# Circuit Theory/Dependent sources

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 *I _{x}* is applied to the input or output node, all external sources are set to zero, and the corresponding alternating voltage

*V*across the test current source determines the impedance seen at that node as

_{x}*R = V*.

_{x}/ I_{x}- ↑ It is a curiosity to note that this table is a "Zwicky box"; in particular, it encompasses all possibilities.