hFE vs hfe

[demonstar]

I was wondering, at a given collector current and value for the collector-emitter voltages does h_FE ever vary from h_fe, for instance due to internal capacitive reactances of the transistor? I guess I could rephrase this question as does h_fe change with frequency?

Thanks.

[alanlan]

In high frequency models, the frequency dependent behaviour is usually provided by capacitors i.e. the transconductance is viewed as being not dependent on frequency, but the overall model is, due to the addition of capacitance.

[demonstar]

Thanks alanlan.

I understand that at higher Frequencies coupling capacitors emitter bypass capacitors etc. affect the frequency response but what I wasn't sure of is due to parasitic capacitances in the transistor would the h_fe change with frequency.

Am I correct in thinking that you are saying models usually don't take into account these internal parasitic capacitances just external capacitances?

[Myriad Society]

As I understand it, what you are describing Demonstar, is an effect that is particularly noticeable in a common emitter BTJ configuration at higher frequencies. Basically in a common emitter gain stage, bandwidth is limited by gain - by this I mean that as the gain of the stage goes up, the available bandwidth goes down and conversely, as the gain of the stage goes down available bandwidth goes up. This is called the "Gain Bandwidth Product".

This effect is inherently dominated by the feedback capacitance intrinsic to the transistor between the collector and the base. Consequently as frequency increases, feedback is increased via the collector/base junction's capacitive reactance which in turn does reduce the overall gain (hfe).

I've never run into this being a problem for anything I've worked on as it is all pretty low frequency stuff but if you are having issues with this, I believe the easiest way to help overcome the problem is to switch the offending amplifier to a common base configuration. By doing this you are grounding the base and disconnecting the pathway between collector to base where this capacitance is happening.

I'm sure one of the bigger brains on this site can add to this and probably make some corrections to what I've just said here and hopefully they do. Also you can reasearch the "Miller Effect" for more information.

[demonstar]

Thanks.

I'm actually just reading a book, "Electronic Circuit Analysis And Design" by Hayt and Neudeck. I've been following through the sections on analysing and designing common emitter amplifiers predominately using the hybrid-pi model to deal with small signal analysis. I can follow the example for mid. frequencies but I'm working on the low and high where all the capacitors get involved. It has just got me thinking and prowling through datasheets and raised a few thoughts that was all. I've just found this site...

"http://jas.eng.buffalo.edu/education/system/bjtequiss/index.html#"

which is a bit sidetracked from this post really but I've found it useful in visualising better where the model arises from for anyone who drags this topic up in a search in the future. The actual thing that sparked me asking the question was some datasheets quote a h_fe and a h_FE value (usually the same) for a given V_CE and I_C but the h_fe is also quoted for a given frequency.

[brett]

Hi
the transition frequency (Ft ?) for most modern silicon BJTs is really high (e.g. a minimum of 300MHz for a 2N3904).  You'll notice that this is also called the gain-bandwidth product ("product" being the term for the results of a multiplication).  This implies that you can get a gain of at least 300 at 1MHz (if the hFE is >300) or a gain of 2 at 150MHz.  Although the detail might not be as simple as this exactly, you can see that the frequency limits are very high in terms of audio reproduction (our upper limit is between 6 and 20 kHz, depending on age and lifetime exposure to loud sounds).
cheers

[demonstar]

So if a datasheet said h_fe is 100 (min.) at I_C=1mA, V_CE=5V and f=1kHz then at 1khz the maximum gain from a transistor of that type with poorest the minimum allowed h_fe would be 100? If I then operated the same transistor at I_C=1mA, V_CE=5V and f=2kHz then the maximum gain from a transistor of that type with the poorest allowed h_fe would be 50?

[R.G.]

I was wondering, at a given collector current and value for the collector-emitter voltages does h_FE ever vary from h_fe, for instance due to internal capacitive reactances of the transistor? I guess I could rephrase this question as does h_fe change with frequency?

On the face of it, yes, h_FE is different from h

fe

, if only by the way they are calculated. The DC value is calculated by computing the offset from zero base current and zero collector current. The AC value is calculated as the ratio of differential offsets around the operating point. The two numbers are different, but since current gain (notice I weenied out and slyly used another term which isn't either one we're talking about) varies so much from device to device and with operating point, it's common to refer to them as one.

But your real question is whether AC (differential) current gain varies with frequency. It's been a long time since I delved this deep into the matter, so I probably should go look it up. What follows is my first-cup-of-coffee understanding, what I would say if I was *not* designing an RF amplifier.

As a practical matter for design, the device capacitances are put into the model to provide a way to calculate the effect of frequency on gain, and the AC current gain is considered to be constant with frequency. The device capacitances themselves are part fixed (mechanical pin-to-pin spacing, etc.) and part variable with operating point, which includes the signal if you're considering quite high frequencies.

This is one of those imponderables where as part of the design process you have to compute to three or four decimal places, then figure what happens when everything varies 2:1. Real EE always involves the idea that you will make more than a few of whatever you're designing, at least in today's world. If you will only ever make one, then the right design procedure is to measure the tarnation out of the device(s) then design to the measurements and be done with it. But not much of that kind of EE happens. Mostly you want to make at least theoretically more than one, even if (as for effects on the internet) you only tell others how to make their own. So it gets really important to understand the variations in different parts even of the same type number very quickly.

Transistor modeling is one of those things which I took to be approximate. There are different models, of course. The Hybrid-Pi model is different from the h-paramaters models and those are both different from s-parameters used at RF. To survive the classroom tests and course final, you had to learn to memorize and then select the right equations, know where to plug the numbers, and get the right answer. However, to keep your job after school, you need to understand the variations in available parts, calculate minimums and maximums for production spreads, and ensure that whatever devices you get will work with no adjustments on the assembly line.

Germanium devices, largely because of crude processing, had to struggle to give audio frequency response. They were in the high-frequencies, everything-matters ranges at 20kHz. Modern silicon devices don't depart much from DC values until you're up at VHF where you need to start worrying about PC traces and component leads as transmission lines. For modern transistors, Anything audio might as well be DC as far as the silicon die is concerned.

[demonstar]

Thank you, I really appreciate all the help people have given me here. I feel I understand this much better than I did around 2 hours ago.

To survive the classroom tests and course final, you had to learn to memorize and then select the right equations, know where to plug the numbers, and get the right answer. However, to keep your job after school, you need to understand the variations in available parts, calculate minimums and maximums for production spreads, and ensure that whatever devices you get will work with no adjustments on the assembly line.

Sidetracking a bit (again  ) but when I first started to look into trying design and I was seeing this in posts I didn't really get it. However it didn't take long though before I started realising when I was going to the local shop and paying high prices for a single transistor my design had to cater for any possible outcome even if I got a non-typical one (I didn't want to have to buy several and go for trial and error and I didn't have a transistor tester.). By non-typical I mean even a relatively small variation from the datasheet's typical value. I then started to realise that when designing for a spread of device characteristics it can be quite a different approach to designing gain stages based on questions in a text book where Beta_dc is fixed. I found the book above in a charity shop and ever since I've delved in and out of it when I get time. The beauty of it is it deals with how to design amplifier stages for varying device characteristics using real datasheets. The book is very modular so you can jump in and out. Like I said I'm following the books through for BJTs in a common-emitter configuration looking at mainly hybrid-pi for small signal analysis but will go back and look  at the other models and configurations. I haven't really paid that much attention to FETs yet although I have looked briefly. It claims to explain how to bias JFETs taking into account device characteristics which should be interesting. 

I am mentioning some of the above because this book is proving extremely useful to me and I think it may help others out there. It takes a very critical approach then gives the simple approach then compares the two. It can get heavy at times. I'm getting to a point where soon I may have to go and brush up on complex numbers before going much further (I may get away with it). After the summer I hope to be starting an EEE undergraduate degree after the summer so I guess although designing for device variation isn't critical now it may be in a few years so might as well start now.

Once again thank you!

[R.G.]

I did some looking. That looks like an interesting book. I checked and found used copies of it available on line for prices from US$0.37 (yep, thirty-seven cents!) to over US$150. So I bought a cheap one for a buck plus three dollars shipping.

To all the would-be designers: plan to be reading textbooks for your entire design career. 

[demonstar]

Be sure to let me know what you think when you get it. I have the hard back second edition. Hope you like it!

[brett]

Hi again

For modern transistors, Anything audio might as well be DC as far as the silicon die is concerned.

Arrggh! RG says in less than 20 plain words what I tried to say in my long, jargon-loaded reply.
cheers

PS For the experimenters:  Has anyone checked the gain-bandwidth product of piggybacked Si transistors? (If necessary, Search piggybacked)

[R.G.]

Has anyone checked the gain-bandwidth product of piggybacked Si transistors? (If necessary, Search piggybacked)

Hmmm. Interesting question. I ran a bunch of simulations on this and found no significant (that is, within the audio band) change in frequency response from normal to piggybacked.

Caveats:
- There were changes out from 1MHz to 1GHz, the limit of my simulator. I believe these were from the addition of the extra device capacitances in the simulation models.
- Simulation results are highly suspect here. Designing RF stuff, as opposed to sniffing of it, especially 100MHz to GHz stuff, needs a better simulator.
- I do not have the equipment to even approach actually testing the responses of circuits at UHF and above. In this case the simulator is much better than the equipment, which is not, of course, saying very much.
- Adding external capacitances to the base-emitter and base-collector produced the expected responses in terms of bandwidth.

Netting this out, a crude first look indicates that for audio stuff at least, piggybacking does not lower bandwidth in an approximation of germanium, but adding capacitances does. That makes sense, as the low bandwidth of germanium is largely a result of the poor processing, not the inherent capabilities of the material itself, at least as concerns us down in the DC/audio backwater.