Voltage Divider: Formula, Circuits, and Applications

A voltage divider is a simple but essential concept in electronics used to produce a desired output voltage from a higher input voltage. By using two resistors connected in series, a voltage divider circuit can reduce voltage to levels appropriate for sensors, analog inputs, or logic circuits. This post explains the voltage divider formula, how to calculate voltage dividers, and where to apply them.

What Is a Voltage Divider?

A voltage divider is a basic resistive network that splits an input voltage into smaller output voltages. This is achieved using two (or more) resistors in series. The voltage across one of the resistors is taken as the output.

The following circuit shows the principle of operation of a voltage divider. In the sections that follow, the voltage divider circuit and formula are explained in more details. In the circuit below, the voltage between A and C is the input voltage. The voltage between B and C is the output voltage.

Series resistor voltage divider circuit — Series Resistor Voltage Divider Circuit

In the above series resistor circuit, current flows from the 12V supply, through resistors R1 and R2 and down to ground (GND), which is where 0V of the power supply is connected.

We have the supply voltage of the circuit and the resistance of the circuit. As a result, we can use Ohm’s Law to calculate the current in the circuit. The total resistance in the circuit is 10k + 4k7, which is 10,000 + 4,700 and results in 14,700 ohms.

In Ohm’s law, current = voltage divided by resistance. In our example this is 12V divide by 14,700 ohms. The result is 0.0008163A, which is better written as 816.3 micro amps.

We can now use Ohm’s law again to calculate the resistance across each resistor:

V = I x R = 816.3uA x 10,000 = 8.163V across R1 (measured between A and B)

V = I x R = 816.3uA x 4,700 = 3.836V across R2 (measured between B and C)

Building a Voltage Divider Circuit

A basic voltage divider circuit includes:

A voltage source
Two resistors connected in series
The output voltage taken from the junction between the resistors

Example Schematic / Circuit Diagram

In this resistor divider, the input voltage is divided proportionally based on the resistor values. The following circuit is the same as the previous circuit, but it is drawn slightly differently. That is, it is drawn vertically, rather than horizontally, and the input and output voltages are labelled.

Voltage divider circuit — Voltage Divider Circuit

Common Uses of this Circuit

Scaling voltages for analog-to-digital converters (ADCs)
Biasing transistor bases
Reading higher voltages on low-voltage microcontrollers

Voltage Divider Formula

The voltage divider formula for a circuit with two resistors, R1 and R2, is:

$$ V_{\text{out}} = V_{\text{in}} \times \left( \frac{R_2}{R_1 + R_2} \right) $$

Where:

V_out is the output voltage
V_in is the input voltage
R₁ is the resistor connected to the input voltage
R₂ is the resistor connected to ground (GND)

This formula allows you to calculate voltage divider output for various resistor values.

Voltage Divider Circuit Working Principle

The principle behind the voltage divider circuit is Ohm’s Law, which states that the voltage across a resistor is directly proportional to the current flowing through it, and inversely proportional to its resistance. When two resistors are connected in series across a voltage source, the total voltage drop across them is equal to the source voltage (V = V1 + V2). The voltage across each resistor can be calculated using the voltage divider formula.

Example: Calculating a Voltage Divider for 3.3V from 5V

Let’s say you have a 5V DC input logic level and you need to reduce it to 3.3V to safely connect to a microcontroller’s input pin. You can use the voltage divider formula to calculate appropriate resistor values.

We want:

V_in = 5V
V_out = 3.3V

Step 1: Use the voltage divider formula

We solve for the resistor ratio:

$$ V_{\text{out}} = V_{\text{in}} \times \left( \frac{R_2}{R_1 + R_2} \right) $$

Rearranged to find the ratio:

$$ \frac{R_2}{R_1 + R_2} = \frac{V_{\text{out}}}{V_{\text{in}}} = \frac{3.3}{5} = 0.66 $$

Step 2: Choose resistor values

Choose one resistor and then calculate the other as follows.

From the previous step, we know the required ratio is:

$$ \frac{R_2}{R_1 + R_2} = 0.66 $$

To proceed, choose a value for either R₁ or R₂. Let’s choose a common and easy-to-find value for R₂, such as:

R₂ = 2.0 kΩ

Now solve for R₁:

We start from:

$$ \frac{R_2}{R_1 + R_2} = 0.66 $$

Substitute R₂ = 2.0 kΩ:

$$ \frac{2.0}{R_1 + 2.0} = 0.66 $$

Multiply both sides by R₁ + 2.0:

$$ 2.0 = 0.66 \times (R_1 + 2.0) $$

Divide both sides by 0.66:

$$ \frac{2.0}{0.66} = R_1 + 2.0 \\[10pt] 3.03 \approx R_1 + 2.0 $$

Now subtract 2.0 from both sides:

$$ R_1 \approx 1.03\,\text{k}\Omega $$

Step 3: Use standard resistor values

If exact resistor values aren’t available, choose the nearest E12 or E24 series resistors.

The calculated value of 1.03kΩ from the previous step is close to a standard resistor value of 1.0 kΩ, so let’s try using:

R₁ = 1.0 kΩ
R₂ = 2.0 kΩ

Now verify the output voltage:

$$ V_{\text{out}} = 5 \times \left( \frac{2.0}{1.0 + 2.0} \right) = 5 \times \frac{2.0}{3.0} = 3.33\,\text{V} $$

This is very close to 3.3 V and will work in most 3.3 V logic-level applications.

How to Calculate a Voltage Divider

A summary of the above calculation follows below for easy reference.

To calculate a voltage divider, follow these steps:

Choose your input voltage (V_in).
Decide the output voltage you need (V_out).
Select a resistor value for R2.
Use the voltage divider formula to solve for R1:

$$ R_1 = R_2 \times \left( \frac{V_{\text{in}}}{V_{\text{out}}} – 1 \right) $$

Alternatively, use a pair of known resistor values and calculate the output voltage using the formula provided earlier.

Practical Applications of Voltage Divider Circuits

A voltage divider circuit or voltage splitter circuit has many applications:

Sensor Interfaces: Adjusting signal levels to match ADC input range
Battery Monitoring: Reducing battery voltage to measurable levels
Biasing: Providing fixed DC voltages for amplifier stages

Further details of practical applications for this type of circuit follow below.

Reference Voltage Generation: Voltage divider circuits are commonly used to generate a stable reference voltage for analog circuits. By selecting appropriate resistor values, a specific voltage level can be obtained reliably.

Sensor Interface: Voltage dividers are used to interface sensors with microcontrollers or analog circuits. For example, in a simple temperature sensor circuit, the output voltage from a thermistor can be converted into a proportional voltage using a voltage divider.

Signal Conditioning: In signal processing applications, voltage dividers are used for signal attenuation or level shifting. They can scale down voltages to match the input range of subsequent stages in a circuit.

Biasing Circuits: Voltage divider circuits are often employed in biasing configurations for transistors and operational amplifiers. They set the operating point or quiescent point of these components to ensure proper amplification or switching behavior.

Power Supply Regulation: Voltage dividers can be used in conjunction with voltage regulators to fine-tune output voltages in power supply circuits. They provide a means of adjusting the output voltage within a certain range.

The following circuit diagram shows an example of a voltage divider built from resistors R1 and R2, that is used in a regulator circuit for a L5973D switching regulator. The divider circuit feeds back part of the output voltage VOUT from the circuit to pin 5 of the L5973D IC, which is the feedback or FB pin.

Circuit diagram example of a voltage divider in a regulator circuit

Tips for Voltage Divider Circuits

Choose Standard Resistor Values: Use values from the E12 or E24 resistor series for easier sourcing.
Avoid Low Resistance Values: Using low-ohm resistors increases power consumption.
Use High Resistance for Minimal Load: To minimize current draw, use resistors in the tens or hundreds of kilo-ohms.
Buffer the Output: If the divider output feeds a load, use a buffer like an op-amp to prevent voltage drop.
Verify With a Multimeter: Always test your output voltage to ensure accuracy.

Did You Know?

Old Concept, Still Useful: The voltage divider has been used since early analog electronics and remains a staple in modern circuit design.
Found in Every Device: From radios to smartphones, resistive divider circuits help regulate voltage levels internally.
Not Just Resistors: You can create a voltage divider using capacitors or even active components, depending on AC or DC needs.

Frequently Asked Questions

What is a voltage divider used for?

A voltage divider is used to reduce a high voltage to a lower one. It’s commonly used in signal conditioning, sensor interfacing, and biasing circuits.

Can I use a voltage divider to power a device?

Generally, no. A voltage divider is not suitable for powering loads because the voltage drops significantly under current draw. It is best used for signal-level applications.

How accurate is a resistor divider?

The accuracy depends on resistor tolerance and loading effects. For critical applications, use precision resistors and buffer the output.

What is the difference between a voltage splitter and a voltage divider?

These terms are often used interchangeably. However, “voltage splitter” sometimes refers to circuits that produce both positive and negative voltages from a single supply, while “voltage divider” specifically describes a resistive network.

Can I use more than two resistors in a voltage divider?

Yes, you can use multiple resistors to create stepped voltages or to divide voltage across multiple points, but the same principles apply.

Conclusion

A voltage divider is a fundamental circuit that every electronics enthusiast should understand. By applying the voltage divider formula and selecting the right resistor values, you can design a voltage divider circuit that safely scales voltage for a wide range of components.

Whether you’re building a resistor divider for a microcontroller input or a voltage splitter circuit for a sensor, this simple concept is a building block of countless electronic designs.

For more tutorials and practical guides, explore the Electronics Theory section of Starting Electronics.

Voltage Divider: Everything You Need to Know

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