# Converters Of Electrical Quantities

Voltage and current are the basic electrical quantities. They can be converted into one another depending on the requirement. **Voltage to Current Converter** and Current to **Voltage Converter** are the two circuits that help in such conversion. These are also linear applications of op-amps. This chapter discusses them in detail.

## Voltage to Current Converter

A **voltage to current converter** or **V to I converter**, is an electronic circuit that takes current as the input and produces voltage as the output. This section discusses about the op-amp based voltage to current converter.

An op-amp based voltage to current converter produces an output current when a voltage is applied to its non-inverting terminal. The **circuit diagram** of an op-amp based voltage to current converter is shown in the following figure.

In the circuit shown above, an input voltage ViVi is applied at the non-inverting input terminal of the op-amp. According to the **virtual short concept**, the voltage at the inverting input terminal of an op-amp will be equal to the voltage at its non-inverting input terminal . So, the voltage at the inverting input terminal of the op-amp will be ViVi.

The **nodal equation** at the inverting input terminal’s node is −

Thus, the **output current** I0I0 of a voltage to current converter is the ratio of its input voltage ViVi and resistance R1R1.

We can re-write the above equation as −

The above equation represents the ratio of the output current I0I0 and the input voltage ViVi & it is equal to the reciprocal of resistance R1R1 The ratio of the output current I0I0 and the input voltage ViVi is called as **Transconductance**.

We know that the ratio of the output and the input of a circuit is called as gain. So, the gain of an voltage to current converter is the Transconductance and it is equal to the reciprocal of resistance R1R1.

## Current to Voltage Converter

A **current to voltage converter **or **I to V converter** is an electronic circuit that takes current as the input and produces voltage as the output. This section discusses about the op-amp based current to voltage converter.

An op-amp based current to voltage converter produces an output voltage when current is applied to its inverting terminal. The **circuit diagram** of an op-amp based current to voltage converter is shown in the following figure.

In the circuit shown above, the non-inverting input terminal of the op-amp is connected to ground. That means zero volts is applied at its non-inverting input terminal.

According to the **virtual short concept**, the voltage at the inverting input terminal of an op-amp will be equal to the voltage at its non-inverting input terminal. So, the voltage at the inverting input terminal of the op-amp will be zero volts.

The **nodal equation** at the inverting terminal’s node is −

Thus, the **output voltage,** V0V0 of current to voltage converter is the (negative) product of the feedback resistance, RfRf and the input current, ItIt. Observe that the output voltage, V0V0 is having a **negative sign**, which indicates that there exists a 180^{0} phase difference between the input current and output voltage.

We can re-write the above equation as −

The above equation represents the ratio of the output voltage V0V0 and the input current IiIi, and it is equal to the negative of feedback resistance, RfRf. The ratio of output voltage V0V0 and input current IiIi is called as **Transresistance**.

We know that the ratio of output and input of a circuit is called as **gain**. So, the gain of a current to voltage converter is its trans resistance and it is equal to the (negative) feedback resistance RfRf .