# 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?

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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 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).

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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 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

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That reminds me of XKCD (except for the drawing style) - at least in terms of brilliance! –  Volker Siegel Apr 23 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.

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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.

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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.

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