op-amp reaction to the input intervention against the virtual ground is used as an output.

Intentionally worsened virtual ground. In some single-supplied circuits with positive feedback (for example, an op-amp inverting comparator with hysteresis [7] or 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 is frequently used in the single supply op-amp circuits with negative feedback.

[edit] ...an output

Fig. 12. Op-amp parallel diode limiter

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 (click Exploring in [8] and go to Page 7-1, in order to see an animated presentation of this phenomenon). Actually, this voltage is a part of the input voltage. For example, in the circuit of an inverting amplifier (Fig. 7a), 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 clipping.

Diode limiter. In some circuits (for example, a parallel diode limiter), the virtual ground point is the output of the circuit.

[edit] See also

• Voltage-to-current converter, Current-to-voltage converter (transimpedance amplifier)
• Negative resistance, Negative impedance converter

[edit] External links

The external links in this article may require cleanup to comply with Wikipedia's content policies. Please improve this article by removing excessive or inappropriate external links. Please remove this tag when this is done. (talk)

• How do we create a virtual ground? reveals the nature of the phenomenon (in ten steps)
• Reinventing transimpedance amplifier in eight consecutive logically connected steps
• Reinventing op-amp inverting summer - an animated flash movie revealing the secret of the circuit
• Inverting op-amp current source is based on a virtual ground concept
• Op-amp circuit builder shows how to build various op-amp inverting circuits keeping virtual ground (an animated flash movie)
• Virtual Ground Circuits
• Single Supply Op Amps, Designing Single Supply, Low-Power Systems