Current-to-voltage converter

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Three kinds of devices are used in electronics: generators (having only outputs), converters (having inputs and outputs) and loads (having only inputs). Most frequently, they use voltage as input/output quantity.

In some cases, there is a need for converters having current input and voltage output. A typical situation is the measuring of a current using instruments having voltage inputs.

Fig. 1. Current-to-voltage converter (a block diagram)
Fig. 1. Current-to-voltage converter (a block diagram)

A current-to-voltage converter is a circuit that performs current to voltage transfomation. In electronic circuitry operating at signal voltages, it usually changes the electric attribute carrying information from current to voltage. The converter acts as a linear circuit with transfer ratio k = VOUT/IIN [V/mA] having dimension of resistivity. That is why, the active version of the circuit is referred also as a transresistance or transimpedance amplifier.

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

Ideal current-to-voltage converters have zero input resistance (impedance), so that they actually short the input source. Therefore, in this case, the input source has to have some resistance; ideally, it has to behave as a constant current source. Otherwise, the input source and the current-to-voltage converter can saturate.

Contents

[edit] The basic idea behind the passive version

[edit] Non-electrical domain: Flow causes pressure

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 causes 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 flow, pressure and impedement like attributes are interrelated. Usually, the output pressure like variable is proportional to the input flow like one; in this way, the flow like quantity creates (is converted to) a pressure like one.

In order to induce a pressure, an impediment has to be put in flow's way.

[edit] Electrical domain: Current causes voltage

Fig. 2. The passive current-to-voltage converter is based on the current-causes-voltage phenomenon.
Fig. 2. The passive current-to-voltage converter is based on the current-causes-voltage phenomenon.

Building the circuit. Similarly, in electricity, if a current IIN flows through a resistor R (Fig. 2), the latter impedes (resists) the current; as a result, a proportional voltage drop VR = R.IIN appears across the resistor according to current-causes-voltage formulation of Ohm's law (V = R.I). In this current-supplied circuit, the voltage drop VR acts as an output voltage VOUT (the voltage drop VR is created not by the resistor; it is created by the excitation voltage source inside the input current source). In this way, the current IIN is converted to a proportional voltage VOUT; the resistor R serves as a current-to-voltage converter - a linear circuit with transfer ratio k = VOUT/IIN [V/mA] having dimension of resistivity.

Circuit operation. Fig. 2 represents graphically the circuit operation by using a current loop and voltage bars. The thickness of the current loop is proportional to the magnitude of the current and the height of the voltage bars is proportional to the corresponding voltages (see also an interactive animation).

A graphoanalytical interpretation of the circuit (and of the Ohm's law) is shown on Fig. 3. As the current through and the voltage across the two components (the current source and the resistor) are the same, their IV curves are superimposed on a common coordinate system. The intersection of the two lines is the operating point A; it represents the present magnitudes of the current IA and the voltage VA. When the current IIN of the input current source varies, its IV curve moves vertically (see also an interactive animation). As a result, the working point A slides over the IV curve of the resistor R; its slope represents the converter's ratio.

Fig. 3. A graphoanalytical presentation of the circuit operation
Fig. 3. A graphoanalytical presentation of the circuit operation
Fig. 4. Voltage distribution over the resistor R
Fig. 4. Voltage distribution over the resistor R

Fig. 4 shows another attractive graphical interpretation of Ohm's law - the voltage diagram (the voltage distribution along the resistive film inside a linear resistor). When the input current varies, the local voltages along the resistive film vary decreasing gradually from left to right (see also another interactive animation). In this arrangement, the angle α represents the input current IIN.

[edit] Passive version applications

[edit] I-to-V converter acting as an output device

Fig. 5. Current-controlled voltage source
Fig. 5. Current-controlled voltage source

Current-controlled voltage source. Although there are enough constant voltage sources in nature (primary and secondary batteries), if a current source is available but there is a need of a voltage source, it may be build. For this purpose, a current-to-voltage converter has to be connected after the current source, according to the building formula below:

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

The simplest implementation of this idea is shown on Fig. 5 where a humble resistor R is connected in parallel to the input current source IIN (the Norton's idea in electricity).

If the load is ideal (that is, it has an infinite resistance), a constant voltage VOUT = R.IIN will be generated. This voltage will affect the current, if the input current source is imperfect (see the section below about passive version imperfections).


Fig. 6. V-to-V RC differentiator = V-to-I C differentiator + I-to-V converter
Fig. 6. V-to-V RC differentiator = V-to-I C differentiator + I-to-V converter

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

V-to-V CR differentiator = V-to-I C differentiator + I-to-V converter

V-to-V LR integrator = V-to-I L integrator + I-to-V converter

V-to-V DR antilog converter = V-to-I D antilog converter + I-to-V

For example, a classic capacitive-resistive differentiator is built on Fig. 6 by using the simpler voltage-to-current capacitive differentiator (a bare capacitor) and a current-to-voltage converter.

In these circuits, the resistor R acting as a current-to-voltage converter introduces some voltage drop VR, which affects the excitation voltage VIN. As a result, the current decreases and an error appears (see the section about passive version imperfections).


Fig. 7. The collector resistor Rc acts as a current-to-voltage converter
Fig. 7. The collector resistor Rc acts as a current-to-voltage converter

Transistor collector resistor. Transistor is a current-generating device. Therefore, in order to obtain a voltage as an output, a collector resistor is connected in the output circuit of the transistor stage (Fig. 7). Examples of this technique are the common-emitter, common-base and differential amplifier, a transistor switch, etc.

Voltage-output transistor = Current-output transistor + I-to-V converter

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

Since the voltage drop VRc is floating, usually the complementary (to the power supply) voltage drop VCE is used as an output. As a result, these transistor circuits are inverting (when the input voltage rises, the output voltage drops and v.v.)

A similar technique is used, in order to obtain a voltage in the transistor emitter (see the section below about negative fedback current source). Examples of this technique are all the transistor circuits using series negative feedback.

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


[edit] I-to-V converter acting as an input device

Fig. 8. Compound ammeter = I-to-V converter + voltmeter
Fig. 8. Compound ammeter = I-to-V converter + voltmeter

Compound ammeter. Today's measuring instruments (DVM's, analog-to-digital converters, etc.) are mainly voltmeters. If there is a need to measure a current, a simple current-to-voltage converter (a shunt resistor) is connected before the voltmeter (Fig. 8). This ammeter is a composed device consisting of two components:

Compound ammeter = Current-to-voltage converter + voltmeter

The shunt resistor of a composed ammeter acts as a current-to-voltage converter.

Although the active version is the perfect current measurement solution, the popular multimeters use exactly the passive version, in order to measure big currents (see the section about power considerations below).


[edit] I-to-V converter as a part of negative feedback V-to-I converters

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.

Fig. 9. A transistor current source using a current-to-voltage converter
Fig. 9. A transistor current source using a current-to-voltage converter
Fig. 10. An op-amp current source using a current-to-voltage converter
Fig. 10. An op-amp current source using a current-to-voltage converter


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. 9 (a transistor version of a current source) and on Fig. 10 (an op-amp version of a current source) where a current-to-voltage converter (the bare resistor R) is connected in the negative feedback loop. The voltage drop VR proportional to the load current I is compared with the input voltage VZ. For this purpose, the two voltages are connected in series and their difference dV = VZ - VR 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 = VR/R ≈ VZ/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 a voltage-to-current converter.

[edit] Passive version imperfections

Fig. 11. The resistor R affects the current Iin when the input current source is imperfect
Fig. 11. The resistor R affects the current Iin when the input current source is imperfect

The passive current-to-voltage converter (as all the passive circuits) is imperfect because of two reasons:

Resistor R. The voltage drop VR affects the input current IIN as the resistor R consumes energy from the input source (Fig. 11). A contradiction exists in this circuit: from one side, the voltage drop VR is useful as it serves as an output voltage; from the other side, this voltage drop is harmful as it effectively modifies the actual current-creating voltage VRi. In this arrangement, the voltage difference VIN - VR determines the current instead the voltage VIN (the resistor Ri actually acts as the opposite voltage-to-current converter). As a result, the current decreases.

Load resistance. In addition, if the load has some finite resistance (instead of infinite resistance), a part of the current IIN will diverts through it. As a result, both the current IIN and the voltage VOUT decrease. The problem is again that the load consumes energy from the passive circuit (click Imperfections in [1]).


[edit] Improvement: Active current-to-voltage converter

[edit] The basic idea behind the active version

[edit] Non-electrical domain: Removing disturbance by equivalent "antidisturbance"

The active version of the current-to-voltage converter is based on a well-known technique, where we compensate the undesirable effects caused by ourself using equivalent "anti-quantities" (see the page about virtual ground). This idea is implemented by using an additional power source, which "helps" the main source by compensating the local losses caused by the internal undesired quantity. Example: if we have broken our window in winter, we turn on a heater that compensates the thermal losses; and v.v., in summer, we turn on an air-conditioner. More examples: if our car has come into collision with other car, the insurance company compensates the damages that we have caused to the else's car, if we cause troubles to others, we apologize, if we have spent money from our account, we begin depositing additional money into the account, etc. In all these cases, we have prepared "standby" resources, in order to use them, if there is a need to compensate internal losses.

[edit] Electrical domain: Removing voltage by equivalent "antivoltage"

Fig. 12. Active current-to-voltage converter
Fig. 12. Active current-to-voltage converter

Electrical implementation. In order to show how this powerful basic idea is applied to improve the passive current-to-voltage converter, first, an equivalent electrical circuit is used (Fig. 12). In this active current-to-voltage converter, the voltage drop VR across the internal resistor R is compensated by adding the same voltage VH = VR to the input voltage VIN [2]. For this purpose, an additional following voltage source BH is connected in series with the resistor. It "helps" the input voltage source; as a result, the undesired voltage VR and the resistance R disappear (the point A becomes a virtual ground).

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

Where to take an output from? The magnitude of the compensating quantity is frequently used to measure indirectly the initial quantity (an example - weighing by using scales). This idea is applied in the circuit of active current-to-voltage converter by connecting the load to the compensating voltage source BH instead to the resistor. There are two advantages of this arrangement: first, the load is connected to the common ground; second, it consumes energy from the additional source instead from the input source. Therefore, it might possess small resistance.


[edit] Op-amp implementation

Fig. 13. Op-amp current-to-voltage converter (a classic circuit diagram)
Fig. 13. Op-amp current-to-voltage converter (a classic circuit diagram)

The basic idea above is implemented in the op-amp current-to-voltage converter (Fig. 13, 14) [3]. In this circuit, the output of the operational amplifier is 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 resistor R in the place of the compensating voltage source BH from Fig. 12. As a result, the op-amp's output voltage and the voltage drop VR are subtracted; the potential of the point A represents the result of this subtraction (it behaves as a virtual ground).

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


[edit] Op-amp circuit operation

Fig. 14. Op-amp current-to-voltage converter (+VIN)
Fig. 14. Op-amp current-to-voltage converter (+VIN)

Zero input voltage results in no voltage drops or currents in the circuit (click Exploring in [4]).


Positive input voltage. If the input voltage VIN increases above the ground, an input current IIN begins flowing through the resistor R. As a result, a voltage drop VR appears across the resistor and the point A begins raising its potential (the input source "pulls" the point A up toward the positive voltage VIN). Only, the op-amp "observes" that and immediately reacts: it decreases its output voltage under the ground sucking the current. Figuratively speaking, the op-amp "pulls" the point A down toward the negative voltage -V until it manages to zero its potential (to establish a virtual ground). It does this work by connecting a portion of the voltage produced by the negative power supply -V in series with the input voltage VIN. The two voltage sources are connected in series, in the same direction (traversing the loop clockwise, the signs are - VIN +, - VOA +) so that their voltages are added. However, regarding to the ground, they have opposite polarities.


Fig. 15. Op-amp current-to-voltage converter (-VIN)
Fig. 15. Op-amp current-to-voltage converter (-VIN)

Negative input voltage. If the input voltage VIN decreases under the ground, the input current flows through the resistor R in opposite direction (Fig. 15). As a result, a voltage drop VR appears across the resistor again and the point A begins dropping its potential (now, the input source "pulls" the point A down toward the negative voltage -VIN). The op-amp "observes"' that and immediately reacts: it increases its output voltage above the ground "pushing out" the current. Now, the op-amp "pulls" the point A up toward the positive voltage +V until it manages to zero again the potential VA (the virtual ground). For this purpose, the op-amp puts a portion of the voltage produced by the positive power supply +V in series with the input voltage VIN. The two voltage sources are connected again, in the same direction (traversing the loop clockwise, + VIN -, + VOA -) so that their voltages are added. However, regarding to the ground, they have opposite polarities as above.

In the circuit of an op-amp current-to-voltage converter, the op-amp adds as much voltage to the voltage of the input source as it loses across the resistor.

[edit] I-to-V converters versus transimpedance amplifiers

The active current-to-voltage converter is an amplifier with current input and voltage output. The gain of this amplifier is represented by the resistance R (K = VOUT/IIN = R); it is expressed in units of ohms. That is why, this circuit is named transresistance amplifier or more general, transimpedance amplifier [5]. The both terms are used to designate the circuit considered.

Its input ideally has low impedance, and the input signal is a current. Its output may have low impedance, or in high-frequency applications, may be matched to a driven transmission line; the output signal is measured as a voltage.

[edit] Active version applications

Fig. 16. Op-amp inverting amplifier = V-to-I converter + op-amp I-to-V converter
Fig. 16. Op-amp inverting amplifier = V-to-I converter + op-amp I-to-V converter

Transimpedance amplifiers are commonly used in receivers for optical communications. The current generated by a photodetector generates photo voltage, but in a nonlinear fashion. Therefor the amplifier has to prevent any large voltage by its low input impedance and generate either a 50 Ohm signal (which is by the way considered low impedance by many) to drive a coaxial cable or a voltage signal for further amplification. But note that the most linear amplification is current amplification by a bipolar transistor, so you may want to amplify before the impedance conversion.


Fig. 17. Inverting amplifier configuration of an op-amp becomes a transimpedance amplifier when Rin is 0 ohms
Fig. 17. Inverting amplifier configuration of an op-amp becomes a transimpedance amplifier when Rin is 0 ohms


The circuit considered is also used as a main part of more complex op-amp inverting circuits with (parallel) negative feedback: inverting amplifier (Fig. 16, 17), CR differentiator, LR integrator, inverting voltage summer etc. Here are the building formulas of these circuits:

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

Op-amp V-to-V CR differentiator = V-to-I C differentiator + op-amp I-to-V converter

Op-amp V-to-V LR integrator = V-to-I L integrator + op-amp I-to-V converter

Op-amp V-to-V DR antilog converter = V-to-I D antilog converter + op-amp I-to-V converter

[edit] Active version imperfections (power considerations)

Although the active current-to-voltage converter is a perfect circuit, the popular multimeters do not work that way. In order to measure a current, they use the imperfect passive current-to-voltage converter instead of the almost ideal op-amp current-to-voltage converter. The reason for applying such an old-fashioned approach to current measurements is that all the input current IIN flows through the "helping" voltage source BH in the active version (Fig. 3). Therefore, the source has to be able to endure such a current. Accordingly, in the practical op-amp circuit (Fig. 4), both the power source and the op-amp have to endure the input current measured. For example, if they try to measure a current of 10A (a normal maximum current range in all purpose DVMs), they have to use a car battery as a power supply and a power "op-amp", which is able to dissipate 100W!

The active (op-amp) current-to-voltage converter is a perfect circuit; however, it is suitable only for low-current applications.

[edit] See also

[edit] External links

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