# Transit vs Unity Gain Frequency of a MOSFET

As far as I understand, the unity gain frequency of a transistor is its gain-bandwidth product, and the transit frequency of a transistor is a measure of how fast it is.

I've also read that the transit frequency is the frequency at which the small signal current gain equals 1.

I have the following questions:

• Why does higher transit frequency as per the small signal current imply that the transistor is 'faster'?
• What exactly is the difference between transit and unity gain frequency? Isn't unity gain frequency also the frequency where gain drops to 1?
• Which of these values is usually higher for a MOSFET, or is there no way to tell?

Transit frequency of a MOSFET is the frequency at which the small-signal current gain drops to unity while the source and drain are AC grounded.

Unity gain frequency doesn't mean anything unless you say what kind of gain it is. Voltage or current gain? If it's current gain, then it's the same as the previous definition. Otherwise, we need to add context: specify a complete circuit, and what kind of gain we're talking about.

Let's have a MOSFET:

Let's decide on a bias point (Vds, Id) and set the DC operating point accordingly, via Vds voltage source, and Vgs DC bias.

At this operating point, the tranistor has a transconductance gm and:

$$\ I_d = g_m V_{gs} \$$

In this context, $$\ V_{gs} \$$ does not mean voltage between the pins on the outside of the transistor, but voltage across the gate inside the transistor. Between the two is the internal gate impedance, Rg plus pin inductance etc.

In AC, FETs have gate current due to capacitance, so we can define its current gain.

$$\ "hFE" = \frac{I_d}{I_g} \$$

Due to Cgs and Cgd, $$\ I_g \$$ will increase with frequency. Neglecting Rg, we get:

$$\ I_g = j 2pi f (C_{gd}+C_{gs}) Vgs \$$

Thus:

$$\ "hFE" = \frac{g_m}{2pi f (C_{gd}+C_{gs})} \$$

So we get a definition of "transit frequency":

$$\ f_t = \frac{g_m}{2pi (C_{gd}+C_{gs})} \$$

Note this is a simplification, it neglects internal impedances, inductance, etc, but the idea is that high gm and low capacitance mean the transistor is "faster", ie it will have current gain up to higher frequency.

gm strongly depends on current, thus fT does too. FET capacitances strongly depend on voltage. So this fT has to be specified at a known bias point for Vds and Id, and it can only be used to compare two transistors if both were measured at the same bias point.

The above MOSFET does not have any voltage gain because source and drain are AC grounded. This is similar to a cascode configuration. In a common source amplifier, while the properties of the transistor remain the same, you would have to consider Miller effect which greatly magnifies the influence of Cgd. Thus voltage gain in a common source non-cascode amplifier depends a lot more on Cgd than on Cgs.

I have read over the years that term transit frequency is associated with both MOSFETs and BJTs, and its the frequency at which the current gain becomes unity. It's usually understood as a figure-of-merit. The unity gain frequency is usually associated with the frequency at which an op-amp has 0dB of voltage gain.

Going back to the transit frequency term. Since this is evaluated for a transistor whose drain/collector is shorted (we're talking about a current transfer, after all), and it is given by, in the case of a MOSFET: $$f_{T,MOS} = \frac{g_m}{C_{gd}+C_{gs}}$$ Or, in the case of a BJT: $$f_{T,BJT} = \frac{g_m}{C_{\pi}+C_{\mu}}$$

This means you'll not see the usual miller-influenced pole $$\\frac{1}{r_{\pi}(C_{\pi}+(1+g_mr_o)C_\mu)}\$$ term in the current transfer. Therefore, it might not directly apply to your particular situation if the $$\f_T\$$ of transistor x is higher than transistor y (unless this difference is of an order of magnitude).

Use it as an indication, but not as the hard truth. For instance, in an IC, this figure of merit does not take into account collector-to-subtrate capacitance or its series resistance, which could render this figure of merit useless when these parasitics dominate.

According to this answer, the unity gain frequency and transit frequency have the same definition but in difference context.

We mostly use transit gain with discrete BJT by looking at the frequency that make the current equals to one.

In other hand, for unity gain frequency, we talking about amplifier by looking at voltage signal amplification.

For the faster response, you can think about the nature of the bjt that follow the low frequency quit well but when the frequency is higher, it need to react faster to keep up with a rapid change of signal. As we assumed all BJTs will have the same characteristics or same mathematics model so if the current reach unity gain first, it means that transistor is slower in every frequency.

We can't compare mosfet with BJTs by that given definition but you can compare amplifier based on BJT with CMOS however the answer to this question depended on technology progression.