VCVS (Dependent Voltage Source) Symbol
Definition: The VCVS symbol represents a voltage-controlled voltage source — a dependent source whose output voltage equals a dimensionless gain μ (V/V) times a controlling voltage measured elsewhere in the circuit — drawn per IEEE 315 / ANSI Y32.2 convention as a DIAMOND containing + and − marks, the diamond shape distinguishing dependent sources from the circles used for independent sources.
Also known as: voltage-controlled voltage source, dependent voltage source, controlled voltage source, E source, E element, ideal voltage amplifier.
What the VCVS (Dependent Voltage Source) symbol means
The VCVS symbol denotes an idealized circuit element with two ports: a controlling port (Ctrl+, Ctrl−) that senses a voltage vx somewhere in the circuit while drawing zero current, and an output port (+, −) that imposes a voltage vout = μ·vx regardless of what current the load demands. The gain μ (often written Av or E) is dimensionless, expressed in volts per volt (V/V). Because the output is a voltage source, the ideal VCVS has zero output impedance; because the control port draws no current, it has infinite input impedance — which is exactly the idealization of a perfect voltage amplifier.
Dependent sources are the modeling backbone of linear electronics: an op-amp with open-loop gain A is a VCVS of gain 100,000+; every small-signal amplifier stage reduces to controlled sources plus resistors. In SPICE the VCVS is the E element (the four dependent sources carry the letters E, G, H, F for VCVS, VCCS, CCVS, CCCS respectively), written as E1 out+ out− ctrl+ ctrl− gain. Unlike an independent source, a VCVS produces nothing on its own — its output exists only insofar as the controlling voltage exists.
How to identify the VCVS (Dependent Voltage Source) symbol
Shape is everything: a DIAMOND (rhombus) marks a dependent source, while a circle marks an independent source. Inside the VCVS diamond are + and − signs indicating the output voltage polarity, exactly as inside an independent voltage source's circle. The controlling connection is drawn either as a separate pair of terminals (Ctrl+, Ctrl−) — often on the left, sometimes only labeled with the controlling voltage vx — or simply annotated with an expression like 'μvx' next to the diamond.
The diamond-with-± must be read against its three siblings: a diamond with an internal arrow is a dependent CURRENT source (VCCS or CCCS); the difference between voltage-controlled and current-controlled versions is only the controlling quantity named in the gain expression (vx versus ix). The diamond convention comes from IEEE 315 / ANSI usage and dominates textbooks and SPICE documentation worldwide; classic IEC 60617 drawings did not define a separate diamond and European texts sometimes show controlled sources as circles or squares with the dependency written beside them, so the label is the ultimate arbiter.
Function in a circuit
In analysis, a VCVS enforces one equation: vout = μ·vx. During nodal or mesh analysis it is treated like a voltage source whose value happens to reference another circuit variable, which typically introduces a constraint equation (or a supernode) tying the output nodes to the controlling nodes. The control port is an open circuit — it merely observes vx.
Practically, the VCVS is how ideal amplifiers enter a schematic or a simulation. An op-amp macro-model is a VCVS with gain 10^5–10^7 from the differential input; a unity-gain buffer is a VCVS with μ = 1; an ideal transformer can even be built in SPICE from a VCVS plus a CCCS. Because the ideal element has infinite input impedance and zero output impedance, real amplifier limitations (finite Rin, nonzero Rout, bandwidth) are modeled by adding resistors and capacitors around the E element.
Standards: IEC vs ANSI
| IEC 60617 | IEC 60617 does not define a distinct diamond symbol for dependent sources; European/IEC-style schematics historically draw controlled sources as circles or squares annotated with the controlling relationship (e.g. μ·vx). Modern international textbooks nonetheless overwhelmingly adopt the diamond. |
|---|---|
| ANSI/IEEE 315 | IEEE 315 / ANSI Y32.2 practice draws dependent (controlled) sources as diamonds — ± inside for voltage sources, an arrow inside for current sources — reserving circles for independent sources. SPICE follows the same taxonomy with letter prefixes E (VCVS), G (VCCS), H (CCVS), F (CCCS). |
| Key difference | The practical difference is diamond versus circle: American/IEEE and textbook convention uses the diamond to signal 'this source's value depends on another circuit variable', while strict IEC drawings may keep a circular source symbol and rely on the value annotation. When reading any schematic, the dependency expression (μvx) — not just the shape — confirms a controlled source. |
Terminals / pins
| Pin | Name |
|---|---|
| pos | + |
| neg | - |
| cp | Ctrl+ |
| cn | Ctrl- |
Typical values
The VCVS gain μ is dimensionless (V/V). Typical modeling values: op-amp open-loop gain 10^5–10^7 V/V (100–140 dB); unity-gain buffer μ = 1; instrumentation-amplifier stages μ = 1–1000; ideal level shifters and attenuators use fractional gains such as 0.5. Ideal element assumptions: input resistance infinite, output resistance zero, unlimited bandwidth and output swing — all deliberately unrealistic, refined with added R and C when realism matters. In SPICE: E1 n+ n− nc+ nc− 1e5 declares a VCVS of gain 100,000.
Where the VCVS (Dependent Voltage Source) symbol is used
- Op-amp macro-models in SPICE, where the open-loop differential gain is a VCVS of 10^5 V/V or more
- Textbook small-signal analysis, representing the voltage-amplification of amplifier stages
- Behavioral simulation blocks — summers, level shifters, ideal buffers — built from E elements
- Controlled-source equivalent circuits for two-port networks described by g- or h-parameters
- Ideal transformer and gyrator constructions in simulators that lack native elements
- Feedback-theory examples, where the forward amplifier of a series-shunt feedback pair is a VCVS
Example
Modeling an op-amp in SPICE, a VCVS named E1 has its Ctrl+ and Ctrl− pins across the op-amp's non-inverting and inverting inputs and its + and − output pins driving the output node against ground, with gain 200,000: the card E1 out 0 inp inn 200k makes vout = 200,000 × (v(inp) − v(inn)), and wrapping external feedback resistors around it reproduces closed-loop amplifier behavior almost exactly.
Key facts
- Diamond = dependent, circle = independent: the diamond shape is the universal flag that the source value is controlled by another circuit variable.
- The VCVS equation is vout = μ·vx with μ a dimensionless gain in V/V; the ± inside the diamond gives the output polarity.
- SPICE letter conventions: E = VCVS, G = VCCS, H = CCVS, F = CCCS; the VCVS card is E<name> out+ out− ctrl+ ctrl− gain.
- The ideal VCVS has infinite input impedance (control port draws zero current) and zero output impedance (output voltage independent of load current).
- An op-amp is, to first order, a VCVS with gain 10^5–10^7 from its differential input — the most common use of the element.
- A dependent source is NOT deactivated when finding Thevenin/Norton equivalents by source-killing: only independent sources are zeroed, and dependent sources force use of the test-source method.
- Dependent sources can deliver net energy to a circuit (they model active devices), unlike passive elements.
- The four dependent sources form a complete set: voltage or current output, controlled by voltage or current — VCVS, VCCS, CCVS, CCCS.
Frequently asked questions
Why is a VCVS drawn as a diamond instead of a circle?
The diamond is the standard flag (from IEEE 315 / ANSI practice, adopted by virtually all textbooks and SPICE documentation) that the source is DEPENDENT — its value is set by a voltage or current elsewhere in the circuit. Circles are reserved for independent sources whose value is fixed. Seeing a diamond tells you immediately that killing independent sources will not remove this element and that its value expression references another circuit variable.
What does the E in 'E source' stand for?
It is the SPICE element letter for a VCVS. SPICE assigns one letter to each dependent source type: E for the voltage-controlled voltage source, G for the voltage-controlled current source, H for the current-controlled voltage source, and F for the current-controlled current source. A netlist line beginning with E, such as E1 out 0 inp inn 1e5, declares a VCVS.
What are the units of VCVS gain?
Volts per volt (V/V) — a dimensionless ratio, since both the controlled quantity and the controlling quantity are voltages. This distinguishes it from the other dependent sources: VCCS gain is transconductance in siemens (A/V), CCVS gain is transresistance in ohms (V/A), and CCCS gain is a dimensionless current ratio (A/A).
Do I set a VCVS to zero when finding a Thevenin equivalent?
No. Source-killing (shorting voltage sources, opening current sources) applies only to INDEPENDENT sources. Dependent sources like the VCVS stay live because they model the active behavior of transistors and op-amps — removing them would delete the amplifier itself. When dependent sources are present, find Thevenin resistance by applying a test source at the port and computing Rth = vtest/itest, or by Rth = Voc/Isc.
How does a VCVS model an op-amp?
The op-amp's core action — output voltage equals open-loop gain times differential input voltage — is exactly the VCVS equation vout = A(v+ − v−). A minimal macro-model is a single E element with gain 10^5 or more between the input pins and the output. More refined models add input resistance, output resistance, and an RC pole for gain-bandwidth, but the VCVS remains the amplifying heart of the model.
What is the difference between VCVS and VCCS?
Both are controlled by a voltage, but the VCVS outputs a VOLTAGE (vout = μ·vx, gain in V/V, diamond with ± inside, zero output impedance) while the VCCS outputs a CURRENT (iout = gm·vx, gain in siemens, diamond with an arrow inside, infinite output impedance). A VCVS models an ideal voltage amplifier such as an op-amp; a VCCS models a transconductance device such as a FET's small-signal channel or an OTA.
Related symbols
- Amplifier Block symbol
- Current Source symbol
- Differential Amplifier symbol
- Op-Amp symbol
- Voltage Source (AC) symbol
- Voltage Source (DC) symbol
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