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I am having trouble understanding how the different amplifier networks actually do "their magic". In these networks a nullor is a unite that has always 0 voltage over the input and no current through it. The output has infinite power to match the requirement set. The "easiest" version -a voltage to voltage amplifier- I can easily understand: enter image description here

Because the current and voltage over the input of the nullor is 0 the voltage at the output must follow the equation \$V_s = V_{load} \cdot \frac{R_2}{(R_1 + R_2)}\$

However I do not see how this works in other types of amplifiers; say the following standard "voltage-to-current" amplifier setup: enter image description here
What is the gain here? And what is the equality equation to solve?

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  • \$\begingroup\$ This makes no sense without a clear definition of what "nullor" is. \$\endgroup\$ – Andy aka Nov 5 '13 at 15:48
  • \$\begingroup\$ @Andy aka Nullor is a well know theoretical circuit component. \$\endgroup\$ – AndrejaKo Nov 5 '13 at 16:04
  • \$\begingroup\$ @AndrejaKo I recognize the op-amp and transistor implementation but I've never heard of it before!! \$\endgroup\$ – Andy aka Nov 5 '13 at 16:07
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Hmm, never heard of a Nullor before. Go figure. Sometimes it is easier to think of these things in terms of control systems. The amplifier tries to set the two input voltages equal to each other. One input voltage is the current command. The other one is the voltage across R1. So what it tries to do is set the voltage across R1 to the input voltage. The voltage on R1 comes from the current flowing through R1. The amplifier will increase the supply to the load until the voltage across R1 is equal to the input. In this case, Iload = Vin / R1. This circuit is called a transconductace amplifier because the gain is actually Iload / Vin = 1 / R1, which has the units of conductance.

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The definition of a nullor is that it has zero voltage drop at its input, zero current flowing in or out its input and that any voltage/current could be delivered at its output. Knowing this, we can say that the voltage over R1 equals the source voltage, as zero current flows through the internal source resistor. This allows us to find the current through R1 using Ohm's Law. As a nullor should be examined as a two port (with a chain matrix consisting of only zero's), we know that the current flowing into one terminal of the port must equal the current flowing out of the other terminal on the same port, i.e. the current flowing through R1: Vsource/R1 = -Iload. Notice the minus sign due to the definition stated above.

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