DS-1 transistor boost frequency response

[antonis]

Nice and clear said, Sir..

[Scribe]

(If the transistor was not there, we would still see a similar curve but far lower in amplitude...)   

Pardon me if I'm sounding like a broken record, but I'm not sure why this is the case given the frequency curve that electrosmash simulated. I understand that the frequency curve at the base of the transistor gets boosted across all frequencies (within reason), however none of the math adds up that will link the frequency response curve to what I would expect to see at the transistor base.

So we have the booster stage, which has two HPF RC filters formed by C2/R4 (3.39Hz) and C3/R5 (33.9Hz):


And the Spice simulation for this stage's output is as follows:


If we take away the gain, the frequencies on the simulation start to roll off around 3.3kHz. This is WAY above any passive HPF filtering from the passive filter network at the base. This is what I am confused about. Is it an error, or is this actually what is happening?

[Scribe]

*sorry double post*

[antonis]

Below is frequency response of a simple (1^st order passive) 470nF/100k filter..
(take a look on vertical axis..)

[iainpunk]

its the miller effect.
you can calculate the miller impedance of the bias circuit, the resistive element of the equivalent Z is only about 1kOhm.
essentially, the actual 2nd filter in this gain stage is 47nf and 1kohm, giving about 3.3kHz.

*mic drop* 

cheers, Iain

[Scribe]

its the miller effect.
you can calculate the miller impedance of the bias circuit, the resistive element of the equivalent Z is only about 1kOhm.
essentially, the actual 2nd filter in this gain stage is 47nf and 1kohm, giving about 3.3kHz.

*mic drop* 

cheers, Iain

There it is! Now the response curve making sense!

Again, thanks to all of you who responded- greatly appreciated.

[jatalahd]

Just interfering this to clarify that the miller effect does not play role here in the high-pass filter behaviour. Here it boils down to what drunk Antonis was trying to say ...

The emitter resistor is not bypassed with a large cap, so the the term to describe it is emitter degeneration. With that, the value of the emitter resistor is scaled by the hfe of the transistor, (hfe+1)*RE. So for a typical hfe of 200, the emitter resistor in this case will show itself as 22*200 = 4400 ohms. This is in series with the transistors internal input resistance rpi, which is affected by the collector current Ic, namely via

gm = IC/0.025   (BJT transconductance in room temperature) and from here
rpi = hfe/gm       (the internal input resistance in series with emitter resistance of the BJT)

If the math is done, the rpi will be around 10k, so the effective input resistance of the BJT configuration is about 15k in this case. BUT ...

What makes this almost impossible to analyse easily is that the feedback from collector to base via 470k resistor makes this a feedback amplifier and the properties of feedback (mainly the loop gain) scales the input impedance of the transistor gain stage lower in this case. I have earlier made an online calculator for this configuration: http://www.guitarscience.net/calcs/cecbemf.htm

When plugging in the values with hfe = 200, I get the AC input resistance of the transistor configuration as tad over 3000 ohms.

When using the common RC filter formula for 3dB corner frequency

f3db = 1/(2*pi)*1/(RC) = 1/(2*pi)*1/(3000*47e-9) => 1100 Hz,

When looking at the simulated graph, the 3db attenuation is quite close to 1 kHz in this case so the calculation give correct ballpark.

Just wanted to point out that this configuration is not easily analysed with simple equations because of the feedback configuration involved.

[antonis]

......

[antonis]

Just interfering this to clarify that the miller effect does not play role here in the high-pass filter behaviour.

I think Iain deals with 470k feedback resistor apparent value, which is its nominal value divided by stage gain plus unity..
That value is set in parallel with R7 and transistor input impedance, severely dominating equivalent input impedance..

Just wanted to point out that this configuration is not easily analysed with simple equations because of the feedback configuration involved.

It definately isn't 'cause "open loop" gain (without 470k resistor in place) value can't be considered "high enough" for calculating close loop gain just using the feedback resistor divided by source impedance formula..

[jatalahd]

Just interfering this to clarify that the miller effect does not play role here in the high-pass filter behaviour.

I think Iain deals with 470k feedback resistor apparent value, which is its nominal value divided by stage gain plus unity..
That value is set in parallel with R7 and transistor input impedance, severely dominating equivalent input impedance..

Yes, Iain is correct in that sense, but that is not Miller effect, he's just referring to Miller Theorem.

So using that we can estimate the gain of the transistor stage as K = -RC/RE --> -10000/22 --> -455

And the Miller Theorem:  Z' = Z/(1-K) --> 470000/454 --> approx 1000...

As a crude approximation that works, but getting the -3dB using that value to 3.3 kHz does not match the simulated graph, where the -3dB point seems to be just below 1 kHz.

[antonis]

Yes, Iain is correct in that sense, but that is not Miller effect, he's just referring to Miller Theorem.

Yes, you're also correct in the mean of Miller effect is only refered on capacitance multiplication.. 

P.S.1
Shall we all correct guys shake hands and go for a coffee (due to beer forbidden local time..)..??

P.S.2
Kudos again for your excellent work in guitarscience..!!!

[jatalahd]

Yes, Iain is correct in that sense, but that is not Miller effect, he's just referring to Miller Theorem.

Yes, you're also correct in the mean of Miller effect is only refered on capacitance multiplication.. 

P.S.
Shall we all correct guys shake hands and go for a coffee (due to beer forbidden local time..)..??

Yes, coffee break and hand shaking sounds good 

I did not want to be against anyone here, but just wanted to get some better clarity to the terms used. The Miller one and then the use of RC filter formula to get -3dB point, not the point where the curve starts to decrease.

In feedback configurations, the open loop gain + Miller theorem impedance do not always apply to yield good results. It is a bit sad that in the common literature this is stated as the correct way to analyse feedback circuits.

[antonis]

In feedback configurations, the open loop gain + Miller theorem impedance do not always apply to yield good results. It is a bit sad that in the common literature this is stated as the correct way to analyse feedback circuits.

But it's a very "convenient" brute approximation, isn't it..?? 
(otherwise we should deal with martixes and Blackman's theorem etc)

P.S.
I'm pretty sure that nobody here thinks you're against him.. 

[iainpunk]

Just interfering this to clarify that the miller effect does not play role here in the high-pass filter behaviour. Here it boils down to what drunk Antonis was trying to say ...

miller effect - miller theorem .... poh-tay-toh - poh-tha-toh...
i just had therms confused a bit. Dyslexia is a B1tch

But it's a very "convenient" brute approximation, isn't it..?? 
(otherwise we should deal with martixes and Blackman's theorem etc)

please don't force me to do matrix calculations without computer again,

cheers

[GibsonGM]

I just make an educated guess...approximation It works well for what I do!  Ha ha.  Nice explanation gentlemen, and with ALL your input you appear to have arrived at the correct solution!  Interesting maths.


It is never 'forbidden time' for beer, Antonis...