Circuit Theory/Dependent sources

The four types of dependent sources ... the control variable is on the left, the output variable is on the right

Electronic amplifiers use two variables: current and voltage. Either can be used as input, and either as output leading to four types of amplifiers. In idealized form they are represented by each of the four types of dependent source used in linear analysis, as shown in the figure, namely:

Input Output Dependent source Amplifier type
I I current controlled current source CCCS current amplifier
I V current controlled voltage source CCVS transresistance amplifier
V I voltage controlled current source VCCS transconductance amplifier
V V voltage controlled voltage source VCVS voltage amplifier

Each type of amplifier in its ideal form has an ideal input and output resistance that is the same as that of the corresponding dependent source:[1]

Amplifier type Dependent source Input impedance Output impedance
Current CCCS 0
Transresistance CCVS 0 0
Transconductance VCCS
Voltage VCVS 0

In practice the ideal impedances are only approximated. For any particular circuit, a small-signal analysis often is used to find the impedance actually achieved. A small-signal AC test current Ix is applied to the input or output node, all external sources are set to zero, and the corresponding alternating voltage Vx across the test current source determines the impedance seen at that node as R = Vx / Ix.

  1. It is a curiosity to note that this table is a "Zwicky box"; in particular, it encompasses all possibilities.