A dependent (frequently searched and misspelled as 'dependant') current source is an active circuit element that delivers a specific current determined by a voltage or current measured elsewhere in the same circuit, rather than a fixed internal value. Unlike a battery or an independent current supply, its output is entirely enslaved to a controlling variable. This changes everything about how you analyze the circuit: you can no longer rely on simple series/parallel reductions or basic Ohm’s law sweeps. Instead, the source introduces a constraint equation that forces you to use modified nodal analysis, supermesh, or supernode techniques to solve the network. People most commonly confuse it with an independent current source (which outputs a fixed value regardless of the rest of the circuit) or a dependent voltage source (which dictates voltage, not current).

The Core Concept: What It Changes in Real Circuit Analysis

When you drop an independent 5A source into a loop, Kirchhoff's Current Law (KCL) at that node is instantly satisfied for that branch. A dependent source breaks this simplicity. Because its output is a variable—say, $3 \times I_x$ or $0.5 \times V_y$—you now have an unknown current that is mathematically chained to another unknown in the circuit.

The Analysis Shift: In SPICE simulators and hand calculations, this requires adding a constraint equation to your system of linear equations. If you are doing mesh analysis and a current-controlled dependent source sits on the boundary of two meshes, you must form a supermesh, bypassing the source for the KVL loop but enforcing the dependency via KCL at the nodes.

To visualize this, think of a water pump whose flow rate isn't set by a dial on the pump itself, but by a sensor measuring the water pressure in a completely different pipe across the facility. You cannot calculate the flow of the pump until you first calculate the pressure in the remote pipe.

Worked Numeric Example: VCCS in a MOSFET Small-Signal Model

The most common place you will calculate a dependent current source by hand is in the small-signal hybrid-pi model of a MOSFET or BJT. Let's look at a Voltage-Controlled Current Source (VCCS) representing the drain current of an NMOS transistor in a common-source amplifier.

The Setup

  • Transconductance ($g_m$): $4 \text{ mA/V}$
  • Gate-to-source small-signal voltage ($v_{gs}$): $0.25 \text{ V}$
  • Drain resistor ($R_D$): $2 \text{ k}\Omega$
  • Supply voltage ($V_{DD}$): $12 \text{ V}$ (DC, treated as AC ground for small-signal analysis)

The Math

The dependent current source is defined by the equation $i_d = g_m \times v_{gs}$.

$i_d = 4 \text{ mA/V} \times 0.25 \text{ V} = 1 \text{ mA}$.

This 1 mA current flows down through the dependent source and up through the drain resistor $R_D$ (in conventional small-signal AC ground terms). The AC voltage drop across $R_D$ is:

$v_{rd} = i_d \times R_D = 1 \text{ mA} \times 2 \text{ k}\Omega = 2 \text{ V}$.

Because the current flows from the AC ground (where $V_{DD}$ is tied) down to the drain node, the output voltage at the drain is inverted: $v_{out} = -2 \text{ V}$.

Constraint Check: Notice how we couldn't solve for $v_{out}$ until we first solved the input node for $v_{gs}$. The output is strictly dependent on the input state. If $v_{gs}$ drops to 0V, the dependent source outputs 0mA, regardless of the 12V supply sitting above $R_D$.

Where You Meet This in Practice (Physical Implementations)

In theoretical textbooks, a dependent source is a diamond-shaped symbol. On your workbench, you build them using specific topologies and integrated circuits. Here is where the theory meets physical silicon:

  • Operational Transconductance Amplifiers (OTAs): ICs like the LM13700 or CA3080 are literal physical VCCS devices. You feed a differential voltage into the inputs, and the output pin sources or sinks a current proportional to that voltage, scaled by an external bias current ($I_{ABC}$). These are the backbone of analog synthesizers and voltage-controlled amplifiers (VCAs).
  • Current Mirrors: Using matched discrete transistors (like a pair of 2N3906 PNPs), you force a reference current through one leg, and the second leg acts as a Current-Controlled Current Source (CCCS), mirroring the exact same current to a high-impedance load. To combat the Early effect and improve output impedance, designers use a Wilson current mirror topology.
  • The Howland Current Pump: An op-amp circuit that converts an input voltage into a precise, load-independent output current. It effectively creates a high-power VCCS, but it requires a tightly matched resistor network (typically four 10kΩ 0.1% resistors) to achieve the high output impedance required of an ideal dependent source.

Decision Tree: Choosing Your Physical Implementation

When you need to generate a controlled current in a physical build, use this decision matrix to select the right topology and part number.

Application Requirement Topology / Implementation Concrete Part Pick
Audio VCA, analog synth filters, low-frequency current control Dual OTA (Voltage-Controlled) TI LM13700 (or NJM13700)
Precision DC biasing for RF stages or differential pairs Wilson Current Mirror (Current-Controlled) Matched 2N3906 (PNP) or 2N3904 (NPN) pair
High-speed, high-bandwidth signal routing GaAs FET Current Source Mini-Circuits GALI-84+ (as active bias)
General lab testing, driving moderate loads (up to 50mA) with high precision Howland Current Pump (Voltage-Controlled) TI OPA445 (High voltage op-amp)
Default Recommendation: If you are building a general-purpose lab tool or an automated test fixture and need a voltage-controlled current source that can drive moderate loads with high precision, build a Howland Current Pump using a Texas Instruments OPA445. It offers the best balance of bandwidth, output compliance voltage (up to ±40V), and ease of tuning. Just ensure you use 0.1% tolerance resistors for the feedback network; a 1% mismatch will drop your output impedance and ruin the ideal dependent source behavior.

Common Confusions and FAQ

What is the difference between a dependent and independent source?

An independent source (like a 9V battery or a 5A lab power supply in constant current mode) maintains its output regardless of what the rest of the circuit is doing. A dependent source's output is a mathematical slave to another node's voltage or current. If the controlling variable drops to zero, the dependent source drops to zero.

Why do some textbooks spell it 'dependant'?

'Dependant' is an archaic or British-English variant spelling of the noun form, while 'dependent' is the standard adjective and the universally accepted spelling in modern electrical engineering and SPICE documentation. Both refer to the exact same diamond-shaped circuit symbol.

Can a dependent source deliver power?

Yes. In small-signal models (like the MOSFET example above), the dependent source represents the energy conversion happening inside the transistor. It is mathematically capable of delivering power to the load resistor, which is how amplifiers achieve voltage gain. For deeper insights into small-signal modeling and active devices, refer to the MIT OpenCourseWare Circuits and Electronics materials on incremental analysis.

How do I model this in LTspice?

LTspice uses arbitrary behavioral sources. For a VCCS, place a 'G' component (voltage-dependent current source). For a CCCS, place an 'F' component (current-dependent current source). You define the gain and the controlling nodes in the component properties dialog.