**Voltage to Current Converter **or **V-I converter** is an electronic circuit that creates a current that is proportional to the applied input voltage. Basically it maintains the load current at a value that is independent of the load impedance variation. In this article, we will see the different op-amp based V-I converter, its working and its applications. Basically three circuits are there for V-I converter.

**Contents**show

## Floating Load Voltage to Current Converter

Floating load voltage to current converter circuit as shown in figure 1. The input V_{i }is applied at the non-inverting terminal. V_{o} is the output voltage. The resistance R connected to the inverting terminal of the op-amp is grounded. The load resistor (R_{L}) is floating in this V-I converter circuit. It is said to be floating because the load resistance is not connected to the ground.

### Analysis

The analysis of the V-I converter circuit is shown in figure 2. Since the op-amp is ideal and negative feedback is present, the voltage of the inverting terminal (V_{−}) is equal to the voltage of the non-inverting terminal (V_{+} = V_{i}), according to the **virtual short concept**.

V_{− }= V_{+} = V_{i}

The currents entering both terminals of the op-amp are zero since the op-amp is ideal.

Let current I flows through the resistor R.

(1)

Apply KCL at node **Q**

(2)

From equations (1) and (2), we have

If input voltage V_{i} and Resistance (R) is fixed then the load current (I_{L}) is independent of the load resistance (R_{L}).

## Ground Load Voltage to Current Converter

Ground load voltage to current converter circuit as shown in figure 3. The input V_{i }is applied as shown in figure 3. V_{o} is the output voltage. The resistance R_{1} connected to the inverting terminal of the op-amp is grounded. The load resistor (R_{L}) is grounded in this V-I converter circuit. It is said to be grounded because the load resistance is connected to the ground.

### Analysis

The analysis of the V-I converter circuit is shown in figure 4. Let the voltage of node Q is V_{1}. Since the op-amp is ideal and negative feedback is present, the voltage of the inverting terminal (V_{−}) is equal to the voltage of the non-inverting terminal (V_{+} = V_{1}), according to the **virtual short concept**.

V_{− }= V_{+} = V_{1}

The currents entering both terminals of the op-amp are zero since the op-amp is ideal.

Let current I_{1} and I_{2} flows through the resistor R_{1} and R_{2} respectively.

(3)

(4)

Apply KCL at node **P**

(5)

From equations (3), (4), and (5), we have

Therefore

or we can write it as

(6)

The current I_{3} , I_{4} and I_{L }flows through the resistor R_{3 }, R_{4} and R_{L} respectively.

(7)

(8)

Apply KCL at node **Q**

(9)

From equations (7), (8), and (9), we have

Now put value of V_{1} from equation (6)

If

Then

If input voltage V_{i} and Resistance (R_3) is fixed then the load current (I_{L}) is independent of the load resistance (R_{L}).

## Ground Load Voltage to Current Converter Circuit 2

Ground load voltage to current converter circuit 2 as shown in figure 5. The input V_{i }is applied as shown in figure 5. V_{o} is the output voltage. The resistance R_{3} connected to the non-inverting terminal of the op-amp is grounded. The load resistor (R_{L}) is grounded in this V-I converter circuit. It is said to be grounded because the load resistance is connected to the ground.

### Analysis

The analysis of the V-I converter circuit is shown in figure 6. Let the voltage of node Q is V_{1}. Since the op-amp is ideal and negative feedback is present, the voltage of the inverting terminal (V_{−}) is equal to the voltage of the non-inverting terminal (V_{+} = V_{1}), according to the **virtual short concept**.

V_{− }= V_{+} = V_{1}

The currents entering both terminals of the op-amp are zero since the op-amp is ideal.

Let current I_{1} and I_{2} flows through the resistor R_{1} and R_{2} respectively.

(10)

(11)

Apply KCL at node **P**

(12)

From equations (10), (11), and (12), we have

(13)

or we can write it as

(14)

The current I_{3} , I_{4} and I_{L }flows through the resistor R_{3 }, R_{4} and R_{L} respectively.

(15)

(16)

Apply KCL at node **Q**

(17)

From equations (15), (16), and (17), we have

put value of

from equation (13), we haveIf

Then

If input voltage V_{i} and Resistance (R_{3}) is fixed then the load current (I_{L}) is independent of the load resistance (R_{L}).

## V-I Converter Applications

This converter has applications in the following

1. Low voltage ac and dc voltmeters

2. LED and Zener diode testers

3. Diode match finders