# Some kind questions on linearity and distortion

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#### ginetto61

Hello to Everyone !

i ask here because i do not know where to ask :
I have a big confusion in mind
1) linearity means a flat freq response at least in the audio band ?
2) i see sometimes those distortion spectra. Why if i send a monotonic signal to a transistor i get at the output also the harmonics ? why this happens ?
3) feedback has only influence on the point 2) ?
4) can i create feedback with only one active device ?

Thanks a lot indeed and sorry if these are silly questions
Kind regards,
gino

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#### jxdking

1) No. Linearity means Vout / Vin is Constant, at any time!
2) Transistor is not linear enough.
3) Feedback will correct some non-linearity. In some cases, it corrects almost all non-linearity, but can not eliminate all non-linearity.
4) Yes.

#### ginetto61

1) No. Linearity means Vout / Vin is Constant, at any time!

I rephrase the question a little.
I am interested in a flat freq response in audio range
A single bjt circuit is capable of a flat freq response from 20 to 20kHz ?

... 4) Yes

An externally hosted image should be here but it was not working when we last tested it.

How can i connect a single bjt circuit to have feedback ?
is it enough a resistor between the collector and the emitter ?
are there any examples in literature ?
I have seen circuit with feedback but at least with two bjts, never with just one and I am very curious about this. Really.
Thanks a lot and kind regards,
gino

#### dmills

There are a fair number of ways to arganise feedback around a single transistor, here are a few:

A resistor in the emitter lead will create feedback because the voltage across it will increase with increasing current flow. A very common trick for stabilising the dc operating point, and if you split the resistor and decouple the junction then you can set the DC operating point and the AC gain almost independently. Note all transistors have some intrinsic Re' so this mechanism always exists to some extent.

Connect the bias resistor to the collector, run common emitter and place a load resistor in the collector circuit. Not as stable as the first design, but it works and is often seen in simple minded mic preamps for things like baby monitors. You sometimes see this combined with the first idea.

Run the stage common base, more usually seen at RF this one, but if you need a low Z input and very good isolation it is not a bad approach at audio.

Then once you get away from audio, there are things like the norton noiseless feedback circuit wrapping a transformer around a common base stage to make a very broadband flat amplifier which is quiet but trades **VERY** poor reverse isolation for its other good bits (You never see this one at audio).

There are (probably) other circuits but I think the emitter degeneration and collector bias are the big ones at audio.

Regards, Dan.

#### bear

Distortion is any deviation in amplitude (or phase) from the input signal.

In order to get the distortion down, engineers use a variety of techniques and methods.

A simple single transistor circuit can sound good, but will not measure free of distortion. It can have a bandwidth far in excess of the audio band.

To keep this simple, making a circuit is not usually simple. First you have to determine what you are going to use it for. Next you need to figure out how much gain it needs, and then the input signal level and input impedance, and then the same for the output - level (gain) and impedance.

The next step is to decide how to accomplish that.

Opamps are the simple way to get good results fast with minimum design.

Discrete transistors (or jfets, mosfets) are more complicated, and often end up being rather similar to what is stuffed inside an opamp.

For a good overview of electronics engineering and design that you can read without much math at all, and is written very clearly, buy a copy of Horowitz and Hill "The Art Of Electronics". It is not inexpensive, but if you want to learn, this is a very very good book. If you can find the first edition, used, and save money that is fine.

Otherwise you have to study and read up on how transistors (or tubes) work, and figure out how circuits work with other books, or online.

It's at once simple on some levels and exceedingly complex and detailed on another...

Hope this helps some.

#### ginetto61

There are a fair number of ways to arganise feedback around a single transistor, here are a few:
A resistor in the emitter lead will create feedback because the voltage across it will increase with increasing current flow. A very common trick for stabilising the dc operating point, and if you split the resistor and decouple the junction then you can set the DC operating point and the AC gain almost independently. Note all transistors have some intrinsic Re' so this mechanism always exists to some extent.
Connect the bias resistor to the collector, run common emitter and place a load resistor in the collector circuit. Not as stable as the first design, but it works and is often seen in simple minded mic preamps for things like baby monitors. You sometimes see this combined with the first idea.
Run the stage common base, more usually seen at RF this one, but if you need a low Z input and very good isolation it is not a bad approach at audio.
Then once you get away from audio, there are things like the norton noiseless feedback circuit wrapping a transformer around a common base stage to make a very broadband flat amplifier which is quiet but trades **VERY** poor reverse isolation for its other good bits (You never see this one at audio).
There are (probably) other circuits but I think the emitter degeneration and collector bias are the big ones at audio.
Regards, Dan.

Good morning Dan and thank you very much for the reply
First, i have limited knowledge ... very limited
My question is very basic
Given this general schema

can i connect with a resistor the output to the emitter of the NPN ?
will it work ? whit what results ?
I am obsessed with the idea of getting the most from the least
I understand that this is quite a technical challenge
But first I would like to understand what is possible with extreme simple typology
And only then, if the results are unsatisfactory, I would pass to more complex designs.
I have two "principles " stuck in mind
1) the KISS principle
2) act on parts selection and design fine-tuning to improve performance of very basic design
I have the feeling, it is clearly onlt a feeling, that very simple design can give astonishing results in terms of sound
Maybe it is just an illusion of a confused mind
Thanks a lot and kind regards,
gino

#### jan.didden

Paid Member
Gino,

If you remove CE you introduce local feedback on the emitter (also sometimes called degeneration).

If you connect the top of R1 not to the supply but to the collector, you also introduce feedback, also called loop feedback.
Of course R1 should be changed in value because the DC conditions are now changed.
Does that help?

jan

#### ginetto61

Distortion is any deviation in amplitude (or phase) from the input signal.
In order to get the distortion down, engineers use a variety of techniques and methods.
A simple single transistor circuit can sound good, but will not measure free of distortion. It can have a bandwidth far in excess of the audio band.

Thank you sincerely for your kind and valuable reply, but i do not understand.
you say

A simple single transistor circuit can sound good, but will not measure free of distortion.
It can have a bandwidth far in excess of the audio band

Maybe i am missing something.
Should not this be the real aim of any audio design ?
Given that there are still problems to correlate sound and figures.
I would be a little trivial (it is my nature, sorry ) but for me if it sounds good is good.
Even if it is just a little bjt doing all the amplification work.

To keep this simple, making a circuit is not usually simple.
First you have to determine what you are going to use it for.
Next you need to figure out how much gain it needs, and then the input signal level and input impedance, and then the same for the output - level (gain) and impedance.
The next step is to decide how to accomplish that.
Opamps are the simple way to get good results fast with minimum design.
Discrete transistors (or jfets, mosfets) are more complicated, and often end up being rather similar to what is stuffed inside an opamp.
For a good overview of electronics engineering and design that you can read without much math at all, and is written very clearly, buy a copy of Horowitz and Hill "The Art Of Electronics".
It is not inexpensive, but if you want to learn, this is a very very good book.
If you can find the first edition, used, and save money that is fine.
Otherwise you have to study and read up on how transistors (or tubes) work, and figure out how circuits work with other books, or online.
It's at once simple on some levels and exceedingly complex and detailed on another...
Hope this helps some

I am trying to study schematics of commercial amps buying service manuals
At least they are working and tested design
But apart all the added complexity for protections, input selection, tone control ...
For istance ... i do not understand why high end equipment do not have tone controls and cheap products have them
I understand saving in parts quality, but not bigger complexity in design
This is even perverse for me
I will look for the book you mention anyway
Thanks a lot.
Kind regards,
gino

#### ginetto61

Gino,
If you remove CE you introduce local feedback on the emitter (also sometimes called degeneration).
If you connect the top of R1 not to the supply but to the collector, you also introduce feedback, also called loop feedback.
Of course R1 should be changed in value because the DC conditions are now changed.
Does that help?
jan

Yes Sir ! it helps a lot indeed
It is what I wanted to know. How to connect a basic circuit
I need gain of 2 and no more than 2-300 ohm of output impedance
about 24V for the supply (two 12V batteries in series).
For a one npn line stage
If it will not sound good i will pass to other designs, more elaborated i mean
Thank you very much again
Kind regards,
gino

#### godfrey

I am trying to study schematics of commercial amps buying service manuals
You can get a lot of schematics and service manuals for commercial amps on Jan Dupont's website for free.

#### ginetto61

You can get a lot of schematics and service manuals for commercial amps on Jan Dupont's website for free.

Thanks !!!
I do not want to sound naive, but i was implying that a more complex design sounds better than a basic design
and this of course justifies the added complexity
I was correct, wasn't I ?
Thanks a lot again !
Kindest regards,
gino

#### godfrey

How to connect a basic circuit
I need gain of 2 and no more than 2-300 ohm of output impedance
about 24V for the supply (two 12V batteries in series).
For a one npn line stage
Here you go.

Input impedance is 10K, gain = 2, and according to my simulator:
• Frequency response is flat up to about 1MHz.
• Output impedance is about 200 Ohms, depending on the transistor, except at low frequencies, where the output capacitor dominates.
• Distortion for 1V rms input, 2V rms output is about 0.2% with no load, and double that with a 10K load.

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#### ginetto61

Here you go.
Input impedance is 10K, gain = 2, and according to my simulator:
• Frequency response is flat up to about 1MHz.
• Output impedance is about 200 Ohms, depending on the transistor, except at low frequencies, where the output capacitor dominates.
• Distortion for 1V rms input, 2V rms output is about 0.2% with no load, and double that with a 10K load.

Thank you very much indeed
This is the approach that i like and I intend to study and follow initially for a line stage
The PS is not difficult. I can find something with building instructions at least up to 30V easily.
I did it with a LM317 based design and it worked nicely.
One last question because i do not want to annoy too much
Starting from this schema and keeping it like this, which could be the moves to get lower distortion ?
I mean, I understand that figures are not everything
But i think that the exercise of fine tune a very simple circuit is both very challenging but also very intriguing.
I do not know, maybe increase the voltage supply ? change bjt ? increase bias current ?
Have you simulated the circuit ? what software do you use ?
I read that some simulation software are quite reliable in predicting a circuit performance
To end this is the most interesting topic for me presently
Kindest regards,
gino

P.S. for me op-amps can also be good, but are very difficult. Too difficult.
Better stick with discretes.

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#### godfrey

The PS is not difficult. I can find something with building instructions at least up to 30V easily.
I did it with a LM317 based design and it worked nicely.
That was quick - you built it less than an hour after I posted it!
Using the LM317 regulator was a good idea - simple circuits like this really do need a smooth clean power supply.

Have you simulated the circuit ? what software do you use ?
I read that some simulation software are quite reliable in predicting a circuit performance
I simulated it with SIMETRIX SIMplis. Many others on the forum use LTSpice. Both are free and good, giving very similar results. I've tried LTSpice, but found SIMETRIX much simpler and easier to learn and use.

Starting from this schema and keeping it like this, which could be the moves to get lower distortion ?
I mean, I understand that figures are not everything
But i think that the exercise of fine tune a very simple circuit is both very challenging but also very intriguing.
I do not know, maybe increase the voltage supply ? change bjt ? increase bias current ?
Good questions. Let's look at a few options:

• change bjt
I chose BC547C because it has a very high current gain. All else being equal, higher gain => higher feedback => lower distortion. There may well be other (esp. more modern) transistors that would be better, but I don't know what they are.
Other reasons I chose the BC547C are that it's inexpensive, widely available and I can remember the part number offhand.

• increase the voltage supply
Higher voltage supply is definitely better than lower. One good reason is that, for the same quiescent conditions (i.e. same idling current and collector voltage), it lets you use a higher value for R3. This reduces the load that the transistor has to drive, which reduces distortion. It also increases open loop gain, resulting in higher feedback, which reduces distortion further.

• increase bias current
I'm not sure about that. I actually suspect reducing the bias current may give better results. It's easy to experiment with this: Just increase R3 to reduce the current or vice versa. e.g. doubling R3 will roughly halve the idling current. Reducing it too far will obviously limit the maximum output swing though.

• reducing collector voltage
I originally aimed to have the collector at about 12V (half the supply voltage), and the collector current at about 3mA which is in the BC547's "comfort zone" where it works well. FWIW, the simulator gives 11V and 3.5mA for the component values I showed.

However, I'm starting to think it may be better to set the collector voltage lower, at about 6V. This will limit the output to about 4V rms, but should reduce distortion at lower levels like 1V or 2V rms. For example: first increase R1 to 2K7. This reduces the collector voltage to about 6V, but also increases collector current. Then increase R3 to 6K8 to bring the collector current back down to about 2.5mA. Increasing R1 and R3 reduces the loading at the input and output respectively, both of which should result in less distortion.

I wouldn't expect any of these changes to make a big difference, but there may be a small but noticeable improvement. e.g., IIRC, the last change mentioned (reducing collector voltage) reduces distortion by about half, according to my simulation.

#### ginetto61

That was quick - you built it less than an hour after I posted it!
Using the LM317 regulator was a good idea - simple circuits like this really do need a smooth clean power supply

Hello ! no ! i said that i did built the PS with a kit sometimes ago
But of course I can do it again, The build is easy with pcb and instruction
I do not know why the lm317 is not more popular. It is a great regulator i think and kits are available. I like it
Unfortunately it can be used up to 30V max

I simulated it with SIMETRIX SIMplis. Many others on the forum use LTSpice. Both are free and good, giving very similar results.
I've tried LTSpice, but found SIMETRIX much simpler and easier to learn and use.

Thank you for the advice ! I will look for it. Great tools these SW.

Good questions. Let's look at a few options:

• change bjt
I chose BC547C because it has a very high current gain.
All else being equal, higher gain => higher feedback => lower distortion.
There may well be other (esp. more modern) transistors that would be better, but I don't know what they are.
Other reasons I chose the BC547C are that it's inexpensive, widely available and I can remember the part number offhand.

• increase the voltage supply
Higher voltage supply is definitely better than lower. One good reason is that, for the same quiescent conditions (i.e. same idling current and collector voltage), it lets you use a higher value for R3. This reduces the load that the transistor has to drive, which reduces distortion.
It also increases open loop gain, resulting in higher feedback, which reduces distortion further.

• increase bias current
I'm not sure about that. I actually suspect reducing the bias current may give better results. It's easy to experiment with this: Just increase R3 to reduce the current or vice versa. e.g. doubling R3 will roughly halve the idling current. Reducing it too far will obviously limit the maximum output swing though.

• reducing collector voltage
I originally aimed to have the collector at about 12V (half the supply voltage), and the collector current at about 3mA which is in the BC547's "comfort zone" where it works well. FWIW, the simulator gives 11V and 3.5mA for the component values I showed.

However, I'm starting to think it may be better to set the collector voltage lower, at about 6V. This will limit the output to about 4V rms, but should reduce distortion at lower levels like 1V or 2V rms. For example: first increase R1 to 2K7. This reduces the collector voltage to about 6V, but also increases collector current. Then increase R3 to 6K8 to bring the collector current back down to about 2.5mA. Increasing R1 and R3 reduces the loading at the input and output respectively, both of which should result in less distortion.

I wouldn't expect any of these changes to make a big difference, but there may be a small but noticeable improvement. e.g., IIRC, the last change mentioned (reducing collector voltage) reduces distortion by about half, according to my simulation.

Thank you very much for this crash course in audio electronics !
It is interesting to see that fine tuning of a simple circuit can lead to better electric performance. This could be a way to nice sound also.
The sim SWs are very nice and useful.
The possibility to predict the performance of a circuit without having to build it is very intriguing
Being ignorant I would use them extensively because they seem also quite reliable
Thanks a lot for the kind and valuable help
Best regards,
gino

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#### dmills

Simulation is useful to a point, and a godsend for some things, but is only ever as good as the models used.

Even in simple audio things sometimes layout can make a significant difference, and while possible to simulate, it is hard to model accurately.

I would argue that until you gain the experience to know when the simulation is lying (And they all do upon occasion), paper and a pencil is pretty much as good.
Get yoursef a copy of "The Art Of Electronics" for a little light beadtime reading (Warning, the binding is well known to be crap), and Doug Selfs "Small signal audio design" contains some stuff that you will seldom see in one place elsewhere.

For learning, you will do as well to look at a few simple stages, and sit down with a pad of graph paper, a calculator, ohms law and Ebbers-Moll or such, simulations are good and quick, but to get the real insights you need to do the math yourself, Ebbers-Moll is good for DC conditions, and good enough for audio band, you don't need Gummel-Poon for that.

The LM317 is fairly noisy, has poor HF PSRR (As do many integrated regulators), and fairly poor load transient response, it also has quite a high idle current consumption when compared to more modern parts, it is however easy to use and robust, which is sometimes all that is required.

Regards, Dan.

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#### ginetto61

Simulation is useful to a point, and a godsend for some things, but is only ever as good as the models used.
Even in simple audio things sometimes layout can make a significant difference, and while possible to simulate, it is hard to model accurately.
I would argue that until you gain the experience to know when the simulation is lying (And they all do upon occasion), paper and a pencil is pretty much as good.

Hi ! i am sure that there is much more like the layout you are mentioning
it is complex to get things very right.
But how could you get a distortion spectrum with paper and pencil ?
i know that sim software can do this easily and this is quite important i guess
with the SW you have just to change component values and press enter
i like this very much
Once you have got a nice distortion graph the pcb design part begins
I understand that this impacts a lot on the overall outcome

Get yoursef a copy of "The Art Of Electronics" for a little light beadtime reading (Warning, the binding is well known to be crap), and Doug Selfs "Small signal audio design" contains some stuff that you will seldom see in one place elsewhere.
For learning, you will do as well to look at a few simple stages, and sit down with a pad of graph paper, a calculator, ohms law and Ebbers-Moll or such, simulations are good and quick, but to get the real insights you need to do the math yourself, Ebbers-Moll is good for DC conditions, and good enough for audio band, you don't need Gummel-Poon for that

I have to tell you that at school i was much better with instruments than on theory
I like the practical part ... measurements in particular
and i am a avid reader of lab reports, even if i do not understand them completely
I trust the instruments so much more than my ear
and i am not good at theory ... quite limited actually

The LM317 is fairly noisy, has poor HF PSRR (As do many integrated regulators), and fairly poor load transient response, it also has quite a high idle current consumption when compared to more modern parts, it is however easy to use and robust, which is sometimes all that is required.
Regards, Dan.

is there any monolithic variable regulator with better performance than the LM317 ?
I mentioned it because kits using this part are very common
Kind regards,
gino

#### CopperTop

I would argue that until you gain the experience to know when the simulation is lying (And they all do upon occasion), paper and a pencil is pretty much as good.

Doesn't the pencil and paper lie too? Most paper and pencil 'simulations' start with "let's assume it's an ideal transistor and passive components, and the power supply is a perfect voltage source". The slightest nod towards real components renders your simulation an hour's hard graft with the potential for many mistakes. I would say that the potential for the software simulator lying is lower than the average back-of-an-envelope manual calculation.

I also sometimes feel that discussions of amplifier design are somewhat circular, based on a priori 'knowledge' about what an amplifier does, exclusively in the frequency domain. The circuit simulator is quite happy to let us see what's going on in the time domain, which I find very revealing.

#### DF96

ginetto61 said:
I like the practical part ... measurements in particular
Without theory you have no framework in which to interpret measurements. A measurement is simply a raw number without interpretation; it is data but contains no information.

#### ginetto61

Without theory you have no framework in which to interpret measurements.
A measurement is simply a raw number without interpretation; it is data but contains no information

I am not so convinced .. anyway i am not convinced of something else
As usual i am confused

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