# Circuit Theory/Dependent sources

!The four types of dependent sources \... the control variable is on
the left, the output variable is on the
right{width="500"}

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~x~* across the test
current source determines the impedance seen at that node as *R = V~x~ /
I~x~*.

## References


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