# 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 $V_{i}$ 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 $V_{i}$.

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

$$\frac{V_i}{R_1}-I_{0}=0$$

$$=>I_{0}=\frac{V_t}{R_1}$$

Thus, the **output current** $I_{0}$ of a voltage to current converter is the ratio of its input voltage $V_{i}$ and resistance $R_{1}$.

We can re-write the above equation as −

$$\frac{I_0}{V_i}=\frac{1}{R_1}$$

The above equation represents the ratio of the output current $I_{0}$ and the input voltage $V_{i}$ & it is equal to the reciprocal of resistance $R_{1}$ The ratio of the output current $I_{0}$ and the input voltage $V_{i}$ 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 $R_{1}$.

## 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 −

$$-I_{i}+\frac{0-V_0}{R_f}=0$$

$$-I_{i}=\frac{V_0}{R_f}$$

$$V_{0}=-R_{t}I_{i}$$

Thus, the **output voltage,** $V_{0}$ of current to voltage converter is the (negative) product of the feedback resistance, $R_{f}$ and the input current, $I_{t}$. Observe that the output voltage, $V_{0}$ 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 −

$$\frac{V_0}{I_i}=-R_{f}$$

The above equation represents the ratio of the output voltage $V_{0}$ and the input current $I_{i}$, and it is equal to the negative of feedback resistance, $R_{f}$. The ratio of output voltage $V_{0}$ and input current $I_{i}$ 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 $R_{f}$ .