Calculate Loaded Voltage Divider

Online calculator for calculating the values ​​of a loaded voltage divider

Loaded Voltage Divider

Loading Effect

A load resistor RL parallel to R₂ changes the division ratio. Enter either the desired output voltage U₂ or the load resistance RL.

Choose Load Parameter
Results
Voltages
Voltage U₁:
Voltage U₂:
Resistances
Load resistance RL:
R₂ || RL:
Total resistance:
Currents
Current through R₁:
Current through R₂:
Current through RL:

Loaded Voltage Divider

Circuit diagram of a loaded voltage divider

Circuit diagram: Loaded voltage divider with load resistance RL

Loading Effect

The load resistance RL parallel to R₂ changes:

  • The voltage division ratio
  • The output voltage U₂ (becomes smaller)
  • The total current (becomes larger)
  • The current distribution in the circuit
Main Formula
\[U_2 = U_{in} \cdot \frac{R_{2L}}{R_1 + R_{2L}}\]
\[R_{2L} = \frac{R_2 \cdot R_L}{R_2 + R_L}\]
R2L = Parallel resistance of R₂ and RL
Important Note
The smaller the load resistance RL, the more the output voltage U₂ is reduced. For stable output voltages, RL should be >> R₂.

Formulas for Loaded Voltage Divider

1. Calculate parallel resistance

Equivalent resistance of R₂ and RL:

\[R_{2L} = \frac{R_2 \cdot R_L}{R_2 + R_L}\]

Product formula for parallel connection

2. Output voltage

Modified voltage divider formula:

\[U_2 = U_{in} \cdot \frac{R_{2L}}{R_1 + R_{2L}}\]

With parallel resistance R2L

3. Calculate currents

According to Ohm's law:

\[I_1 = \frac{U_1}{R_1}\]
\[I_2 = \frac{U_2}{R_2}, I_L = \frac{U_2}{R_L}\]
Additional formulas

Calculate load resistance from R2L:

\[R_L = \frac{R_2 \cdot R_{2L}}{R_2 - R_{2L}}\]

Calculate R2L from voltages:

\[R_{2L} = \frac{U_2 \cdot R_1}{U_{in} - U_2}\]

Practical Calculation Example

Example: Loading effect of a voltage divider

Given: Uin = 15V, R₁ = 10kΩ, R₂ = 20kΩ, RL = 30kΩ

Step 1: Unloaded voltage divider (reference)
\[U_{2,unloaded} = 15V \cdot \frac{20kΩ}{10kΩ + 20kΩ} = 15V \cdot \frac{20}{30} = 10V\]
Step 2: Calculate parallel resistance R₂ || RL
\[R_{2L} = \frac{20kΩ \cdot 30kΩ}{20kΩ + 30kΩ} = \frac{600k}{50k} = 12kΩ\]
Step 3: Calculate loaded output voltage
\[U_{2,loaded} = 15V \cdot \frac{12kΩ}{10kΩ + 12kΩ} = 15V \cdot \frac{12}{22} ≈ 8.18V\]
Step 4: Calculate currents
Total current: \[I_1 = \frac{15V}{22kΩ} ≈ 0.68mA\]
Current through R₂: \[I_2 = \frac{8.18V}{20kΩ} ≈ 0.41mA\]
Current through RL: \[I_L = \frac{8.18V}{30kΩ} ≈ 0.27mA\]
Step 5: Evaluate loading effect
Voltage drop: 10V - 8.18V = 1.82V (18% reduction)
Current increase: 0.68mA vs. 0.5mA unloaded (36% increase)
Conclusion: The load resistance of 30kΩ reduces the output voltage from 10V to 8.18V. For a stable voltage, RL should be chosen significantly larger than R₂.

Applications and Design Guidelines

Typical Applications

  • Signal sources: Voltage dividers with changing loads
  • Sensor interfaces: Adaptation to different input resistances
  • ADC preamplifiers: Considering input impedance
  • Audio circuits: Volume controls with headphone loads
  • Measurement circuits: Voltage dividers with measuring device resistances
Design Guidelines
  • Load factor: RL should be at least 10× larger than R₂
  • Voltage regulation: For ±5% accuracy: RL ≥ 20 × R₂
  • Current consumption: Voltage divider current >> Load current
  • Buffering: Use operational amplifiers for high-impedance loads
Comparison with unloaded voltage divider
Parameter Unloaded Loaded
Output voltage Constant (ideal) Reduced by load
Total current Uin/(R₁+R₂) Higher due to parallel resistance
Application Reference voltages Signal sources with load
Stability Very good Depends on RL
Important Notes
  • Load effect: Every connected load changes the output voltage
  • Current consumption: Higher current consumption due to parallel load
  • Temperature drift: All resistors affect stability
  • Frequency response: Capacitive loads can cause instability
Related Calculators

For unloaded applications:

Unloaded Voltage Divider
Practical Tips
  • Use buffer amplifiers for variable loads
  • Calculate worst-case scenarios
  • Consider tolerances of all resistors
  • Monitor power dissipation

Symbol Definitions

UinInput voltage of the voltage divider
U₁Voltage across R₁
U₂Output voltage across R₂ || RL
R₁, R₂Voltage divider resistances
RLLoad resistance parallel to R₂
R2LParallel resistance of R₂ and RL
I₁, I₂, ILCurrents through the respective resistances

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