# What's the difference between the maximum and cut-off frequencies of a single transistor compared to those of a circuit? [closed]

Many publications, when they speak about a single transistor, the maximum and cut-off frequencies are way higher than of the final circuit.

Example: A modern FinFET, some report a maximum oscillation frequency of 150GHz or higher. On the other hand, a CPU runs at only at a base clock of 3GHz.

What is the difference?

If you have any bibliographic references that answer this in detail, could you please share them?

• well, the transistor isn't the only thing in a circuit, and obviously, it's properties depend on how it's used, so I'm not sure what you're asking here – how deep is your understanding of the dynamic behaviour of a transistor? And of basic transistor configurations? – Marcus Müller Jan 18 at 19:32
• you can speak technical. Basically, those who do TCAD simulations always report such measurements. the thing I don't follow is where exactly this huge cut in frequency happens.(regardless of the gain and power losses). – ali_05 Jan 18 at 19:36
• moreover, at such frequencies, dynamic power loss would be so high that it might melt the chip itself (ofc, not a single transistor would do that but a millions of them can definitely do that) – Sanmveg saini Jan 19 at 7:43
• Consider - if all the transistors in a CPU switched infinitely fast, what would limit CPU speed? Consider the effects of propagation velocities, inductance and capacitance resistance, clocking data through muliple operations, ... . – Russell McMahon Jan 19 at 9:53
• This question has been thoroughly answered enough to understand operational frequency for components as simple as a single transistor or as complicated as a CPU, or any circuit with a complexity in between, from component limitations such as needing a gain greater than one that derate its rated maximums, to the factors in a real circuit that affect propagation delay and therefore maximum output frequency. You should upvote all of the answers since they all represent effort and are factually correct, and mark one correct if you find it more correct than the others. – K H Jan 20 at 5:22

A CPU's logic design is highly tuned to minimise the number of gates between registers (made of flip-flops); some CPUs have 12 or 14 or 16 gates on the longest path. That means a signal has to propagate through 2 FFs, 13 wires and 12 amplifiers (gates) before the next clock pulse.

(This paper suggests the optimal would be 6 to 8 gates before the FF delays started reducing performance : scanning it, it appears to be a hypothetical paper, and I haven't heard of any practical CPU with as few as 10 gate delays. I vaguely recall Andy Glew upset a lot of fast RISC CPU designers when his Pentium Pro at about 12 gates upset most expectations of what an x86 CPU could do)

So one shouldn't expect it to work at clock frequencies more than about 1/25 the speed you can get a single element to oscillate.

That would get you down from 150GHz to maybe 6 GHz right there; but it's clearly not the whole story.

Given millions of elements on a CPU, you can't afford to power them as much as you can a single transistor, both from power supply and interconnection issues, and from thermal (heat dissipation) issues. So they are tuned to somewhat less than the maximum power (and higher speed requires higher power)

• Thanks for the reply, I think you made a very interesting argument about the signal path length, basically the interconnect. But, I don't think it is the full picture, for an example a fully integrated inverter (NOT gate). will still have a very low frequency. I guess what I am looking for is an accurate physical modeling (switching wise) from a single transistor to where the frequency cut. Thanks again ! – ali_05 Jan 18 at 20:05
• You didn't ask about a simple device like an inverter, you asked about a 3 GHz CPU, @ali_05. Also, obviously, in an inverter, the external circuitry is the limiting factor, especially considering the purpose of the inductor in an inverter. – Marcus Müller Jan 18 at 20:06
• "discrete gate" inverters come in buffered and unbuffered versions (e.g.74HC04/74CHU04). The buffered version has an extra amplification stage to increase fanout. – Brian Drummond Jan 18 at 20:08

150Ghz or higher. while -for example- a CPU runs at only at a base clock of 3Ghz.

Well, a CPU isn't a single transistor; it's billions, and even the speed of light wouldn't allow for a CPU core to distribute a clock consistently across a die at 150 GHz.

It gets worse, though: your transistor might switch incredibly fast, but it has to (dis-)charge the gate of the next transistor, and since even in fully switched state, your drain-source impedance isn't 0 Ω, and your power supply can't supply infinite current that simply takes time.

Now, a single transistor doesn't make a logic gate, you need multiple; a single logic gate doesn't make a complex unit such as floating point multiplier, you need hundreds. So, you get complex networks of connected gates and typically CMOS pairs. There's going to be a longest path there, which simply takes a lot of time from the first CMOS pair switching to the last CMOS pair switching. That's the ultimate limiting factor: you can't get faster than that, even if you ignore all other problems.

(I don't think you actually need a bibliographic reference to that, that's kind of "common knowledge"; else, pick your arbitrary VLSI textbook.)

And there's plenty of other problems: You can't increase voltages to speed up charging of gates, simply because ohmic losses go with the square of your voltage, and ho boy, is your CPU thermally limited.

You can't work with a "oh, it doesn't have to be at 99% of supply voltage, 80% is enough charge that is achieved within a cycle", because, again, billions of transistors: Reducing the "acceptable threshold", then you get cascading probabilities of things not being in the correct state. Do that a billion time at once, and you basically guarantee that something goes wrong in your CPU.

Atop of that, you, being a TCAD engineer, will definitely have to deal with a lot of interactions that say "many transistors on a die do not behave like a lot of independent transistors".

• Thanks for the reply. I think you are write about whether the power supply can handle that. you spoke about charging rates being a limitation, I think this particular argument doesn't hold as a study of a single transistor, that take into account charging rates, parasitic resistances and capacitances , still give very high frequencies. Brian Drummand gave an interesting point. thanks again ! – ali_05 Jan 18 at 19:56

Many publications, when they speak about a single transistor, the maximum and cut-off frequencies are way higher than of the final circuit.

Think about what $$\f_{\mathrm{max}}\$$ actually means. It is the frequency at which the transistor has unity power gain. In other words the transistor cannot be considered an active device above this frequency. In practise this limits the operation frequency to at most half of $$\f_{\mathrm{max}}\$$, since you actually want to have a reasonable power gain for the transistor to be useful.

The book "High-Frequency Integrated Circuits" by S. Voinigescu even states:

"Over the years, circuit designers have established an empirical rule that transistor $$\f_{MAX}\$$ values four to five times higher than the frequency of operation of the circuit are needed to develop robust, high-yielding commercial ICs. For example, today’s first commercial 77GHz automotive radar and 60GHz radio transceivers are fabricated in technologies with transistor $$\f_{MAX}\$$ values in the 250–300GHz range."

Today there is research done in a lot of fields where operation frequencies up to hundreds of GHz are a reality. But this still requires for the transistor to have a several times larger $$\f_{\mathrm{max}}\$$ and transistors like that do exist.

Large CPUs are not a good example for a comparison with the technology's transistor $$\f_{\mathrm{max}}\$$ because there are reasons like power dissipation (density) putting a much lower limit to the operating frequency. In RF circuits the number and density of transistors is a lot lower so that power dissipation, in terms of cooling the chip, is less critical.