# BJT High Frequency Effects?

I am studying high frequency common emitter amplifier and I came across a model where parasitic capacitances C_CB, C_BE, C_CE of BJT are included. In my textbook the small signal current gain beta of the transistor then becomes frequency dependent because of the parasitic capacitances. My question: Is the small signal current gain beta cut-off frequency responsible for the upper frequency limit of the transistor amplifier? Because I also read about the Miller-Effect. Does this result in another cut off frequency?

• Can you clarify your question to reference one or more specific amplifier topologies? Not all capacitances have strong effects on all topologies, and likewise the Miller effect is pronounced in some topologies but has negligible practical effect in others. Commented Jan 20, 2022 at 20:36
• thanks. i totally forgot to add that i am referring to the common emitter amplifier Commented Jan 20, 2022 at 20:51
• No problem. I have to run to meetings and other committments, so I won't be able to write out a good answer since this is a fairly rich topic that merits a thoughtful and thorough answer, but I'll try to circle back if time permits later on and there aren't good answers yet. In short, some of these capacitances directly lead to poles in the transfer function, and Miller effect leads causes the effective capacitance of C_cb to be much more than it really is (leading to a much more significant pole) -- a good answer would include a decent explanation why. Commented Jan 20, 2022 at 20:58

BJTs are voltage controlled devices. On first order, they're voltage controlled current sources, with collector current depending on internal Vbe.

Current gain does not exist at the physical level. There is no mechanism by which base current is multiplied by hFe and turned into collector current.

Current gain is an observed effect at low frequency: Vbe controls Ic, but Vbe also causes a current to flow through the B-E junction. They happen to be quite proportional because Ic has an exponential dependence on Vbe, and Ib also has an exponential dependence on Vbe. So this results in a convenient and easy to use "current gain" metric.

At high frequency, collector current is still controlled by internal Vbe. However, the base has capacitance to both C and E. In order to vary the base collector current quickly, these two capacitances have to be charged and discharged, which implies a base current i=C dv/dt in addition to the current going through the B-E junction. On top of that, quite a large amount of charge is stored in the base, which makes the B-E capacitance appear surprisingly large and difficult to discharge at turn-off.

So the observed current gain of the transistor, which doesn't exist at the physical level but is still convenient, does appear to go down with increasing frequency. This is not due to any "current gain" mechanism, but simply the fact that whatever circuit is providing base current must also provide current to charge and discharge Cbc and Cbe. So at high frequency, more AC base current is needed, because more goes into the capacitance and less into doing useful work moving Vbe, and therefore current gain goes down.

Even if the transistor base is driven by a current in your circuit, the device is still voltage driven internally. The B-E junction and capacitances convert the driving base current into voltage, which then controls Ic. When base is current driven, due to capacitances, internal voltage gets lower at high frequency, which looks like current gain is dropping.

Because i=C dv/dt, if the transistor is wired as common emitter amplifier and has a large voltage swing on its collector, the smaller Cbc sees a large dv/dt, thus it takes much more current than the tiny capacitance value (usually a few pF for small transistors) would imply. This is Miller effect, which is basically the product of Vcb voltage swing and Cbc. Miller effect only occurs if there is a voltage swing on the collector, hence the useful cascode circuit.

And since voltage swing is tiny on the B-E junction, the much larger Cbe sees a low dv/dt, and takes much less current.

In addition, the base has resistance and inductance, which means even if it was driven by an ideal voltage source, it would still have a lowpass effect.

• Btw, can you recommend a book where things like that are explained in detail? Commented Jan 20, 2022 at 23:28
• @user2276094 I really like the Sedra/Smith textbook for introductory usage, and Razavi's microelectronics as a further text. Commented Jan 21, 2022 at 1:15