Voltage-to-current converter

Introduction

For a variety of reasons, in low-voltage electronics, voltage is a more frequently used data carrier. Thus electronic devices tend to be labeled with voltage inputs and outputs. However some devices are labeled in terms of current-input and -output (for example, a bipolar transistor). In such cases, a component is needed to convert (change) the electric attributes into a relay of information.

A voltage-to-current converter changes the electric attribute carrying information from voltage to current. It acts as a linear circuit with transfer ratio k = I_OUT/V_IN [mA/V] having dimension of conductivity. That is why, the active version of the circuit is referred also as a transconductance amplifier.

Typical applications of voltage-to-current converter are measuring voltages by using instruments having current inputs, creating voltage-controlled current sources, building various passive and active voltage-to-voltage converters, etc. In some cases, the simple passive voltage-to-current converter works well; in other cases, there is a need of using active voltage-to-current converters. There is a close interrelation between the two versions - the active version is come from the passive one.

The basic idea behind the passive version

In life, there are many situations where a pressure like quantity puts in motion a flow like one through an impediment: pneumatic (a constant pressure pump moves air through a closed loop of pipes), water (height difference between two communicating vessels cause water to flow), thermal (if a metal bar is warmed up on the one side, heat begins flowing to the other side), mechanical (a motor drives a belt), informational (someone tells a story to somebody else - data flows through the phone line), money (the rich give money to poor) etc. In this arrangement, the pressure like, flow like and impediment like attributes are interrelated. Usually, the output flow like variable is proportional to the input pressure like one; in this way, the impediment converts the pressure like variable into a flow like one.

Similarly, in electricity, if a voltage V_IN is applied across a resistor R (Fig. 2), a proportional current I_OUT = V_IN/R begins flowing through the circuit according to the voltage-causes-current formulation of Ohm's law (I = V/R). In this voltage-supplied circuit, the resistor R determines the current flowing through it thus converting the voltage V_IN into a proportional current I_OUT. In this way, the resistor R serves as a voltage-to-current converter - a linear circuit with transfer ratio k = I_OUT/V_IN [mA/V] having dimension of conductivity.

Passive version applications

V-to-I converter acting as an output device

Voltage-controlled current source. Almost all the natural electrical sources are constant voltage sources (primary and secondary batteries). Actually, there are not constant current sources in nature (excepting inductor, Van der Graaf generator and photodiode); if there is a need of a current source, it has to be build. For this purpose, a voltage-to-current converter may be connected after the voltage source, according to the building formula:

Current source = Voltage source + Voltage-to-current converter

The simplest implementation of this idea is shown on Fig. 5 where a humble resistor R is connected in series with the input voltage source V_IN. If the circuit output is shortened with an ideal current load (a piece of wire), a constant current I_OUT = V_IN/R will be generated.

V-to-I converter acting as an input device

Compound voltmeter. A meter movement (a galvanometer) is actually an ammeter. In order to measure a voltage by an ammeter, a voltage-to-current converter (the so called "multiplier" resistor R) is connected before the ammeter. Therefore, the classic voltmeter is a composed device consisting of two components:

Compound voltmeter = Voltage-to-current converter + Ammeter

The multiplier resistor of a classic voltmeter acts as a voltage-to-current converter.

Compound passive converters: Similarly, in the popular passive circuits of capacitive integrator, inductive differentiator, logarithmic converter, etc., the resistor acts as a voltage-to-current converter (Fig. 6):

V-to-V RC integrator = V-to-I converter + I-to-V C integrator

V-to-V RL differentiator = V-to-I converter + I-to-V L differentiator

V-to-V RD log converter = V-to-I converter + I-to-V D log converter

Transistor base resistor. Transistor is a current-controlled device; it actually "shorts" the input source. Therefore, in order to drive a transistor by a relatively high voltage (for example, in the circuit of a transistor switch), a base resistor acting as a voltage-to-current converter is connected in series with the base-emitter junction (Fig. 8.)

Voltage-input transistor = V-to-I converter + current-input transistor

With the same purpose, resistors are connected to the inverting and non-inverting inputs of a Norton op-amp [1], in order to apply a voltage.

The transistor's base resistor acts as a voltage-to-current converter.

Op-amp inverting amplifier (an input part). In the op-amp inverting circuits the op-amp keeps the voltage of the inverting input at zero level (the so-called virtual ground). As a result, the circuit behaves as a current-controlled device, which "shorts" the input source connected to the inverting input. In order to drive the op-amp by a voltage (for example, in the circuit of an op-amp inverting amplifier), a resistor acting as a voltage-to-current converter is connected between the input voltage source and the inverting input (Fig. 9):

Op-amp inverting amplifier = V-to-I converter + op-amp I-to-V converter

Op-amp V-to-V RC integrator = V-to-I converter + op-amp I-to-V C integrator

Op-amp V-to-V RL differentiator = V-to-I converter + op-amp I-to-V L differentiator

Op-amp V-to-V RD log converter = V-to-I converter + op-amp I-to-V D log converter

Passive version imperfections

Real loads act as imperfect current loads dissipating energy (for example, simple ammeter, current measuring resistor, a diode, etc.) or storing energy (a capacitor, secondary battery, an inductor, etc.) They have some resistance (liner or non-linear), capacitance or inductance, which causes a voltage drop V_L to appear across the load (Fig. 5 - Fig. 8). In this way, the voltage difference V_IN - V_L determines the current I_OUT instead only the voltage V_IN; as a result, the current decreases.

A contradiction exists in these circuits: from one side, the voltage drop V_L is useful as it serves as an output voltage; from the other side, this voltage drop is harmful as it decreases the actual current-creating voltage V_R across the resistor R. This contradiction may be solved by using active elements.

Improvement: Active voltage-to-current converter

Removing a disturbance by an equivalent "antidisturbance". The active version of the voltage-to-current converter is frequently based on a well-known technique from human routine, where we compensate the undesirable effects caused by others using equivalent "anti-quantities". This idea is implemented by using an additional power source, which "helps" the main source by compensating the local losses caused by the undesired external quantity (conversely, in the opposite active current-to-voltage converter, the additional power source compensates the losses caused by the internal quantity). Examples: if someone has broken our window in winter, we turn on a heater (in summer, we turn on an air-conditioner), if a car has come into collision with our car, the insurance company compensates the damages caused by the else's car, if someone is spending money from our account, we begin depositing money into the account to restore the sum, etc. (see virtual ground page for more examples). In all these cases, we have prepared (just in case) "standby" resources, in order to use them, if there is a need to compensate eventual external losses.

Negative feedback. Another popular technique for compensating the undesirable quantities is to monitor and control the quantity, in order to keep up the desired magnitude; it is referred to as negative feedback. The advantage of this approach is that all kinds of disturbances are compensated.

In electricity, the problem of creating an active voltage-to-current converter is actually the well-known problem of creating a voltage-controlled constant current source. For this purpose, two popular techniques are used according to the general ideas above, in order to compensate the losses in the load.

Compensating the voltage drop across the load by adding a voltage

Basic idea. In order to show how this powerful basic idea is applied to improve the passive voltage-to-current converter, first, an equivalent electrical circuit is used (Fig. 10). In this active voltage-to-current converter, the voltage drop V_L across the external load L is compensated by adding the same voltage V_H = V_L to the input voltage V_IN. For this purpose, an additional following voltage source B_H is preliminarily connected in series with the input voltage source. This supplementary source "helps" the input source when a real load is connected; as a result, the undesired external voltage V_L disappears and the point A becomes a virtual ground.

Active V-to-I converter = passive V-to-I converter + "helping" voltage source

Op-amp implementation. The basic idea above is implemented in the op-amp voltage-to-current converter (Fig. 11). In this circuit, the output of the operational amplifier is preliminarily connected in series with the input voltage source; the op-amp's inverting input is connected to point A. As a result, the op-amp's output voltage and the input voltage are summed.

From other viewpoint, the output of the operational amplifier is connected in series with the load L in the place of the compensating voltage source B_H from Fig. 10. As a result, the op-amp's output voltage and the voltage drop V_L are subtracted; the potential of the point A represents the result of this subtraction.

Op-amp V-to-I converter = passive V-to-I converter + "helping" op-amp

Conclusion. In the circuit of an op-amp voltage-to-current converter, the op-amp adds as much voltage to the voltage of the input source as it loses across the external load. The op-amp compensates the local losses caused by this external load (conversely, in the opposite op-amp current-to-voltage converter, the op-amp compensates the losses caused by the internal resistor).

Keeping a constant current by applying a negative feedback

Negative feedback systems have the unique property to reverse the causality in the electronic converters connected in the feedback loop. Examples: an op-amp non-inverting amplifier is actually a reversed voltage divider, an op-amp integrator is a reversed differentiator and v.v., an op-amp logarithmic converter is a reversed antilogarithmic converter and v.v., etc.

Similarly, an op-amp voltage-to-current converter (a voltage-controlled constant current source) built by using a negative feedback is actually a reversed current-to-voltage converter. This powerful idea is implemented on Fig. 12 (a transistor version of a negative feedback current source) and on Fig. 13 (an op-amp version of a negative feedback current source) where a current-to-voltage converter (the bare resistor R) is connected in the negative feedback loop. The voltage drop V_R proportional to the load current I is compared with the input voltage V_Z. For this purpose, the two voltages are connected in series and their difference dV = V_Z - V_R is applied to the input part of the regulating element (the base-emitter junction of the transistor T or the differential input of the op-amp OA). As a result, the regulating element establishes the current I = V_R/R ≈ V_Z/R by changing its output resistance so that to zero the voltage difference dV. In this way, the output current is proportional to the input voltage; the whole circuit acts as an active voltage-to-current converter.

In this negative feedback arrangement, all kinds of disturbances (not only the voltage drop across the load) are compensated (for example, power supply and temperature variations).

External links

Passive voltage-to-current converter, Op-amp inverting summer - animated flash tutorials
Build to understand circuits: Voltage causes current (Unit 1) - another animated flash tutorial about voltage-to-current converter
Op-amp circuit builder shows how to build an active voltage-to-current converter (an animated flash interactive builder)
Voltage to Current Conversion - App Note 13 - shows a variety of voltage-controlled current sources (VCCS)
Voltage-to-current signal conversion - discusses the classic op-amp non-inverting voltage-to-current converter with a floating load
Voltage to Current Converter - shows an op-amp inverting voltage-to-current converter with a grounded load
LM3900 "Norton" amplifier - describes the famous National's voltage-to-current op-amp