# Multistage voltage amplifier

1. Apr 5, 2013

### sherrellbc

I am having trouble figuring out how to design multistage amplifiers in general. I am working on a project in which I take the small signal from a condenser mic ( ± 5mV ), amplify and filter it a sufficient amount such that I can read into a microcontroller and process the information. I would like to use the full resolution of the Arduino due. (10bit, 5V), therefore an amplification of 1000 is needed.

I designed an input stage BJT common-emitter amplifier with a gain of approximately 50; the gain was actually 54. Then, I used an active filter to get the remaining 20 gain required to meet the spec of 1000.

Now, both amplifiers work great if taken by themselves. The issue is that when I place the two stages in series,[STRIKE] my overall gain diminishes to about 800. [/STRIKE]The change that I noticed was that the input stage (the BJT) now has a gain of 84, [STRIKE]and the second stage dwindeled to about 9.6.[/STRIKE]

I realized I never changed the default rail supplies. The loading affect of the input stage's amplification increasing from 50 to 85 still persists. Can anyone help me to understand this? I now get 7.3V output. The associated gain is about 1460V/V. almost 1.5X what I designed for.

What am I missing here? I assumed it has something to do with loading the stages by placing them in cascade, but that reason is specifically why I included a buffering stage. The input resistance of the LM741 ( at 2kHz ) is approximately 9MΩ, and the associated input resistance is approximately 75Ω.

I have attached the schematic used below.
Thank you.

http://tinypic.com/r/339sv8y/6

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Last edited: Apr 5, 2013
2. Apr 5, 2013

### Staff: Mentor

It looks like there is a typo for the Vcc/Vee supplies. Are they backwards? Vcc would normally be the + voltage, and Vee would be the - voltage.

The drop in gain may be a stability problem. When you have two cascaded gain stages like that, you need to take care to keep the larger output signal from coupling back into the low-level first stage. Output signal coupling back to the first stage can cause stability problems and oscillations, or it can just alter the overall gain. Similarly, you need to keep the noise on the 2nd stage's power supply rails from feeding back into the first stage's power supply. Depending on the PSRR of the input stage, this can also cause stability and gain issues.

Maybe try separating the two stages better electrically. Can you run them off of separate power supplies? Or at least do some filtering for each power supply rail at each gain stage...

3. Apr 5, 2013

### sherrellbc

How would you suggest to filter the power supply rails more effectively? And yes, originally I had the voltages placed on the wrong pins. After checking the data sheet I just switched the names.

I have yet to construct and test this circuit. I ran the simulation to see the effect of the buffer on the input stage. The gain does become 85V/V if the second stage is disconnected from the circuit. Apparently, the buffer is somehow adding additional amplification to the BJT amp. By looking at the circuit model for the buffer, the input impedance is 9M. How is the input stage being changes so dramatically?

4. Apr 5, 2013

### sherrellbc

Oh boy, I just realized one of the major issues. If you look at the original design, I only supplied +-5V rails on the second stage. If I was expecting 5V, I certainly cannot only use 5V rails. So, after adjusting the rails, I get 7.3V output. The associated gain is approximately 1460V/V. I am still getting some sort of a loading affect by introducing the buffer stage.

Can anyone help me to understand this?

5. Apr 5, 2013

### cabraham

I computed the 1st stage gain at 94. A 2N2222A bjt device has a gain of roughly 100 or so, 50 minimum. I was just wondering how you computed a 1st stage gain of 50. I assumed a condenser mic impedance of 150 ohms.

Claude

6. Apr 5, 2013

### technician

I assumed a condenser mic impedance of 150 ohms.

What model condenser microphone does this relate to? Seems a bit on the low side

7. Apr 5, 2013

### cabraham

Electra Voice condenser mics typically go 150 to 200 ohms. Other condensers from AKG, AT, & Shure are usually around 200 ohms, AFAIR. Anyone know differently?

Claude

8. Apr 5, 2013

### sherrellbc

How did you go about calculating the gain to be 94? I used the small signal
model. I am away from my notes at the moment. I did, however, assume an ideal source.

If you run this circuit in a simulation software, I used Multisim, the gain without the buffer is 54. After the buffer is added, the gain increases to 85.

9. Apr 5, 2013

### cabraham

Tonight I will compute the gain long hand, scan, then post it for all to see. Maybe I erred, so I will carefully check my own work tonight.

Claude

10. Apr 5, 2013

### f95toli

Slightly OT:
You are aware of the fact that the ADC on the Due only have an input range of 0.55V to 2.75V?

Hence, if you want to use the full range you will not only have to amplify, but shift the voltage level.
I've just made an amplifier for exactly this purpose, shifting the level was fortunately easy since I used a couple of cascaded op-amps.

11. Apr 5, 2013

### sherrellbc

My apologies. I am actually using the duemilanove for this project.

12. Apr 5, 2013

### gnurf

If your ADC is 0-5V and your input signal is 5mV, you want a gain of 500 (5Vpk-pk) and a 2.5V DC offset, no?

EDIT: Sorry, I'm not paying attention. I didn't see the duemilanove posts. I have no idea what that is.

Last edited: Apr 5, 2013
13. Apr 5, 2013

### gnurf

FWIW, I also got a gain of 94 when I simulated the first stage in LTspice.

14. Apr 5, 2013

### jim hardy

Small signal amplification operates on the slope not on the DC value .

Presence of C5 means all ac input is dropped across internal resistances of the transistor's emitter and base, and most of it across emitter resistance because of hfe .
Let's call internal emitter resistance Reinternal .

Without going to lengthy equations,
a common emitter amplifier gives ac gain of approximately the ratio of resistances in series with collector and emitter, the latter including internal resistance..
Of course that's because the emitter and collector have essentially the same AC current through them.

Fairchild's 2N2222 datasheet gives an estimate of 60 ohms for input resistance in common emitter configuration .
http://www.fairchildsemi.com/ds/PN/PN2222A.pdf
see "small signal characteristics"

R8 doesn't count for AC because he's bypassed for AC by C5. That's what C5 is for, to give the circuit the most gain the transistor can deliver.

So a rough estimate of that stage's gain would be $\frac{R5}{Re_{internal}}$, 5000/60 = 83.3

When you add the second stage, R7 shunts R5 so the gain drops to $\frac{R5 {parallel} R7}{Re_{internal}}$, 4000/60 = ~66.

Are these gains anything like your measured results?

If you want the circuit's gain to be more predictable and less reliant on individual transistor characteristics, place a few ohms in series with its emitter. Gain will be lower but circuit will be more tolerant of variations in temperature and individual transistor parameters.

Here's a refresher I visited, :
common emitter starts on page 11.

it was fifty years ago I studied this stuff so please excuse my rustiness.

old jim

Last edited by a moderator: May 6, 2017
15. Apr 6, 2013

### Carl Pugh

Transistors were never my speciality, however let me put in my 2 bits (25 cents).
The time constant of C3/(R4-R6) and C4/R7 are too high. Operate the circuit at a higher frequency and see what happens.
Why not get rid of Q1 and have the signal go directly to the buffer stage? Buffer stage would have to have some gain. (May have to use a better operational amplifier)

16. Apr 6, 2013

### jim hardy

changed default rail supplies? Did you change supply voltage? That'll change your DC operating point and hfe varies with emitter current, see curves in Fairchild datasheet.
That might explain your gain change.

Is this a real circuit or a simulation?

I like the LM386 for general purpose audio amp. Its gain is settable from 20 to 200 and operates from single supply.
Might save you a lot of work .

I also like LM324 for low frequency and DC , it's single supply like LM386 and there's four in one package. It has lower input currents than 741.
This datasheet shows your filter in fig16 and a biquad in fig 17:

Both come in DIP package which is handy if this is a real circuit. If it's just a simulation, you might pick a faster opamp. But even Radio Shack carries these two.

17. Apr 7, 2013

### sherrellbc

Alright, I am not sure what I have been doing. The gain is most certainly 84 in Multisim when I run it. I was using the T model transistor model and could not come up with the same gain.

Looking at the datasheet, Hfe for the small-signal current gain has a minimum of 50, and a max of 375. Taking the average of the two, I used a value of 163 to compute the gain.

Where did you see the value of collector and emitter impedances? I see from the data sheet that you provided that it refers to the P2N2222A transistor. I am using the Q2N2222. Although they may be from the same family of transistors, can the datasheets be interchanged like that? Also, the 60 ohm input impedance row states that it behaves with such a characteristic at high frequencies (300MHz). Although, I adjusted my model to have a split emitter resistance of 40 in series with the cap and 5k. The associated output was then 50V/V gain. Thus, what you said was true with respect to the 60 ohm emitter impedance. (5000/(60+40)) = 50. However, you must also consider the impedance of the capacitor at the operating frequency, 2kHz. It turns out to be approximately 32.

http://alltransistors.com/pdfview.php?doc=p2n2222a.pdf&dire=_motorola

The above link indicates that the input impedance is 2-8k. Is this value referring to the base impedance? The only other mention I find it output admittance, which is 5 - 35 μmhos.

Last edited: Apr 7, 2013
18. Apr 7, 2013

### sherrellbc

I was thinking of using the LM348 quad amp. I changed the power supply rails on the op amp. My original confusion ended up being that I was saturating the op amp.

19. Apr 7, 2013

### jim hardy

Very reasonable.

I didn't. I was just shooting for approximations.
For emitter resistance I used that 60 ohms which is given by Farichild as the real portion of zin. and yes at 300 mhz. But I assumed the real part shouldn't be f(frequency)

I think that was the purpose of jedec standards, so parts would be interchangeable. I treat them that way, though for important projects I try to buy from a good US supplier.
In my plant days we cut the tops off some imported metal can transistors we'd got as replacements and looked with a microscope. We decided to not use that vendor anymore.

yes it's specified at 300 mhz. But I assumed the real part shouldn't be frequency dependent - it is resistive.
Whatever base resistance is, only base current flows through it.
Emitter resistance gets hfe X more, so to be precise one should do a proper voltage divider calculation. But he'd have to know how much is rb so I assumed the majority of drop is across re.

The alltransistors link gives me a blank page, so I don't know what they mean...

Touche on the 32 ohm Xc ! You got me...
Since it's a simulation, maybe you'd try making R8 into two resistors and just bypass one of them.

I think you've got the hang of it now.
I use the thought tool of taking things to extremes.
At one extreme we have common collector(aka emitter follower) with gain very well defined ~1.
At other extreme we have common emitter with gain loosely defined by re, rb. and hfe which itself is function of temperature and emitter current..

If you want better defined AC gain move a little toward the common emitter by only bypassing part of the emitter resistor.. it costs you gain but gives you more predictable gain.
It's the simples form of negative feedback I know.

Nowadays everybody just uses an opamp - I was delighted to see somebody doing old fashioned circuit design. Good for you !

Best of luck on your project !
old jim

20. Apr 7, 2013

### sherrellbc

I read that op amps, unless very high quality, provide a lot of unwanted noise. That's why I designed the two stage design with majority gain in the first stage.

I really couldn't find a definitive reason why op amps provide such gain, but to be on the safe side I designed it like I did.

I needed an overall gain of 1000.