BSIAB 2 Analysis in SPICE

[Vivek]

In my quest to find out what gains and equalisations do pedal designers use when they claim to target the Brown sound,

I decided to first analyse the BSIAB 2 using SPICE (and make a new thread for it, so its less cluttered, and more easily searchable)


I found, like most electronic endeavors, someone already did it 10 years or more ago!!

Drschwartz' Analysis of the BSIAB 2 in October 2008

https://www.diystompboxes.com/smfforum/index.php?topic=71466.0

I know I'm very late to the party, but I will try to add more data and graphics to that initial effort.


Given that Through Hole FET are getting harder to find, and their huge vagaries, I might try and see if it is possible to get somewhat similar response with Opamps and diodes since they are more easily available, more predictable and more repeatable. I would need assistance since my knowledge and experience is very limited.

That would then be a emulation of an emulation, but still might be worth it, if it simplifies, standardises, makes more stable final pedals.



The original schematic is here http://www.generalguitargadgets.com/pdf/ggg_bsiab2_sc.pdf
Thanks to the great experimenters who developed BSIAB 2



I will need help from all of you, so please let's treat this as a community project !!

PS: It is not my intention to "teach Grandma how to eat eggs". Please pardon me if my analysis and comments appears too basic and unnecessary.

[Vivek]

STAGE 1



It's a mu-amp stage

The mu-amp is a very old circuit. It was reasonably common during the vacuum tube era, where it offered the opportunity to get a lot of gain and signal output out of common, garden variety triodes. Later, National Semiconductor published a JFET adaptation of the mu-amp in their JFET applications notes in a collection of JFET cookbook circuits. Later, effects experimenter Jack Orman used the mu-amp for a guitar gain circuit, renaming the circuit the "minibooster". The use of the mu-amp has been adapted into several DIY effects circuits from there. You can see the original circuit on National Semi's web page at http://www.national.com/an/AN/AN-32.pdf

- http://www.geofex.com/Article_Folders/modmuamp/modmuamp.htm
.

Now that same Application note can be found at https://www.ti.com/lit/pdf/snoa620


Graph of output waveshape from the first stage :


Here I ran signals of 10mvp, 50mvp, 100mvp, 200mvp, 500mvp, and 1000mv peak sine waves at 1Khz into the input and plotted the output of the first stage

An input of 50mvp leads to an output of 976mvp, ie a gain of 19.5 times. Visually, it appears that there is very low distortion for this signal level.

We also see very little distortion also in the 100mvp curve

With inputs of 1Vp, we see that the output swing is getting rail saturated at ~ +3.6Vp and =4.1Vp. This is asymmetrical. 

The tops are rounded for input 1vp

Let's see what happens when we drive the first stage with 2Vp input signals :




We see rail saturation +3.72vP and we see asymmetry of output waveshape.


Now looking at the frequency response of the first stage :



and with some annotation and measurements (Extended X axis):



It is expected that there will be a serious bass cut before a distortion stage. This is to prevent harmonics from the thicker strings from overpowering the fundamental and harmonics of the thinner strings. Indeed, pre-distortion bass cut exists in almost every high gain Amp and every distortion pedal. What makes each pedal sound different is the slope of the cut and the corner frequencies.

In the BSIAB 2, the output at 5Khz is 48 db more than output at 10 Hz, while output at 10 Khz is 53 dB more than the output at 10 Hz.

This means that the gain and saturation will depend on frequency. Earlier we saw graph of outputs with different inputs of 1Khz. Now lets see same graph but with signals of 5 Khz




Now we see that a 100mvp signal at 5Khz is distorted while a 100mvp signal at 1Khz was not distorted. This is because the gain depends on the frequency. Gain was 19.5 at 1Khz but is 58 at 5Khz.

Signals of higher frequency will saturate faster than signals of lower frequency.


Now lets use FFT to have a look at the harmonic content with 200mvp input at 1Khz




We see a mix of odd and even harmonics at output of the first stage.

[Vivek]

Now we look at the filter and drive controls in between the First Mu-Amp stage and second Mu-Amp stage




It's frequency response looks like this (for different settings of the Drive knob):



For low drive settings, there is considerable treble boost due to the treble bleed capacitor. The amount of treble boost reduces as gain increases.

This is a common strategy since high gain has more shrill harmonics, which need to be removed to sound good.

( However, seeing that the first stage already did a bit of clipping, an alternate strategy could have been to have a flatter response for low drive settings and a treble cut on the higher gain settings. I guess listening tests would have determined the better approach)

Now we analyse the interstage filter/Drive knob + Second Mu-Amp + Buffer

First we biased the buffer stage trimmer for roughly 4.5V DC




For this analysis, we run sine waves into the input of the 2nd stage (not the output of the fist stage)



We see that 100mvp at 1Khz gave an output of 550mvp hence a gain of 5.5x

Hence input signals of more than 500mvp will be clipped due to saturation.

Combined with the roughly 19x gain of the first stage, we now have 104.5x gain till the end of stage 2

Here is the output of the second and third stage combined (drive knob at 25%) :



We see that 10mvp input lead to a 151mvp output from the third stage ie total gain of second and third stage is 15.1
But second stage had gain of 5.5, hence third stage has gain of 2.75x


The total gain from input to end of 3rd stage is (Drive knob at 25%)

19.5 x 5.5 x 2.75 = 295

Which is in the normal range for distortion pedals

At max drive setting, the situation is different !!!
19.5 x 60.47 x 2.77 = total gain of 3333 from input till output of 3rd stage. This is an extreme amount of gain !!!!



Here is the frequency response from gate of stage 2 till output of stage 3 (not including intermediate filter and drive)

[Vivek]

TRANSFER FUNCTION OF FIRST MU-AMP STAGE IN BSIAB 2






X axis is input voltage in mv Peak, from -1200mvp to +1200mvp

Y axis is output of 1st mu-amp in volts peak


This looks very tube like !!!

Asymmetric

Harder clipping on one side, softer clipping on the other. It will have great crunch and still have dynamics !!!

No wonder people love the BSIAB 2 !

And here are actual readings from LTSPICE, for the boffins amongst us:

Code Select Expand


-1199.90 -5.22503
-1069.97 -5.19632
-912.967 -5.15237
-809.9588 -5.11507
-610.936 -5.02147
-461.914 -4.9245
-343.878 -4.7977
-252.860 -4.4698
-181.927 -3.8878
-120.955 -2.5879
-82.9600 -1.6638
-23.96500 -0.44859
0          0
7.0000  0.13846
28.547 0.5319
60.461 1.1182
86.459 1.45482
122.5 1.8787
129.64 1.9609
133.47 1.9868
141.49 1.9848
156.47 1.9799
173.52 1.9929
215.53 2.0347
299.54 2.1025
404.58 2.1828
557.72 2.2558
773.69 2.3258
831.59 2.34044
1026.00 2.3793
1199.6 2.4055




Suggested reading: Yamaha and Line6 have patents that explain their transfer curves for different Amp emulations and also propose mathematical equations to fit the curves (for easier computation in the digital domain)




https://patents.google.com/patent/US5789689A/en

[Vivek]

reserved 4

[POTL]

Hello About a month ago, I wondered what could help us make an amp in a box without the classic ROG-style circuits, with single Jfets and their cons. Alternatives found 3 1) Mu - amp, which, although it works on jfet, is devoid of a number of disadvantages 2) Op-Amp, flexible, affordable and modern, but the problem is I haven't heard any good examples of op amp sound, the closest way to simulate is using Bajaman 3) Mosfets - These are available but have many disadvantages, however I recently learned about LND150 circuits as a good way to simulate amplifiers. I haven't tried them yet and I don't have a simulation model.

[POTL]

Now let's talk about mu amp I simulated the frequency response of the triodes in multisim by comparing both at the same time. 1) C2 must be 22uf or more 2) To reduce the output impedance and gain loss, there must be a resistor between the transistors (1k-10k) 3) R3 gave the desired response at a large value, about 18k 4) C3 was calculated at the desired frequency, usually there is a resistor between it and ground, which attenuates the gain. I simulated this about a month ago, the calculation was fast, it is possible to recalculate the circuit bypassing the "extra" resistor in step 4.

[marcelomd]

Hi,
I really like these analysis-es-es-es post and I appreciate the work.

I bet most BSIABs try to copy the general topology of Marshall amps, with the same inter-stage eq (such as that 470k//470p between stage 1 and 2) and different amp/clipping elements.

[iainpunk]

instead of the mu-amp, you can try SPRR gain stages, they work a bit differently but sound great as well, with similar gain range, but a different sound when clipping.

this one uses diode bias instead of resistance bias, using 1n4004 diodes. swapping out the JFETs makes a big difference in sound, and they need to be somewhat close to sound good, but matching is a fun activity IMHO.


originally done with resistors, they are praised for their sound quality by the DIY HiFi community.


i haven't tried combining them, tubes with diode bias, might give that a try later today.

cheers, Iain

[Vivek]

instead of the mu-amp, you can try SPRR gain stages...

cheers, Iain

I want to try and redesign something equivalent with Opamps and diodes.

By matching the amplitude, frequency response, clipping of each stage as close as possible

[deadastronaut]

^ interesting , i for one would like to see what an opamp equivalent to a mu-amp

looks and sounds like....


i like mu-amp dirts...they have a certain ampy type flavour.

as you were....

[Vivek]

^ interesting , i for one would like to see what an opamp equivalent to a mu-amp

looks and sounds like....


i like mu-amp dirts...they have a certain ampy type flavour.

as you were....

Let's work on it together !

What would you recommend to acheive same transfer function distortion curve as the first stage mu-amp but using Opamp and diode function generator ?

[deadastronaut]

No idea....just along for the ride really...

I have wondered how an op amp would be configured to replicate a mu-amp though.....

Lets hope some more knowledgeable, and also curious chaps chime in...

[Vivek]

Pertinent thread


https://www.diystompboxes.com/smfforum/index.php?topic=123269.0

[Ice-9]

There is a paper from 2004 by Dimitri (Daniuk) about triode emulation which is using op amps along with a single jfet. I don't have the paper to hand at the moment but will try and find the link to it asap.

[Vivek]

i like mu-amp dirts...they have a certain ampy type flavour.

I posted the Transfer function of the first mu-Amp of the BSIAB2.

Yes indeed it looks quite tube like !!!

I feel that an Amp sound is basically a mix of

Correct pre-distortion EQ
Correct transfer response curve
Correct post-distortion EQ

So far into my analysis, BSIAB is great,
1. Cut bass before distortion
2. Tube like transfer response
3. some interstage filter ( Which I feel should have been a treble cut instead of a treble boost)
4. More clipping stages ( I hope they too have same tube-like transfer function)
5. Tone controls ( Some reports say that could be improved / had been improved but I dont have schematics of the Mods)
6. Sufficient output to drive / overdrive an Amp


Maybe the fortuitous transfer curve was a serendipitous discovery, since the Mu-amp was designed for high linear gain and all bets were off when the Mu-amp is overdriven. Great respects for experimenters like Jack AMZ who bravely went where no man had been before !!!

[niektb]

what is on the x-axis of the mu-amp transfer curve? Can you convert it to Vin? (So you have Vin plotted against Vout )

[Vivek]

X axis is input voltage in mv Peak, from -1200mvp to +1200mvp

Y axis is output of 1st mu-amp in Volts peak



To be able to generate these graphs with automatically increasing Vin, I use as V(in), a BEHAVIORAL VOLTAGE SOURCE which uses the formula V(sine source) * time

as time increases, the Vin increases automatically.

Hence the X axis shows as time units

But I have standardised it so that 1 second = 1000mvp linearly.

[iainpunk]

i strongly suggest a CMOS inverter gain stage to simulate ''tube style'' clipping.
have been experimenting with a Marshall / Tube amp in a Box type sound using some CMOS and opamp gain stages. currently battling the ''high gain hiss'' sound that it also has on lower gains. i base my tone off of the clean channel of my Bugera V55 when over driven using a mid boost pedal, instead of a Marshall.

cheers

[POTL]

All amplifier in a box projects have one limitation, they try to simulate a triode in a class A amplifier mode with hot biased and standard anode resistor value. This, of course, is interesting, but the study narrows our possibilities, guys.
Let's discuss some of the obvious things that strongly affect tonality in real preamplifiers, but we are not paying attention to them.
1) DC cathode follower. Roughly speaking, this is a triode operating in buffer mode, it is located between the last stage of amplification and the tonstack.
A) It reduces the output impedance and your circuit does not lose high frequencies in the tonstack.
B) It compresses the signal, and only 1 (!) Half of the wave. Almost asymmetrical clipping that is loved in overdrive pedals.
C) This is part of the sound of cult amps, almost all Marshall amps (except the Silver Jubilee and a couple of other models), Vox, Fender Tweed (later models), Soldano, Diezel, etc. have it and that's part of their sound.

2) The absence of a cathode follower, it is easy to simulate, you need to install a resistor between the tonstack and the last stage of amplification, the resistor will be equal to the output impedance of the triode.

3) The stages of cold clipping, this is a cathode resistor with a large value, part of the sound of JCM800, Soldano, Mesa Rectifier, Peavey 5150/6505, Framus, PRS Archon / MT15. the resistor value is 10k-39k, this also gives an asymmetric distortion, 39k, looks almost like a half-wave rectifier. some amplifiers (Friedman, Bogner) can switch the clipping mode between cold and hot.

4) The value of the anode resistor. the sound feature of some amplifiers is the larger anode resistor value (220k-330k versus standard 100k). it affects the gain, tone, distortion and how the cathode resistor and capacitor filter changes. As examples Engl, Soldano, Mesa, Friedman. 5) Tonstek, yes yes yes, he plays a huge role in shaping the tone, which is why ancient schemes like Bsiab with a tone ala Big Muff look strange.
6) phase inverter and power amplifier (look at the PAL pedals, which were inspired by the early designs of R.O.G.), Presence, reaonanse, response controls are important. In addition, my personal experience says that all pedals on field-effect transistors, after the tonstack, MUST have an amplification stage otherwise they will sound bad.
Now let's think about what every possible way can give us.

1) Jfet class A, they cannot simulate different values ​​of the anode resistor, the stage of cold clipping (more than 10k), without the selection of transistors, the circuit is poorly repeated and requires adjustment. Pros, sounds good, but the choice of circuits to simulate is small.

2) Mosfet (2n7000 / bs170), are noisy, have a large miller capacity and require an input buffer to prevent high frequency losses. Poyes, they are more flexible in tuning, do not require selection of transistors and bias tuning.

3) Mu Amp, about the same as a mosfet, but prone to sagging when heavily distorted.
Also I have often seen reports that the Mu Amp does not simulate a Class A amplifier, but rather a Push-Pull amplifier.

4) Op amps, the most flexible, but I am a skeptic and have never heard of a good amp in a box using op amps. Perhaps the problem is high speed and square distortion without diodes.

5) LND150, potentially the main candidate for the title of the new king of field-effect transistors (so far j201, 2n5457, 2n7000, bs170). Judging by the description, this transistor has the best of jfet and mosfet, but does not have their drawbacks, does not require selection, is used in real tube amplifiers, in cathode follower circuits (good as a buffer, bad as a wave amplifier), amplification stages, effect loops, able to replace the lamp without reworking the circuit.

In my humble opinion, it is worth paying attention to operational amplifiers and LND150, as the least used (unlike jfet, mosfet, mu amp) devices for simulating an amplifier in a box. Mu Amp, I would put it in third place in terms of potential (it has a lot of limitations).