Voltage to Current Converter

A voltage-to-current converter produces an output current proportional to an input voltage, regardless of the load resistance. It drives LEDs, deflection coils, and platinum resistance thermometers where a stable current, not a voltage, controls the device.

Core Concept

In the simplest V-I converter, the load sits in the feedback path of an inverting op-amp. The virtual ground keeps the inverting input at 0V. The current through R1 must equal the current through the load, so IL = Vin/R1. This current is set entirely by Vin and R1, not by the load impedance. This is the defining property of a transconductance amplifier.

The drawback of this topology is that the load must float (neither terminal is grounded). Most practical loads (motors, LEDs) have one terminal grounded. For grounded loads, the Howland current pump is used. It employs four equal resistors and both input terminals of the op-amp to achieve load-independent current with one end of the load tied to ground.

The LM741 works for audio and DC applications. For precision current sources driving platinum resistance thermometers (PT100), a low-offset op-amp such as the OP07 is used because any input offset error directly adds to the current error multiplied by 1/R.

Key Equations

Load current for the floating-load topology:

IL = Vin / R1

This is independent of the load resistance RL. The transconductance (Gm) of this converter is:

Gm = IL / Vin = 1 / R1 (in siemens, S or A/V)

For the Howland current pump with sense resistor Rs and all other resistors equal to R:

IL = Vin / Rs

Maximum output current is limited by the op-amp output current capability. For LM741, this is approximately 25 mA. The compliance voltage (maximum voltage across the load) is limited by the supply:

VL_max = VCC - Vout_sat - IL * R1

Given:
  V-I converter, floating load topology
  R1 = 10 kΩ = 10,000 Ω
  Vin = 2V
  RL = 500 Ω (LED string)
  Supply = ±15V, LM741

Why this formula:
  IL = Vin / R1 (virtual ground forces all Vin current through RL)

Formula:
  IL = Vin / R1

Substitution:
  IL = 2 / 10,000

Calculation:
  IL = 0.0002 A = 0.2 mA

  Verify compliance:
  Voltage across RL = IL * RL = 0.2 mA * 500 = 0.1V
  This is well within the ±15V supply range.

  Transconductance Gm = 1/R1 = 1/10,000 = 0.1 mA/V

Final Answer:
  IL = 0.2 mA, Gm = 0.1 mA/V
  Current is independent of RL.

Exam Tip: GATE asks to identify whether a given circuit is a V-I or I-V converter, and to derive the transfer function. For V-I, current through the feedback element equals Vin/R (virtual ground argument). The load must be in the feedback path. For grounded loads, expect a Howland pump. Also note: transconductance Gm = 1/R1 is in A/V or mA/V. Do not write Gm in ohms.

Key Properties

• IL = Vin/R1 is constant regardless of load resistance RL (within compliance limits).
• Transconductance Gm = 1/R1 in siemens (A/V or mA/V).
• Maximum output current from LM741 is about 25 mA. Exceed this and the output voltage clips.
• Floating-load topology: neither load terminal is grounded.
• Howland current pump allows grounded load using four matched resistors and both op-amp inputs.
• OP07 is preferred for precision DC current sources due to its 75 µV maximum input offset voltage.
• Used in LED drivers, galvanometers, motor speed control, and precision resistance measurement.

Quick Revision

• Output is current, input is voltage. IL = Vin/R1.
• Load sits in op-amp feedback path.
• IL is independent of RL (ideal current source behaviour).
• Gm = 1/R1 in A/V.
• Floating-load: simple circuit. Grounded load: use Howland pump.
• Op-amp output current limit (~25 mA for LM741) sets maximum IL.
• OP07 preferred for precision current sources.
• Exam trap: Students write Vout/RL for the output current, treating the circuit as a voltage source with load. The whole point is that the op-amp forces a constant current regardless of RL. The virtual ground argument gives IL = Vin/R1, and RL is irrelevant.