EMRFD Message Archive 12458

Message Date From Subject
12458 2016-02-28 11:40:42 mleblanc0 Beta Cutoff for BJT

On p 2.9 of EMRFD Revised, Fig. 2.27 illustrates the concept of "beta cutoff", which is defined in the text as "the frequency where beta begins to depart from beta-subscript-zero." In the last paragraph on that page, it uses 2N3904 as an example, where F-subscript-t = 300 (Current Gain-Bandwidth Product in most datasheets, I presume) and it has a low frequency beta-subscript-zero (hFE in most datasheets) = 100. The next sentence reads: "This places the beta cutoff at about 3 MHz." Beta cutoff is not shown in most datasheets I've looked at.

Is beta cutoff determined by simply dividing Current Gain-Bandwidth Product by hFE, or is there something I've missed further back in the text?

-Michael VE1LEB

12459 2016-02-28 16:17:28 vasilyivanenko Re: Beta Cutoff for BJT

Yes --- you've got it correct.

Beta cutoff is the frequency where the beta has dropped to 0.707 times the low frequency value.  The product of that frequency times the low-frequency beta is the current GBW.
12460 2016-02-28 18:29:10 iq_rx Re: Beta Cutoff for BJT
I'd like to suggest that beta cutoff is a useful concept, rather than a number.  The key word in the quote from EMRFD is "about."

Beta may be easily measured at dc for a particular individual transistor, but we expect that other transistors with the same part number may have very different values.  In many data sheets and textbooks, beta = 100 is used as a convenient ballpark number that makes calculations easy.  But LTspice models often have beta = 300 for a 2N3904, which is perhaps a more typical value.  A good designer's circuits work over a very wide range of dc beta.

Here's how the concept of beta cutoff for a 2N3904 might be put into words:

"At some frequency in the low MHz range, a 2N3904 will have a beta lower than the value measured at dc, and beta will typically decrease above that point by a factor of about ten per decade up to some low UHF frequency."

For example, if the beta at 5 MHz is about 200, then it is about 20 at 50 MHz.

All of that is academic, because I'll design my small-signal amplifiers using transconductance and device parasitics rather than beta.  Transconductance is wonderfully easy to set with bipolar transistors, and it is designed in as a very useful value with a favorite FET, the J310.

Beta cutoff is a still useful concept, because if we understand it, we know that we can expect HF beta to be lower than dc beta, and increasingly lower as frequency increases, right up to the frequency at which we can no longer easily build an amplifier.  But several assumptions and variables make any calculated numerical value of "beta cutoff" suspect.  The first of these is dc beta, which might be anywhere from perhaps 50 to 500 for a 2N3904.  The second is the frequency at which beta = 1.  If rolloff of beta with increasing frequency were a single RC time constant, then we would know the shape of the rolloff from that point all the way down to the point at which the high frequency beta = dc beta.  But there are more terms in the device model.  Transistor device physics is interesting!

For general high frequency design, it's not the number that is important, it is the concept.  A beta cutoff number would be unlikely to appear on a data sheet, since it is derived from two variables with such large uncertainty.

Best Regards,

Rick KK7B