Types of controlled sources

A controlled (dependent) source is a source whose voltage or current is not fixed but depends on a voltage or current elsewhere in the circuit. It is drawn as a diamond. Transistors and op-amps are modelled with such sources. There are four types:

1. Voltage controlled voltage source (VCVS)

Output voltage = μ × control voltage: Vo = μ Vx (μ is a dimensionless gain). Model of an op-amp or voltage amplifier.

2. Current controlled voltage source (CCVS)

Output voltage = r × control current: Vo = r Ix (r in ohms, transresistance).

3. Voltage controlled current source (VCCS)

Output current = g × control voltage: Io = g Vx (g in siemens, transconductance). Model of a FET or BJT (gm vbe).

4. Current controlled current source (CCCS)

Output current = β × control current: Io = β Ix (β dimensionless). Model of a BJT: Ic = β Ib.

    VCVS            CCVS            VCCS            CCCS
     /\              /\              /\              /\
    /+ \            /+ \            / ^\            / ^\
   < mu Vx>        < r Ix >        < g Vx>         < b Ix>
    \- /            \- /            \ |/            \ |/
     \/              \/              \/              \/
 voltage out     voltage out     current out     current out
 (+/- marks)     (+/- marks)     (arrow)         (arrow)

A dependent source is drawn with a diamond symbol, while an independent source uses a circle. The polarity (+/−) or arrow shows the reference direction of the output.