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**Building a Passive Current-to-Voltage Converter**

**Circuit idea:** *A current passing through a resistor makes a proportional voltage drop appear across the resistor.*

## Contents

## Problem: *How to convert current into voltage*Edit

As regards the circuit inputs, we prefer voltage to current as an input quantity. Only, some devices have a current input (an ammeter, a bipolar transistor, a transimpedance amplifier, a Norton amplifier, etc.) In these cases, we connect a voltage-to-current converter before the device; as a result, it acquires a voltage input.

Similarly, we prefer voltage to current as an output quantity. Only, there many devices having a current output (actually all the active electronic components - a current source, a bipolar transistor, a tube, a FET transistor, etc.) In these cases, we need to connect the reverse current-to-voltage converter after the device, in order to get a voltage output. Since the current-output devices are more widespread than current-input ones, this circuit is more popular than the opposite voltage-to-current converter. Then, let's build it!

As usual, there are two versions of the circuit - passive ("bad") and active ("good"); here, we begin with the "bad" passive version. Then, in another story dedicated to the "good" active version, we will show that again there is a close interrelation between the two circuits: the active version is come from the passive one (the active version comprises the passive one, it is just an improved passive version). In this way, we will show the evolution of the famous circuit moving, step-by-step, from simple to complex.

## Basic non-electrical idea: *Flow causes pressure*Edit

Trying to find an answer to the question, "What causes what?" in the previous story, we assumed that *pressure causes flow*. Conversely, there are many situations in our routine where *flow causes pressure*. In these case, something moving encounters an obstacle; as a result, a pressure appears. Here are some examples: *mechanical* (if we try to stop a moving car with our, it exerts pressure to us), *pneumatic* (imagine a constant flow pump moving air through a closed loop of pipes -pinch the hose in the middle and you will see that a pressure appears across the bottleneck), *social* (stand in someone's way and you will experience "pressure"), etc. Let's finally generalize all these situations.

In order to induce a pressure, we have to put an impediment in flow's way. In this arrangement, *the flow-like, pressure-like and impediment-like attributes are interrelated* as before. Usually, *the output pressure-like variable is proportional to the input flow-like one*; so, we may say that *the impediment converts the flow-like variable into a pressure-like one*.

## Basic electrical idea: *Current causes voltage*Edit

### Building the circuitEdit

In electricity, we may observe an analogous *current-causes-voltage phenomenon*: if a current I_{IN} flows through a resistor R (Fig. 2), the latter impedes (resists) the current; as a result, a proportional voltage drop V_{R} = R.I_{IN} appears across the resistor.^{[1]} In this current-supplied circuit, the voltage drop V_{R} acts as an output voltage V_{OUT}. Only, note that the voltage drop V_{R} is created not by the resistor; it is created by the excitation voltage source inside the input current source. We may say that this is a *current-causes-voltage formulation* of Ohm's law: **V = R × I**

In this current-supplied circuit, the resistor R determines the voltage across it. We usually say that the resistor converts the current I_{IN} into a proportional voltage V_{OUT} or it serves as a simple current-to-voltage converter - a linear circuit with transfer ratio k = V_{OUT}/I_{IN} [V/mA].

*A bare resistor can convert current into voltage.*

### Exploring the circuit operationEdit

We may present the circuit operation and Ohm's law in a more attractive manner than V = R × I, if we visualize the invisible electrical quantities by means of voltage bars and current loops (Fig. 2). If you remember, in this "geometrical" presentation, 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 or drop (see also an interactive animation).

Then, we may present the circuit operation (and Ohm's law) graphoanalytically (Fig. 3). As the voltage across and the current through the two 2-terminal components (the voltage source and the resistor) are the same, we may superimpose their IV curves on a common coordinate system. The intersection of the two lines is the operating point A; it represents the current magnitudes of the current I_{A} and the voltage V_{A}.

When we vary the current of the input current source, 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.

As before, we may use again the attractive graphical interpretation of Ohm's law called a voltage diagram (the voltage distribution along the resistive film inside a linear resistor, Fig. 4). Here, 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 I_{IN}.

## ApplicationsEdit

### I-to-V converter acting as an output deviceEdit

**Current-controlled voltage source.** Although there are enough constant voltage sources in nature (primary and secondary batteries), if there is a current source but we need a voltage source, we may build it. For this purpose, we connect a current-to-voltage converter after the current source:

*Voltage source = current source + current-to-voltage converter*

That means just to connect a humble resistor R in parallel to the input current source I_{IN} (the Norton's idea in electricity) - Fig. 5.

If the load is ideal (that is, it has an infinite resistance), this compound voltage source will generate a constant voltage V_{OUT} = R.I. This voltage will affect the current, if the input current source is imperfect (see imperfections).

**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 on Fig. 6 is built by using the simpler voltage-to-current capacitive differentiator (a bare capacitor) and a current-to-voltage converter.

In these circuits, the respective I-to-V converters introduce some voltage drop, which affects the excitation voltage V_{IN}. As a result, the current decreases and an error appears (see the section about imperfections).

**Transistor collector resistor.** A BJ 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. 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 V_{Rc} is floating, usually the complementary (to the power supply) voltage drop V_{CE} 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 of the negative feedback 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.*

### I-to-V converter acting as an input deviceEdit

**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, we connect a simple current-to-voltage converter (a shunt resistor) before the voltmeter. 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 power considerations).

## I-to-V converter as a part of active V-to-I convertersEdit

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. We can implement this powerful idea as a transistor version (Fig. 9) or as an op-amp version of a current source (Fig. 10). In these circuits, we connect a current-to-voltage converter (the bare resistor R) in the negative feedback loop. Then, in order to compare the voltage drop V_{R} proportional to the load current I with the input voltage V_{Z}, we connect the two voltages in series and apply their difference dV = V_{Z} - V_{R} 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 a voltage-to-current converter.

## What are the input/output resistances?Edit

Do you remember that when we were considering the opposite voltage-to-current converter, we were investigating the input and output resistances? Let's do the same for the present current-to-voltage converter. Again, let's for concreteness assume a resistive load R_{L}.

**What is the input resistance?** First, connect an ammeter in series with and a voltmeter in parallel to the converter's input; then vary the input current to investigate the input resistance. Looking from the side of the input source we see two resistors connected in parallel - R and R_{L}; so, the input resistance is R_{IN} = R||R_{L}. As you can see, it depends on the load resistance RL. Only, we choose R << R_{L}; so, R_{IN} ≈ R.

**What is the output resistance?** Now, connect a voltmeter in parallel to and an ammeter in series with the converter's output; then, vary the load resistance (voltage) and observe the current to investigate the output resistance. Looking from the side of the load, we see two resistors connected in parallel - Re (the equivalent resistance of the input circuit) and R; so, the output resistance is R_{OUT} = Re||R. If the input current is created by an ideal current source, the output resistance is only R_{OUT} ≈ R.

## ImperfectionsEdit

**A problem.** Only, a strange contradiction appears here. From one side, the voltage drop V_{R} across the resistor R is useful for us (this is the output voltage needed!). From the other side, this voltage drop is troublesome as it enervates the excitation voltage V_{IN} (here we suppose that the input current is created by a voltage source V_{IN} through the resistor Ri). Now the voltage difference V_{IN} - V_{R} determines the current instead the voltage V_{IN}. It turns out that measuring the current we disturb it! As a result, the current I_{IN} decreases:( What do we do to solve this contradiction?

You can explore the circuit operation in a more attractive way, if you click *Exploring* button in the interactive flash movie ^{[2]} or if you go to *Stage 2* in the interactive flash builder.^{[3]}

## ImprovementEdit

**Classic remedy.** We can decrease the error caused by the resistor R just by decreasing its resistance. Only, the output voltage will decrease as well and probably we have to amplify it. Doing that, we will also amplify the noise... How to solve the problem then?

**Looking for a perfect remedy.** Obviously, we have to solve the contradiction so that the resistance R to exist and, at the same time, not to exist!?! How do we do this magic? A tip: remember what we do in life when something bad appears. If you do not manage to find a remedy, visit the related story about active voltage-to-current converter to get an answer.

## ReferencesEdit

The passive current-to-voltage converter is a more popular circuit than the opposite passive voltage-to-current converter. It is well presented in the electronics books and web resources. Here are some of them.

- ↑ Elementary passive converters with voltage output is a teacher's story about the simplest electric converters producing a current.
- ↑ Passive current-to-voltage converter is an animated
*Flash*tutorial revealing the philosophy of the passive version. - ↑ Op-amp circuit builder (movie philosophy) is an interactive
*Flash*tutorial that shows how to transform any passive converter into an active one.

## Related Wikimedia resourcesEdit

### WikibooksEdit

**Circuit Idea (this book):**

Passive voltage-to-current converter reveals the basic idea behind the opposite passive circuit.

Reinventing the op-amp inverting voltage-to-current converter reveals the basic idea behind the opposite active circuit.

**Electronics:** Resistors is a comprehensive story about the simplest resistive components.

### WikipediaEdit

Current-to-voltage converter introduces the passive and active versions of the circuit.

Voltage-to-current converter introduces the passive and active versions of the "mirror" circuit.

How electrical and electronic engineers use Ohm's law is an interesting story about the relation between the electrical attributes.

## External web resourcesEdit

Reinventing current-to-voltage converter is a similar circuit story but it is better structured and easier to navigate.

Reinventing transimpedance amplifier is a story especially intended to the active version.

How do we build an op-amp ammeter? is a similar story about simpler active version.

Resistors and Transistors show that a collector resistor can serve as a simple current-to-voltage converter (well illustrated and animated).

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