DS-1 transistor boost frequency response

[Scribe]

Hey all,
I was reading up on the electrosmash DS1 analysis and noted that the transistor boost phase has a really high bass roll off starting around 3.3KHz, but couldn't find the explanation for why. Can anyone shed some light on this, perhaps provide a rough calculation?

Link for reference, section 5.1: https://www.electrosmash.com/boss-ds1-analysis

Thanks!

[ElectricDruid]

Where did you find 3.3KHz? I'm not seeing it.

The first part of this stage are 2 consecutive high pass filters:

C2 and R4 with a cut frequency of 3.3Hz
C3 and R5 with a cut frequency of 33Hz.

[antonis]

It clearly states C2/R4 HPF cut off frequency at 3.3Hz (not Kilo)..

P.S.
3.3kHz (3,300Hz) should only stand for an ultra-high treble booster.. 

[GibsonGM]

Hi Scribe,

They pretty much 'tell us' here: "The first part of this stage are 2 consecutive high pass filters:

    C2 and R4 with a cut frequency of 3.3Hz
    C3 and R5 with a cut frequency of 33Hz.

The basic idea behind this filters is to remove the excess of bass before the (next) distortion stage, a guitar signal with too much bass harmonics could make the distortion slow, dumped or muddy."

The calculation there is: 1 /2 pi (R) (C)  =  the cutoff frequency.  It is helpful to use Megohms for resistance and microfarads for capacitance.   That is, .1 for the R, the cap stays .47u and so on.   

Looks like a 2 pole HP filter to ENSURE no low end flub-dub crap gets boosted and makes a muddy mess later on - primarily noise signals.   You could shift that higher to trim low end, which is a very common practice, often after the first stage.

[iainpunk]

It clearly states C2/R4 HPF cut off frequency at 3.3Hz (not Kilo)..

P.S.
3.3kHz (3,300Hz) should only stand for an ultra-high treble booster.. 

isn't the RangeMaster cut off at 3.3kHz?

cheers

edit; its 2.6kHz

[Scribe]

I get the explanation for the 33Hz and 3.3Hz roll off, but the frequency response curve confused me.

Final sentence of section 5.1:
"The signal has a raw gain of 35dB (56 times bigger) on frequencies above 3.3KHz that makes this stage to boost the guitar signal to the (soft) clipping."

Initially I thought it was a typo, but the frequency response curve shows a roll off well above 33Hz, unless I'm reading it wrong.

[antonis]

isn't the RangeMaster cut off at 3.3kHz?
cheers

isn't the RangeMaster an ultra-high treble booster..?? 

Cheers ..

[GibsonGM]

They're just talking about the input filtering there, Scribe.  The STAGE itself has a lower, and upper, freq. response, of course.  As you see in their graph, the response goes back to flat about 3.3khz, and everything above is boosted more (than what was cut on input).   The ramping up of the curve is due to the network on the input; otherwise that 'curve' would be fairly flat (disregarding the feedback cap on the transistor)

[Scribe]

They're just talking about the input filtering there, Scribe.  The STAGE itself has a lower, and upper, freq. response, of course.  As you see in their graph, the response goes back to flat about 3.3khz, and everything above is boosted more (than what was cut on input).   The ramping up of the curve is due to the network on the input; otherwise that 'curve' would be fairly flat (disregarding the feedback cap on the transistor)

Perhaps I worded my initial question incorrectly: can you explain a bit more why the stage is boosting more above 3.3Khz? I can't figure out why the transistor isn't boosting all frequencies equally.

Thank you all for the responses!

[antonis]

Final sentence of section 5.1:
"The signal has a raw gain of 35dB (56 times bigger) on frequencies above 3.3KHz that makes this stage to boost the guitar signal to the (soft) clipping."

You have to study a bit about first order Low/High Pass Filters attenuation..
3.3kHz is 2 decades above 33Hz and 3 decades above 3.3Hz corner frequency..
Particular HPF forms -3dB corner frequency with a slope of 20dB per decade, hence 40dB (x100) or 60dB (x1000) voltage "gain" at 3.3kHz..(*)
This practically means negligible attenuation due to particular HPF action so 35dB is the actual (frequency independent) boost stage Gain ..

(*) it actually works in reverse - 33Hz signal voltage is 100 times lower than 3.3kHz one, in the ideal case of infinite booster stage gain..

[antonis]

Perhaps I worded my initial question incorrectly: can you explain a bit more why the stage is boosting more above 3.3Khz? I can't figure out why the transistor isn't boosting all frequencies equally.

The transistor DOES boost all frequencies equally..!!!
NOT ALL frequencies come into transistor equally....!!! 

[antonis]

Electrosmash analysis is an elementary level one 'cause 2^nd HPF isn't formed by C2/R5(only)..

In place of R5 should be R5 // R7/(Stage gain + 1) // [(h_FE+1)*R9 + h_FE*26/I_Collector]

[Scribe]

Electrosmash analysis is an elementary level one 'cause 2^nd HPF isn't formed by C2/R5(only)..

In place of R5 should be R5 // R7/(Stage gain + 1) // [(h_FE+1)*R9 + h_FE*26/I_Collector]

Ah, so that's the missing piece. So the decreased gain below 3.3KHz is mostly due to the fact that R9 is only 22 ohms, which ends up pushing the cutoff higher than simply using C3 and R5 as the RC network?

[antonis]

Ah, so that's the missing piece. So the decreased gain below 3.3KHz is mostly due to the fact that R9 is only 22 ohms, which ends up pushing the cutoff higher than simply using C3 and R5 as the RC network?

No.. 
(for two independent reasons..)

1. R9 is seen h_FE + 1  times bigger (resistance reflection rule) and is considered in series with h_FE times intrinsic Emitter resistance (26 ohms divided by Collector quiescent current)..
So, for 450μA Collector current and transistor h_FE 150, say, resistance "seen" from Base is about 12k.. 

2. There isn't any decreased (or increased) transistor gain (ignoring C4 and some other "hidden" transistor properties)..!!
You can consider transistor amp as purely linear device with constant gain all over frequency range..
What matters is the Base input signal amplitude..!!
That amplitude varies according to particular frequency, due to input HPFs and is subsequently amplified by stage constant gain..

e.g. for a X100 stage gain (40dB) and a 1kHz HPF corner frequency, 1V input signal of 100Hz comes out as 10V (10 times attenuated and 100 times amplified)

P.S.
Sorry but both late Saturday night here (hard drinking day) and my teaching skills suck, anyway..

[GibsonGM]

I was going to write something similar, Antonis, but you say it better!        The transistor is amplifying what it 'sees' just fine....the R/C networks on the base are 'showing' the transistor a curve, which is then amplified....while the emitter R IS part of it, a very small part...it has far more control over the OVERALL gain of the transistor...increasing the value of the C's on the base would lower the cutoff and thus move the curve down...

Playing with stages like this in LT Spice or other software can really show what's going on!

[Scribe]

I think I'm understanding these explanations, but I still am a little confused why the curve looks the way it does.

Maybe I need to find a good article explaining this, but if the highest HPF corner frequency at the input is 33Hz, how is it that frequencies well above that (like in the 300Hz-1kHz range) are not receiving the full amount of gain? With a HPF cutoff that low, I would think those frequencies should get a gain similar to what we are seeing at 3.3kHz. Why is the input 'seeing' a curve that 'starts' around 3.3kHz? Is there some other aspect of the network that is making the input 'see' a higher cutoff?

Again, thank you all for taking the time to try to explain this to me. I have a harder time wrapping my head around some of these transistor networks 

[antonis]

if the highest HPF corner frequency at the input is 33Hz, how is it that frequencies well above that (like in the 300Hz-1kHz range) are not receiving the full amount of gain?

But they DO receive it..!!
The issue is that 300Hz - 1kHz input signals are still attenuated, according to input HPF curve slope..
Despite filter's particular corner frequency, there is NO signal coming out with NO attenuation at all, except for INFINITE frequency one..
(absolute zero cap impedance)

For particular stage gain (35dB), all signal frequencies higher than 3.3kHz are clipped due to booster headroom whereas all frequencies lower than 3.3kHz are equally amplified (also 35dB) but not clipped/distorted due to their individual attenuation before amplification..

Consider (brute approximation) a 1V signal amplified by a X10 stage gain with 11V headroom..
The lower the signal frequency the lower the output signal voltage but there shouldn't be any frequency for which output voltage is 10V..!!
If headroom was 5V, all signal frequencies above "some" frequency should exhibit 5V output (the higher the frequency the higher the distortion but the same the output amplitude..) 

[Scribe]

if the highest HPF corner frequency at the input is 33Hz, how is it that frequencies well above that (like in the 300Hz-1kHz range) are not receiving the full amount of gain?

For particular stage gain (35dB), all signal frequencies higher than 3.3kHz are clipped due to booster headroom whereas all frequencies lower than 3.3kHz are equally amplified (also 35dB) but not clipped/distorted due to their individual attenuation before amplification..

Got it, but what is causing the signal attenuation for the frequencies between 33Hz and 3.3kHz? I don't get what attenuated those frequencies given the decently sized 47nF input cap. Treble boosters like the rangemaster have a higher roll off due to a smaller cap size, but I don't see anything in the DS1 circuit that would do that.

[antonis]

Curve slope..

https://www.electronics-tutorials.ws/filter/filter_3.html

http://www.learningaboutelectronics.com/Articles/High-pass-filter-calculator.php

http://sim.okawa-denshi.jp/en/CRhikeisan.htm

[GibsonGM]

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


The active device (the transistor) does have an effect on the signal level, and some on the frequency response due to the things mentioned above...emitter resistor, feedback components, Miller capacitance)...but most of its job is just to amplify.   The network on its input (its base) is calling most of the shots!

If we swapped the components, Cs for Rs, we'd see the opposite curve.