I was searching the net and found this article by D.Feucht:
http://www.analogzone.com/col_1017.pdf
There is a simple and elegant concept behind all the math. Here is my oversimplified take on this:
1. Bandwidth of a gain device can be divided by three regions: LF, HF and unity gain (VHF).
2. Gain (beta, S, A, whatever) is constant in LF, rolls 6db/octave in HF and is unity beyond Ft.
3. model is valid for HF region only.
4. here is the main idea: because the gain is proportional to 1/s (1/jw), it transforms any parameter of the gain device where gain is a part of the equation (for example: Zin=(beta+1)Ze for an emitter follower. beta is now not a constant but proportional to 1/s. Consequently, Zin is proportional to Ze/s. Thus, Ze is transformed or gyrated to something else. If Ze is a resistor Re, Zin Will appear as a capacitor. Mind you, this has nothing to do with intrinsic input capacitance Cie. If Ze is a capacitor, Zin will appear as a negative resistance). This is a very crude example but describes an idea sufficiently.
5. in HF region you need completely different model for gain device (with transformed parameters). My understanding is that this model is not difficult to make.
6. Now that you know what the players are, you can identify resonant circuits and damp resonances properly.
Cool 🙂
http://www.analogzone.com/col_1017.pdf
There is a simple and elegant concept behind all the math. Here is my oversimplified take on this:
1. Bandwidth of a gain device can be divided by three regions: LF, HF and unity gain (VHF).
2. Gain (beta, S, A, whatever) is constant in LF, rolls 6db/octave in HF and is unity beyond Ft.
3. model is valid for HF region only.
4. here is the main idea: because the gain is proportional to 1/s (1/jw), it transforms any parameter of the gain device where gain is a part of the equation (for example: Zin=(beta+1)Ze for an emitter follower. beta is now not a constant but proportional to 1/s. Consequently, Zin is proportional to Ze/s. Thus, Ze is transformed or gyrated to something else. If Ze is a resistor Re, Zin Will appear as a capacitor. Mind you, this has nothing to do with intrinsic input capacitance Cie. If Ze is a capacitor, Zin will appear as a negative resistance). This is a very crude example but describes an idea sufficiently.
5. in HF region you need completely different model for gain device (with transformed parameters). My understanding is that this model is not difficult to make.
6. Now that you know what the players are, you can identify resonant circuits and damp resonances properly.
Cool 🙂
I'm not certain about the asymptotic gain being unity; I would have thought that many devices exhibit loss at high frequencies. The general point about unexpected reactances appearing is good. I am surprised that he claims that this is relatively unknown outside Tektronix - the oscillating emitter-follower with capacitive load is quite well known.
It might be worth making clear that he is mainly talking about oscillating stages due to parasitics. Whole circuits also oscillate, but usually due to unstable feedback loops.
It might be worth making clear that he is mainly talking about oscillating stages due to parasitics. Whole circuits also oscillate, but usually due to unstable feedback loops.
Putting a small resistor in series with the output is another cure, as it stops the follower from seeing the capacitive load at high frequencies.
Nothing really new here. Miller (of "Miller Effect" fame) discussed the very problem in his original paper describing Miller Effect. "Dirty" admittances do sometimes look like negative resistances at the input of whatever active device you're discussing.
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