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A mosfet can be considered as a transconductance amplifier with unity gain frequency gm/(Cgs + Cgd).

The unity gain frequency is defined as the frequency where the current gain is one. What I am confused is why should we care about this frequency? What is so special about it?

Also because mosfet is a transconductance device meaning that it receives an input voltage and gives out a current.

So why do we focus on current gain Iout/Iin instead of Iout/Vin?

Thank you.

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    \$\begingroup\$ Where do you see "focus on current gain Iout/Iin instead of Iout/Vin"? For BJTs we talk about Iout/Iin (beta or hfe). But for MOSFETs, the usual approach is Iout/Vin. If you are seeing something different, give us a link to the source. \$\endgroup\$ – The Photon Oct 25 '16 at 16:07
  • \$\begingroup\$ Here is the link: ittc.ku.edu/~jstiles/412/handouts/… \$\endgroup\$ – anhnha Oct 25 '16 at 16:16
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I suspect it's because "unity" means unity, not some value with units attached. So we can talk about unity current gain or unity voltage gain independent of any choice of unit system. But if we say a transimpedance is "unity" that depends on our rather arbitrary choice of definition of the amp and volt.

And we can't talk about the voltage gain of a MOSFET in isolation, because (at least in the common-source configuration) determined partly by external components.

So the author chose to find the unity current gain frequency because that's a meaningful value.

why should we care about this frequency?

It's a figure of merit that gives a rough idea of the maximum frequency where the device can provide useful gain in a circuit.

If output impedance is higher than input impedance we could provide voltage gain above this frequency, but usually we want the opposite: low output impedance and high input impedance.

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The MOS transistor is a voltage controlled current source with the emphasis on current source. In order to produce an AC current at the output another AC current at the input is required to drive the gate. The gate is mainly a capacitive load and therefore the current to drive it increases with increasing frequency.

The frequency where the input current equals the output current is called the transition frequency. Above this frequency the transistor needs more current to be driven than it generates, it's useless.

The transition frequency depends on the parasitics and therefore on the technology. It is an important figure-of-merit that increases with smaller technologies.

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The gate of a MOSFET is essentially a capacitor. Remember that if an AC voltage (V) at frequency (f) is put into a capacitor (C) the resulting current (I) is..

I = V * 2 * pi * f * C

Also note that the output of a MOSFET is a current. The unity gain frequency, as you have defined it in your question, is important because it defines the frequency, above which, you must put more AC current into the gat than you will get at the output. It therefore defines the maximum useful frequency for that transistor if you want to get amplification in terms of AC current in vs AC current out.

For example, if you had a MOSFET with a unity gain frequency of 100MHz, then you could not use it to amplify a 1GHz signal.

Also, suppose we have a circuit consisting of multiple MOSFETs of the same type (like most integrated circuits) where the output (drain) of one MOSFET is used to drive the input (gate) of another MOSFET. We will only get signal amplification if we can get more current out of the MOSFET than we put in. So if we were constructing amplifiers or digital circuits out of MOSFETs the unity gain frequency would serve as a maximum limit on the operating frequency of the circuit.

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