Library / Circuits, electronics and noise / ELN-02
Circuits, electronics and noise
Loaded voltage divider output
Output voltage of a resistor divider with a load RL across the lower resistor R₂.
- Ref
- ELN-02
- Rev
- v1
- Field
- Circuits, electronics and noise
- Result
- Vo [V]
A load RL across the lower resistor R₂ sits in parallel with it, so the output is Vs·(R₂∥RL)/(R₁ + R₂∥RL). The calculator’s form Vs/(1 + R₁/R₂ + R₁/RL) is the same expression. The load always lowers the output compared with the unloaded divider Vs R₂/(R₁ + R₂), unless RL is much bigger than R₂.
Output voltage of a resistor divider with a load RL across the lower resistor R₂. The load is in parallel with R₂, which lowers the output compared with the unloaded divider.
Calculator
- Unloaded output, Vs R₂/(R₁ + R₂)8 V
- Parallel resistance of R₂ and RL2,000 Ω
- Voltage lost to loading2 V
What drives the result
Each variable is moved across its typical range while the others stay at the values above. The longest bar is the key driver.
- With a 4,000 Ω load the 12 V divider gives 6 V instead of 8 V unloaded.
- To keep the loading error under 1 %, the load should be at least about 100 times the lower resistor, or the divider resistances should be lowered.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing (V) | Local step | Change in result |
|---|---|---|---|---|---|---|
| Vs Source voltage | 0.1 to 1,000 V | 0.05 | 500 | 499.9 | +10% | +10 % |
| R1 Upper resistor to the source | 10 to 1,000,000 Ω | 0.02395 | 11.94 | 11.92 | +10% | −4.76 % |
| R2 Lower resistor to ground | 10 to 1,000,000 Ω | 0.05955 | 7.989 | 7.93 | +10% | +2.33 % |
| RL Load resistance | 10 to 1,000,000 Ω | 0.05955 | 7.989 | 7.93 | +10% | +2.33 % |
Sweep of Load resistance
| Load resistance (Ω) | Output voltage (V) |
|---|---|
| 10 | 0.05955 |
| 42.17 | 0.2453 |
| 177.8 | 0.9414 |
| 749.9 | 2.88 |
| 3,162 | 5.627 |
| 13,340 | 7.273 |
| 56,230 | 7.815 |
| 237,100 | 7.955 |
| 1,000,000 | 7.989 |
Sweep one variable
Variables and how each one contributes
Output voltage
What the equation gives you. Everything else feeds it.
Source voltage
The source voltage, in V, an ideal source. Scales the output in direct proportion. Raising it by 10 % (to 13.2) moves the result by +10 %, from 6 to 6.6 V.
Upper resistor to the source
The resistor from the source to the output, in Ω. A larger R₁ drops more voltage and lowers the output. Raising it by 10 % (to 2,200) moves the result by −4.76 %, from 6 to 5.714 V.
Lower resistor to ground
The resistor from the output to ground, in Ω. A larger R₂ raises the output. Raising it by 10 % (to 4,400) moves the result by +2.33 %, from 6 to 6.14 V.
Load resistance
The load resistance across the output, in Ω. A larger load resistance gives less loading, so the output rises toward the unloaded value. Raising it by 10 % (to 4,400) moves the result by +2.33 %, from 6 to 6.14 V.
Worked example with the values above
- Divider ratios: R₁/R₂ = 0.5 and R₁/RL = 0.5.
- Denominator: 1 + 0.5 + 0.5 = 2.
- Vₒ = 12 / 2 = 6 V.
Assumptions and limits
- Ideal sources and linear resistors with positive values, all in base SI units.
- The circuit is exactly as described: no extra loads, and instruments that draw no current.
Common mistakes
- Forgetting a load across a divider, which lowers the output.
- Using the resistor on the wrong side of the divider or the wrong branch for the current share.
- Mixing kΩ and Ω in one calculation.
Statistics and uncertainty
Resistor values are only known to their tolerance, typically 1 % to 5 %, so a result built from them carries that scatter. Ratios such as dividers and bridges are less sensitive to a common drift than to differences between the resistors.
Where it is used
- Sensor interfaces, bias networks, bridge circuits and mixers.
- Reducing a network to simpler series and parallel parts.
Maths you need
- Ohm’s law: V = I R
- Kirchhoff’s current law: currents into a node add to zero
- Series and parallel resistors: R₁ + R₂ and R₁R₂/(R₁ + R₂)