# How is a current controlled voltage source different from a resistor?

A current controlled voltage source produces a voltage that is linearly proportional to a current. A resistor has the same behavior. And the gain for a CCVS is measured in ohms, which is the same unit that measures a resistor. So what is the difference between them? Is a resistor just a kind of CCVS (and I guess also a VCCS) and if so, how does it differ from an ideal CCVS?

• One nitpick for better understanding - the relation between control current and produced voltage does not have to be linearly proportional as your ? states, but linearity is often preferred in applications and models of course. – EwokNightmares Apr 22 '14 at 20:43

A resistor is a passive component. A current controlled voltage source is an active component i.e. the voltage will remain proportional to the current controlling it regardless of what else is connected to the source (ideally).

• Few more differences. Unlike real resistors CCVS may have negative resistance. Noise characteristics would also be different -- regular resistors have inherent Johnson (AKA thermal) noise which CCVS may not replicate exactly. – ArtemB Apr 22 '14 at 22:41

A nice graphic answering one half of the question

I don't remember the source of this, since I have stored on my HD

• That reminds me of XKCD (except for the drawing style) - at least in terms of brilliance! – Volker Siegel Apr 23 '14 at 9:32

A resistor produces a voltage that is linearly proportional to the current that flows into it. Moreover the polarity of the voltage is fixed too, you can't have current flowing in a resistor from A to B and have $V_B>V_A$.

A CCVS can be controlled by any current in the network, possibly the one that flows through it but again, this time you get the freedom to choose the voltage polarity.

The following two ideal circuit elements have identical terminal characteristics and are thus indistinguishable:

simulate this circuit – Schematic created using CircuitLab

Thus, if the controlling variable of a CCVS is the current through the CCVS, the CCVS is indistinguishable from a resistor where the gain of the CCVS is the resistance.

If the controlling variable of a CCVS is the current through another circuit element, the gain is the transresistance.

A circuit that is called voltage "SOURCE" must be able to deliver the output to any connected load - otherwise it is not really a "source". Hence, it must have a very small source resistance (ideal: zero). This is the main feature of an active CCVS.

A resistor controls current in same branch. The dependent sources show interdependence of different branches. i.e current through one branch controls voltage through some other branch or current through one branch controls current through some other branch. So, dependent sources can be generalized as the concept of resistance but they are not same as resistance.