A voltage dependent current source (VDCS) is an active circuit element that delivers an output current strictly proportional to a controlling voltage measured across two other nodes in the same network. In practical circuit design, this element fundamentally changes signal processing by converting a high-impedance voltage input into a proportional current output, providing the transconductance gain necessary to amplify weak microphone signals, drive capacitive loads, or control analog synthesizer filters. Rather than generating power from nothing, the VDCS acts as a mathematical and physical valve, using a small voltage to modulate a larger current drawn from an independent DC power supply.
The Core Math and a Worked Numeric Example
The behavior of a VDCS is defined by a single proportionality constant known as transconductance, denoted as gm. Transconductance is measured in Siemens (S), which is equivalent to Amperes per Volt (A/V). In older literature and vacuum tube datasheets, you will frequently see this expressed in micromhos (μmho), where 1000 μmho equals 1 milliSiemen (mS).
The governing equation is straightforward:
Iout = gm × Vcontrol
Where Iout is the generated current, gm is the transconductance, and Vcontrol is the voltage measured across the controlling nodes.
Suppose you are biasing a standard 2N7000 N-channel MOSFET in its saturation region to build a common-source audio preamplifier. Based on your DC bias point, the device exhibits a transconductance (gm) of 120 mA/V (or 0.12 S).
An AC audio signal from an electret microphone introduces a gate-to-source controlling voltage (vgs) of 25 mV (0.025 V) peak-to-peak.
Calculation:
id = 0.12 A/V × 0.025 V = 0.003 A (or 3 mA peak-to-peak).
The VDCS model tells us the MOSFET will output a 3 mA AC current. If this current flows through a 2.2 kΩ drain resistor, it develops an output voltage of 6.6 V peak-to-peak (3 mA × 2200 Ω), achieving massive voltage gain from a tiny input signal.
Transconductance Profiles of Real-World Devices
While the VDCS is often introduced as an abstract diamond-shaped symbol in textbook nodal analysis, it is the exact mathematical model used to describe the gain mechanism of almost every active amplifying component. The table below compares the transconductance characteristics of four distinct amplifying devices you will encounter on the bench.
| Device / Type | Typical gm (Transconductance) | Controlling Voltage Nodes | Max Linear Output Current | Primary Application |
|---|---|---|---|---|
| 2N7000 (N-Channel MOSFET) | ~120 mA/V | Gate-to-Source (VGS) | ~200 mA (pulsed) | Low-power switching, small-signal RF |
| BC547B (NPN BJT) | ~40 mA/V (at IC=1mA) | Base-to-Emitter (VBE) | ~100 mA | General purpose audio amplification |
| LM13700 (Dual OTA IC) | Variable: 19.2 × IABC | Differential Inputs (VIN+, VIN-) | ±2 mA (linear range) | Analog synths, voltage-controlled filters |
| 12AX7 (Dual Triode Tube) | ~1.6 mA/V (1600 μmho) | Grid-to-Cathode (VGK) | ~2 mA per section | Guitar amplifier preamp stages |
Notice the stark contrast in transconductance scaling. A modern MOSFET like the 2N7000 offers high gm with virtually zero input current draw at the gate, making it an excellent voltage-controlled current source. Conversely, the 12AX7 vacuum tube has a very low gm by modern standards, which is why tube preamps require multiple gain stages and high-voltage power supplies to achieve usable output swings. The Texas Instruments LM13700 datasheet highlights a unique feature of Operational Transconductance Amplifiers (OTAs): their gm is not fixed by physics alone, but can be programmed in real-time via an external amplifier bias current (IABC).
Where You Meet This in Practice
If you only build circuits using discrete resistors and capacitors, you might never draw a VDCS diamond on a schematic. However, you interact with the physics of the VDCS constantly in three specific areas:
1. SPICE Simulation and Small-Signal Models
When you run an AC analysis or operating point sweep in LTspice or KiCad, the software does not simulate the physical semiconductor physics of a transistor. Instead, it replaces your MOSFET or BJT with its hybrid-pi small-signal model. The core of this model is a VDCS. If your simulation converges but the gain is wrong, it is almost always because the simulator calculated a DC bias point that resulted in a lower gm than you expected.
2. Analog Synthesizers and Voltage-Controlled Amplifiers (VCAs)
In modular synthesis, control voltage (CV) dictates the behavior of the audio path. Chips like the LM13700 or the SSI2164 act as explicit, macro-scale VDCS elements. A 1V/octave control signal is fed into the programming pin, altering the transconductance of the internal differential pair. This varying current is then mirrored and pushed into an audio signal path to create tremolo, envelopes, and amplitude modulation.
3. Active Loads in Integrated Circuit Design
Inside operational amplifier ICs like the LM358 or TL072, silicon real estate is too precious to waste on large physical resistors. IC designers use current mirrors—circuits built entirely on VDCS principles—to create "active loads." These present an extremely high dynamic impedance to the gain stage, allowing the op-amp to achieve open-loop gains of 100,000+ without requiring massive voltage drops across physical resistors.
Common Confusions and Troubleshooting
Because dependent sources are heavily emphasized in university circuit theory but rarely labeled as such on commercial schematics, several misconceptions frequently trip up hobbyists and students.
What do people commonly confuse the VDCS with?
- Independent Current Sources: An independent source (like an LM334 constant current diode) outputs a fixed current regardless of the voltage across it or the rest of the circuit. A VDCS output will fluctuate wildly if the controlling voltage changes.
- Voltage Dependent Voltage Source (VDVS): A VDVS outputs a voltage proportional to an input voltage. An ideal op-amp in a non-inverting configuration is modeled as a VDVS. A VDCS outputs current, requiring a load resistor to develop a usable voltage.
- Current Dependent Voltage Source (CDVS / Transimpedance): Often seen in photodiode amplifiers, a CDVS converts an input current into a voltage. The VDCS is the exact mathematical inverse (transconductance), converting voltage into current.
If you breadboard a common-emitter BJT amplifier and the AC voltage gain is significantly lower than your hand calculations predicted, check your DC biasing. The gm of a BJT is directly proportional to its collector current (gm = IC / VT, where VT is ~26mV at room temp). If your biasing resistors are off and IC is only 0.1mA instead of 1mA, your VDCS transconductance drops by a factor of 10, killing your AC gain. Always verify the DC operating point with a multimeter before injecting an AC signal.
Frequently Asked Questions
Q: Can I build a discrete VDCS without a specialized OTA chip?
A: Yes. A simple JFET (like the 2N5457) operated in its ohmic/triode region can act as a voltage-dependent resistor, while a standard MOSFET in saturation acts as a VDCS. For better linearity, a discrete differential pair (two matched transistors sharing a tail current source) functions as a highly effective VDCS, which is exactly how the internal stages of the LM13700 are constructed.
Q: Why does the VDCS symbol have a diamond shape in schematics?
A: The diamond shape is an IEEE standard convention used to instantly differentiate dependent (controlled) sources from independent sources, which are drawn as circles. If you see a diamond with an arrow inside, it is a dependent current source; if it has a plus/minus polarity inside, it is a dependent voltage source.
