The voltage across a current source is the exact potential difference the source must dynamically generate to push its designated constant current through the external load resistance. Unlike a battery or bench power supply set to voltage mode, an ideal current source does not have a fixed output voltage; instead, the external circuit dictates the required voltage, while the source dictates the current. If you connect a 10 mA ideal current source to a 100 Ω resistor, the voltage across the source's terminals will be exactly 1.0 V. Understanding this relationship is critical for designing LED drivers, sensor loops, and battery charging circuits.
The Core Principle: Load Dictates the Potential
In a standard voltage source circuit (like a 12V battery connected to a resistor), the source forces a fixed potential, and the load draws whatever current Ohm's Law dictates. A current source operates in the exact inverse manner. It forces a fixed current (I = constant), and the voltage across its terminals adjusts to whatever value is necessary to maintain that current through the total resistance of the external loop.
What this changes in a real circuit is the power dissipation profile. Because V = I × R_load, if the load resistance increases, the voltage across the current source must increase proportionally. This leads to the most common point of confusion for beginners: assuming a current source has a fixed voltage rating. It does not. Instead, real-world current sources have a compliance voltage range—the minimum and maximum voltage limits within which the internal transistors or switching ICs can physically operate before they saturate or break down.
| Load Resistance (Ω) | Required Voltage (V) | Load Power Dissipation (mW) | Source Compliance Status (Max 30V) |
|---|---|---|---|
| 10 Ω | 0.20 V | 4.0 mW | Active (Above minimum headroom) |
| 100 Ω | 2.00 V | 40.0 mW | Active (Nominal operating range) |
| 500 Ω | 10.00 V | 200.0 mW | Active (Nominal operating range) |
| 1,000 Ω | 20.00 V | 400.0 mW | Active (Approaching upper limit) |
| 2,000 Ω | 40.00 V | 800.0 mW | Failed (Exceeds 30V compliance rail) |
Table 1: As demonstrated above, the source attempts to generate 40V for the 2kΩ load, but if its internal supply rail or transistor breakdown voltage is limited to 30V, it can no longer maintain the 20 mA setpoint. The current will drop, and the device effectively becomes a 30V voltage source. For a deeper dive into the internal topology of these limits, refer to the Electronics Tutorials guide on current sources.
Worked Numeric Example: LM317 LED Driver Circuit
Let us look at a practical bench scenario: driving a series string of high-power LEDs using an LM317 linear regulator configured as a constant current source. This is a classic topology for prototyping lighting circuits.
- Current Source IC: LM317 (configured with a sense resistor).
- Target Current (I): 350 mA.
- Load: 3x Cree XP-G3 LEDs in series.
- LED Forward Voltage (Vf): 2.9V each at 350mA (Total Vf = 8.7V).
- Input Supply: 12.0V DC bench supply.
- Assumptions: Ambient temperature 25°C, nominal LED Vf from datasheet, ideal wiring with 0Ω resistance.
Step 1: Calculate the sense resistor.
The LM317 maintains a 1.25V reference between its OUT and ADJ pins. To get 350 mA, the sense resistor (R_sense) must be:
R_sense = 1.25V / 0.35A = 3.57 Ω (We will use a standard 3.6 Ω 1W resistor, yielding an actual current of ~347 mA, but we will use 350 mA for clean math).
Step 2: Calculate the total voltage required by the external load.
The external load consists of the LEDs and the sense resistor.
Voltage across LEDs = 3 × 2.9V = 8.7V.
Voltage across sense resistor = 1.25V.
Total Load Voltage = 8.7V + 1.25V = 9.95V.
Step 3: Determine the voltage across the current source.
The 'current source' in this context is the LM317 itself (from its OUT pin to the ground return). Because the load requires exactly 9.95V to pass 350 mA, the voltage across the current source terminals is exactly 9.95V.
Step 4: Verify compliance and headroom.
The input supply is 12.0V. The load takes 9.95V. The remaining 2.05V is dropped across the internal pass transistor of the LM317 (from IN to OUT). The LM317 requires a minimum dropout voltage of about 2.0V to 2.5V to maintain regulation. In this real-world scenario, we are right on the edge of the compliance limit. If the LEDs heat up and their Vf drops slightly, the circuit will regulate perfectly. If the bench supply sags to 11.5V, the LM317 will drop out of regulation, and the current will fall below 350 mA. For more on linear regulator dropout characteristics, consult the Texas Instruments LM317 datasheet.
Where You Meet This in Practice
Understanding how voltage behaves across a current source is not just academic; it dictates component selection in several major electrical and electronic domains.
- Industrial 4-20mA Sensor Loops: A pressure transmitter acts as a current source, outputting 4 to 20 mA based on the measured process variable. The PLC receives this via a 250 Ω shunt resistor. At 20 mA, the voltage across the shunt is 5V. However, the transmitter itself requires a minimum 'compliance voltage' (often 12V to 36V) across its own terminals to power its internal op-amps and microcontrollers. If the loop wire resistance and shunt resistor drop too much voltage, the voltage remaining across the transmitter falls below its minimum compliance threshold, and the loop fails.
- Lithium Battery Charging (CC/CV Profile): When charging a LiFePO4 or Li-ion cell, the charger acts as a current source during the Constant Current (CC) phase. If you set a 2A charge rate, the voltage across the charger's output terminals starts low (e.g., 3.2V for a depleted cell) and steadily rises as the battery's State of Charge (SoC) increases. The current remains 2A, but the voltage across the source climbs until it hits the battery's absorption voltage (e.g., 4.2V), at which point the charger switches to Constant Voltage (CV) mode.
- Switching LED Drivers (Buck/Boost): ICs like the PT4115 or AL8860 are constant current buck converters. They rapidly switch a MOSFET to maintain a set average current through the LED string. The voltage across the IC's output nodes is strictly defined by the LED string's forward voltage. If you connect a 12V LED string to a driver powered by a 12V battery, the driver cannot boost the voltage; it lacks the compliance headroom, resulting in flickering or dim output.
Common Confusions and Troubleshooting Limits
Why is my current source outputting less current than I set?
You have likely exceeded the maximum compliance voltage. If your load resistance is too high, the required voltage (V = I × R) exceeds the physical supply rail or the breakdown voltage of the source's internal transistors. The source saturates, the voltage caps out at its maximum limit, and the current drops. Fix: Increase the supply voltage to the current source circuit, or reduce the load resistance.
Can a current source have a voltage of zero?
In an ideal theoretical model, yes—if the load resistance is zero (a short circuit), the voltage across the source is zero. In practice, real current sources require a minimum compliance voltage (often 0.5V to 2V) to keep their internal biasing transistors in the active region. If you short the output of an LM317 current source, it will still drop about 2V across its internal junctions, dissipating significant heat.
What is the difference between a current source and a current sink?
Electrically, they perform the same function: regulating current. The difference is purely topological. A current source is placed on the high-side (between the positive supply and the load), pushing current into the load. A current sink is placed on the low-side (between the load and ground), pulling current out of the load. The voltage across the sink is calculated identically to the source, but referenced to ground rather than the positive rail.
Mastering the voltage across a current source means shifting your mindset from 'voltage drives current' to 'current demands voltage.' Always calculate your total load resistance, multiply by your setpoint current, and verify that the resulting voltage falls squarely within your component's compliance window.
